tag:blogger.com,1999:blog-2352762924549184362024-03-18T13:01:01.164-04:00Math HombreA blog for sharing my math interests on the web, to post new materials for elementary, secondary and teacher ed, and vent mathematical steam when needed.
Thanks for visiting!John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.comBlogger441125tag:blogger.com,1999:blog-235276292454918436.post-44791364149240389502024-02-18T15:28:00.000-05:002024-02-18T15:28:17.317-05:00Variable Kings - a Linear Equations Math Game<p><span style="background-color: white; font-family: Helvetica, Arial, sans-serif; font-size: 13px;">I'm still posting games from the Fall 2023 GAMES seminar at GVSU. This senior capstone was begun by Char Beckmann. See many of the games from her seminar in this </span><a href="https://www.youtube.com/watch?v=dEUg3qp6zQo" style="background-color: white; color: #003366; font-family: Helvetica, Arial, sans-serif; font-size: 13px; font-weight: bold; text-decoration-line: none;" target="_blank">YouTube playlist</a><span style="background-color: white; font-family: Helvetica, Arial, sans-serif; font-size: 13px;">. Many of the games completed in my seminar are in </span><a href="https://www.youtube.com/watch?v=wXpyTji0WgY" style="background-color: white; color: #003366; font-family: Helvetica, Arial, sans-serif; font-size: 13px; font-weight: bold; text-decoration-line: none;" target="_blank">this playlist</a><span style="background-color: white; font-family: Helvetica, Arial, sans-serif; font-size: 13px;">. In the seminar, we play lots of games and math games, the future teachers make a first video to promote a class math game that already exists, we develop a group game (a monster-themed middle school </span><a href="https://teacher.desmos.com/activitybuilder/custom/6519f6dda4544090e16cbf2e" style="background-color: white; color: #003366; font-family: Helvetica, Arial, sans-serif; font-size: 13px; font-weight: bold; text-decoration-line: none;" target="_blank">Desmos escape room</a><span style="background-color: white; font-family: Helvetica, Arial, sans-serif; font-size: 13px;"> and </span><a href="https://youtu.be/smQAukReKSQ" style="background-color: white; color: #003366; font-family: Helvetica, Arial, sans-serif; font-size: 13px; font-weight: bold; text-decoration-line: none;" target="_blank">Math Heads</a><span style="background-color: white; font-family: Helvetica, Arial, sans-serif; font-size: 13px;">, a number mystery game this year), and they develop a game of their own.</span></p><p><span style="background-color: white; font-family: Helvetica, Arial, sans-serif; font-size: 13px;">Ryan Brummel made a video for Math Heads, our group game as mentioned above, a game he tested extensively with his algebra students.</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="398" src="https://www.youtube.com/embed/daoKiwF831g" width="478" youtube-src-id="daoKiwF831g"></iframe></div><br /><span style="background-color: white; font-family: Helvetica, Arial, sans-serif; font-size: 13px;">Ryan's original game is a super cool algebra game where students make, evaluate and solve linear equations. The rules are surprisingly simple and the game play can be pretty intense. What follows is his story of making the game, and thoughts on math games in general.</span><p></p><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="415" src="https://www.youtube.com/embed/5VY3i6rllx8" width="499" youtube-src-id="5VY3i6rllx8"></iframe></div><span style="font-family: Arial, sans-serif; font-size: 11pt; white-space-collapse: preserve;"><p><span style="font-family: Arial, sans-serif; font-size: 11pt; white-space-collapse: preserve;"><br /></span></p>When trying to come up with a math game, I wanted something that would apply to the math I was teaching my students.I happen to be teaching linear equations to my 8th Grade Algebra class, and my 8th grade Pre Algebra classes were going to get to linear equations later in the year. I wanted some kind of game I could use in my classroom. I wanted something simple that didn’t need lots of materials or printing out so I wondered if I could make a game where you build linear equations using a deck of cards. With decks of cards having cards with numbers 1-10 using the Ace I figured I could incorporate the face cards as variables somehow. </span><p></p><p><span style="font-family: Arial, sans-serif; font-size: 11pt; white-space-collapse: preserve;">I brought this very rough idea to my Math 496 math games class at Grand Valley. From there my professor and classmates did a great job helping me brainstorm and try to arrange my setup so that it would be as user friendly as we would get it to be. We came to the conclusion of a rough idea of a game with two teams trying to solve a linear equation and create the biggest output. </span></p><p><span style="font-family: Arial, sans-serif; font-size: 11pt; white-space-collapse: preserve;">I took that idea to my Honors class and had them try it. It went over surprisingly well, The students had a blast. They found holes in the game that needed to be addressed, and they begged me to play the next week. I brought their comments back to class and we continued to playtest and mess around with the rules and setup of the game. Once I thought we had a final product I brought it back to my students and had them play it one more time. Having honed in on some of the minor issues of the game a lot better, it went very well and my students were very self-sufficient and able to play in teams of 2-3 the whole hour without my help. That is when I knew the game was pretty well set in stone. </span></p><p><span style="font-family: Arial, sans-serif; font-size: 11pt; white-space-collapse: preserve;">From there the game needed a name. My students did not have any bright ideas like I thought, however my 496 class gave me the idea of “Variable Kings” as the name since the game is all about winning variables and the king cards are the ones that count as variables. From that point I did what I never thought I would really do which was create my own math game that I can effectively use in my 8th grade classroom.</span></p><p><span style="font-family: Arial, sans-serif; font-size: 11pt; white-space-collapse: preserve;"><b>Why Play Math Games?</b></span></p><p><span style="font-family: Arial, sans-serif;"><span style="font-size: 14.6667px; white-space-collapse: preserve;">Coming into the Grand Valley education program I was completely foreign to the idea of math games in the classroom. I have a dad who just retired as a high school math teacher and spent 30 years in the classroom. I went all throughout my 12 year educational journey from kindergarten to high school not remembering any semblance of math games in the classroom as I know of them today. However now that I have taken math education courses, taken a math games course, and have taught in my own classroom I now can see the importance of games in the classroom.<br /></span></span></p><p><span style="font-family: Arial, sans-serif;"><span style="font-size: 14.6667px; white-space-collapse: preserve;">Math classes at the primary or secondary level tend to get the reputation of being very boring. As someone who was good at math, I did well in my math classes and enjoyed them but I enjoyed them more because of my classmates and friends in the class rather than the content itself and the way the classes were run. There were some teachers that had good personalities that made the classes more engaging but again, that is nothing to do with the content and most of my classmates didn’t even feel the way I did. What happens when students say class is “boring”. That means they are not engaged, and don’t have any desire to be engaged. Students who are not engaged have no chance at success. These students who tend to not be engaged, whether it be in math or any class, are the students that are the toughest to reach, but the students we have to try and reach. What I have found when using math games in my classroom is that a lot of the students that normally tune out, or misbehave, will perk up when there is a game to be played rather than the traditional notes or worksheet. I believe the reason for this is that a lot of these games that teachers use in the classroom have a very low entry point. This means that students who feel like they struggle in math or don’t want to share for fear of getting an answer wrong, are much more likely to engage in mathematical conversation during a math game. Math games invite students of all achievement levels to participate and also have fun which is something not always associated with a math class. <br /></span></span></p><p><span style="font-family: Arial, sans-serif;"><span style="font-size: 14.6667px; white-space-collapse: preserve;">The engagement piece is huge when it comes to math games in the classroom. However, if I played dodgeball every day in my Algebra class I’m sure students would be engaged, but they wouldn’t be learning any math. The thing that surprised me the most about math games is that I really feel like students get more out of it. When you pick a good math game it gets students to think deeper about mathematical concepts without even realizing it. With good scaffolding and discussion facilitation students really start to notice things about math while playing games that they wouldn’t using a textbook. The more students are engaged and are invested in the activity they are doing the more they will dig deeper and get out of said activity. <br /></span></span></p><p><span style="font-family: Arial, sans-serif;"><span style="font-size: 14.6667px; white-space-collapse: preserve;">Overall I think that math games are super essential to any math classroom. Not every single part of every day has to be a game, but I think that using math games in your classroom is super beneficial to the students and the teacher. With my experience, math games cause engagement and the depth of mathematical thinking to skyrocket. Both of these are things that can be lacking in traditional math classrooms. I wish my teachers and classrooms would have incorporated math games a lot more in my education experience. And I know classmates that would have benefited greatly from that!</span></span></p>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-73293175181789430142024-01-06T20:36:00.005-05:002024-01-06T20:36:56.981-05:00Multiplication Mazes - a puzzle for fact practice<p> All this month I'll be posting games from the Fall 2023 GAMES seminar at GVSU. This senior capstone was begun by Char Beckmann. See many of the games from her seminar in this <a href="https://www.youtube.com/watch?v=dEUg3qp6zQo" target="_blank">YouTube playlist</a>. Many of the games completed in my seminar are in <a href="https://www.youtube.com/watch?v=wXpyTji0WgY" target="_blank">this playlist</a>. In the seminar, we play lots of games and math games, the future teachers make a first video to promote a class math game that already exists, we develop a group game (a monster-themed middle school <a href="https://teacher.desmos.com/activitybuilder/custom/6519f6dda4544090e16cbf2e" target="_blank">Desmos escape room</a> and <a href="https://youtu.be/smQAukReKSQ" target="_blank">Math Heads</a>, a number mystery game this year), and they develop a game of their own.</p><p>Keri Herman chose Tens Go Fish, a classic addition fluency game. As an extra feature, she demonstrates the game with Tiny Polka Dot cards. (Find them here at <a href="https://mathforlove.com/awg/tiny-polka-dot/" target="_blank">Math for Love</a>.)</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="411" src="https://www.youtube.com/embed/pFIjHcpIZOs" width="494" youtube-src-id="pFIjHcpIZOs"></iframe></div><br /><p>Keri's original game was a new idea for the seminar: she was interested in making a puzzle. I recently saw a description of a puzzle as a game for one person. That certainly fits here. The puzzles are available on a <a href="https://bit.ly/multimaze" target="_blank">Google doc here</a>. What follows is Keri's story of making the game, and her ideas on why we should play games in math class.</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="411" src="https://www.youtube.com/embed/_wvtQlEf-9I" width="494" youtube-src-id="_wvtQlEf-9I"></iframe></div><br /><p><b>Story of my Game</b></p><p><span style="white-space: normal;">I knew when I got the opportunity to create my own game, I wanted to develop something that was related to quick multiplication facts. The reason being that my memory of learning my multiplication tables was always timed and quite stressful for me as a young student. I wanted to create a game where students could get great practice of their multiplication facts, and build in aspects of a good game; strategy, any player can win, etc. </span></p><p><span style="white-space: normal;">My first idea was a game board, moving the amount of spaces of the product. However, I was then drawn to the idea of more of a maze. I started with a small grid and filled in very small multiplication facts, students would have to find their way to the end. This turned into the development of three mazes, 5 x 6, 7 x 8, and 9 x 10, all with their own unique solution. To figure out how to design these mazes took a lot of different approaches, starting from scratch, and overall just thinking about how to make them work. I believe that the final product of these mazes will provide students with a very fun way to practice their multiplication, while being able to try to solve the maze. </span></p><p>The goal was to have a large mathematical objective for the game. Students will be focused on trying to find the solution, even if they are going the wrong way, or have to start over, they are still constantly doing the math and getting practice of their multiplication facts. I think this game would be something that teachers should play with their learners because you can never have enough practice with multiplication. Especially in the 9 x 10 maze, all multiplication facts are used from 1 through 9 (not including zero). These mazes will also help students recognize patterns between multiples, factors, and products. </p><p>These games could be used within a lesson, if students finish early, or simply just given as an opportunity for more practice, without time constraints. I also share within my video the development process of these mazes. With students who have learned multiplication facts, I think it would be a great idea to turn this into a project or performance assessment. Students can work to develop their own maze. Not only does it take strategy, but at the same time students are able to continue working with the facts themselves and continue to recognize patterns. Overall, I am very proud of the way these mazes have turned out. I want to continue to show these to math educators and I hope that students will enjoy solving them as much as I had hoped. </p><p><b>Why Play Games in the Math Classroom?</b></p><p>As a future math educator, incorporating games into the classroom is something that I want to use and will continue to encourage others to consider as well. It is often looked over to play games in the classroom, but the reasons as to why they are beneficial to student education should be considered. There are few specific reasons that are important to point out, including; building mathematical knowledge and skills, collaboration with peers, student engagement, critical thinking skills, and more. Each one of these reasons in its own makes games in a math classroom worthwhile. </p><p><i>Building Mathematical Knowledge</i></p><p>Math games all are built upon their own goals and mathematical objectives. Teachers have the option to choose a game that targets the content that is being focused on. To find a game that can build mathematical knowledge, choosing a game that is relevant to your current learning goals within a classroom can help students extend their skills. There are so many aspects built within games that students can pick up on mathematically, without noticing. This can be beneficial to students because they are still learning, but without the title of class, homework, or assessments. </p><p><i>Collaboration with Peers</i></p><p><span style="white-space: normal;">It is important for a classroom to have communication among students that can lead to quality discussions. Discussions can uncover so many helpful aspects to student learning. In a game setting, a lot of times students will play with each other in teams, or against each other. In both cases, students are able to communicate and learn from each other. Students are able to pick up on each other’s strategies and build off of them. When playing with each other, this can help build a more positive classroom environment. This is because this type of communication is not usually seen in a regular lecture or discussion. </span></p><p><i>Student Engagement</i></p><p><span style="white-space: normal;">Oftentimes we hear negative assumptions about math and negative attitudes are common when stepping into a classroom for some students. It is important as teachers that we are able to increase student interest by engagement and participation. Incorporating math games into the classroom is a great way to develop student engagement. A lot of times, the mathematical objective of games are mixed in with aspects of interaction, surprises, and fun. A game can also change the view of many students. All students can participate and it is important to use games where any student can win. In math class, students can often point out the “smartest” students and become discouraged. When using games that are designed that anyone can win, not just based on skill, this can build a lot of confidence in students. </span></p><p><i>Critical Thinking Skills</i></p><p><span style="white-space: normal;">In many situations, students become disengaged after they reach the level of knowledge and understanding. However, it is things like analysis, critical thinking, and application that get students to really push past that level of reasoning for the content that they are learning. Math games provide a different way to push students to build upon their critical thinking skills. Having to figure out a strategy to finish or win the game is a very important tool when it comes to building these skills. With that being said, games that are chosen to play in a class should have aspects that involve strategy. </span></p><p><span style="white-space: normal;">Overall, math games have so many advantages when it comes to incorporating them into the classroom. Being able to play different types of games this semester has taught me so much about what a good math game should look like. Being able to develop and create our own group </span>game, and my own game has changed my perspective on math games. Math games can help students learn in a unique, fun, and interactive way. </p>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-168562697703825932024-01-05T13:37:00.004-05:002024-01-05T13:37:36.342-05:00Coordistroy - Classroom Graphing Game<p> All this month I'll be posting games from the Fall 2023 GAMES seminar at GVSU. This senior capstone was begun by Char Beckmann. See many of the games from her seminar in this <a href="https://www.youtube.com/watch?v=dEUg3qp6zQo" target="_blank">YouTube playlist</a>. Many of the games completed in my seminar are in <a href="https://www.youtube.com/watch?v=wXpyTji0WgY" target="_blank">this playlist</a>. In the seminar, we play lots of games and math games, the future teachers make a first video to promote a class math game that already exists, we develop a group game (a monster-themed middle school <a href="https://teacher.desmos.com/activitybuilder/custom/6519f6dda4544090e16cbf2e" target="_blank">Desmos escape room</a> and <a href="https://youtu.be/smQAukReKSQ" target="_blank">Math Heads</a>, a number mystery game this year), and they develop a game of their own.</p><p>Kacy Jeffries chose Number Boxes from Jenna Laib for her first video. See Jenna's blogpost for it here. This game was really influential to the seminar this year. Corrina Campau made a <a href="https://www.youtube.com/watch?v=MloUPPNhSVQ" target="_blank">high school/college focused video</a> for it, and Jordan Burnham made a game built on that structure, <a href="https://mathhombre.blogspot.com/2024/01/boxzee-flexible-computation-game.html" target="_blank">Boxzee</a>.</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="409" src="https://www.youtube.com/embed/NHQ47aMGRwo" width="492" youtube-src-id="NHQ47aMGRwo"></iframe></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">Kacy's original game is a spin on Battleship that incorporates some shapes and better game play rules. (IMHO) What follows is her story of the game, and why she feels like we should play games in math class.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="411" src="https://www.youtube.com/embed/tGNb_PUfC80" width="494" youtube-src-id="tGNb_PUfC80"></iframe></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both;"><b>Coordistroy Development</b></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Before thinking of this game, I went through a bunch of trial and errors with games that I could potentially come up with. I knew I wanted to do something with upper grade levels since I couldn’t think of a lot of games that had to do with the upper grades. Additionally, I wanted to create a game that was related to a well-known game that many students would probably already know how to play. This way, they could implement the same strategies they used with that game into my game.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">My first game thoughts had to do with geometry, statistics, addition, etc. However, after playing Battleship with a friend, I knew for certain what I wanted to do. So, I found a small coordinate plane online and decided to try my first attempt on my game: Shape Escape. My first thoughts were that there would be little shape pieces in which students can practice translating on a coordinate plane if that’s how they chose to use their turn. However, I quickly realized that unfortunately it wouldn’t work the way I wanted it to. My class and I then came up with the idea of students drawing shapes on the coordinate plane rather than getting pieces and keeping track of hits/misses with a pencil/pen. This seemed to work a lot better and be a lot more fun with my classmates! Finally, I created the fun scenario of aliens taking over the world to make it more intriguing for the target 6th grade audience. And from there, Coordistroy was born. </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Teachers should be interested in using my game in the classroom because it’s a fun and entertaining way to get students thinking about the coordinate plane. Students must be able to read the coordinate plane, understand how to read coordinates as (x,y), working with area, height, and width on the coordinate plane, and knowing the difference between points in different quadrants. All of these reasons are why I chose 6th grade as the target audience: there are quite a few 6th grade standards revolving around all of these skills with the coordinate plane. Another reason why teachers may be interested is because it could take up however much time needed! It can be used as an activity (taking around 20-30 minutes to find all five shapes) or even just used as filler time (taking around 5-10 minutes to find one or two shapes)! It’s perfect for any classroom where students can play one-on-one or even two-on-two. No matter how it’s used, there’s no denying the immense amount of important practice that students will be involved in with the coordinate plane!</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">After playing this game, students will be more comfortable with the coordinate plane. They will be able to read coordinates, be able to find points after given coordinates, develop shapes with certain elements, and be more excited about working with the coordinate plane! Teachers can always refer back to this game if they find their students having a hard time later on. However this will be nothing but beneficial to students! </div><div><br /></div><div><div><b>Why Play Games in Math Class?</b></div><div><span style="white-space: normal;"><br /></span></div><div><span style="white-space: normal;">It may not be thought that having fun in math class is possible. However, if you think that, you’re dead wrong! Even with topics that students dislike the most (like fractions, geometry, function relationships, etc), it’s always possible for students to have fun learning them! The way to do this is to play math games. </span></div><div><span style="white-space: normal;"><br /></span></div><div><span style="white-space: normal;">Playing games in math classes is extremely beneficial for both students and teachers. From the student’s perspective, it can make math more fun to learn. Many, many students don’t think math is fun to learn because it’s boring or too difficult. However, involving games makes math seem way more fun, exciting, and intriguing. When there’s a bit of competition involved, some points earned here and there, and chance for a comeback win, there’s no backing down! For example, in a game called Number Boxes, students have the opportunity to play each other in trying to create the biggest (or smallest) number possible from randomly generated numbers. Since there is fun and competition involved, students are much more entertained than they would be by simply doing a worksheet about this. </span></div><div><span style="white-space: normal;"><br /></span></div><div><span style="white-space: normal;">From a teacher's perspective, having students learn important mathematical subjects and develop important mathematical skills is much more effective through enjoyment rather than through a lecture. For instance, if a teacher is trying to teach their class about the coordinate plane and having them practice reading coordinates, a handful of students won’t pay attention and begin to struggle. This is because the concept itself sounds kind of boring and not something that will be useful someday. However, through my newly developed game Coordistroy, students practice these same skills in a more enjoyable way. Another reason why playing games in the classroom is encouraged is because students will learn problem solving, communication, teamwork, and strategic thinking skills all while learning about important mathematical ideas. Additionally, if students are doing something they enjoy, the chances of them remembering that topic is much higher than if the teacher is relying on memorization from the lecture. </span></div><div><span style="white-space: normal;"><br /></span></div><div><span style="white-space: normal;">In order to have an effective game used in either the classroom or even at home, it’s important to make sure there’s a good theme first of all. Without a theme, there’s no purpose to the game and there seems to be no point to it. Additionally, there needs to be a clear goal in which players must accomplish. If students can accomplish a goal with little to no time pressure, it will be a hit game! A few more factors that make a great game are if mistakes players make are handled productively and if there is a catchup factor. If a player is losing very badly, it’s never good to have a game that drives the knife even deeper into them. Having a game in which the last round or two is worth more points, then the student who is losing still has hope to make a comeback! </span></div><div><span style="white-space: normal;"><br /></span></div><div><span style="white-space: normal;">Overall, playing math games in the classroom has endless benefits not only revolving around mathematical topics themselves, but also around skills that students will use for the rest of their lives. They’re fun ways to learn about maybe not-so-fun topics and add a bit of competition too (cause who doesn’t like that?)</span></div></div></div>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-90559740270308658632024-01-03T16:31:00.001-05:002024-01-03T16:31:29.192-05:00Algebra Spoons - an Algebra Representations Math Game<p>All this month I'll be posting games from the Fall 2023 GAMES seminar at GVSU. This senior capstone was begun by Char Beckmann. See many of the games in this <a href="https://www.youtube.com/watch?v=dEUg3qp6zQo" target="_blank">YouTube playlist</a>. Many of the games completed in my seminar are in <a href="https://www.youtube.com/watch?v=wXpyTji0WgY" target="_blank">this playlist</a>. In the seminar, we play lots of games and math games, the future teachers make a first video to promote a class math game that already exists, we develop a group game (a monster-themed middle school <a href="https://teacher.desmos.com/activitybuilder/custom/6519f6dda4544090e16cbf2e" target="_blank">Desmos escape room</a> and <a href="https://youtu.be/smQAukReKSQ" target="_blank">Math Heads</a>, a number mystery game), and they develop a game of their own.</p><p>This post is sharing Corrina Campau's games - she was also the lead Desmos engineer on the escape room!</p><p>Her first video was for <a href="https://jennalaib.wordpress.com/2019/05/29/one-of-my-favorite-games-number-boxes/comment-page-1/" target="_blank">Jenna Laib's Number Boxes</a>. Really an all time great classroom math game, it was extra influential to this year's seminar. Like <a href="https://mathhombre.blogspot.com/2024/01/boxzee-flexible-computation-game.html" target="_blank">Jordan Burnham's game Boxzee</a>.</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="411" src="https://www.youtube.com/embed/MloUPPNhSVQ" width="495" youtube-src-id="MloUPPNhSVQ"></iframe></div><br /><p>Corrina's original game has an original deck of cards, which would have multiple uses, but is great in her Math Spoons (<a href="https://bit.ly/mathspoonscards" target="_blank">Cards</a> and <a href="https://bit.ly/mathspoonsrules" target="_blank">Rules</a>). What follows the video is her story of making the game, and some thoughts on why to play games in math class and which games are effective.</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="411" src="https://www.youtube.com/embed/jbyPq2SJbLI" width="494" youtube-src-id="jbyPq2SJbLI"></iframe></div><br /><p><b>The Story of Algebra Spoons</b></p><p>Whenever I take a class at GV I am always trying to see how I can use the class to become a more effective, engaging math instructor. In thinking about what my course content entails I became enthralled with the idea of having students differentiate between different function families. We study linear, quadratic, exponential and logarithmic functions and so this became my starting point. I wanted a game that would allow students to think about all of the function families as a whole. After playing some of the games in class I decided that one of the games that could work would be to design a game like SET where students must match cards based on different attributes. I kept thinking about SET and how I felt when I played the game. Although I like the game, I don’t always have fun playing it because I am not necessarily the fastest player when looking at 12 cards and trying to find matching ones. John mentioned Spoons in class one day, and I thought that was a really great idea. I have always enjoyed playing Spoons and so decided to roll with the idea. Thus, Algebra Spoons was born. I began to think of the number and type of cards needed. I decided to use linear, quadratic, and exponential function families with 4 cards in a set and 4 of each function family giving me a total of 48 cards per deck. I knew I needed to include graphs, stories, equations, and tables, but I wasn’t sure if I should choose a theme or not. I decided to use stories that related to GV students and even chose some stories like they had modeled in class – like the equation of the water as it comes out of the drinking water fountain. I hoped that the stories would appear somewhat familiar to them even if the story was new. Once the stories were written then I needed to make sure that the graphs showed the important characteristics of each story so that students would be able to determine the graphs that matched the stories with relative ease. I also examined the tables and made sure to include the portion of the table that made the most sense when trying to match the cards. For some of the quadratic functions I used vertex form and for some I used standard form. In retrospect, I wish I had included factored form as well. But making these cards took a considerable amount of time and thought, and unfortunately when I thought about factored form it was too late to change. Having finalized the front of the cards, I decided to make something on the back to make the cards more visually interesting. Thus, the spoons motif was added. Ten sets of cards were printed on card stock and printed out in color. </p><p>When I played the game with two of my MTH 109 classes, I first had them sort the cards so they could become familiar with them. After they had a chance to match all the cards, I then passed out the spoons, and they started playing the game. The students had so much fun! I was overjoyed to see how they embraced this game, and this was so much more fun than doing a standard final exam review. I would encourage all teachers to play this game as it really gives students a fun, enjoyable, and deep conceptual learning of different function families.</p><p><b>Why Play Games in the Math Classroom and What Makes a Game Effective?</b></p><p>Research shows that Games Based Learning (GBL), either digital or non-digital, in education is now one of the major learning trends of the 21st century. So, why are teachers playing more games in the classroom, and what makes a game effective as a learning tool? </p><p>First, for a game to be effective, a game needs to meet learning targets. Once an instructor has decided upon what the game should help students learn then a game can be found or created that allows students to meet those goals. In thinking about LeBlanc’s Taxonomy of Game Pleasures, we can understand the eight “primary pleasures” that arise from playing games and see how these game pleasures help to make games more enjoyable and when games are more enjoyable, they are often more effective. </p><p>A game that requires fewer materials is typically better because there is less set-up and typically less time spent learning to play the game. Having fewer rules or simplifying the rules is also important so students are not overwhelmed before they begin playing the game. Games where students’ interaction with other players affects their play attract different types of players and can make the game more fun to play for all players. A game that generates different situations or has the element of surprise can be more exciting and make players want to keep playing the game, and a game where an early advantage always causes a player to win is not as fun or effective as a game that allows all players an equal chance of winning. </p><p>When I play games in my classroom, I look for games that yield the best results in the least amount of time. I ask myself – what game can I play that allows students to understand, apply, analyze, evaluate, and create? Games always make learning fun and interactive, so when I tell students we are going to play a game there is always some excitement in the atmosphere. Games, if set up correctly, can provide low risk competition and meet learning targets in a manner that is more motivating for students. The structure of the game allows students to engage in problem solving in a way which is typically more enjoyable and more effective. Games create a more engaging learning environment and cause more students to pay attention to the teacher’s lessons, and they help students understand the concepts and retain the material better. Games are also able to reach students of all levels and function as confidence builders. In addition, game play encourages and deepens strategic mathematical thinking. Playing games in the classroom also allows educators to easily include active learning in the classroom. </p><p>Spending time creating games or selecting games that are already made is time well spent and worthwhile for students and a very effective way of presenting concepts, creating deep thinking, and motivating and encouraging students, and GBL should be included in every classroom.</p><p><i>Reference</i></p><p>Hui HB, Mahmud MS. Influence of game-based learning in mathematics education on the students' cognitive and affective domain: A systematic review. Front Psychol. 2023;14:1105806. Published 2023 Mar 28. doi:10.3389/fpsyg.2023.11058</p><div><br /></div><p><br /></p><div><br /></div>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-52134157472730451212024-01-02T22:14:00.005-05:002024-01-03T12:20:58.713-05:00Boxzee - Flexible Computation Game<p>All this month I'll be posting games from the Fall 2023 GAMES seminar at GVSU. This senior capstone was begun by Char Beckmann. See many of the games in this <a href="https://www.youtube.com/watch?v=dEUg3qp6zQo" target="_blank">YouTube playlist</a>. Many of the games completed in my seminar are in <a href="https://www.youtube.com/watch?v=wXpyTji0WgY" target="_blank">this playlist</a>. In the seminar, we play lots of games and math games, the future teachers make a first video to promote a class math game that already exists, we develop a group game (a monster-themed middle school <a href="https://teacher.desmos.com/activitybuilder/custom/6519f6dda4544090e16cbf2e" target="_blank">Desmos escape room</a> and <a href="https://youtu.be/smQAukReKSQ" target="_blank">Math Heads</a>, a number mystery game), and they develop a game of their own.</p><p>Jordan Burnham selected Close to Zero, and integer addition game for her first video. <a href="https://bit.ly/ClosetoZero" target="_blank">Handout</a> and <a href="https://mathhombre.blogspot.com/2011/02/integer-games.html" target="_blank">original blogpost</a>.</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="412" src="https://www.youtube.com/embed/aKE5aZEhai8" width="496" youtube-src-id="aKE5aZEhai8"></iframe></div><br /><p>Jordan's original game Boxzee crosses one of my favorite classroom games, <a href="https://jennalaib.wordpress.com/2019/05/29/one-of-my-favorite-games-number-boxes/" target="_blank">Number Boxes by Jenna Laib</a>, with the classic Yahtzee. What follows is Jordan's explanation of the game and thoughts on why play games in math class.</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="409" src="https://www.youtube.com/embed/PMi3HVM7Gw4" width="492" youtube-src-id="PMi3HVM7Gw4"></iframe></div><br /><p><span style="white-space: normal;"><b>Boxzee</b></span></p><p><span style="white-space: normal;">When I was first brainstorming games, I had absolutely no idea what kind of game I wanted to make. It wasn’t until one day when I was sitting on my bedroom floor that the starting ideas of Boxzee came to me.</span></p><p><span style="white-space: normal;">Originally I imagined the game to have more moving parts. I first had players each being dealt 4 cards. From there they would roll a dice twice to determine a specific operation they would be using (odds = subtract, evens = add). Then after finding out those operations you would choose 3 cards from your hand to find a largest total value for that specific round. I found that this became a little confusing and players wouldn’t necessarily be able to truly “compete” if all of their rounds operations were different than each other. If one player only rolled odd values then they would be predetermined to loose solely because the other players would have a better chance of having larger numbers if they rolled more even values. </span></p><p><span style="white-space: normal;">Moving on from here, I decided to instead come up with the number box sets. Rather than using the dice to determine operations I decided this was a more structured way that players could still affect the total value by the cards they put in without having so many moving parts. I first came up with the idea to have four different rounds. The players would both have 4 cards in their hands and needed 3 to fill into the number box sets. I also decided that they would both fill in the top box row, then move downward. After playing this a couple of times I realized it could be very common to tie. So then I chose to create a number box set that would be the final round and would use all of the cards in the players hand. I liked this much more. </span></p><p><span style="white-space: normal;">Then to incorporate more of a feel of Yahtzee, I decided that players should be able to substitute their cards into any of the top 4 number box sets of their choice in any order. This gives them more of a chance to use higher cards and lower cards when they have them for specific rows that those cards would be more valuable for each round. </span></p><p><span style="white-space: normal;">Some final touches were made after play testing with Professor Golden and my classmates. These included allowing players to chance any of the cards they have in their hand. I really enjoyed this change because it gives players more risk opportunities. The queen card was introduced as being a wild card during this time as well. I appreciated this idea because I feel like it allows players to more strategic and intentional about where they substitute certain card values into the number boxes. Finally I made a coupe of variations. I came originally came up with the addition and subtraction version of the game. I then decided to toy around with the idea of multiplication and division and made the multiplication and fractions versions.</span></p><p><span style="white-space: normal;">I think that teachers should play this with their students because it makes basic operations more exciting. I think that allowing students to have so much control over placing values into expressions and solving these is something they will enjoy. I also believe that it allows students to grasp where they may rather place a larger value versus a smaller value. Since the goal is to have the largest total value for each number box set, it will look different for each set. Placing a 9 in the same value that you place a 1 or a 0 has much different affects. </span></p><p><span style="white-space: normal;">I believe that this game can be adapted and used for so many reasons. The framework of the rules and rounds is something that creates such a great skeleton to then use with multiple content areas. I have thought about creating a Binomial Boxzee and think that this would be a great next step as well.</span></p><p><b>Why Play Math Games?</b></p><p><span style="white-space: normal;">Math can sometimes be a very intimidating subject area for some students. Because of this, I believe that it is important to keep the classroom environment exciting and reassuring that every student has the ability to be a mathematician no matter what level of skills they may think they have. To do this, incorporating games into the classroom can be very beneficial.</span></p><p><span style="white-space: normal;">Math games are a great resource for teachers to use to introduce and practice content. When playing games in the classroom in allows students to learn content in a more relaxed environment. This allows students to feel less pressure when making mistakes. This is important because students will be more likely to try and continue trying even after making mistakes which will help them master content areas. Similarly, playing these games allows students to build their strategic and problem solving skills. They want to perform their best and win, so they are able to develop strategies that can help them succeed throughout the game.</span></p><p><span style="white-space: normal;">I also believe math games are beneficial in the classroom because they can be interactive. This allows students to also help each other in teaching the math skills. By not only performing the skills needed for the game, but also using their skills to help teach their classmates they develop a deeper understanding for the content. </span></p><p><span style="white-space: normal;">Finally, playing math games allow students to build a love of math. When students are engaged and having fun playing these games, this is when they will be doing the most learning. Exposing students to games that are centered around math subjects, they will be able to see that math is more than just what they may be learning to compute in class.</span></p><p><span style="white-space: normal;">Now seeing some of the benefits associated with math games, it is also important to identify what makes a good game. One of the biggest things that I believe makes a good math game is having minimal time constraints. When students are practicing their math skills within a certain amount of time some may start to feel discouraged if they are not as fast as their other classmates. With this in mind, choosing games that give students the same opportunity to be successful at completing the game whether they are fast thinkers or need some extra time is very important. </span></p><p><span style="white-space: normal;">I also believe that a good math game allows for catch up. This means that even if a student is “down” in a game or is behind, there are aspects of the game that allow the players to quickly catch up and still have an opportunity to win. Since some students may not succeed right away, offering an opportunity for them to catch up and still have a chance to win this makes the game more fun for all players. This also makes students more likely to want to play and in turn allows them to practice and learn without the fear of losing. </span></p><p>In conclusion, math games being incorporated into the classroom that I urge many educators to try. Not only to practice content, but also to help build up students’ love for the subject and confidence in their own skills.</p><div><br /></div><p><br /></p>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-92190663123960997712024-01-01T13:50:00.003-05:002024-01-02T22:15:55.260-05:00GEO - Middle School Geometry Game<p>All this month I'll be posting games from the Fall 2023 GAMES seminar at GVSU. This senior capstone was begun by Char Beckmann. See many of the games in this <a href="https://www.youtube.com/watch?v=dEUg3qp6zQo" target="_blank">YouTube playlist</a>. Many of the games completed in my seminar are in <a href="https://www.youtube.com/watch?v=wXpyTji0WgY" target="_blank">this playlist</a>. In the seminar, we play lots of games and math games, the future teachers make a first video to promote a class math game that already exists, we develop a group game (a monster-themed middle school <a href="https://teacher.desmos.com/activitybuilder/custom/6519f6dda4544090e16cbf2e" target="_blank">Desmos escape room</a> and <a href="https://youtu.be/smQAukReKSQ" target="_blank">Math Heads</a>, a number mystery game), and they develop a game of their own.</p><p>Leah Barber selected Greater Than for her first video, an integer multiplication game. (<a href="https://bit.ly/GreaterThanGame" target="_blank">Handout</a>)</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="413" src="https://www.youtube.com/embed/Sl72f4hebZM" width="497" youtube-src-id="Sl72f4hebZM"></iframe></div><p><br /></p><p>Leah's original math game is a great spin on Uno called Geo. <a href="https://bit.ly/GEOcards" target="_blank">Cards</a> & <a href="https://bit.ly/GEOrules" target="_blank">Handout</a>. What follows is Leah's explanation of the game and thoughts on why play games in math class.</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="412" src="https://www.youtube.com/embed/XR-h_Zs_D2o" width="496" youtube-src-id="XR-h_Zs_D2o"></iframe></div><br /><p><b>How Geo Came To Be</b></p><p><span style="white-space: normal;">My idea of Geo came from Professor Golden mentioning Uno during one of our classes. I thought that Uno already included a lot of good components of a math game. This included number recognition, being able to categorize and identify different elements of a category, problem solving, catch-up factor, surprise elements, etc. Since Uno already had strong components of a math game I decided to create a game that was based on it. At the start I was thinking about doing a game that had to do with geometry so I began thinking of ways students could categorize shapes. Initially I didn’t know if I wanted students to create their own connections between different shapes, so I considered doing a Guess Who style game. However, after trying out a draft version of it I thought Geo would not only be less complicated but it would still offer students the opportunity to practice identifying shapes based on properties and computing area. From here I decided that instead of colors and numbers, like regular Uno, the two categories would be shape and area. Then I went through and made a rough draft of the game that iterated through many revisions until I was happy with its final form. Throughout these iterations I changed things like what the special action cards would be, what shapes would be included, how many cards would be included, what the shapes looked like, and what information I would include on the individual shape cards. </span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdv_yato7pCatnE7i7T3Oo2dn8pALPrnT-iiDW9TVfjAohzOe_6a-0DE7MCaZ4tRpG5oaJ069NCLUhq7dnnOWjNCb79xEtYf0TO2UZmi8kSZUsidg2ieR7I-FRhL_pUhI2Ds0NMyU9xH_XPAi56SuK1aZa_tT3R1kByldDNKSBEYiNuduyLEziDASTyUI/s1452/Screenshot%202024-01-01%20at%201.44.15%20PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="624" data-original-width="1452" height="276" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdv_yato7pCatnE7i7T3Oo2dn8pALPrnT-iiDW9TVfjAohzOe_6a-0DE7MCaZ4tRpG5oaJ069NCLUhq7dnnOWjNCb79xEtYf0TO2UZmi8kSZUsidg2ieR7I-FRhL_pUhI2Ds0NMyU9xH_XPAi56SuK1aZa_tT3R1kByldDNKSBEYiNuduyLEziDASTyUI/w640-h276/Screenshot%202024-01-01%20at%201.44.15%20PM.png" width="640" /></a></div><br /><span style="white-space: normal;"><br /></span><p></p><p>Why Teachers Should Play GEO:</p><p><span style="white-space: normal;">There are many reasons why teachers should play Geo with their students. Geo covers different Michigan Math Standards such as: CCSM. 6G.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons and CCSM. 5G: Classify two-dimensional figures into categories based on their properties. Beyond letting students practice finding the area of different polygons and identifying shapes by their properties, Geo helps students practice integer multiplication, reason mathematically, and build problem solving skills. Due to Geo being a competitive game, students often become engaged doing math, checking the work of other students, and reasoning mathematically in order to win. This is another reason why teachers should play Geo with their students. Geo allows students to engage in math in a fun, interactive way. Many learners have anxiety around math or think that it is boring, hard, irrelevant, etc. Geo is a way to get learners engaged and have fun while doing math. </span></p><p>Other Uses: </p><p><span style="white-space: normal;">The materials of Geo could be used outside of playing the game. Teachers could use the cards to create a memory style game where students try to match different areas or shapes. Other uses include going through the cards as examples of computing areas with students. Teachers could also play a Polygon Capture style game where students identify all the shapes they can that fit under the different command cards. Following playing Geo teachers could have a discussion with students about what they noticed or wondered when playing the game. This could start a good dialogue about different shape properties, how different shapes are related or different, definitions of shapes, etc. They could also have students discuss strategies and problem solving skills they used to try to win. </span></p><p><b>Why Play Math Games</b>? </p><p>There are many reasons to play games in the math classroom. To start, math games allow students to engage in mathematics in a fun, interactive way. Students often think that math is boring, too analytical, irrelevant, etc. By playing games in the classroom students can experience math in a way that it often isn't presented to them. This can also dispel anxieties many students experience with math. Due to previous bad experiences with math, whether it be a harsh teacher, tough material, or overwhelming course load, students can develop anxiety surrounding math. This can also affect how students think of themselves. Bad experiences with math that cause students to do poorly can lead to them thinking they are dumb or not a “math person”. By involving games into lessons students can create positive experiences with math and start to dispel any anxiety or negative thoughts surrounding math.</p><p>Math games also allow students multiple entry points to engage in math. Oftentimes this idea of not being a “math person” is due to inaccessible lessons. By including a math game in a lesson you can create many opportunities for students to participate in math. A good math game includes some aspect of luck, strategy, catch up, or surprise that allow students who are struggling to still succeed. By creating accessible activities for students they can start to think of themselves as someone who is capable of doing math. </p><p>Getting students to reason and express themselves mathematically can be challenging. Often students don’t want to participate in discussions in math class due to a multitude of reasons. Including a math game however is a great way to get students talking about math. Due to the competitive nature of games students are more likely to reason, argue, make conjectures, and express mathematical ideas in order to win. This creates a great dialogue where students can think through material covered in class together and come to conclusions on their own. By doing this students will continue to grow their self concept as a mathematician and be able to better communicate mathematical ideas. Math games also help students build problem solving skills. A good math game has players interacting with each other and constantly trying to figure out their next move. As stated before a good math game also includes strategy. These elements allow students to build their problem solving skills as they identify what they need to do to win, how they are going to do that, executing their plan, assessing how it worked, and what they will do next time. </p><p>Lastly, including math games in the classroom is a great idea because it is a great way to introduce, explore, or practice mathematical concepts. Teachers or parents may feel that including a game in a lesson will distract students from their learning. This however is not the case. Math games are not something that is just filler. Instead math games are great ways to introduce new concepts by allowing students to get familiar or explore with new ideas in a low stakes, fun environment. Math games can also be used to help students review a concept they already learned by applying their knowledge in a new way. </p><div><br /></div>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-62291038595748191342023-12-28T22:02:00.001-05:002023-12-28T22:02:38.525-05:002023<p> So what have I been up to?</p><p>The biggest project this year has been working on Teaching Like Ted Lasso. 95% or more is Dave Coffey - inspiration, planning, and production. And I get to play along! There's a <a href="https://www.youtube.com/@teachingliketedlasso6034" target="_blank">YouTube channel</a> and the <a href="https://shows.acast.com/teaching-like-ted-lass" target="_blank">home for all the audio</a>. We get to talk to so many interesting researchers and teachers. </p><p>One of my favorite interviews this year was Nicora Placa:</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/QCfaoJbPHto" width="320" youtube-src-id="QCfaoJbPHto"></iframe></div><br /><p>I also get to commute with my son Xavier, a first year high school art teacher, and have an occasional low-tech, barely produced podcast with him, <a href="https://podcasters.spotify.com/pod/show/john-golden5/" target="_blank">Background Noise</a>. It's a little art education, a little math education, and mostly just talking teaching.</p><p>Speaking of teaching, after years of a highly variable teaching load, it has settled into a couple elementary math teacher education courses, a high school math education course, a seminar where a smaller group of students develop math games, and a math history capstone. One of the elementary courses is actually in an elementary school. The future teachers get to actually teach kids every class day, feedback from great teachers, observation by me and another student (when I can get one). The framework my colleague Esther developed for this (with others) is <a href="https://www.researchgate.net/profile/Melinda-Knapp/publication/329388877_WORKING_TO_UNDERSTAND_MEDIATED_FIELD_EXPERIENCES_AND_STUDY_THEIR_IMPACT/links/5c06033f299bf169ae3051d5/WORKING-TO-UNDERSTAND-MEDIATED-FIELD-EXPERIENCES-AND-STUDY-THEIR-IMPACT.pdf" target="_blank">mediated field experience</a>. We spoke about it at a local math teacher education conference. Here's <a href="https://bit.ly/CAC23-MFE" target="_blank">the handout</a>. The course page for the class is <a href="http://bit.ly/226-W23" target="_blank">bit.ly/226-W23</a>, and the lessons I wrote for the teaching (with a wide range of influences, colleagues, articles, curricula...) are <a href="https://docs.google.com/document/d/1oiPULyNUDBNP_8zClUzaXR4MDWo913fu0YA9F8kDMos/edit" target="_blank">here</a>. </p><p>There will soon (fingers crossed) be a series of blogposts with this year's games. We actually wound up with two seminars of five each. Good stuff from elementary to secondary. One group developed a middle school <a href="https://teacher.desmos.com/activitybuilder/custom/6519f6dda4544090e16cbf2e" target="_blank">Desmos Escape Room</a> with a spooky monster theme. As a teaser, here's the video for one of our group games, Math Heads, which has been tested with 6th grade middle school students, algebra students and college math majors. Ryan Brummel made this video. Here's the handout with the rules and a form to support players, <a href="http://bit.ly/MathHeads" target="_blank">bit.ly/MathHeads</a>. </p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/smQAukReKSQ" width="320" youtube-src-id="smQAukReKSQ"></iframe></div><br /><p>I continue to futz about with math/art. </p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgAzRUOrSWiD-E51cbhK5zeGPAcqftDXOxgz9nudWZ9fSoRWsTGdC4LQe3fmyl8o2nPSvdaKyFxrnt4HYvDHRIIaiQJvIg7MZK-e8gYGKS_ra0jisQK5Nnq6WTk3V31tf_uNPmt2J71nRI8rv7kxpNoIY7uESe097BktgsyfD6ME5Kz-ljV6qX3kOoXz8s" style="margin-left: 1em; margin-right: 1em;"></a><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgAzRUOrSWiD-E51cbhK5zeGPAcqftDXOxgz9nudWZ9fSoRWsTGdC4LQe3fmyl8o2nPSvdaKyFxrnt4HYvDHRIIaiQJvIg7MZK-e8gYGKS_ra0jisQK5Nnq6WTk3V31tf_uNPmt2J71nRI8rv7kxpNoIY7uESe097BktgsyfD6ME5Kz-ljV6qX3kOoXz8s" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgZ40a96xYPp9fhCZ8HrvHz2zyIS_5O1eRJNLKVEzr9Ybrdg8h9f5bC-8YkJ38tZl2KXUHgV0LBG-H_ZziS7s5eg_OUf5Hi8bMBlHjDL_ZX-fLT7raeOfXznUT3UXHtZmAJ2ElYkGTibnIfn7e2oRF5KskCmRGEuCXVx1sm7rlbPFOw6DrRBmeWwDnQCH8" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" data-original-height="398" data-original-width="509" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgZ40a96xYPp9fhCZ8HrvHz2zyIS_5O1eRJNLKVEzr9Ybrdg8h9f5bC-8YkJ38tZl2KXUHgV0LBG-H_ZziS7s5eg_OUf5Hi8bMBlHjDL_ZX-fLT7raeOfXznUT3UXHtZmAJ2ElYkGTibnIfn7e2oRF5KskCmRGEuCXVx1sm7rlbPFOw6DrRBmeWwDnQCH8" width="307" /></a></div><img alt="" data-original-height="335" data-original-width="428" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgAzRUOrSWiD-E51cbhK5zeGPAcqftDXOxgz9nudWZ9fSoRWsTGdC4LQe3fmyl8o2nPSvdaKyFxrnt4HYvDHRIIaiQJvIg7MZK-e8gYGKS_ra0jisQK5Nnq6WTk3V31tf_uNPmt2J71nRI8rv7kxpNoIY7uESe097BktgsyfD6ME5Kz-ljV6qX3kOoXz8s" width="307" /></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEga6ZNIsmsDqZm6ruCEd35t4SHcTSUdzqPK7UuhpQme7m2Y47a9SMARqYEp6RNzDvvNqjhVWgYvHJfnOyLzUN_6sukvBxyL8j1D7hzGZi5PSqShU7mmbS0E6RP3o4ctu3YRdu6A9fws-oSt7W8CPx8MbYKTjbxdepOy5oFUOA6NV7bf8YFM7vMAaJ0k8ss" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1016" data-original-width="1298" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEga6ZNIsmsDqZm6ruCEd35t4SHcTSUdzqPK7UuhpQme7m2Y47a9SMARqYEp6RNzDvvNqjhVWgYvHJfnOyLzUN_6sukvBxyL8j1D7hzGZi5PSqShU7mmbS0E6RP3o4ctu3YRdu6A9fws-oSt7W8CPx8MbYKTjbxdepOy5oFUOA6NV7bf8YFM7vMAaJ0k8ss" width="307" /></a></div><br /><p></p><p></p><p></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg7EEXsgSc13nTGvSoQKCLsfOQD0lJAJGW6f9m0kZPbrRjcw1ysg3rpYYUkpeRKq33vQPcaKYRN6CqDy9eydc6rcKMCBtM_N754tJvhP31WRmhsWM18gAAe9W2Z-hIADKCC6zm4HWG0Py5QIVDIaN1k4TORkcjiL3fS4eIK9XN-7HSPHz5NZGufqk7UM-0" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="488" data-original-width="488" height="320" src="https://blogger.googleusercontent.com/img/a/AVvXsEg7EEXsgSc13nTGvSoQKCLsfOQD0lJAJGW6f9m0kZPbrRjcw1ysg3rpYYUkpeRKq33vQPcaKYRN6CqDy9eydc6rcKMCBtM_N754tJvhP31WRmhsWM18gAAe9W2Z-hIADKCC6zm4HWG0Py5QIVDIaN1k4TORkcjiL3fS4eIK9XN-7HSPHz5NZGufqk7UM-0=w320-h320" width="320" /></a></div><p></p><p>From <a href="https://mathhombre.tumblr.com/post/737721085264625664/apollonio-disk" target="_blank">one</a>, <a href="https://mathhombre.tumblr.com/post/735363718809092096/schleifer-turning" target="_blank">two</a>, <a href="https://mathhombre.tumblr.com/post/734714158706278400/vasarely-hexes" target="_blank">three</a>, <a href="http://four." target="_blank">four.</a> The Tumblr posts have variations and links to the GeoGebra for generating them.</p><p>I <a href="https://www.tumblr.com/talkingnumbers" target="_blank">cartoon</a> when I have time or am challenged like in Mathober. They're pretty geeky. Some are college + math and some are elementary.</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEja5F-jFTppsbYI6Iax6wm4fxJxjRPj-6NZq8YrMqhmR3kZ_K7jziV9oQ3koVsxy4UBcueV8q2fyZApfjq4oZwnatby2RdmcLcY03ZQGKA-2Ib96QAZcCNMGlawYenjzGDpgy6Y3GPqK-738goc4oS52cyoRo-LOExlAHqjIBFlFYtGdUYS344tsIjVRBc" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="894" data-original-width="1280" height="448" src="https://blogger.googleusercontent.com/img/a/AVvXsEja5F-jFTppsbYI6Iax6wm4fxJxjRPj-6NZq8YrMqhmR3kZ_K7jziV9oQ3koVsxy4UBcueV8q2fyZApfjq4oZwnatby2RdmcLcY03ZQGKA-2Ib96QAZcCNMGlawYenjzGDpgy6Y3GPqK-738goc4oS52cyoRo-LOExlAHqjIBFlFYtGdUYS344tsIjVRBc=w640-h448" width="640" /></a></div><br />Just a sampler... what have you been working on?<p></p>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-78044880046565116422023-10-30T22:22:00.005-04:002023-11-03T12:55:28.116-04:00Playful Math Carnival 169<p><span style="font-family: inherit;"> Do you want to host the 13^2 Playful Math carnival in October? A month that had a <a href="https://mathhombre.tumblr.com/post/731110785200357376" target="_blank">Friday the 13th</a>? </span></p><p><span style="font-family: inherit;">Yes, please. Should have been on 10/13 instead of 10/31 but... apologies.</span></p><p><span style="font-family: inherit;">169 is a palindrome in two number bases less than 16. Which do you suppose?</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq-T0qNC7PZpE4CSNwiWhKPQQJrurTCN3q232ttmEfYcobiDBEoLB-2e5QEtMUSc74lonnV-RLKqg-ft60d461-G3zUps6RuIxVCcHu93lrIsjxSv5CS9ETrPy-5GzbDPzAJrXf0KrQDkGipmRh_ym31wJVlSP_LB7u9IQ0-Qv50sxgluAkmuBsGVdlj8/s1058/Screenshot%202023-10-30%20at%201.18.34%20PM.png" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><span style="font-family: inherit;"><img border="0" data-original-height="950" data-original-width="1058" height="179" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq-T0qNC7PZpE4CSNwiWhKPQQJrurTCN3q232ttmEfYcobiDBEoLB-2e5QEtMUSc74lonnV-RLKqg-ft60d461-G3zUps6RuIxVCcHu93lrIsjxSv5CS9ETrPy-5GzbDPzAJrXf0KrQDkGipmRh_ym31wJVlSP_LB7u9IQ0-Qv50sxgluAkmuBsGVdlj8/w200-h179/Screenshot%202023-10-30%20at%201.18.34%20PM.png" width="200" /></span></a></div><span style="font-family: inherit;">All odd squares are centered octagonal numbers, but 169 is also a centered hexagonal. (Visualize more with Alex CHIK's <a href="https://www.geogebra.org/m/eccDThJp" target="_blank">GeoGebra</a>.)</span><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">It is the smallest square that is prime upside down! What on earth could the next one be? Also 1666666999999999 is prime. What would you call that property? (Both via <a href="https://t5k.org/curios/page.php/169.html" target="_blank">PrimeCurios</a>.)</span></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">It's the last square in the <a href="https://en.wikipedia.org/wiki/Pell_number" target="_blank">Pell sequence</a>, which are connected to approximations of π. What numerator n makes n/129 an approximation of π?<br /></span><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJKzJoSqszvcx-yiAqLYNjNZA0s8gbd83eGW53Ms3S6sfv8dBGOpCc91F3uJevV3qyDFeb6RFmz7F0yvDYTFQ_T7KQe9YqiBWICUn-rVzFgi6tRD6aYU_wzEqTqbc5DOWhOCWNUg_aL9Jo0vzIAugjkzSuhTfqNRILRIjvm72EYlEXWsk_rxWKtkTak-g/s924/Screenshot%202023-10-30%20at%201.18.54%20PM.png" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="font-family: inherit;"><img border="0" data-original-height="916" data-original-width="924" height="198" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJKzJoSqszvcx-yiAqLYNjNZA0s8gbd83eGW53Ms3S6sfv8dBGOpCc91F3uJevV3qyDFeb6RFmz7F0yvDYTFQ_T7KQe9YqiBWICUn-rVzFgi6tRD6aYU_wzEqTqbc5DOWhOCWNUg_aL9Jo0vzIAugjkzSuhTfqNRILRIjvm72EYlEXWsk_rxWKtkTak-g/w200-h198/Screenshot%202023-10-30%20at%201.18.54%20PM.png" width="200" /></span></a></div><b><span style="font-family: inherit;">Puzzling</span></b></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">I'm using tangrams in an elementary math ed course as our primary manipulative to talk geometry, so I maybe have been too on the lookout. Simona Riva has a great <a href="https://www.geogebra.org/m/kyzukdsr" target="_blank">GeoGebra collection</a> of activities. Polypad has a great <a href="https://mathigon.org/tangram" target="_blank">tangram puzzle</a> collection. Here are some I found on <a href="https://docs.google.com/document/d/1eUwTNgnQeKhhfUCVPYqXmvHTt704h5aA7BpocDpTGyM/edit?usp=sharing" target="_blank">a cereal box</a>! But most of all, you have to see Paula Beardell Krieg's amazing <a href="https://bookzoompa.wordpress.com/category/summertangrams-2023/" target="_blank">series of tangram posts</a> from this summer.</span></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">Futility Closet shared a ridiculous <a href="https://www.futilitycloset.com/2023/10/05/a-panmagic-geomagic-square/" target="_blank">Lee Sallows pangeomagic square</a>.</span></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">Bakingmoomins made a <a href="https://bakingmoomins.tumblr.com/post/732082751432491008/hat-out-of-aperiodic-monotiles-is-finally" target="_blank">Hat Hat</a> with the new Einstein tile.</span></div><div><span style="font-family: inherit;"><br /></span></div><div><b><span style="font-family: inherit;">Games</span></b></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">Always on the lookout for games. Tracy Proffitt has an <a href="https://sites.google.com/view/games4math" target="_blank">awesome collection</a>, well organized.</span></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">Interesting <a href="https://nrich.maths.org/10654" target="_blank">double or halve game</a> from NRICH.</span></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">Sarah Carter shared <a href="https://mathequalslove.net/ghost-game/" target="_blank">the Ghost Game</a>, fun logic/strategy game.</span></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">Sophia Wood and Kate Nowak with a great math game over on Brilliant: <a href="https://brilliant.org/challenges/halfsies/" target="_blank">Halfsies</a></span></div><div><span style="font-family: inherit;"><br /></span></div><div><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhf1g9_df0CwyhGRggvN4lZFC8mvgUa9JRgLzfTbOxivUM_e8tE0zMNZcnX_f_DI0VclTlALa9k8Vc7lebBH7GpJuRCXwyaMLMGFVfXKsvjKKj_vG4bvbVfJcA_ZljgnJmHhNmVn7T1HsWXz448Dy31xdRGdIuNB4fG55BRqCQ40k54MhMMQdeNcwGVTAs" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><span style="font-family: inherit;"><img alt="" data-original-height="534" data-original-width="800" height="214" src="https://blogger.googleusercontent.com/img/a/AVvXsEhf1g9_df0CwyhGRggvN4lZFC8mvgUa9JRgLzfTbOxivUM_e8tE0zMNZcnX_f_DI0VclTlALa9k8Vc7lebBH7GpJuRCXwyaMLMGFVfXKsvjKKj_vG4bvbVfJcA_ZljgnJmHhNmVn7T1HsWXz448Dy31xdRGdIuNB4fG55BRqCQ40k54MhMMQdeNcwGVTAs" width="320" /></span></a><b><span style="font-family: inherit;">Content</span></b></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">Jenna Laib interviewed Kindergartners about zero. <a href="https://jennalaib.wordpress.com/2023/09/19/is-zero-a-number-interviews-with-a-whole-class-of-kindergartners/" target="_blank">Great read</a>!</span></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;"><span style="font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Steve Phelps is the most amazing teacher with tech I know. He has a </span><a href="https://teacher.desmos.com/activitybuilder/custom/653d86374d825f5d866ad736" style="text-decoration-line: none;"><span style="color: #1155cc; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; text-decoration-line: underline; text-decoration-skip-ink: none; vertical-align: baseline; white-space-collapse: preserve;">geometric constructions Desmos activity</span></a><span style="font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">.</span></span></div><div><span><span style="font-family: inherit; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><br /></span></span></div><div><span><span style="font-family: inherit; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Eugenia Cheng on NPR addressing "<a href="https://www.npr.org/transcripts/1193035114" target="_blank">Is math real</a>?"</span></span></div><div><span><span style="font-family: inherit; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><br /></span></span></div><div><span><span style="font-family: inherit; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Mathigon now has an <a href="https://mathigon.org/multiply" target="_blank">online implementation of Multiply by Heart</a> by Dan Finkel.</span></span></div><div><span><span style="font-family: inherit; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><br /></span></span></div><div><span><span style="font-family: inherit; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">NCTM has a new line of kids books on <a href="https://www.nctm.org/store/powerfulmath/" target="_blank">Powerful Mathematicians Who Changed the World</a>.</span></span></div><div><span><span style="font-family: inherit; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><br /></span></span></div><div><span><span style="font-family: inherit; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Karen Campe has a calendar of problems every month, solutions at the end of the month. <a href="https://karendcampe.wordpress.com/2023/10/02/october-calendar-problems/" target="_blank">Here's October</a>.</span></span></div><div><span><span style="font-family: inherit; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><br /></span></span></div><div><span style="font-family: inherit;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEil6IMslCV9HiT9hN3Yvf-UpqIEvbYELSnhC7_HFV-_ISw89pV3H6jgOBFDrDyzPMFCuL_FZthPQ4ouB459UB_8ZGBxhySzVwhBZ8nLNIPa3fvpJuUrgMetE5wuojJmPaFPLVWsX-IBmt4iKTYWVIFFRofx7scIGSeBL3Zy6Sx2tKkzOymmEqJ7u6zqYd0" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><span style="font-family: inherit;"><img alt="" data-original-height="333" data-original-width="500" height="213" src="https://blogger.googleusercontent.com/img/a/AVvXsEil6IMslCV9HiT9hN3Yvf-UpqIEvbYELSnhC7_HFV-_ISw89pV3H6jgOBFDrDyzPMFCuL_FZthPQ4ouB459UB_8ZGBxhySzVwhBZ8nLNIPa3fvpJuUrgMetE5wuojJmPaFPLVWsX-IBmt4iKTYWVIFFRofx7scIGSeBL3Zy6Sx2tKkzOymmEqJ7u6zqYd0" width="320" /></span></a></div><b><span style="font-family: inherit;">Humor</span></b></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">Sara VanDerWerf pointed out that SNL did a <a href="https://www.youtube.com/watch?v=JYqfVE-fykk" target="_blank">measurement skit</a>. Warning: actually funny.</span></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">Kassia Wedekind shared a <a href="https://www.mcsweeneys.net/articles/you-must-teach-this-new-curriculum-with-fidelity" target="_blank">McSweeney's post</a> from a teacher about teaching a curriculum with fidelity. Warning: a little too close to reality.</span></div><div><span style="font-family: inherit;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEieuZxx4WMlnVBJHQBMYAzlplewrp3M6dtfAGGiWC7DzHmm_GW-rfKzJdk8lplto-LiSqILepGb2uzsBxOEwZ8HSy41BAwv54Es9PifAsITXctuaBhsfQkJakMhpqTwXDoULQWB658C4IdNJePW6yluAwaceMdcUXluOIsDdekhEBb1Fs_9r06xKRJPLnw" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><span style="font-family: inherit;"><img alt="" data-original-height="375" data-original-width="500" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEieuZxx4WMlnVBJHQBMYAzlplewrp3M6dtfAGGiWC7DzHmm_GW-rfKzJdk8lplto-LiSqILepGb2uzsBxOEwZ8HSy41BAwv54Es9PifAsITXctuaBhsfQkJakMhpqTwXDoULQWB658C4IdNJePW6yluAwaceMdcUXluOIsDdekhEBb1Fs_9r06xKRJPLnw" width="320" /></span></a></div><b><span style="font-family: inherit;">Fashion</span></b></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">Fashion? Libo Valencia has #mathplay <a href="https://www.bonfire.com/store/math-play/" target="_blank">t-shirts</a> to go with <a href="https://www.amazon.com/dp/1990566561" target="_blank">his cool book</a>.</span></div><div><span style="font-family: inherit;"><br /></span></div><div><b><span style="font-family: inherit;">Mathober</span></b></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;"><a href="https://fractalkitty.com/2023/10/01/mathober-pieces/" target="_blank">Sophia Wood</a> started #Mathober a few years ago. Art and more on a math theme. Find many posts on <a href="https://twitter.com/search?q=%23mathober2023&src=typed_query&f=live" target="_blank">Twitter</a> or <a href="https://mathstodon.xyz/deck/tags/mathober2023" target="_blank">Mastodon</a> or <a href="https://bsky.app/search?q=mathober2023" target="_blank">Bluesky</a>. I've been liking <a href="https://www.youtube.com/watch?v=8W-hYyN8Yw4" target="_blank">Katie Steckles</a>' π minute GeoGebra videos.</span></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;"><b>Last Stop</b><br /><br /></span><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgqpNRYdjWJfD4ZwZTFEln467gGwYRusGXtwZQK8UzZii0hXv3Wu1-3NMBfKoaIXCHALj0VMIjDnQPUqZmXNgjFyF5cE1s7bP6WX7P0H1h6cLhFHU1N0J0dy6QkfO4bU7lcsrg8jkQteeHPnE7xzROwma6OSQ4PwMuJ3_QbYb_keLzYcL2lDs57dZv1b1Q" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><span style="font-family: inherit;"><img alt="" data-original-height="450" data-original-width="600" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgqpNRYdjWJfD4ZwZTFEln467gGwYRusGXtwZQK8UzZii0hXv3Wu1-3NMBfKoaIXCHALj0VMIjDnQPUqZmXNgjFyF5cE1s7bP6WX7P0H1h6cLhFHU1N0J0dy6QkfO4bU7lcsrg8jkQteeHPnE7xzROwma6OSQ4PwMuJ3_QbYb_keLzYcL2lDs57dZv1b1Q" width="320" /></span></a></div><span style="font-family: inherit;">Last but not least, two playful bits from my students! Corinna, Leah, Jordan, Kacy and Jill made a <a href="https://teacher.desmos.com/activitybuilder/custom/6519f6dda4544090e16cbf2e" target="_blank">Spooky Monster Escape Room</a> in Desmos Activities. Ryan, Keri, Alex, Anna, and Emma have a new headbandz inspired math game for grades 5 and up called <a href="https://docs.google.com/document/d/1qMQltDeqx29hCAEpJI6iMA2u3xM2je76nHyZTibbqWw/edit" target="_blank">Math Heads</a>. And by up, we mean up to college math majors!<br /><br />At the home of the <a href="https://denisegaskins.com/mtap/" target="_blank">Playful Math Carnival</a>, you can find previous, like <a href="https://findthefactors.com/2023/08/25/the-168th-playful-math-education-blog-carnival/" target="_blank">168</a> at find your factors, or connect to host yourself. I'd highly recommend it! Find the next one, Nov/Dec at the <a href="https://fairymathmother.com/" target="_blank">Fairy Math Mother</a>. Should be magical.<br /></span><p><span style="font-family: inherit;">This is my stop! Hope you had fun.</span></p><p><span style="font-family: inherit;">P.S. This will get you to go. Ed Southall asked AI to make images of people enjoying math...</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiqRCM098BFAzowTweHJLHNa9r0tjbYYNxuIb5bSKCyEHs67bVSc8Ljkkinfn8kmVCFltDWr6SVTdN7hNjERh5p0vvgK3MnPYfICji9SVxEFxNebuUkaxTT-RCMXTMbAPBtr0vaNxcHvRzDOSQQZVnUivLKWoTioZa-h_VJxs_F5IkT2SgTTf4x23rxgz8" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: inherit;"><img alt="" data-original-height="538" data-original-width="934" height="230" src="https://blogger.googleusercontent.com/img/a/AVvXsEiqRCM098BFAzowTweHJLHNa9r0tjbYYNxuIb5bSKCyEHs67bVSc8Ljkkinfn8kmVCFltDWr6SVTdN7hNjERh5p0vvgK3MnPYfICji9SVxEFxNebuUkaxTT-RCMXTMbAPBtr0vaNxcHvRzDOSQQZVnUivLKWoTioZa-h_VJxs_F5IkT2SgTTf4x23rxgz8=w400-h230" width="400" /></span></a></div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: inherit;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhuEDMcE5yQ05oOzSRQjgg7v4ZJavNUHt5H20IjPr1aWKvToxRRsSutuYTlrI_8ASIxDwYaAHPDpy_ZB6wTymqYMFh0Nm8M_hkTsrjJluGaUTuL9gpvxpp-HT6tSVKWDCHA1S3pBpYOZDQBTEndTHD3SU314oSx6N7oxrUWFS1v4sdnZa8CtVTjsl0pntc" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: inherit;"><img alt="" data-original-height="592" data-original-width="1036" height="229" src="https://blogger.googleusercontent.com/img/a/AVvXsEhuEDMcE5yQ05oOzSRQjgg7v4ZJavNUHt5H20IjPr1aWKvToxRRsSutuYTlrI_8ASIxDwYaAHPDpy_ZB6wTymqYMFh0Nm8M_hkTsrjJluGaUTuL9gpvxpp-HT6tSVKWDCHA1S3pBpYOZDQBTEndTHD3SU314oSx6N7oxrUWFS1v4sdnZa8CtVTjsl0pntc=w400-h229" width="400" /></span></a></div><span style="font-family: inherit;"><br /><br /><br /></span><p></p><p><span style="font-family: inherit;"><br /></span></p><p><span style="font-family: inherit;"><br /></span></p><p><span style="font-family: inherit;"><br /></span></p><p><span style="font-family: inherit;"><br /></span></p><p><span style="font-family: inherit;"><br /></span></p><p><span style="font-family: inherit;"><br /></span></p><p><br /></p></div>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-64074434086089986362023-10-05T13:51:00.002-04:002023-10-05T13:51:22.910-04:00Elicit Student Thinking<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiR5hCrTznscdzjYUbdq_yrVj1mnfmz7xXW3dkU5w5Skbc4mc08O8F0IGbwjfWPwiNhiqRycxiXVizsaG7fNya-x52rvJVYWWaatyQMMLCV2W8JU3PGabwRptAm37DKXeb-8-2d9ARJb7ByIF-dtAHFXf0PRVYLs5EOAEwXdEuVtWF-lP_14pUdPq9ek-0/s571/Hulk-thinking.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="571" data-original-width="566" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiR5hCrTznscdzjYUbdq_yrVj1mnfmz7xXW3dkU5w5Skbc4mc08O8F0IGbwjfWPwiNhiqRycxiXVizsaG7fNya-x52rvJVYWWaatyQMMLCV2W8JU3PGabwRptAm37DKXeb-8-2d9ARJb7ByIF-dtAHFXf0PRVYLs5EOAEwXdEuVtWF-lP_14pUdPq9ek-0/s320/Hulk-thinking.jpg" width="317" /></a></div><br />In Michigan, at least, the <a href="https://library.teachingworks.org/curriculum-resources/high-leverage-practices/" target="_blank">high leverage practices</a> are dominating the teacher preparation conversation. For our new certification programs, the state waaants to know where are we doing it. Nothing new there, just... enumerated. Some are beyond what we can do in math classes. But where it all starts for us, I think, is <a href="https://library.teachingworks.org/curriculum-resources/teaching-practices/eliciting-and-interpreting/" target="_blank">eliciting student thinking</a>. I have an interview project coming up, in an elementary teaching class I'm teaching for the first time, and thought to ask on social media what teachers do or think about this core process. (Used to just be <a href="https://x.com/mathhombre/status/1708809091844350210?s=20" target="_blank">Twitter</a>, now I'm trying <a href="https://mathstodon.xyz/@mathhombre/111165234235512743" target="_blank">Mastodon</a> and <a href="https://bsky.app/profile/johngolden.bsky.social/post/3kard3dnbhi2l" target="_blank">BlueSky</a>.)<p></p><p><span class="r-18u37iz" style="-webkit-box-direction: normal; -webkit-box-orient: horizontal; background-color: white; color: #0f1419; flex-direction: row; font-family: TwitterChirp, -apple-system, "system-ui", "Segoe UI", Roboto, Helvetica, Arial, sans-serif; font-size: 17px; white-space-collapse: preserve;"><a class="css-4rbku5 css-18t94o4 css-901oao css-16my406 r-1cvl2hr r-1loqt21 r-poiln3 r-bcqeeo r-1ny4l3l r-1ddef8g r-tjvw6i r-qvutc0" dir="ltr" href="https://twitter.com/hashtag/classroommath?src=hashtag_click" role="link" style="background-color: rgba(0, 0, 0, 0); border: 0px solid black; box-sizing: border-box; color: #1d9bf0; cursor: pointer; display: inline; font: inherit; list-style: none; margin: 0px; min-width: 0px; outline-style: none; overflow-wrap: break-word; padding: 0px; text-align: inherit; text-decoration-thickness: 1px; white-space: inherit;">#classroommath</a></span><span class="css-901oao css-16my406 r-poiln3 r-bcqeeo r-qvutc0" style="background-color: white; border: 0px solid black; box-sizing: border-box; color: #0f1419; display: inline; font-family: TwitterChirp, -apple-system, "system-ui", "Segoe UI", Roboto, Helvetica, Arial, sans-serif; font-feature-settings: inherit; font-kerning: inherit; font-optical-sizing: inherit; font-size: 17px; font-stretch: inherit; font-variant-alternates: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; font-variant-position: inherit; font-variation-settings: inherit; line-height: inherit; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space-collapse: preserve;"> </span><span class="r-18u37iz" style="-webkit-box-direction: normal; -webkit-box-orient: horizontal; background-color: white; color: #0f1419; flex-direction: row; font-family: TwitterChirp, -apple-system, "system-ui", "Segoe UI", Roboto, Helvetica, Arial, sans-serif; font-size: 17px; white-space-collapse: preserve;"><a class="css-4rbku5 css-18t94o4 css-901oao css-16my406 r-1cvl2hr r-1loqt21 r-poiln3 r-bcqeeo r-qvutc0" dir="ltr" href="https://twitter.com/hashtag/mtechat?src=hashtag_click" role="link" style="background-color: rgba(0, 0, 0, 0); border: 0px solid black; box-sizing: border-box; color: #1d9bf0; cursor: pointer; display: inline; font: inherit; list-style: none; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-align: inherit; text-decoration-line: none; white-space: inherit;">#mtechat</a></span><span class="css-901oao css-16my406 r-poiln3 r-bcqeeo r-qvutc0" style="background-color: white; border: 0px solid black; box-sizing: border-box; color: #0f1419; display: inline; font-family: TwitterChirp, -apple-system, "system-ui", "Segoe UI", Roboto, Helvetica, Arial, sans-serif; font-feature-settings: inherit; font-kerning: inherit; font-optical-sizing: inherit; font-size: 17px; font-stretch: inherit; font-variant-alternates: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; font-variant-position: inherit; font-variation-settings: inherit; line-height: inherit; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; white-space-collapse: preserve;"> one of the main objectives with preservice teachers is to work on the practice of eliciting student thinking. What advice do you have for them? How did you get better at it? What are you working on now?</span></p><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px; text-align: left;"><p>Lani Horn had a quick, impactful response (bsky). "I find that the work of eliciting needs to be followed with some work on listening and interpreting. i have seen some folks stop at just eliciting, and it becomes "what do you think? what do you think?" without any connections built."</p><p>Elizabeth continued: "OMG yes. Learning to listen is a challenge for many pre-service & new teachers, and I often wonder if this is because they feel so rushed/anxious themselves.</p><p>Listen, swallow, take a breath -- just because a student has spoken in response to a prompt doesn't mean I've heard them yet.</p><p>Another thought -- could we also stipulate that asking a clarifying question can also be also an essential part of teacher listening?"</p></blockquote><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><p style="text-align: left;">Shelby Strong also responded to Lani: "YES. It's not enough just to hear a bunch of different ideas; what is similar and different about those ideas?"</p></blockquote><p>Learners are definitely interested when they know you are interested. How many times have they had a teacher gloss over their answer while really just looking for what they want to hear. "Tell me more" is a phrase I try to use a lot.</p><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><p style="text-align: left;">Mike Steele said: "When you catch yourself thinking about what to say next when students are talking… don’t. Focus on listening. Take a beat before speaking."</p></blockquote><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px; text-align: left;"><p>Nick Smith noted: "I like the other replies here and I'll add, "Never say anything a student can say." </p></blockquote><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px; text-align: left;"><p>I think too often I'm doing the thinking for them. The less I talk, the more I hear their thinking instead of my own." </p></blockquote><p>Good indicator. Especially tough as a novice, maybe, when you have to think more about what's next.</p><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px; text-align: left;"><p>Shelby also said: "Get students to turn and talk and prep them that you are going to ask them to share what their partner said. It lowers the stakes because it's just one other person listening to their ideas, and it takes the pressure off of sharing their own ideas."</p><p>Karen Campe responded: "Oooh I like that... encourages careful listening to your partner!"</p><p>Coutney Flessner added: "I LOVE using this strategy. I also don’t have students share their work. They already know it! The class analyzes it and we ask the author if we missed anything. Kids are significantly more engaged with each other and math with both these instructional routines. Ryan Flessner introduced both to me!"</p></blockquote><p>Your students who always talk will still try to say what they said, but I think this is a moment for them to hear what others see them as saying. </p><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px; text-align: left;"><p>Karen was also thinking about wait time: "An important step is to give Ss individual think time before talking to partners/groups or sharing out to class -- the T shouldn't solicit any responses until that essential time has happened. </p><p>That way, everyone engages, & no priority to fast thinkers or those who can do it in their head. </p><p>Then you can elicit their thinking.</p><p>I was so bad at wait time early in my career that I had to actual count on my fingers (behind my back) to be sure I gave thinking time before discussing. </p></blockquote><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><p style="text-align: left;">Tierney Kennedy also has a teacher hack: "My advice: take a drink bottle with you to groups. When kids ask a question or when you ask them one, take a mouthful. It builds in an automatic thinking moment. Plus sometimes they end up answering their own question." </p></blockquote><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px; text-align: left;"><p>Trey Goesh thinking similarly: "I like to have students take 60 seconds to record their ideas silently before having them talk to a partner.</p><p>You can feel the tension ratcheting up as they collect the ideas they want to share."</p></blockquote><p>Wait time is such an amazing tool. Really lets learners know you are really asking, not just checking 'any questions.' </p><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><p style="text-align: left;">Dee Crescitelli has the objective in mind: "Listen to student thinking with an ear for the mathematical goal of the lesson… we should be thinking about the math story the classroom discussion is telling. How do student responses & representations connect to tell that story?"</p></blockquote><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><p style="text-align: left;">Peg Cagle also thinking about what you're asking: "Make sure that you ask about their ideas/thinking not their “answer”, and make sure they know you are genuinely curious about & interested in what they tell you. Answers w/o thinking-worthless. Ideas w/o answers, immensely valuable…& to everyone in the room!" </p></blockquote><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><p style="text-align: left;">Tara Maynard: "Try to always find a positive in their thinking and then find the misconception. Ask students to write, draw, sketch how they found their solution, not just verbal interaction. Always trying to provide feedback that is helpful yet doesn’t take hours." </p></blockquote><p>This might violate Mike's advice to keep your mind where it's at, but I do this a lot, thinking about the summary/reflection for the lesson. I probably open floor question too much to summarize, but if there is an idea missing, I like knowing whom to call. </p><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><p style="text-align: left;">Arika Byman said: "Model genuine curiosity every chance you get. Provide sentence/question stems to help students organize and articulate their thinking. Be patient and persistent!" </p></blockquote><p>The stems idea is another idea of which I don't do enough. The curiosity is crucial. There are so many things I genuinely want to know about learner thinking, why not ask?</p><p>Another few people were thinking about the math about which you're asking:</p><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px; text-align: left;"><p>Rose said: "# talks and visual patterns tell Ss you want to know what they 💭 esp bc everyone has dif ideas. Shifted my mindset too!</p><p>Working on: design small group tasks/materials that encourage Ss to share their ideas w/each other. Generally ⬆️ S talk. S talk = window into their thinking."</p></blockquote><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><p style="text-align: left;">Sian Zelbo said: "One aspect of eliciting student thinking is asking questions that are open-ended enough that you get a range of answers. If you ask something that is essentially procedural students can't share their thinking bc they have none."</p></blockquote><p>Lastly, is sharing thinking a part of your class culture?</p><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><p style="text-align: left;">Susan Russo said: "One thing that helps is to model your own thought process out loud. Not: this is what I’m doing but: First I notice this, and that leads me to think it might be good to go this way so I’ll try that and see where it leads. But now I wonder… </p></blockquote><p>If you are also sharing genuine thinking it is a great model for when you ask for theirs. </p><p>What did you notice about these responses? What would you add or emphasize? There's a comment section below just waiting for you.</p><p>I'm really grateful to all who responded. Whatever media site we wind up on, I'll be there, because talking to teachers is the best way to teach better.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjftEgbAhk04tEm31oywDJKd56W8i1j8zwzvtEZgY_yJIDddu9Ulxo7kwsgYFwnXpitHu7lHxalCyP7fpnfCnEe7VQBapsPia6i4GLyc0WuOlT2w8DZDWmWwFLEMQ0KW7dCsh28MWIAvCgXkGSvgmFzhtSBUWJVht3ikm9cKy9x-_MKE8kQTH55xTBJL5I/s600/stop-think-sam-gross-it-sort-of-makes-you-stop-and-think-cartoon.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="451" data-original-width="600" height="482" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjftEgbAhk04tEm31oywDJKd56W8i1j8zwzvtEZgY_yJIDddu9Ulxo7kwsgYFwnXpitHu7lHxalCyP7fpnfCnEe7VQBapsPia6i4GLyc0WuOlT2w8DZDWmWwFLEMQ0KW7dCsh28MWIAvCgXkGSvgmFzhtSBUWJVht3ikm9cKy9x-_MKE8kQTH55xTBJL5I/w640-h482/stop-think-sam-gross-it-sort-of-makes-you-stop-and-think-cartoon.jpg" width="640" /></a></div><br /><p><br /></p><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><p style="text-align: left;"> </p></blockquote><p><br /></p><p><br /></p><p> </p>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-51287708217922393272023-08-15T16:20:00.003-04:002023-08-16T08:20:04.470-04:00Old Dog, New Complex<p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqVkP-cM6fIyNODiSssXlvtw95LpBNyMIZhMdjpVJLXl2GwOS6v3z0wHZkHOjqFnt9nXO5fcFNueZtiyMbMw0gjuI4lpOWk7e94H-YuYkquj6QYZgNRWp0p_kevhFHjkfhR6rNNnQ3codDs6CBVxzULXaUXH9mZxNSvfQZZERCEpPLZitkn9gEG8n6kkQ/s346/smto.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="346" data-original-width="243" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqVkP-cM6fIyNODiSssXlvtw95LpBNyMIZhMdjpVJLXl2GwOS6v3z0wHZkHOjqFnt9nXO5fcFNueZtiyMbMw0gjuI4lpOWk7e94H-YuYkquj6QYZgNRWp0p_kevhFHjkfhR6rNNnQ3codDs6CBVxzULXaUXH9mZxNSvfQZZERCEpPLZitkn9gEG8n6kkQ/s320/smto.jpg" width="225" /></a></div> I was very excited when we were able to hire Joy Oslund last year. Great teacher, experienced professor, and she brought expertise in complex instruction (CI) which was completely new to our department. She wrote the book!<p></p><p>OK, a book, <a href="https://www.nctm.org/store/Products/Smarter-Together!-Collaboration-and-Equity-in-the-Elementary-Math-Classroom/" target="_blank">Smarter Together</a>, which, appropriately, was collaborative itself. </p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p>Dave Coffey and I interviewed her for Teaching Like Ted Lasso, if you'd like to hear her for yourself.</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/YGxakYF1QNs" width="320" youtube-src-id="YGxakYF1QNs"></iframe></div><br /><p>She's leading a professional development for faculty in CI here in the math department. Small group, supported by the U and by our state AMTE chapter.</p><p>There's a few texts people have for it. Everyone has <a href="https://www.tcpress.com/designing-groupwork-9780807755662" target="_blank">Designing Groupwork</a> by Cohen and Lotan, 3rd edition of the seminal text. The book presents the case for why group work is helpful, and examines why it so often is not helpful in practice.</p><h4 style="text-align: left;">Day 1</h4><p>Introductions. Why are we here?</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwqgpFbOLzEHT61ZMKJVG0D8tO6X6MOW8dl8or1qmuqT6bzbMxuj9Fuhh4VUcRJbipsRdLuHaAkDZfjDLxlPdFywVEqIQOEflPneG7F1skkgvLeSTJrsROjobk8PUSILT3ww1_yZwGccP-PnD7WJYpLWRBiw-q6pgu-samtqI6WxB2kGWcAFpWHm5kNI4/s3609/IMG_3056.JPG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="3609" height="284" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwqgpFbOLzEHT61ZMKJVG0D8tO6X6MOW8dl8or1qmuqT6bzbMxuj9Fuhh4VUcRJbipsRdLuHaAkDZfjDLxlPdFywVEqIQOEflPneG7F1skkgvLeSTJrsROjobk8PUSILT3ww1_yZwGccP-PnD7WJYpLWRBiw-q6pgu-samtqI6WxB2kGWcAFpWHm5kNI4/w640-h284/IMG_3056.JPG" width="640" /></a></div><br /><p>One feature of Joy's classroom is a smartness wall. We were each asked to write one way we are smart in math. Learners add to it throughout the year or course. Lisa Hawley, another new colleague, does one at the beginning and one at the end for them to compare. She noted that they often shift from content claims to process claims, and how many more ways they think there are to be smart at the end. The decision to use 'smart', which is loaded, is that they do already have ideas about that, and using it gives us an opportunity to intervene.</p><p>Community Agreement. What do we need to have a safe classroom, where we are free to take risks?</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjf-cbS33HThmOgEgQOhVqjECr9HdPw54Dzn5MmzyHvrHGSKKR2w3J0je-k9sk-cJhiW45Np07n0YaZd3HvW1hL-QxGBUeszJbCGaWELLGRhnjpWLeuDXxOPY7iIKGiVVTCj7I3nKpMy6lyPZIqcngAgbVeMjdBayyIZ-Dgk4hp8RGLMcj3qMoGNQotj6U/s1982/IMG_3054.JPG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1190" data-original-width="1982" height="384" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjf-cbS33HThmOgEgQOhVqjECr9HdPw54Dzn5MmzyHvrHGSKKR2w3J0je-k9sk-cJhiW45Np07n0YaZd3HvW1hL-QxGBUeszJbCGaWELLGRhnjpWLeuDXxOPY7iIKGiVVTCj7I3nKpMy6lyPZIqcngAgbVeMjdBayyIZ-Dgk4hp8RGLMcj3qMoGNQotj6U/w640-h384/IMG_3054.JPG" width="640" /></a></div><br /><p>Groupwork norms: </p><p></p><ul style="text-align: left;"><li>quick start, </li><li>no one is done until everyone understands (each step!), </li><li>work the whole time, (trying this year)</li><li>call the instructor for group questions only, </li><li>middle space - there was a table whiteboard in the middle of the table which we were encouraged to keep open and collaborative. </li></ul><p>Groupworthy tasks require multiple abilities and can't be done alone. "If it can be done alone, it will be." We did an activity with instructions for folding an open-top box (not quite <a href="https://pretend2work.com/origami-box-instructions-pdf" target="_blank">this one</a>, a little simpler) from squares of different sizes and then measured volume with beans and cubes, then had to predict the volume of a different size box. There were two copies of the task instructions, one copy of the origami instructions, a few beans, a few cubes. Plenty of interest even for mathematicians and math educators to get engaged and want to keep going. </p><p><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidypKT8JePfyihWs5wE7l7_fGMEEYfXNnCrnfGjBK9Mn7fgclxe2pFhrn7F2rLlJbIds5X26LusxyfJNHjqnVqhB7wMVBCRBhcqpXZJXBA_ObZeOtyLE7nppWXdGy3-nx3hj0KIjqNoyArk__V6Voknc4XeLAXiQPwtlWXFFhEz0xSMW5BdIFEbhiyQTo/s4032/IMG_3050.JPG" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="3024" data-original-width="4032" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidypKT8JePfyihWs5wE7l7_fGMEEYfXNnCrnfGjBK9Mn7fgclxe2pFhrn7F2rLlJbIds5X26LusxyfJNHjqnVqhB7wMVBCRBhcqpXZJXBA_ObZeOtyLE7nppWXdGy3-nx3hj0KIjqNoyArk__V6Voknc4XeLAXiQPwtlWXFFhEz0xSMW5BdIFEbhiyQTo/w640-h480/IMG_3050.JPG" width="640" /></a></p><p>Afterwards, we discussed what we noticed about the task. There was a lot to notice. We really could not have done it alone in the time allotted, and there was meaningful work for everyone.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoWkH1_h3E0a1StdtnUrVuBj9y98bVPutcAfd_66oZVCatM6IrzOqkAO36O0gJdHW0Zn-obL7uEJ4MAZBjgG4GdZREzRuGUJQ7bQDGd6CGNG1URSB6-nDwmX5aj-vnk0clsR6HFeoGSw_52yoavXWEmfxYkQkXFlFaDr2gEsFcZhva8WZ6APu2l_z2ZfM/s4032/IMG_3053.JPG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3024" data-original-width="4032" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoWkH1_h3E0a1StdtnUrVuBj9y98bVPutcAfd_66oZVCatM6IrzOqkAO36O0gJdHW0Zn-obL7uEJ4MAZBjgG4GdZREzRuGUJQ7bQDGd6CGNG1URSB6-nDwmX5aj-vnk0clsR6HFeoGSw_52yoavXWEmfxYkQkXFlFaDr2gEsFcZhva8WZ6APu2l_z2ZfM/w640-h480/IMG_3053.JPG" width="640" /></a></div><p><br /></p><p>Working on the task, we had roles. I have not been able to get roles to work for me before, but I've really been thinking about how I haven't pushed for them, and never really done anything to teach how to do them. These feel less made up than some other roles, and, I think, are really another implementation of the norms.</p><h4 style="text-align: left;">Roles</h4><p></p><p></p><p></p><p></p><ul style="text-align: left;"><li>Team Captain - fills in missing roles, moves people along</li><li>Resource Monitor - call instructor, distribute supplies </li><li>Facilitator - task gets read, everyone understands task</li><li>Recorder/Reporter</li></ul><div>Our names were slotted into groups and roles randomly. It doesn't have to be completely random, but visible randomness is recommended. (This is not the only overlap with building thinking classrooms.)</div><p>Individual and group accountability. Joy often follows an activity with the groups sharing results, and learners writing an individual reflection, responding to one or more prompts. In addition, while we were working, Joy did a "Participation Quiz" - teacher notes in a public space on what they observed groups doing. Great at beginning of course and when group work starts declining in quality/evidencing the norms. </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXOAzHB5ALVLfshQedJft1sLOnDiSgb6SPyqMFi-KbPoLHswkT13K9Z8NPVqoB1ZV1TU6VYwvLxUMgHwuwbPNfb2M5EtpLHTl-twDf9hmjFDhs7gyjqcc4mkZEO_oQZ5dCklvjcwNskzJRMWICudy0Nw3tbbfvbVkg3QUIuFsgitrebG2tLiveerUrE-g/s1462/Screenshot%202023-08-15%20at%203.37.02%20PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="766" data-original-width="1462" height="336" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXOAzHB5ALVLfshQedJft1sLOnDiSgb6SPyqMFi-KbPoLHswkT13K9Z8NPVqoB1ZV1TU6VYwvLxUMgHwuwbPNfb2M5EtpLHTl-twDf9hmjFDhs7gyjqcc4mkZEO_oQZ5dCklvjcwNskzJRMWICudy0Nw3tbbfvbVkg3QUIuFsgitrebG2tLiveerUrE-g/w640-h336/Screenshot%202023-08-15%20at%203.37.02%20PM.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><h4 style="clear: both; text-align: left;">Status</h4><div class="separator" style="clear: both; text-align: left;">Academic, Social, and the perception of that by the student, their peers and the teacher. This is really what complex instruction is about. We watched the first half of this. </div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="439" src="https://www.youtube.com/embed/ZUKue1upMv0" width="528" youtube-src-id="ZUKue1upMv0"></iframe></div><div><br /></div>Painful, and familiar. How many times have I seen similar in my class and not intervened? Perpetuating status.<div><br /></div><div>Worse, we discussed how often we blame learners for the lack of involvement which their status denies them. In the video, to these kids' credit, you can see how much they still want to join in, despite what has been clearly repeated hurtful exclusions.</div><div><br /></div><div>We spent a few minutes with an excellent teacher activity, filling out a <a href="https://docs.google.com/document/d/1moPomU_J2dnvZNcrfpUXtG92gFOVqFZOTdJCb6JlE3Q/edit?usp=sharing" target="_blank">smartness chart</a> for a few students, then discussing about whom we were writing, and what made them notable to us. I mostly thought about my summer class, which started better than it ended. I lost a couple students, and have thought a lot about what I should be doing. At the beginning of the semester, I was trying to implement what I knew about CI, but fell back into my old habits, which allowed students to work in parallel rather than really in groups. At first, I could remind them to discuss, but then that had diminishing returns, too.</div><div><br /></div><div>There's a CI site at Stanford with some of the <a href="https://web.stanford.edu/class/ed284/csb/" target="_blank">skill builder activities</a>. We closed with the <a href="https://web.stanford.edu/class/ed284/csb/BuildIt/BuildIt.doc" target="_blank">Broken Circles</a> activity (link to .doc file), which was a really good one for promoting collaboration and noticing.</div><div><br /></div><div>Definitely looking forward to days 2 and 3. Which, bloggods willing, I will also try to write about.</div><div><br /></div>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-15001989146869242162023-07-08T23:00:00.002-04:002023-07-09T10:01:12.285-04:00Games Before Class<p> I'm teaching a quick 6 week Intermediate Algebra (linear/quadratic/exponential) for incoming freshman this summer. Part of my goal is to convince them that math is different than how they might have been exposed to it. On day 1, we started with <a href="https://www.nytimes.com/games/wordle/index.html" target="_blank">Wordle</a>. A few learners had played it before, but quickly the whole class picked up the idea, and there were several good deductions about which letters could go where. The rest of the week, we played the daily Wordle before class the rest of the week.</p><p>This week, we started with SET. A little harder to understand, but there's so much logic. The <a href="https://www.setgame.com/set/puzzle" target="_blank">daily puzzle</a> has up to six solutions, which seems to allow for more participation. (Kelly Spoon noted <a href="https://setwithfriends.com/" target="_blank">Set with Friends</a> for online actual game play, plus variants.)</p><p>I had ideas about what I wanted to do in subsequent weeks, but I was curious what others think and <a href="https://twitter.com/mathhombre/status/1675853642451091459?s=20" target="_blank">asked on Twitter</a>. BOOM, people exploded with a bevy of resources. I used to have a blog where I shared resources, where did I put that...? After <a href="https://samjshah.com/2023/07/01/mastodon-mathstodon-join-us/" target="_blank">Sam</a> and <a href="https://ispeakmath.org/2023/07/03/lets-get-mathstodoning-together-prompt-1/">Julie</a> posted about moving to Mastodon (because of Twitter's Troubles), I tried <a href="https://mathstodon.xyz/@mathhombre/110650303845076797" target="_blank">posting there</a>, too.</p><p><b>Math Online Games & Apps</b></p><p></p><ul style="text-align: left;"><li><a href="https://www.fiddlebrix.com/" target="_blank">FiddleBrix</a> suggested by Benjamin Dickman. He suggested downloading the app, then handwrite a previous puzzle. This is a super challenging puzzle, to me, but Benjamin's suggestions are gold.</li><li><a href="https://sumit.clontz.org/" target="_blank">SumIt puzzle</a> suggested by Kelly Spoon. Lots of stuff there.</li><li>Beast Academy <a href="https://beastacademy.com/all-ten" target="_blank">All Ten</a> also via Kelly. Really great arithmetic challenge.</li><li><a href="https://brising.com/" target="_blank">Draggin Math</a> pay app, </li><li>Shirley McDonald suggested a lot of great stuff: <a href="https://beastacademy.com/all-ten" target="_blank">All Ten</a> by Beast Academy (always an open tab in my browser), <a href="https://play.numberhive.org/" target="_blank">Number Hive</a> (like the Product Game on a hexagon board), <a href="https://www.brainbashers.com/skyscrapers.asp" target="_blank">Skyscrapers</a> (Latin square with clues, from a site with lots of puzzles) and Digit Party (implementation of a Ben Orlin game; also an open tab, I may have a tab problem).</li><li>Shirley also recommended Mathigon's <a href="https://mathigon.org/task/puzzle-of-the-day" target="_blank">Puzzle of the Day</a>. I've been playing that in an app more days than not. (I think I'm getting better?)</li><li>Kathy Henderson suggested the NYT <a href="https://www.nytimes.com/games/connections" target="_blank">Connections game</a>, which I hadn't seen yet. That is very much in the spirit of what I'm looking for!</li></ul><p></p><p><b>IRL Math Games</b> (Free and Commercial)</p><p></p><ul style="text-align: left;"><li>David Butler has a great collection of activities, his <a href="https://www.adelaide.edu.au/mathslearning/play#one-hundred-factorial" target="_blank">100 Factorial</a>. He singled out <a href="https://blogs.adelaide.edu.au/maths-learning/2019/09/21/digit-disguises/" target="_blank">Digit Disguises</a> and <a href="https://blogs.adelaide.edu.au/maths-learning/2020/08/18/which-number-where/" target="_blank">Which Number Where</a></li><li>Neal W recommended: <a href="https://gamewright.com/product/Qwixx" target="_blank">Quixx</a> is a great dice game and very easy to learn. My students love <a href="Tom Cutrofello suggested the excellent Turnstyle puzzle he designed for Brainwright! Prime Climb by Dan Finkel, suggested by Amie Albrecht. She notes, especially David Butler's human scale Prime Climb. (Which I have played and love." target="_blank">20 Express</a>. There are rules and scoresheets online.</li><li>Tom Cutrofello suggested the excellent <a href="https://gamewright.com/product/turnstyle" target="_blank">Turnstyle puzzle</a> he designed for Brainwright!</li><li><a href="https://mathforlove.com/games/prime-climb/" target="_blank">Prime Climb</a> by Dan Finkel, suggested by Amie Albrecht. She notes, especially David Butler's human scale Prime Climb. (Which I have played and love.</li><li>Anna Blinstein suggested Anna Weltman's <a href="https://recipesforpi.wordpress.com/2013/10/16/snugglenumber/" target="_blank">Snugglenumbers</a>, which is a great variation on a target number game.</li><li>Pat Bellew said remember the original: <a href="https://mastermindgame.org/" target="_blank">Mastermind</a>. Erick Lee has a Desmos activity implementarion of the math version, <a href="https://teacher.desmos.com/activitybuilder/custom/63ceac97e0216eace8bd6fd0" target="_blank">Pico, Fermi, Bagel</a>.</li><li>Sian Zelbo claims <a href="https://en.m.wikipedia.org/wiki/Jotto" target="_blank">Jotto</a> is better than the either Wordle or Mastermind. (<a href="http://jotto.augiehill.com/single.jsp" target="_blank">Online version</a>.)</li><li>Becky Steele cited David Coffey for <a href="https://boardgamegeek.com/boardgame/253664/taco-cat-goat-cheese-pizza" target="_blank">Taco Cat Goat Cheese Pizza</a> as well as Farkle.</li><li>Chris Conrad recommended Quarto, amazing strategy game. Amie mentioned you can play with SET cards - how amazing is that idea. Karen Campe remembered this great <a href="https://aperiodical.com/2022/07/mathematical-objects-quarto/" target="_blank">Aperiodical article</a> about the game.</li><li>Mardi Nott, Bradford Dykes and Jenna Laib vouch for <a href="https://boardgamegeek.com/boardgame/278413/charty-party" target="_blank">Charty Party</a> - that's a strong recommendation. Bradford also brought up this stats version of Spot It, the <a href="https://policyviz.com/2018/04/18/the-graphic-continuum-match-it-game/" target="_blank">Graphic Continuum Match It Game</a>.</li><li>Ms. Morris suggested <a href="https://playpager.com/mill-game/" target="_blank">Nine Men's Morris</a>. Interesting game idea.</li></ul><p></p><p><b>Puzzles</b></p><p></p><ul style="text-align: left;"><li>Kim McIntyre suggested Sarah Carter's <a href="https://mathequalslove.net/puzzles/" target="_blank">big collection of classroom puzzles</a>. I have learned so many puzzles from her over the years, but especially the <a href="https://mathequalslove.net/?s=inaba" target="_blank">Naoki Inaba</a> puzzles.</li><li>Speaking of Japanese puzzles, Gregory White suggests <a href="https://www.puzzle-shikaku.com/" target="_blank">Shikaku</a>.</li><li>Benjamin Dickman and Shirley and Gayle Herrington suggested <a href="https://www.kenkenpuzzle.com/" target="_blank">KenKen</a>. I've used those with younger learners and college students.</li><li>Karen Campe had several suggestions, some in this blogpost. Times UK <a href="https://feeds.thetimes.co.uk/puzzles/public/homepage/" target="_blank">puzzle page</a>, <a href="https://krazydad.com/starbattle/" target="_blank">StarBattle</a>, <a href="https://www.transum.org/software/Puzzles/Suko.asp" target="_blank">Suko</a>, </li><li>suggested Mobiles. Love those, and we do lessons based on them. Here's a challenge problem I asked them!</li><li>Druin suggested <a href="https://www.puzzleoftheweek.com/puzzle-library" target="_blank">the Puzzle Library</a>, which I can't access for some reason. Looks like they're intentionally made for schools.</li><li>Susan Russo linked <a href="https://cryptograms.puzzlebaron.com/" target="_blank">Cryptograms</a>, which are some cool cruptographic puzzles. I haven't tried anything like this and am curious.</li><li>Sarcasymptote brought up Sideways Arithmetic from Wayside School, which is what I was expecting from Cryptograms, thinking it was <a href="https://nrich.maths.org/cryptarithms" target="_blank">cryptarithms</a>. But somehow have never seen that book despite loving Wayside.</li><li>Ms. Morris linked a <a href="https://www.transum.org/software/SW/magic_square/magic_square.asp" target="_blank">Magic Square app</a>.</li></ul><div><b>Activity Ideas</b></div><div><ul style="text-align: left;"><li>Joanne Growney suggested <a href="https://poetrywithmathematics.blogspot.com/search?q=acrostic" target="_blank">making acrostic poems</a>. </li><li>Rational Tangle, John Conway's amazing envisioning of <b>Q </b>as rope tangles with two allowed moves. David Butler had the link to Amie Albrecht's <a href="https://amiealbrecht.com/2017/05/25/noticewonder-and-rational-tangles/" target="_blank">notice and wonder implementation</a> of it.</li><li>Gregory White suggested Sean Sweeney's Desmos Escape Rooms, <a href="https://teacher.desmos.com/activitybuilder/custom/61d37598e72fa548182dbd2e?collections=5f6bf12d4f8544403327f4bb" target="_blank">the first</a> or <a href="https://teacher.desmos.com/activitybuilder/custom/62e414940e0fc666b51422eb?collections=5f6bf12d4f8544403327f4bb" target="_blank">the second</a>.</li><li>Erick Lee brought up Gord Hamilton's <a href="https://www.kickstarter.com/projects/mathpickle/the-infinite-pickle" target="_blank">Infinite Pickle book</a>, which is great. I 100% will be using it for elementary math ed class.</li><li>Erick also linked <a href="https://playwithyourmath.com/" target="_blank">Play With Your Math</a> which has some classic fun math activities.</li><li>Mike Lawson linked his <a href="https://mikesmathpage.wordpress.com/2018/03/25/15-1-bonus-math-ideas-for-a-6th-grade-math-camp/" target="_blank">6th grade math camp ideas</a>, which are awesome problems.</li><li>Ms. Morris' <a href="https://haubergs.com/hanoi" target="_blank">Tower of Hanoi</a>, which sometimes I'll do as exponential data collection.</li></ul></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_W5nQKAnz16kxzFAupR53-9LjAQkgn4DonZhMtu-P3tggDt2psVI5JaEUVgkn-jWITWuqgnkdF5E6zgdfA1EE9QEynp8Tkpc_nYBjUrKZgOGPM7XTw693OuheQ8CxPHxbSeNEO670Z4HbKif-muE6gOSnY_oHHN29ik6w_3lNcEBK5XJOuw5D6KhyP8/s1462/obscuremath.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="472" data-original-width="1462" height="185" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_W5nQKAnz16kxzFAupR53-9LjAQkgn4DonZhMtu-P3tggDt2psVI5JaEUVgkn-jWITWuqgnkdF5E6zgdfA1EE9QEynp8Tkpc_nYBjUrKZgOGPM7XTw693OuheQ8CxPHxbSeNEO670Z4HbKif-muE6gOSnY_oHHN29ik6w_3lNcEBK5XJOuw5D6KhyP8/w574-h185/obscuremath.png" width="574" /></a></div><br /><div>So my plans as of now are:</div><div><ul style="text-align: left;"><li>Wordle</li><li>SET (both in the books and worked well)</li><li>Connections (I like that this will alternate word and math)</li><li>All Ten (Digit Party would make a better game, but is harder to kibbitz on as people come in.)</li><li>Mastermind</li><li>Henri Picciotto's Supertangrams. (a- recently got them! b - they are so amazing. c- be nice to close with something tangible.)</li></ul><div>Thanks to everyone who replied! Wherever the math teachers are chatting, I'll continue to be there.</div></div><p></p>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com3tag:blogger.com,1999:blog-235276292454918436.post-49844612348798931162023-02-03T13:05:00.004-05:002023-02-03T13:05:42.527-05:00G.L.A.S. Game<p> I'm very excited to share this game with you. Jenisa Henry invented it for our senior math game seminar, and it shows a LOT of promise. As she pitches it, it's an early elementary game, but it is highly suited for variations I'll discuss after you hear from Jenisa.</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/pPMIDa8OToY" width="320" youtube-src-id="pPMIDa8OToY"></iframe></div><br /><p>Her rules printout in on Google drive: <a href="https://bit.ly/GLASrules">bit.ly/GLASrules</a>. She writes this about the game development:</p><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px; text-align: left;"><p>My brainstorming for G.L.A.S. first started because I knew I wanted to create a game I can play in my future lower elementary classroom. Knowing that these years it is important to learn simple addition and subtraction facts while understanding equalities I toyed around with the first version of this game. It started with players using their top four cards to create an equality, then use their biggest sum to compare to the opponents biggest sum. It was rough to begin with, until I found the game <a href="https://mathhombre.blogspot.com/2022/02/early-el-math-games.html" target="_blank">more or less</a>. This game solidified my idea on wanting to pursue designing a game with equalities. Though, I knew I wanted to add in another element to it, that was the addition and subtraction. Once I added that element to the game, I knew I had to think of a method for making the calls. I knew adding this element would offer choice to the players. I’ve learned to value games that have choices for the players as it makes them feel more active in playing. Once I added that, the game was great. I loved it and it was fun to play.</p><p>However, there was still something missing. An element of surprise was just what the game needed and that is when the Queen chance card came into play. This added the perfect amount of randomness that the game needed. After the playtesting went well, I knew it was exactly what I wanted the game to become.</p><p>G.L.A.S. is a great game that all teachers for 2nd-3rd grade should have their students playing. There are many reasons students should play this game, many benefits for the students to gather. Most simply, addition and subtraction facts are majorly important for the students to recall as they progress through their schooling. Additionally, the exploration of greater than and less than is the beginning of a building block for equalities. It is also a game of strategy. By using the cards in the players’ hand they need to strategically pick what they want to call. Further, they have to decide what two cards to operate on to get a sum that may satisfy the called equality. My personal favorite is when we have greater than for the equality and subtraction for the operation or less than and addition.</p><p>There is another variation to this game that has an emphasis on place value. Players will still call an equality, though instead of an operation they’ll pick the desired length of the number 1 digits-4 digits. All other rules still apply as far as card values, though 10’s do represent 2-digits. This game is very interesting as many variations can be created. As another example, this game can be played where the operation is strictly multiplication, a fraction version could even be created. Changing the game in these ways extends it to reach more grade levels as well as more areas within the mathematics realm.</p></blockquote><p>For me, the break through of this game is the double choice. Giving both players significant choices each turn really makes this one of the best computation games I've seen. The adaptability is significant. In addition to place value, they experimented with multiplication and division, which would be good 5th-8th grade. You could do two digit computations (draw 6 cards), or even mix, 2 cards +/– 1 card.</p><p>Also for the course, teachers make a video for a game they want to promote. Jenisa chose +/– 24.</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/_VJjMoUoMLw" width="320" youtube-src-id="_VJjMoUoMLw"></iframe></div><div><br /></div>Explaining why this game, she writes: <div><br /></div><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><div><div style="text-align: left;">+/- 24 makes a phenomenal classroom game because of its quick nature and simple materials. Only requiring three simple materials that typically already reside in the classroom requires less preparation time for any teacher or helper. With simple rules, students will be able to grasp the game fairly easily. With there being many ways to create the desired outcome, there are multiple entry points for any and all students. This allows for students to stick to addition and subtraction, if they need or use the alternative operations if they feel comfortable. This is also a great game to use to bring attention to the associative and commutative properties. All the while, students are manipulating numbers to get their desired result. There is both strategy and critical thinking within this game, allowing students to be challenged when playing.</div></div></blockquote><div><p>I agree! </p><p>If you get a chance to play GLAS or try it with kids, I would love to hear about it!</p><p><br /></p></div>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-69298646050354420512022-09-30T00:30:00.002-04:002022-09-30T09:18:07.585-04:00Playful Math Carnival 159<p>Welcome one and all! Come on in and have a ball. 159 is semiprime and that's just fine.</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0T2Djl3m8V-y_Jqm_oPGK3IHsA_K54wbk44FMeWG84PbXKHRsAKT5n0m_513zOBKKeM6cHfUutgLc24N1doDHADi2shwmMnzkYLtCF6WmAZBS6oOwxLdEX85nHBFV98UgKvpZqUMwm2JcWAxx3egI1easRbZH5XwS-_ixHBEMUeN4OHtb5sadyhCW/s800/159bus.png" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="561" data-original-width="800" height="224" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0T2Djl3m8V-y_Jqm_oPGK3IHsA_K54wbk44FMeWG84PbXKHRsAKT5n0m_513zOBKKeM6cHfUutgLc24N1doDHADi2shwmMnzkYLtCF6WmAZBS6oOwxLdEX85nHBFV98UgKvpZqUMwm2JcWAxx3egI1easRbZH5XwS-_ixHBEMUeN4OHtb5sadyhCW/s320/159bus.png" width="320" /></a></div>Lucky that I'm hosting this, or is it just that 159 is lucky. How do you get lucky? Start with the counting numbers. Delete every 2nd number, leaving 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45... odd. The 2nd number remaining is 3, so delete every 3rd number, leaving 1 3 7 9 13 15 19 21 25 27 31 33 37 39 43 45... now that's interesting in and of itself. Next delete every 7th number, leaving 1 3 7 9 13 15 21 25 27 31 33 37 43 45 ...; now delete every 9th number; etc. How far do we have to go before we know 159 is lucky? Does knowing 151 is the previous lucky number help? Interesting to look at the gaps in each step, and the cutlist for each step.<p></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgXnh-Ew7pb_5ymgrGvcjVDMDfN6Vb85fC0EsNYuX0ErSDu4bpx0zjtKMRL7f_JqwmXkPzHIgUYG5JIOCcIaXfA29xV1RhEe2bMIr8a4jBIbOqRIDJZAU_gNihO8s5Oq83u5i0jBGyP4bZqSGg1cRL8BfUaTUP0OGyic0KVvoszPmGQsxz2ksi9dkd-" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" data-original-height="971" data-original-width="960" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgXnh-Ew7pb_5ymgrGvcjVDMDfN6Vb85fC0EsNYuX0ErSDu4bpx0zjtKMRL7f_JqwmXkPzHIgUYG5JIOCcIaXfA29xV1RhEe2bMIr8a4jBIbOqRIDJZAU_gNihO8s5Oq83u5i0jBGyP4bZqSGg1cRL8BfUaTUP0OGyic0KVvoszPmGQsxz2ksi9dkd-" width="237" /></a></div><p><br /></p>Is it rarer to be a semiprime or a number with only odd digits? Odd increasing digits? Linear pattern in its digits? Alyssa would like it as is.<p></p><p>Pat Bellew's 159 facts are that 159 is the sum of 3 consecutive prime numbers (which?) and can be written as the difference of two squares in two different ways (don't you want to find them?).</p><p>He also has that __ __ •159 = __ __ __ __ using all 9 nonzero digits. Of course, you can brute force it, but can you deduce this digitally complete product?<br /></p><p><br /></p><p><br /></p><p>What #playfulmath have you seen this month? Here's some of what I have noticed.</p><p>September started with <a href="https://twitter.com/MathOnAStick" target="_blank">Math on a Stick</a> in full swing. Doesn't get more playful than that!</p><p>Katie Steckles and Jimi <a href="https://www.youtube.com/watch?v=-9kxO14jUb4" target="_blank">went over the math</a> in the Spider-Man No Way Home end credits. I lost my mind when watching it in the theatre, and am so glad someone's sharing it. SO MANY MC Escher references.</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/hfVzUMGxauY" width="320" youtube-src-id="hfVzUMGxauY"></iframe></div>And as if the visuals weren't sufficient, the song is De La Soul's great cover of the Schoolhouse Rock classic, Three is a Magic Number.<div><br /></div><div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjHQ3Fy6SsDYBVbsyqqkjX9AhCZTG8W9pGk4xY-o76ECLI-tUJ2Ui80v6E01z3zrkkIjkc394bkWWhWx3Ae2jXSL6Ds5oVNAaNWntxDpTxei1k4HrVjE58wRHe_qggu4L4d3pcptFj5CUqdip7r8BNjvJn7n8iKTWODUCkgYGrynvBn8nofEHPaphgC" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="" data-original-height="1536" data-original-width="2048" height="331" src="https://blogger.googleusercontent.com/img/a/AVvXsEjHQ3Fy6SsDYBVbsyqqkjX9AhCZTG8W9pGk4xY-o76ECLI-tUJ2Ui80v6E01z3zrkkIjkc394bkWWhWx3Ae2jXSL6Ds5oVNAaNWntxDpTxei1k4HrVjE58wRHe_qggu4L4d3pcptFj5CUqdip7r8BNjvJn7n8iKTWODUCkgYGrynvBn8nofEHPaphgC=w443-h331" width="443" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Live human scale Prime Climb at NCTM-LA<br />photo Liesl McConchie</td></tr></tbody></table><br /></div><br /><div>Is that Howie Hua? (Yes - He and Annie Forest won.)</div><div><br /></div><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivf9H-sWydOZml4aZ1lLMbBe_HHFTAaafN8oK_m6h-7ShYnDZGv7JmZ4VIZUvnf9WXw_jOvdCdRxAjMmoNd-L2PmuXYemSIIblH_Ml7b7FcLn7MhS_XkjlNkX18aCpGNaRTB6zLi6k72G5Fg882QfwTEB6JRBSfKMOZkpTboiDtORaJfJUNY0AaAjk/s300/159.gif" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="300" data-original-width="300" height="248" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivf9H-sWydOZml4aZ1lLMbBe_HHFTAaafN8oK_m6h-7ShYnDZGv7JmZ4VIZUvnf9WXw_jOvdCdRxAjMmoNd-L2PmuXYemSIIblH_Ml7b7FcLn7MhS_XkjlNkX18aCpGNaRTB6zLi6k72G5Fg882QfwTEB6JRBSfKMOZkpTboiDtORaJfJUNY0AaAjk/w248-h248/159.gif" width="248" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">as yet undiscovered unpentennium</td></tr></tbody></table>Christine Thielen tweeted about her class' enjoyment of the <a href="https://mathigon.org/task/puzzle-of-the-day" target="_blank">Mathigon puzzle of the day</a>.</div><div><br /></div><div>Speaking of puzzle of the day, Michael Pershan wrote about this new Beast Academy (upper elementary and higher) daily arithmetic puzzle, <a href="https://beastacademy.com/all-ten" target="_blank">Make Ten</a>. I enjoy his <a href="https://buttondown.email/mpershan" target="_blank">PershMail newsletter</a> each week.<br /><p>The Erikson Institute is a great source for early math insights, and here they cover <a href="https://earlymath.erikson.edu/books-about-numbers/" target="_blank">four playful number books</a>.</p><p>Charlotte Sharpe <a href="https://twitter.com/getting_sharper/status/1572572224502272002?s=20&t=Ao_lv794QbHO0sypI1iDhg" target="_blank">shared a quick, rich early math game</a> with dice and subitizing cards.</p><p>Michael Minas & helpers are back with an inequality game, <a href="https://www.youtube.com/watch?v=th4HAwnCK9I" target="_blank">Big Bad Wolf and the Three Little Pigs.</a> </p><p>Australian Math Circles shared this <a href="https://www.numbershapes.com/interactives/saami/saami" target="_blank">online interactive math game</a> with lots of nice number recognition and sense images.</p><p><a href="https://twitter.com/MrValencia24/status/1570833824371867649?s=20&t=Ao_lv794QbHO0sypI1iDhg" target="_blank">Libo Valencia tweeted</a> about his class playing this angle game, Daniel Mentrard's <a href="https://www.geogebra.org/m/gzzp5whu" target="_blank">Polar Battleship</a>. </p><p>He also shared his daughters <a href="https://twitter.com/MrValencia24/status/1568970428319768578?s=20&t=Ao_lv794QbHO0sypI1iDhg" target="_blank">catmathart</a>... a perfect transition to the next section.</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj-5dz0qb9sp_TfQXZ6YsUNu1tzL1W7slUUgTbFd1SD0J30tv3PfmBCAutAu3qKOytfIZQv2Is6QGZzuZWkaBHVxQP-dU-srpBCptN6auuLqTxM1ZhgFqH6tRS9vj4uZv5lwgGrTpWVJ9xjCfu8-JhUO42CyN_wvJSxl3aeO9BkR9gt-VGM4C9TYSv3" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" data-original-height="1600" data-original-width="1200" height="291" src="https://blogger.googleusercontent.com/img/a/AVvXsEj-5dz0qb9sp_TfQXZ6YsUNu1tzL1W7slUUgTbFd1SD0J30tv3PfmBCAutAu3qKOytfIZQv2Is6QGZzuZWkaBHVxQP-dU-srpBCptN6auuLqTxM1ZhgFqH6tRS9vj4uZv5lwgGrTpWVJ9xjCfu8-JhUO42CyN_wvJSxl3aeO9BkR9gt-VGM4C9TYSv3=w218-h291" width="218" /></a></div><br /><p></p><p><a href="https://twitter.com/zarahkhussain/status/1575077176416010246?s=20&t=Ao_lv794QbHO0sypI1iDhg" target="_blank">Zarah Hussain</a> shared her icosahedron statue on public display in London.<br /><br /></p><p>Paula Beardell Krieg is always busy with something creative and beautiful. For instance, <a href="https://bookzoompa.wordpress.com/2022/09/09/rather-strange-solids/" target="_blank">her Rather Strange Solids</a>. (But while you're there, poke around.)</p><p><br /></p><p>Sophia Wood does programming, teaching and art. Her <a href="https://fractalkitty.com/2022/09/25/white-breasted-nuthatch/" target="_blank">latest bird</a> is perched on an unorientable branch...</p><p><br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgorDeMa44-RXnec3ksp-2crJI7Bez__Rth48a7p_Ix67UIyhzHSjpHdlvT_rqLXGOj4CpmSmQrhCA-CHD6-nq0q6FIuWLwwWcnBcdP1KWH3vM9ltAYLnG3uV7uGXTZ4FqUtJ78jSGEN21bIzGau6VVm4C9FFP9eWZlQPPYKtEnA_oUgKsi_Lt9qqgF" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="1200" data-original-width="900" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgorDeMa44-RXnec3ksp-2crJI7Bez__Rth48a7p_Ix67UIyhzHSjpHdlvT_rqLXGOj4CpmSmQrhCA-CHD6-nq0q6FIuWLwwWcnBcdP1KWH3vM9ltAYLnG3uV7uGXTZ4FqUtJ78jSGEN21bIzGau6VVm4C9FFP9eWZlQPPYKtEnA_oUgKsi_Lt9qqgF" width="180" /></a></div><p></p><p><br /></p><p><a href="https://www.youtube.com/watch?v=tHgdjrDnIbo" target="_blank">Sam Hartburn sang to some Ayliean artwork</a> for a recent Clopen Mic Night.</p><p>SimonLav with a <a href="https://www.desmos.com/calculator/yovfpr2bmy" target="_blank">Marvel-ous Desmos animation</a>.</p><p>David Reimann nods to Magritte with this piece, related to his <a href="https://archive.bridgesmathart.org/2022/bridges2022-399.html#gsc.tab=0" target="_blank">Bridges article</a>.</p><p><br /><br /></p><p></p><p><br /></p><p>Last but not least, I'm very happy to be a part of David Coffey's newest project: the Teaching Like Ted Lasso Podcast. Episode 1 is out, and it's on... PLAY! Check the show notes for scoonches of resources on play in math class.</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="361" src="https://www.youtube.com/embed/HzGm7afXcxs" width="434" youtube-src-id="HzGm7afXcxs"></iframe></div><br /><p>As long as I'm on the pitch... just after this post on this blog are some very fun, well developed <a href="https://mathhombre.blogspot.com/search/label/math%20game" target="_blank">math games</a> from my students.</p><p>And what's next? #Mathober! Sophia Wood has put together a list of prompts.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZFapdmFmCm-jVFm5w3l1bJM1HT2QP4eK8X9d6i3vfwcKcAUHKX63qG9BSHZML9zzxMCGHGXXWnYAfTwBh_3PHT7ybuHXRW6ElK0U36PUHtU9Cs-bOErDe93tgNoUlmbM8nlJ-x13tO-qSZ5epNe2geTsL07E0PHjxialRgQwXsPPt9xrJxLQI58zD/s1200/mathober22.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1033" height="427" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZFapdmFmCm-jVFm5w3l1bJM1HT2QP4eK8X9d6i3vfwcKcAUHKX63qG9BSHZML9zzxMCGHGXXWnYAfTwBh_3PHT7ybuHXRW6ElK0U36PUHtU9Cs-bOErDe93tgNoUlmbM8nlJ-x13tO-qSZ5epNe2geTsL07E0PHjxialRgQwXsPPt9xrJxLQI58zD/w367-h427/mathober22.jpeg" width="367" /></a></div>Each day there's a theme. Share a bit of math, a doodle, a comic, some art on the theme. Play along one day, or all 31. Tweet or send it to Sophia or myself and we'll share.<div><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-BAad2jR0LIqRZUlZDPpn5R15pcqDr4kv_GgjUsf8FRA0vTwQNim1Y_-OLuWcTs_Le12jF--qWyBjvvSAypNIVB4ZJjeVLXJm_qSi-b1txeRR3LfgVozUDBGO3SRkMFtG_Y9PyPXIFmqjcQMjdEtt3QcIqO3R_Hh6Uyvfsz4vkYlftVVvHeq-MeUX/s700/ferrari159s.png" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="459" data-original-width="700" height="210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-BAad2jR0LIqRZUlZDPpn5R15pcqDr4kv_GgjUsf8FRA0vTwQNim1Y_-OLuWcTs_Le12jF--qWyBjvvSAypNIVB4ZJjeVLXJm_qSi-b1txeRR3LfgVozUDBGO3SRkMFtG_Y9PyPXIFmqjcQMjdEtt3QcIqO3R_Hh6Uyvfsz4vkYlftVVvHeq-MeUX/s320/ferrari159s.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Ferarri 159S </td></tr></tbody></table></div><div><br /></div><div><br /></div><div><br /></div><div>See you next month at <a href="https://denisegaskins.com/" target="_blank">Denise Gaskins' place</a>, the founder of this here blog carnival. Info there on how to ask to host. I highly recommend it! So much playful math to celebrate. While you're there, check out her weekly <a href="https://denisegaskins.com/tag/math-game-monday/" target="_blank">Math Game Monday</a>.</div><div><br /></div><div>Vroom!<br /><p><br /></p></div></div>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com1tag:blogger.com,1999:blog-235276292454918436.post-45844138523538616012022-09-06T10:32:00.003-04:002022-09-10T11:49:14.140-04:00College Algebra: Quadratics<p> I had my elementary ed class canceled for low enrollment this fall. Make of that what you will.</p><p>The replacement course is College Algebra. Ironically named, since it is mostly Algebra 2. Which is required in Michigan. Our sequence has been 097 (prealgebra) -> 110 intermediate algebra (algebra 1) -> 122 College Algebra. It used to be + 123 (trigonometry) to go on to Calculus, but we have a nice precalc class now (124) so people needing to take calculus that don't place into it can just take 1 semester. The audience for 122 then, is now general education, and people who need courses that require it, like the basic chemistry, intro physics, and statistics. It's a 3 credit course, and my section meets twice a week.</p><p>The course has traditionally been quadratics -> polynomials -> rational functions -> exponentials -> logarithms -> light touch of statistics. So what do we want from the quadratics unit? This post is me trying to think out loud to get it straight for myself. The schedule is pretty packed, so I have 2-3 weeks per topic, 4-6 class periods.</p><p>The instructional sequence I have planned is visual patterns -> modeling (<a href="https://teacher.desmos.com/activitybuilder/custom/586ab17c2f8cd5bc3bcaf259?collections=featured-collections%2C5da649da5a46437eff2441d0" target="_blank">Penny Circle</a> and <a href="https://teacher.desmos.com/activitybuilder/custom/56e0b6af0133822106a0bed1?collections=featured-collections%2C5da649da5a46437eff2441d0" target="_blank">Will It Hit the Hoop?</a>) -> graphing/equation forms (<a href="https://teacher.desmos.com/activitybuilder/custom/5605bb6200701ed10fb0931a?collections=featured-collections%2C5e73b204d560367270838c4b" target="_blank">Match My Parabola</a> & <a href="https://teacher.desmos.com/activitybuilder/custom/61019827de3200e299b3fdfe" target="_blank">Form Fix</a>) -> solving equations (vertex form & graphing), mostly in a modeling context.</p><p><span id="docs-internal-guid-6d6c34a7-7fff-d0b6-52c4-5d3c05b4a9d7"><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="border: none; display: inline-block; height: 381px; overflow: hidden; width: 660px;"><img height="381" src="https://lh3.googleusercontent.com/TG7E9cJsXjJAitqOfKQhcyFAAMUqSupzD1uztm9yJartRbK4fHZJ9kaygG17oJOMWYqfxKiAjoxQ2V3leRDtrvIjyOxF2S2bbzEMtUx7dIs-Z2hMEuMm0ztc6yEoWh9V5s173358zSnaRMeIdu--ekaGL_RRaOzP2yz3WhbmJ7aB2tjIr23Jf_ifHA" style="margin-left: 0px; margin-top: 0px;" width="660" /></span></span></span></p><p>The visual patterns do a lot of work. They offer a hook, they give learners a chance to notice and wonder, they give us a chance to problem solve. They are also different from what most students have seen in algebra, sadly, so offer a <span style="font-family: inherit;">way to let them know that this course might be different. I also have them read Elizabeth Statmore's post on <a href="http://cheesemonkeysf.blogspot.com/2018/08/a-course-in-thinking.html" style="text-decoration-line: none;"><span style="color: #1155cc; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-decoration-line: underline; text-decoration-skip-ink: none; vertical-align: baseline; white-space: pre-wrap;">math as a thinking class</span></a><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. I asked them, "What do you think the main idea is? How does this compare with your own ideas about learning math or your previous experiences?" and you can read their responses on </span><a href="https://docs.google.com/document/d/1gotb6fqxmal7iLYE_01YKhfFN7eWZrkAEvZ7h_6uYK8/edit?usp=sharing" style="text-decoration-line: none;"><span style="color: #1155cc; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-decoration-line: underline; text-decoration-skip-ink: none; vertical-align: baseline; white-space: pre-wrap;">this doc</span></a><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">.</span> I think they get it. Mathematically, I think my main point is the use of variable as a relationship rather than an unknown. The transition from step number to <i>x</i> is very natural. Secondarily, they get to see multiple equivalent expressions. Which is one of those math ideas which many learners see as a bug, but mathematicians think is a central feature. Part of the richness of these problems is what the old NCTM standards called the representation process standard. Tables, expressions, visual and the connections between them all move us forward. Here's <a href="https://docs.google.com/document/d/1c9cliE-z6Pc5oVO3yXAh774PbaGxgo_o4I_GfoifIdo/edit?usp=sharing" target="_blank">a handout</a> with four quadratic patterns. The bricks and the darts and kites are very difficult to visual make a symbolic rule for. I might have made them or might have found them at Fawn Nguyen's <a href="http://visualpatterns.org">visualpatterns.org</a> or it could be a mix.</span></p><p><span style="font-family: inherit;">Modeling is a key theme of the course, and Penny Circle and Will It the Hoop? are a good start to it. I was surprised how many learners went with an exponential form, and the reveal is the perfect way to settle it. We will be using Desmos activities a lot, and those are pretty slick introductions. The Penny Circle builds on the covariation use of variables, and the basketball leads into the graphing we'll be working on next. </span></p><p><span style="font-family: inherit;">This is where we are as I write.</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjidmAJtEgnjKBlWOvJ6nJkqEUHIQpNWMI8M2zF_AppmtBpc1Mj4qY7V8YueyLLXf8wN6G026vXaoNE_D8OMKUSza_YEx4Cm73Fu4RISqGtEi7-PXBn5SPoH28BDkjLO59UCPWR-YZwU2_xskMM2XMM50ZMew1O13ATMvfDIJeiJtSbk-y65RlyG0EQ/s462/parabolas-Jesus.jpg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="462" data-original-width="458" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjidmAJtEgnjKBlWOvJ6nJkqEUHIQpNWMI8M2zF_AppmtBpc1Mj4qY7V8YueyLLXf8wN6G026vXaoNE_D8OMKUSza_YEx4Cm73Fu4RISqGtEi7-PXBn5SPoH28BDkjLO59UCPWR-YZwU2_xskMM2XMM50ZMew1O13ATMvfDIJeiJtSbk-y65RlyG0EQ/s320/parabolas-Jesus.jpg" width="317" /></a></div><span style="font-family: inherit;">I'm convinced that one of the barriers for these students is understanding graphs. Thankfully, making them is easier than ever. But I don't think that many know how to think with them. Again with the representation standard, the connections between the symbolic expression and the graph is mostly taxonomical, and I want it to have meaning. Though this is a place where I could use some help. Regression supports this goal, as it brings tables into the web of connections. Activities where they vary parameteers and observe the effect on the graph help, at least in terms of taxonomy. Solving equations with graphs is an opportunity to build some of the understanding I want, as, especially for applications, the context is another piece of the representation. Writing this, I'm a little surprised by how hard it is for me to put my goal here into words. That would undoubtedly help with the teaching!</span><p></p><p><span style="font-family: inherit;">Solving equations is last for me, partly because it is so much what they perceived the focus to be in their previous math courses. I don't care especially for a lot of symbolic skill here. I don't teach solving by factoring, though the factored form in connection with graphs is something I emphasize. I do like the approach of solving from quadratic form, because it builds on a theme in math I love about doing and undoing. This leads better into exponentials and logarithms than it does polynomials and rational functions. The symbolic fluency that I want is being able to see a quadratic as series of steps. Take a number, subtract 2, square it, double it, add five is the same as </span><img alt="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" data-is-equatio="1" data-latex="2\left(x-2\right)^2+5=13"><mn>2</mn><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>x</mi><mo>−</mo><mn>2</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>=</mo><mn>13</mn></math>" height="20" src="https://lh4.googleusercontent.com/Fs9uj0sWWuf2AOW68O01Nb3uOlhd-w486mu4_gJOj-HeA-7cIMR7EbVp45IQLV66ScFwoV1V0XIJ6vftoTb-aGb8hkJH45E4l2RN3kBDWlqNk0VaztsU6EGZRqGtEgc6YjB0_Pex4HODGDcIYBTXOnT2NsZa-gtvjLPLNO7Wvuh-VOFRRqSiJjfpFQ=w139-h20" style="font-family: Arial; font-size: 11pt; margin-left: 0px; margin-top: 0px; white-space: pre-wrap;" title="2 times open paren x minus 2 close paren squared plus 5 equals 13" width="139" />. To find what numbers make 13 from that function, we can do by undoing. I love Graspable Math for this, as the dragging to undo seems to really help get across the idea, though it doesn't work on the balance nature of equations. Here's an example <a href="https://gmacts.com/s/TRWA3" target="_blank">GM activity</a> with 3 quadratics to solve.</p><p>I'm very interested in your thoughts. What are the key ideas you want in a quadratics unit? What am I leaving out that you love? What understanding do you want your learners to develop or skills do you want them to have for graphing? Why?</p><p>P.S.</p><p><span style="font-family: inherit;">Probably violating some internet rule here, but really liking the <a href="https://twitter.com/mathhombre/status/1567159573731053569?s=20&t=Dq6QN9H98uIz5slyjhANZA" target="_blank">Twitter discussion</a> about this post.</span></p><p>@DavidKButlerUoA: This line was very interesting: "multiple equivalent expressions... is one of those math ideas which many learners see as a bug, but mathematicians think is a central feature". I'd love to hear more about that.</p><p>@joshuazucker: My interpretation is that beginners may want there to be only one answer and experts see how useful it is to have multiple representations that make different behaviors immediately visible.</p><p>@mathcurmudgeon: When 90% of calculus (and every math course, really) is rewriting expressions in an equivalent form that we can work with more easily.</p><p>@mathhombre: it starts with fractions. All these different ways to write the same thing. One of them must be right. (Often supported by teachers insisting on one.) But that we can transform, rewrite and tinker leads to fluency, connections, and meaning.</p><p>@mathforge: The belief that out of all the ways of writing it there must be a RIGHT way is SUCH an interesting belief. I've never thought before that people might believe this.</p><p>I suspect that this is more prevelant than we might admit. As experienced mathematicians we might chuckle at people who think that there is a "best" way to write, say, a quadratic or a fraction. But we probably fall into the same trap with ideas.</p><p><span></span></p><p>I might, to take a random example, think that there is a "right" way to think about differentiation, or Pythagoras theorem, or a topology, or the category of smooth functions. What I mean is, "this is the way I find most intuitive".</p><p><span style="font-family: inherit;">===</span></p><p>@KarenCampe: Love the visual patterns start & modeling focus. </p><p>When you do graphing equation forms & use match my graph/form fix you will surely cover symmetry of the graphs & how factoring gives x-ints. I like how graphing & alg manipulation of quadratics are interconnected...</p><p>Use graphing as tool to support any algebraic rearranging we might want. Look for hidden parabola that shows complex roots. Axis of symm hidden in quadratic formula.</p><p>===</p><p>[In response to "Quadratics unit in a college algebra course. What goes in, what's left out? "]</p><p>@theresawills: Probably too vague, but worth saying: RICH PROBLEM SOLVING.</p><p> </p>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com2tag:blogger.com,1999:blog-235276292454918436.post-1622644070641517282022-09-04T20:23:00.000-04:002022-09-04T20:23:04.474-04:00Fraction Reaction<p><span style="font-family: inherit;">Some years I'm fortunate to be able to lead a capstone seminar where future teachers research math games and develop a math game of their own.</span></p><p><span style="font-family: inherit;">Gretchen Zeuch developed Fraction Reaction to be a simple to learn, easy to play, fast game that works on fraction magnitude and mixed number fraction equivalence. </span></p><p><span style="font-family: inherit;">She writes:</span></p><p><span style="font-family: inherit;">The process of making this game had many stages. The first stage was deciding what kind of materials I wanted to use in my game. I decided to use a standard deck of cards because I really wanted to make a game that was accessible to every classroom. I then had to pick the mathematical content I wanted my game to be based on. I started by just laying out all the cards in a standard deck and brainstorming different mathematical content. I finally landed on fractions because I liked the students being able to physically see it. I then decided that making the connection between improper fractions and mixed fractions would be the most helpful. I then went through a lot of trial and error by playing the game with a variety of people. This helped me decide how points would work, specialty cards, and general playing rules.</span></p><p><span style="font-family: inherit;">This game is great to teach in a classroom when students are learning about improper and mixed fractions. It is very easy to teach to students as well as all students will be able to play at the same time because of the accessibility of the materials. This game will help students make the connection between an improper fraction and a mixed number. They will also be able to compare the sizes of mixed numbers and improper fractions so identify which is larger and which is smaller. Overall, this game is simple to understand and helps to solidify students' understanding of improper fractions and mixed numbers.</span></p><p><span style="font-family: inherit;">There are a few different uses for this game in a classroom. The first use is that, while students play, you can have them record all of their improper fractions turned into mixed numbers and then have them sort them on a number line. Another use is for students to record their answers during the game and then answer some comparison questions at the end. Lastly, another in class use for this game is to have students discuss the differences between fractions and mixed numbers and how they relate to each other.</span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: inherit;"><iframe allowfullscreen="" class="BLOG_video_class" height="416" src="https://www.youtube.com/embed/ASiXjPvCGhE" width="501" youtube-src-id="ASiXjPvCGhE"></iframe></span></div><span style="font-family: inherit;"><br /></span><p><span style="font-family: inherit;">Rules - <a href="https://bit.ly/FractionReactionRules" target="_blank">https://bit.ly/FractionReactionRules</a></span></p><p><span style="font-family: inherit;">In addition, Gretchen made a video to promote the integer game, Zero Rummy. She writes: This is a great game to use with young children to get them working on their addition and subtraction or to help introduce the concept of negative numbers. This game should be used as a fun exercise rather than to teach a skill. The great thing about this game is that it is stimulating for children so that they are doing math without knowing they are. It is very easy to use in the classroom with minimal materials and does not take up a large chunk of time. Children really enjoy this game and it is a very easy game to play for many ages with multiple variations.</span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: inherit;"><iframe allowfullscreen="" class="BLOG_video_class" height="416" src="https://www.youtube.com/embed/vJr-N_ng4lw" width="501" youtube-src-id="vJr-N_ng4lw"></iframe></span></div><span style="font-family: inherit;"><br /></span><p><span style="font-family: inherit;"><span style="background-color: white; color: #0d0d0d; white-space: pre-wrap;">Rules: </span><span style="background-color: white; color: #0d0d0d; white-space: pre-wrap;"><a href="https://bit.ly/ZeroRummy-rules" target="_blank">https://bit.ly/ZeroRummy-rules</a></span></span></p><p><br /></p>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-56631964515952719972022-09-04T14:58:00.000-04:002022-09-04T14:58:51.913-04:00polyGONE<p><span style="background-color: white;"><span style="font-family: inherit;">Some years I'm fortunate to be able to lead a capstone seminar where future teachers research math games and develop a math game of their own.</span></span></p><p><span style="background-color: white;"><span style="font-family: inherit;">Melanie Hanko came into seminar with a vision of making a math game inspired by <a href="https://boardgamegeek.com/boardgame/11/bohnanza" target="_blank">Bohnanza</a>, a collecting and trading game with a lot of strategy and a fair amount of luck. She really worked on the details for this game. Often times we focus on making games that use minimal materials, but this is much like a commercial game, with a lot of necessary components. For a teacher wanting to give it a try, I would love to see the learners get involved with making the cards. </span></span></p><p><span style="background-color: white;"><span style="font-family: inherit;">Melanie writes:</span></span></p><p><span style="font-family: inherit;">In the hopes of making an exceptional game, I set off looking for game structures that were simple but had a lot of potential. Then, interested in the structure of Bohnanza: The Bean Game, I started looking at mathematical content that involved some sort of sorting. Eventually, I landed with organizing shapes into hierarchies - specifically quadrilaterals. This is largely based on a 5th grade standard. polyGONE: The Shape Game is the sort of game that engages students with mathematical discourse and reasoning minus the negative attitudes about math. While players need to have a good base understanding of the hierarchy of quadrilaterals and the different types of triangles, this game will help players to create more connections between shapes and gain a broader understanding of what gives a shape its name. </span></p><p><span style="font-family: inherit;">A lot of the pieces of the game are designed with specific purposes, either to clear up misunderstandings or confusion in early versions or to clear out some of the underlying confusion. The part of the game with the most meaningful design, is the deck of cards. These cards are created to broaden player’s understanding of shapes. Included in the cards are traditional and non-traditional shapes. Different cards show different attributes of a family, like parallel lines, congruent lines or angles, and even lines of symmetry. Different cards show different looking shapes - for example both a concave and a convex kite. This differentiation within the cards, will broaden player’s understanding of shapes and relationships between shape families.</span></p><p><span style="font-family: inherit;"><span style="background-color: white;"></span></span></p><p><span style="font-family: inherit;">Another purpose of the design of the cards is to increase their usefulness. With all of the cutting and printing, the cards better be usable for multiple occasions. Since there is so much differentiation between the cards, you can easily use them in a sorting or a matching activity. Even before playing the polyGONE, you could match cards based on if they have certain attributes. For example, matching cards that have two pairs of congruent sides. The cards can be used in explorations of the “rules” for each shape family. For example, deciding if a right angle is necessary for a trapezoid, or if it is something that only occurs in some trapezoids. These and other activities can be easily supported with these cards and will help to broaden students’ understanding of shapes and the shape hierarchy. </span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: inherit;"><iframe allowfullscreen="" class="BLOG_video_class" height="415" src="https://www.youtube.com/embed/N57aE69Ohjs" width="499" youtube-src-id="N57aE69Ohjs"></iframe></span></div><span style="font-family: inherit;"><br /></span><div><div><span style="font-family: inherit;">Rules - <a href="https://bit.ly/PolyGONERules" target="_blank">https://bit.ly/PolyGONERules</a></span></div><div><span style="font-family: inherit;">Board - <a href="https://bit.ly/PolyGONEBoard" target="_blank">https://bit.ly/PolyGONEBoard</a></span></div><div><span style="font-family: inherit;">Shape Cards - <a href="https://bit.ly/PolyGONECards" target="_blank">https://bit.ly/PolyGONECards</a></span></div></div><p><span style="background-color: white; font-family: inherit;">The teachers also make a video for a good math game which they would like to promote. Melanie found one of </span><a href="https://www.gamesforyoungminds.com/blog/2018/4/20/the-100-game" style="background-color: white; font-family: inherit;" target="_blank">Kent Haines' games</a><span style="background-color: white; font-family: inherit;"> that is a very good Nim variant. She writes: </span></p><p><span style="font-family: inherit;">The 100 Game is a part of the math game genre of nim, which are mathematical strategy games in which players take turns removing objects from distinct piles or groups. Not only does the 100 Game require almost no materials and setup, but it is a fun game full of mathematical reasoning. In the forefront, the game makes practice subtracting within 100 enjoyable. Behind this practice, players strategize how to not be the last person to take away from the total. This requires deductive reasoning, an important mathematical skill. Besides the math, this game is quick to learn and engages players quickly - even unwilling players.<span style="background-color: white;"> </span></span></p><p></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: inherit;"><iframe allowfullscreen="" class="BLOG_video_class" height="416" src="https://www.youtube.com/embed/-yN9jihULRo" width="501" youtube-src-id="-yN9jihULRo"></iframe></span></div><span style="font-family: inherit;"><br /><br /></span><p></p><p><span style="font-family: inherit;">Mathematical Applications: practice subtraction, strategy and deductive reasoning</span></p><p><span style="font-family: inherit;">Materials: paper and pencil, two players</span></p><p><span style="font-family: inherit;">Object of the Game: Players start at 100 and subtract any number 1-10 from the total. The goal is to NOT be the last person to subtract a number. So you want to subtract the second to last number from the total.</span></p><p><span style="font-family: inherit;">How to Play:</span></p><p></p><ul style="text-align: left;"><li><span style="font-family: inherit;">Player one will start the game by saying “100 minus [blank] equals [insert new total]. You can only subtract numbers from 1-10.</span></li><li><span style="font-family: inherit;">Then both players will write out the subtraction sentence player one just said out loud.</span></li><li><span style="font-family: inherit;">Now, it’s player two’s turn. This player will pick a new number to subtract, say the subtraction sentence, and both players will write down the sentence.</span></li></ul><p></p><p><span style="font-family: inherit;">Example Play: Here is an example of what each player would say for a few turns. Remember that BOTH players are writing down the subtraction sentences as well.</span></p><p></p><ul style="text-align: left;"><li><span style="font-family: inherit;">Player One (P1): “100 minus 5 equals 95”</span></li><li><span style="font-family: inherit;">Player Two (P2): “95 minus 10 equals 85”</span></li><li><span style="font-family: inherit;">P1: “85 minus 7 equals 78”</span></li><li><span style="font-family: inherit;">P2: :78 minus 9 equals 69”</span></li><li><span style="font-family: inherit;">...</span></li><li><span style="font-family: inherit;">P2: “23 minus 9 equals 14”</span></li><li><span style="font-family: inherit;">P1: “14 minus 3 equals 11”</span></li><li><span style="font-family: inherit;">P2: “11 minus 10 equals 1”</span></li><li><span style="font-family: inherit;">P1: “1 minus 1 equals 0”</span></li></ul><p></p><p><span style="font-family: inherit;">In this game, player one lost because they were the last person to subtract a number from 100.</span></p><p><span style="font-family: inherit;">Notes: </span><span style="font-family: inherit;">After you play this game a few times, you might start to develop a sure strategy. In fact </span><span style="font-family: inherit;">there is something special about the number 12. Finding this strategy is what engages </span><span style="font-family: inherit;">players in deductive reasoning. Some questions you might want to ask yourself or your </span><span style="font-family: inherit;">students/children include the following:</span></p><p></p><ul style="text-align: left;"><li><span style="font-family: inherit;">What should your strategy be?</span></li><li><span style="font-family: inherit;">How can you ensure that you will win?</span></li><li><span style="font-family: inherit;">At what point in the game do you need to start using your strategy?</span></li><li><span style="font-family: inherit;">Does it matter who goes first?</span></li></ul><p></p><p><span style="font-family: inherit;">Be sure to check <a href="https://www.gamesforyoungminds.com/blog/2018/4/20/the-100-game" target="_blank">Kent's blogpost</a> for more ideas.</span></p>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-33661620773294221552022-09-04T13:44:00.002-04:002022-09-04T13:44:59.831-04:00Sorry, It's Fractions<p> Some years I'm fortunate to be able to lead a capstone seminar where future teachers research math games and develop a math game of their own.</p><p>This is Alaina Murphy's game, Sorry, It's Fractions. She was really persistent in the playtesting for this game, and did a lot of work to make it fun while keeping the math content front and center in a natural way.</p><p>She writes:</p><p>When coming up with this game, I knew I wanted to make a game that dealt with some aspect of fractions. In my opinion, fractions are one of the first aspects of math that students begin to lose interest, lack understanding, and start to hate this subject. So fractions it was. Next, I wanted the game to peak their interest, while having some mechanics that they might be familiar with. Thus, I chose to utilize a board game that many kids have played at some point in their life - SORRY. This would allow kids to focus more on learning the math of this game in comparison to first trying to figure out how to play the game. So, I had the content area and the mechanics. The next step was deciding how this was going to work. I wanted to make sure that thirds and fifths were included in this game because I believe these are the scary fractions to students. I find that students have an easier time with even numbers, but give them an odd denominator and they are out. The best denominator for including halves, thirds, fourths, and fifths was 60. So what better way to help students understand the numerical value of fractions and become more comfortable with them than using a clocklike numberline! </p><p>The rest of designing this game involved play testing to decide how exactly I would apply the mechanics and actually designing the game board. The best way to get students to want to do the math and find the most reduced fraction was to make the fractions they landed on special, rather than the cards. I wanted to ensure that the materials of this board game would be resources a teacher could acquire. So, the board can be printed or they can have students make their own, place markers can be anything - sticky notes, erasers, beads, paper clips it doesn’t really matter - and I either wanted to use dice or playing cards to move around the board. By using a deck of playing cards, students would be able to draw larger numbers and make it further around the board to larger fractions, because the probability of getting a card with a higher value is higher than if they were to roll dice. Plus, the probability of getting any value is equivalent between cards where it is not when rolling dice. In order to make the game faster for classroom use, I incorporated four entrances to home that all players can enter and reduced the number of place markers to two, requiring only two pawns to make it home for the game to end. I incorporated a lot of DRAW AGAIN fractions as a way to make it further around the board and as a catch-up mechanic. Bumping, swapping and sorry’s are also catch-up mechanics and they make the game more competitive, creating more interaction and discussion. Lastly, I wanted to use the colors of SORRY, but I also wanted to create a board similar to Prime Climb where the colors have meaning. So based on the factors of 60 I wanted to color coordinate the prime denominators.</p><p></p><ul style="text-align: left;"><li>½ is blue which is a primary color because 2 is a prime number.</li><li>Thirds are red which is a primary color because 3 is a prime number.</li><li>Fourths are a dark blue because 4 = 2 x 2 so it is the combination of two blues, producing a darker shade.</li><li>Fifths are yellow which is a primary color because 5 is a prime number.</li><li>Sixths are purple because 6= 2 x 3 so it is the combination of blue and red, producing purple.</li><li>Tenths are green because 10 = 2 x 5 so it is the combination of blue and yellow, producing green.</li><li>Twelfths are a dark purple because 12 = 6 x 2 = 3 x 2 x 2 so it is the combination of red and two blues or red and a dark blue, producing a dark purple.</li><li>Fifthteenths are orange because 15 = 3 x 5 so it is the combination of red and yellow, producing orange.</li><li>Twentieths are teal because 20 = 10 x 2 = 5 x 2 x 2 so it is the combination of yellow and two blues or green and blue, producing teal.</li><li>Thirtieths are gray because 30 has many factors so it is a combination of many colors but one less than 60 making it gray.</li><li>Sixtieths are black because 60 also has many factors so it is a combination of many colors and they are irreducible so I wanted it to be the same color as the outline. </li></ul><p></p><p>This is a great game for all types of learners to become more comfortable with fractions. Visual learners will be able to utilize the clock model and color scheme, hands on learners will be able to use the structure and game aspect, auditory learners will be able to use the discussions and verbal addition and reducing, and if teachers had students make their own boards it would be useful for those who learn from writing. </p><p>This game is a great way to get students excited about adding and reducing fractions while becoming more familiar with factors of 60, exploring prime numbers, and ultimately improving their understanding of fractions. Other applications of this game would be to refine subtracting fractions skills by playing the game counter clockwise and subtracting the value of the drawn card, rather than adding. In order to incorporate more unlike denominators, the game board could be labeled in the most reduced form (i.e. rather than 30/60, label it as ½) and the students would add the cards in the same way. This board could be used at a younger age range to better understand adding or subtracting and number sense by labeling the board with whole numbers and playing in a similar way - this variation could be useful for learning to read a clock as well! Lastly, this game could be modified to the unit circle with pi/12 radians or 15 degrees and played with dice - here it would be beneficial for students to create their board as they go using trig to come up with the value of each position. </p><p>Some problems that apply to this context:</p><p></p><ul style="text-align: left;"><li>Reduce 24/60</li><li>Reduce 13/60</li><li>Which fraction is closer to one, ⅔ or ⅗? </li><li>If there are 60 people at a party and 12 are vegetarian and 4 have a nut allergy what fraction of people at the party have a dietary restriction.</li><li>If it takes me ⅚ of an hour to get ready for school and the bus leaves in 48 minutes, do I have time to make it to the bus if it takes me 1/15 of an hour to walk to the bus stop? If not, how much time do I have to get ready?</li><li>If I am 3 minutes away from the bus stop and it takes the bus 1/10 of an hour to get to my stop, and my sister walks 11 minutes home from school. Who will get home first? What fraction of an hour will it take each of us to get home?</li></ul><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="429" src="https://www.youtube.com/embed/jrj4TF56LWc" width="516" youtube-src-id="jrj4TF56LWc"></iframe></div><br /><p>Rules: <a href="https://bit.ly/SorryItsFractions-rules" target="_blank">https://bit.ly/SorryItsFractions-rules</a></p><p>Board: <a href="https://bit.ly/SorryItsFractions-board" target="_blank">https://bit.ly/SorryItsFractions-board</a></p><p><br /></p><p>The teachers also made a video for a math game they wished to promote. While there are other videos for games called Guess My Rule, Alaina wanted to share her own take. I heartily endorse this, and have used it myself from 2nd grade to university. She writes:</p><p>There are various reasons why Guess My Rule should be used in your classroom. First of all, this game requires little to no materials - no printing, cutting, or random pieces needed. As long as students have a way to record numbers they will be set. Games, such as this one, will get students thinking about math in a fun, hands-on way that encourages collaboration and critical thinking. With this version of the game, students are encouraged to explore functions and identify patterns that will allow them to predict outputs and eventually deduce a rule. This game will give students an opportunity to experiment with expressions, practice solving equations, and familiarize themselves with symbolic representations. </p><p>If you are not convinced yet, there are so many ways that we can apply the framework of this game to learn and practice math! If you plan to use this game in an algebra class you will not be wasting your time, because it can be applied to any algebraic function and even graphs. In geometry this game could be used for guessing what axiom a figure or statement applies to or for learning terminology by grouping correct shapes. It can also be used with younger kids to learn simpler arithmetic. Lastly, we can extend this problem to higher level learners and explore various rules at the same time, not limiting the rule keepers to linear functions but allowing them to pick from any range of functions. So why not use this game?</p><p>Standards: </p><p></p><ul style="text-align: left;"><li>CCSS.MATH.CONTENT.8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear).</li><li>CCSS.MATH.CONTENT.8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.</li><li>CCSS.MATH.CONTENT.8.F.A.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). </li><li>CCSS.MATH.CONTENT.8.F.A.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1</li></ul><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="426" src="https://www.youtube.com/embed/kGf6MegV-mg" width="513" youtube-src-id="kGf6MegV-mg"></iframe></div><br /><div><br /></div><p>Rules:</p><p></p><ul style="text-align: left;"><li>Rule Keeper makes a rule</li><li>Rule Guessers take turns giving an input</li><li>Rule Keeper records input, calculates output (secretly), and records the output</li><li>Rule Guessers continue to one by one give inputs until they feel they have found the rule</li><li>ON THEIR TURN, Rule Guessers must say I would like to guess, then they must give an input AND predict the output of their given input.</li><li>Rule Keeper informs the guesser if the output is correct</li><li>If the output is CORRECT, the Rule Guesser guesses the rule</li><li>If the output is INCORRECT, the next Rule Guesser continues giving an input or they can choose to guess.</li><li>If the Rule Guesser successfully guesses the rule, they will become the next Rule Keeper and the current Rule Keeper becomes a Rule Guesser</li></ul><p></p><p>Link to John's <a href="http://mathhombre.blogspot.com/2012/05/guess-my-rule.html" target="_blank">version of the game</a>.</p><div><br /></div><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-66217828635904851462022-09-04T12:24:00.004-04:002022-09-04T12:38:06.819-04:00Binomial Battleship<p><span style="font-family: inherit;">Some years I'm fortunate to be able to lead a capstone seminar where future teachers research math games and develop a math game of their own.</span></p><p><span style="font-family: inherit;">One such is this high school algebra game from Lucas Pohl. He writes about this in what follows.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: inherit; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">When thinking about creating a math game myself, I knew I had a couple goals in mind. We had done multiple readings about what makes a good classroom game, and obviously I wanted to fulfill those criteria. Things such as being engaging, strategic, and grounded in coursework were very important to me. I had two initial thoughts: at first, I wanted to do a game that is based on statistics. Statistics is one of my favorite areas of math, and I think that it could lead to a great board game. However, I ended up going to my second thought, which was an adaptation of Battleship.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: inherit; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">The initial idea was that the coordinate system used in battleships reminded me of different methods I had seen to multiply polynomials together. In school I remember myself and classmates having trouble multiplying polynomials together, so I thought that would be a good context of the game. Luckily, making an adaptation of a game checks some game design criteria for you. Because of this, I felt like I could focus on the subject area of the game. After trial and error, I had figured out the best setup for the game. Each team gets two grids, an attack and defense grid. The attack grid had the binomials on the sides, and the attackers would have to calculate the trinomials to attack, however, the defense grid was completely filled out. The sequence and fluidity of gameplay was then discovered through playtester feedback.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: inherit; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">I think that teachers should want their learners to play this game because it is very effective at its job. Even creating the game, I became much more efficient multiplying binomials together. There is very little to suggest that playing this game is off topic, or unuseful. The game essentially is essentially getting students to do homework level repetitions, but in a context that makes it more competitive and fun. Another reason for teachers to implement this game is the opportunity for variations, and classroom connections. I feel this game has great flexibility and potential to be implemented in not only a lesson plan, but even lecture, or assessment questions. For example, teachers could use this game to get into conversations about common factors, and factoring trinomials. The game could become more engaging by letting students choose their own binomials for the grid.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: inherit; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">These are just a few examples of the advantages of implementing Binomial Battleship into the classroom. The truth is, this game is very young, but the potential it has to advance student learning is very high.</span></p><p><span id="docs-internal-guid-8ca265bf-7fff-b23f-748e-a2127bdb0010" style="font-family: inherit;"></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span class="Apple-tab-span" style="font-family: inherit; white-space: pre;"></span></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: inherit;"><iframe allowfullscreen="" class="BLOG_video_class" height="418" src="https://www.youtube.com/embed/GMqHYSRp3Vs" width="503" youtube-src-id="GMqHYSRp3Vs"></iframe></span></div><span style="font-family: inherit;"><br />Handout: <a href="https://bit.ly/BinomialBattleship-handout" target="_blank">https://bit.ly/BinomialBattleship-handout </a></span><div><span style="font-family: inherit;">Game board: <a href="https://bit.ly/BinomialBattleship-board" target="_blank">https://bit.ly/BinomialBattleship-board</a> <br /></span><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">These teachers also make a video to promote an excellent math game they found. I couldn't agree more with this one, a classic from Joe Schwartz. I first saw it in </span><a href="https://exit10a.blogspot.com/2016/01/i-like-this-game-because-you-have-to.html" style="font-family: inherit;" target="_blank">this blogpost</a><span style="font-family: inherit;">.</span></div><div><p></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="color: black; font-family: inherit; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre;"><span class="Apple-tab-span">Lucas writes: </span></span><span style="font-family: inherit; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span class="Apple-tab-span" style="white-space: pre;"> </span></span><span style="font-family: inherit; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The hundreds chart game is a great game for you to bring into your classroom for many reasons. I am going to give you three reasons why you should adopt this game into your classroom. First of all, it is incredibly engaging for students. This game will have students thinking of math in a more fun way, and they will likely find themselves enjoying math. Second, it encourages strategic thinking, and helps students develop that part of their brain. Developing this type of critical thinking will not only help them in your class, but all of their classes. Thirdly, it is incredibly easy to set up. There are almost no required materials for it. All you need is a 10x10 grid, and two different color pens. This game is the definition of minimal time and setup for the teacher, and maximum benefit for the students. </span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: inherit;"><iframe allowfullscreen="" class="BLOG_video_class" height="420" src="https://www.youtube.com/embed/oFUBoZ0T-PM" width="505" youtube-src-id="oFUBoZ0T-PM"></iframe></span></div><span style="font-family: inherit;"><br /></span><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span><p></p></div></div>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-40011233443523634442022-04-30T16:07:00.001-04:002022-04-30T16:07:40.634-04:00Playful Math 155<p> Welcome to the Playful Math Carnival, 155th edition!</p><p>155, tell us your secrets.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiN4wv3EK2kWITYeZ8hSx0bXwaosl7Ucs0CZPl5JZRt5AU9ykVLTA309yRX7rAErw0lL6o47i3Ee-8WQmiDkTAPF1D7dZRkdngQ4AC8EPRBuYoMHVuwwGqPU48xkUFVd7_vgIYRFm1Xzrsb39MAH9a7O8UGCGLNnWpmYKnk-M1l4oA0hzSHTRLldg1Y/s800/155house.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="800" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiN4wv3EK2kWITYeZ8hSx0bXwaosl7Ucs0CZPl5JZRt5AU9ykVLTA309yRX7rAErw0lL6o47i3Ee-8WQmiDkTAPF1D7dZRkdngQ4AC8EPRBuYoMHVuwwGqPU48xkUFVd7_vgIYRFm1Xzrsb39MAH9a7O8UGCGLNnWpmYKnk-M1l4oA0hzSHTRLldg1Y/s320/155house.jpeg" width="320" /></a></div><br /><p></p><p>Via <a href="https://pballew.blogspot.com/2021/06/on-this-day-in-math-june-4.html" target="_blank">Pat Bellew</a>, 155 is the sum of the prime numbers between its smallest and largest prime factors, 5 and 31. 5+7+11+13+17+19+23+29+31=155. How would you go about finding more of these? What would you call them? Pat also notes that 155 is the number of primitive permutation groups of order 81. Which is odd, because it is more than double the number of groups for any order less than 81. And there's <a href="https://oeis.org/A000019/b000019.txt" target="_blank">not another larger</a> (than 75 even!) until you get to order 256 (which has 244). Do 81 and 256 have anything in common?</p><p>Wait, 5 and 31? That means 155 is semiprime. What is the previous and what is the next semiprime? (They're both even...) Are there more primes or semiprimes smaller than 100?</p><p>The coolest thing I found is that 155 is a toothpick number. You start with a toothpick, then add a perpendicular toothpick anywhere there is an exposed endpoint. Here is 1, 3, 7, 11, 15, 23, 35, 43, 47, 55, 67. How many more steps to 155? Is it a fractal? Is it a cellular automaton? Mathematicians have also studied T(n)/n^2. Does it have a limit? Does it have an extremum? Here's some <a href="https://www.geogebra.org/m/m8xtbmar" target="_blank">GeoGebra</a> to make your own.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH00kozZLmQyKuvEvmTkxAse3BoCvthyEWUBrKCxIK7UG6-ReU-YIFTJXSP5yhCqkU81sm70KSJW282J9IXbS6mYAev78DjnfF9x83s9x4pcyjxDfJy3E-JiAUxCK3FkkvRdKtFKTNyuB4eQEaapqLvHNrqneSWd-8lxXJZV90d6b27l4K67KRvsW8/s480/merged.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="480" data-original-width="480" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH00kozZLmQyKuvEvmTkxAse3BoCvthyEWUBrKCxIK7UG6-ReU-YIFTJXSP5yhCqkU81sm70KSJW282J9IXbS6mYAev78DjnfF9x83s9x4pcyjxDfJy3E-JiAUxCK3FkkvRdKtFKTNyuB4eQEaapqLvHNrqneSWd-8lxXJZV90d6b27l4K67KRvsW8/s320/merged.gif" width="320" /></a></div><br /><p>155 is also a <i>generalized</i> pentagonal number. The <a href="https://www.geogebra.org/m/Pt87zyD5" target="_blank">pentagonal numbers</a> have a rule n(3n-1)/2, usually for n =1, 2, 3... , giving 1, 5, 12, 22, 35, ... But there are also positive outputs for negative integers, 2, 7, 15, 26, 40 ... which pleasantly fit between the usual pentagonal numbers. What patterns do you notice? Which negative number gives 155? I've been trying to think about how to visualize these negative pentagonals, to no avail so far. Have you got any ideas?</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrTDV_0EMZdm2QV5XZF3o3zEnP149va1S-nNtLksY-_5CCLNinGUTWsVOgBHNruiE1uRHCN9qn_ZOBx82CQz-vE-7C8uyANQb33bFvui7ciqJaSq4bbtvsG9J77qlNnIRUqoQuWQXRe1TxJ_inEj2bd17-R7KTlWeizhNPhjk8TBnwtP1SbjVcwPbu/s1014/Screen%20Shot%202022-04-30%20at%2012.45.25%20PM.png" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="516" data-original-width="1014" height="163" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrTDV_0EMZdm2QV5XZF3o3zEnP149va1S-nNtLksY-_5CCLNinGUTWsVOgBHNruiE1uRHCN9qn_ZOBx82CQz-vE-7C8uyANQb33bFvui7ciqJaSq4bbtvsG9J77qlNnIRUqoQuWQXRe1TxJ_inEj2bd17-R7KTlWeizhNPhjk8TBnwtP1SbjVcwPbu/s320/Screen%20Shot%202022-04-30%20at%2012.45.25%20PM.png" width="320" /></a></div><p><br /></p>Maybe the toothpick was a little too crazy of a visual patten? Here's one I was trying to make to have 155. Did it work? If so, which step? Fawn always asks for the 43rd step... what's that? Is there a rule? What if step 1 had -1 square, what would the rule be?<p></p><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9Z4XkLpiT8wf_jG-q0si2jgKZhwzAFCLoOQz0faQtx638JzZpHASmjQN4rj1WkvKBV5G1VUgClfvwZA0lc_zEp6Euq6Iox8_oxa6ZIAnDRpiyNSnOAYaGSAjKUGPkIWFBdIYm-fbcDI007TH6BrQTN6gEmh2DROTHUyMl_uKW6DslXEG-Rk6pigCn/s980/Screen%20Shot%202022-04-30%20at%2012.52.45%20PM.png" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="980" data-original-width="476" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9Z4XkLpiT8wf_jG-q0si2jgKZhwzAFCLoOQz0faQtx638JzZpHASmjQN4rj1WkvKBV5G1VUgClfvwZA0lc_zEp6Euq6Iox8_oxa6ZIAnDRpiyNSnOAYaGSAjKUGPkIWFBdIYm-fbcDI007TH6BrQTN6gEmh2DROTHUyMl_uKW6DslXEG-Rk6pigCn/s320/Screen%20Shot%202022-04-30%20at%2012.52.45%20PM.png" width="155" /></a></div><div><br /></div><div><br /></div><div><br /></div><div>I also found this pattern over at <a href="https://oeis.org/A028387" target="_blank">OEIS</a> from Ilya Gutskovskiy. Which step is 155? How would you write the rule? What is a Fibonacci polynomial? From where did that question come?</div></div><div><br /></div><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvy7U3PIhwlxVvd8UiZSYlguel23XuHipOz_HSWjn54H0Y4k5pG5RNUmxUjzTtaAWzMwOKTTtUKotfu5Nh8kSf0ajShgRWEpgZ6SIG4zEwOypN9QgmXAucidh9FkjYRY6frLsCXWu2iUOivak9vIJZaJhQfYgtrghvh-_OQhsWwDZnTXtcdY7mppaT/s570/155brass.jpeg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="526" data-original-width="570" height="184" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvy7U3PIhwlxVvd8UiZSYlguel23XuHipOz_HSWjn54H0Y4k5pG5RNUmxUjzTtaAWzMwOKTTtUKotfu5Nh8kSf0ajShgRWEpgZ6SIG4zEwOypN9QgmXAucidh9FkjYRY6frLsCXWu2iUOivak9vIJZaJhQfYgtrghvh-_OQhsWwDZnTXtcdY7mppaT/w200-h184/155brass.jpeg" width="200" /></a></div><div><i>On to the goodies...</i></div><div><br /></div><div><b>Blogger of the Month</b></div><div>Jenna Laib is killing it. Creator of Slow Reveal Graphs, she has so much good writing on so many different topics, it is amazing. For example, THIS MONTH, <a href="https://jennalaib.wordpress.com/2022/03/31/what-will-help-plan-for-tomorrow/" target="_blank">planning</a> (with a great pattern/multiplication activity), the <a href="https://jennalaib.wordpress.com/2022/04/06/the-ramadan-calendar/" target="_blank">Ramadan calendar</a>, <a href="https://jennalaib.wordpress.com/2022/04/19/the-learning-that-led-to-today/" target="_blank">learning progressions</a>, <a href="https://jennalaib.wordpress.com/2022/04/26/changing-how-i-mathematize-childrens-literature/" target="_blank">mathematizing children's literature</a> plus <a href="https://jennalaib.wordpress.com/2022/04/27/the-bossy-owl-mathematizing-two-many-birds-in-first-grade-part-1/" target="_blank">part 1</a> and <a href="https://jennalaib.wordpress.com/2022/04/28/how-many-birds-mathematizing-two-many-birds-in-first-grade-part-2/" target="_blank">part 2</a> examples. In addition, she edits the Illustrative Math blog, where she also sometimes writes gems <a href="https://illustrativemathematics.blog/2019/10/13/using-instructional-routines-to-inspire-deep-thinking/" target="_blank">like this</a> on instructional routines Plus Slow Reveal Graphs, which just this week included <a href="https://slowrevealgraphs.com/2022/04/22/how-loud-is-too-loud-english-espanol/" target="_blank">How Loud is Too Loud?</a>, <a href="https://slowrevealgraphs.com/2022/04/21/amazon-warehouse-workers-suffer-muscle-and-joint-injuries-at-a-rate-4-times-higher-than-industry-peers/" target="_blank">Amazon Worker Injuries</a>, and <a href="https://slowrevealgraphs.com/2022/04/21/moving-out-share-of-population-by-age-that-rents-in-australia/" target="_blank">Australian Housing</a>.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaK3x7QQ4DzIvW4H5gl60mYqQrC8FmBPLwVUPHwHfN84fEQsKVcDg7M6V5EqTjshbDH8rhthlG1BgYCvFoA8IBpYs1D4Z5R35yfRAD8oxcgLr-TPR0D56jiayU4HPh19wzHiQ_gbVOrBWlQ1feYkJFPeio--lYVXhAV09D5oqvaFeusHkXZiFxGLGL/s1600/4228060461_86b0de9af0_h.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaK3x7QQ4DzIvW4H5gl60mYqQrC8FmBPLwVUPHwHfN84fEQsKVcDg7M6V5EqTjshbDH8rhthlG1BgYCvFoA8IBpYs1D4Z5R35yfRAD8oxcgLr-TPR0D56jiayU4HPh19wzHiQ_gbVOrBWlQ1feYkJFPeio--lYVXhAV09D5oqvaFeusHkXZiFxGLGL/s320/4228060461_86b0de9af0_h.jpeg" width="320" /></a></div><br /><div><br /></div><div><b>Elementary and Middle</b></div><div>Math for Love shared their <a href="https://mathforlove.com/lesson/forty-faces/" target="_blank">40 Face Puzzle</a>. 100% will try, as I've loved the <a href="http://faceshundred.blogspot.com/" target="_blank">100 Face activity</a>, too.</div><div><br /></div><div>Brian Bushart got playing <a href="https://twitter.com/SplashSpeaks/status/1513623560690016260" target="_blank">Heads and Tails</a>, a game/probability exploration.</div><div><br /></div><div>Andrew Fenner made a <a href="https://app.knowledgehook.com/app/Teacher/da9eaa90-93bc-ea11-974a-0050568c42b6/Content/249c5cea-76ac-ec11-9756-0050568c42b6//View" target="_blank">hundred chart game</a> in KnowledgeHook. (Free account but you have to log in to see it.)</div><div><br /></div><div>Karen Campe wrote about <a href="https://karendcampe.wordpress.com/2022/04/22/powerful-pairs/" target="_blank">special number pairs</a> in math. The game I love adapting for these is Go Fish. For example, my preservice teachers were playing 1s Go Fish with some <a href="https://drive.google.com/file/d/1cSQ84IuzHMXtAML4s85Eeb1N5NhTSLTo/view?usp=sharing" target="_blank">fraction cards</a> they made with 4th and 5th graders. (2 cards each of: ½, ¼, ¾.⅓, ⅔, ⅙,⅚, 1/12, 5/12, 7/12, 11/12, one choice or can make two more different 1/2s, or a 0 and a 1.) I also made these <a href="https://drive.google.com/file/d/12R8Z87yMnOTDFextSqs_eqnaK92PiShu/view?usp=sharing" target="_blank">fraction card blanks</a>, but they might be more middle school...</div><div><br /></div><div>Not this month, but there is a collection of tiny elementary math games here <a href="http://mathhombre.blogspot.com/2022/02/early-el-math-games.html" target="_blank">on this blog</a>. Pointed for specific content, but low effort, low materials. As wih the fractions above, I love playing them with <a href="https://mathhombre.tumblr.com/post/682551607656923136/number-cards" target="_blank">student made cards</a>.</div><div><br /></div><div>Wow. Rajeev Raizada made <a href="https://www.desmos.com/calculator/lkdwtulfwr" target="_blank">paper pool in Desmos</a>!</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjB5cx946HgsJjp0FzV7X2vkaKJWvIxI5ToiD39sPf1a8rdvMCnlSoVuQK689_XTEEGIod1FSFfo4ELyD-ohEwRCxsefkBSfzABNTsBYTscpcEkEcRvN5pou3O6iMQla2X9_SHprUrZsadJ4Ktm5AZwO2J04a-fIRVkTLziRw4i5cAq_Qh5NXhbAOQw/s316/sports155.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="316" data-original-width="240" height="316" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjB5cx946HgsJjp0FzV7X2vkaKJWvIxI5ToiD39sPf1a8rdvMCnlSoVuQK689_XTEEGIod1FSFfo4ELyD-ohEwRCxsefkBSfzABNTsBYTscpcEkEcRvN5pou3O6iMQla2X9_SHprUrZsadJ4Ktm5AZwO2J04a-fIRVkTLziRw4i5cAq_Qh5NXhbAOQw/s1600/sports155.jpeg" width="240" /></a></div><br /><div><br /></div><div><br /></div><div><b>High School and Beyond</b></div><div>Henri Picciotto shared a <a href="https://blog.mathed.page/2022/04/13/lab-gear-the-great-connector/" target="_blank">blogpost from Liz Caffrey</a> using his Lab Gear for algebra. </div><div><br /></div><div>Deana Sample shared a fun <a href="https://twitter.com/shoutitout314/status/1520096136077271040?s=20&t=WK98de3_Frk4Du7WMOfhVg" target="_blank">bodyscale similar triangles activity</a>.</div><div><br /></div><div>Matt Enlow shared his progress on <a href="https://twitter.com/CmonMattTHINK/status/1520425040852013056?s=20&t=WK98de3_Frk4Du7WMOfhVg" target="_blank">a crazy problem</a> cutting up spheres to get different surface areas.</div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjvdC-8XYsh5Ep_FV4K3RV3RGj59QI1MTn8-rvr22tzGAb-I1AKQxIUp-x8Sthw9-mmTRM9x7aH5jFedILy098nWvCm54Z-1xz5xjbs4oj7UZXP-tAG05ld3sRDDOzPnzA155kzbdzzUn4kHHbxfnVwDPGsbYT-w7AQGDalBToCdnB3Nk5RLtLw9V4f/s972/Screen%20Shot%202022-04-30%20at%201.23.07%20PM.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="600" data-original-width="972" height="198" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjvdC-8XYsh5Ep_FV4K3RV3RGj59QI1MTn8-rvr22tzGAb-I1AKQxIUp-x8Sthw9-mmTRM9x7aH5jFedILy098nWvCm54Z-1xz5xjbs4oj7UZXP-tAG05ld3sRDDOzPnzA155kzbdzzUn4kHHbxfnVwDPGsbYT-w7AQGDalBToCdnB3Nk5RLtLw9V4f/s320/Screen%20Shot%202022-04-30%20at%201.23.07%20PM.png" width="320" /></a></div>Also 3D, Sophia Wood shared <a href="https://twitter.com/fractalkitty/status/1520410588848918529?s=20&t=WK98de3_Frk4Du7WMOfhVg" target="_blank">her learners' work</a> making nets for some interesting polyhedra in Polypad. (Which lets you fold them! Select all the tiles in the net, and a fold option appears. Select a polyhedron and an unfold option is there.)</div><div><br /></div><div>Erin and Taylor, two of my seniors, put together a sweet 1 <a href="https://sites.google.com/mail.gvsu.edu/baird-magennis/home" target="_blank">week graph theory unit</a> for high school, which ends with a math game built on some pretty cool discrete ideas.</div><div><br /></div><div>Mathigon shared their <a href="https://mathigon.org/task/timelinehunt" target="_blank">timeline scavenger hunt</a>, using their excellent timeline of math and mathematicians.</div><div><br /></div><div>Dave Richeson investigates <a href="https://twitter.com/divbyzero/status/1515042610007707655?s=20&t=WK98de3_Frk4Du7WMOfhVg" target="_blank">Möbius strips with zippers</a> with his learners.</div><div><br /></div><div>James Propp <a href="https://mathenchant.wordpress.com/2022/04/17/tricks-of-the-trade/" target="_blank">applies proof by contradiction constructively</a> in this month's post.</div><div><br /></div><div><b>Math Art & Puzzles</b></div><div>Melynee Naegele sent the <a href="https://mathequalslove.net/hexaflexagons/" target="_blank">hexaflexagons</a> from Sarah at Math Equals Love. These are always amazing! Sarah is also the queen of <a href="https://mathequalslove.net/puzzles/" target="_blank">classroom puzzles</a>, so check them out while you're over there.</div><div><br /></div><div>Margie Pearse collected a bunch of <a href="https://twitter.com/pearse_margie/status/1518214706393194496?s=20&t=ElnpRWyI_HWnebvpEFp2Xw" target="_blank">math puzzles for May</a>. (Gdoc)</div><div><br /></div><div>Via James Propp and Daniel Kline, the <a href="https://twitter.com/JimPropp/status/1512256809385533442?s=20&t=WK98de3_Frk4Du7WMOfhVg" target="_blank">Jumping Julia puzzle</a>. </div><div><br /></div><div>Speaking of puzzles, Ms. Messineo sent <a href="https://twitter.com/JustinAion/status/1506640108010848260?s=20&t=WK98de3_Frk4Du7WMOfhVg" target="_blank">Justin Aion's pride</a> in solving Will M Dunn's puzzle. Feels like some kind of planar Ramsey Theory problem... Keep reading, the #mtbos discussion was pretty cool.</div><div><br /></div><div>Patrick Vennebush wrote & joked about <a href="https://mathjokes4mathyfolks.wordpress.com/2022/04/12/idk-puzzles/" target="_blank">I Don't Know Puzzles</a>.</div><div><br /></div><div>Obviously I love using Polypad at Mathigon. Well they're having <a href="https://mathigon.org/art-contest" target="_blank">an art contest</a>! For the under 18 crowd, but I'm planning to go gawk. HT Sophia.</div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglO22yYTgaROGCG6gJa7v_vFUL3jIDKrrkT2X0x8GktW3QKIZH9RumF67yU0X6ykJ7eOIKWcxeEB1C5oYK9IX9Y-xYzN42PdcpQxte8fBG55xq9pbhpiKbwOf6VfLIcRQiW9Jb42sj2DRNAdJcM_1790QjgJplMI44GOQsJxNRGyPfkbu0Mq4Typ7T/s1200/FPtACmmXMAMmk-w.jpeg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1200" data-original-width="1200" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglO22yYTgaROGCG6gJa7v_vFUL3jIDKrrkT2X0x8GktW3QKIZH9RumF67yU0X6ykJ7eOIKWcxeEB1C5oYK9IX9Y-xYzN42PdcpQxte8fBG55xq9pbhpiKbwOf6VfLIcRQiW9Jb42sj2DRNAdJcM_1790QjgJplMI44GOQsJxNRGyPfkbu0Mq4Typ7T/s320/FPtACmmXMAMmk-w.jpeg" width="320" /></a></div>Speaking of art, Paula Beardell Krieg sent Celeste Bancos' <a href="https://bancosparenting.wordpress.com/2022/03/24/origami-pockets-and-a-paper-pickup-truck/" target="_blank">Origami Pockets post</a>, which also had some great informal measurement investigation and what if thinking. Paula has been blowing me away with her <a href="https://twitter.com/hashtag/MathsArtMonday?src=hashtag_click&f=live" target="_blank">#mathsartmonday</a> tweets, like <a href="https://twitter.com/PaulaKrieg/status/1518580484812455936?s=20&t=WK98de3_Frk4Du7WMOfhVg" target="_blank">this one</a>.</div><div><br /></div><div>Lee Trent was playing with <a href="https://vacuously-true.tumblr.com/post/680827686547046400/vacuously-true-minerva-studies" target="_blank">fractal cats</a>. Fracatals? Not <a href="https://vacuously-true.tumblr.com/post/614747546243514368/programmerhumour-incatption-or-catception" target="_blank">her first</a>...</div><div><br /></div><div>Speaking of tumblr, this poster described this viral video as <a href="https://this-is-trivial.tumblr.com/post/680507244353355776/stochastic-continuous-nim" target="_blank">stochastic continuous nim</a>. Spot on.</div><div><br /></div><div><br /></div><div><br /></div><div><b>Tik Tok?</b></div><div><a href="https://www.tiktok.com/@howie_hua" target="_blank">Howie Hua</a> is the king of math TikTok. Check out gems like his <a href="https://www.tiktok.com/@howie_hua/video/7092417961826340139?is_from_webapp=1&sender_device=pc&web_id=7062050613333444102" target="_blank">mixture puzzle</a>.</div><div><br /></div><div>The undisputed master of math tech, <a href="https://www.tiktok.com/@mathtechcoach" target="_blank">Steve Phelps</a> is there.</div><div><br /></div><div>Ms. Callahan is the <a href="https://www.tiktok.com/@funny_math_teacher" target="_blank">funny math teacher</a>.</div><div><br /></div><div><a href="https://www.tiktok.com/@mathletters" target="_blank">Math Letters</a> is shooting for a Math with Bad Drawings vibe for TikTok. </div><div><br /></div><div>But there must be more! Help us find them...</div><div><br /></div><div><b>Off Ramp</b></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMDBa7Zzq5aS6f7J1_XPiGQdqm33s9LQbcdFL-W0wJj8uGQV1nQslsx4FCQvPeFzyGtoxCCoTVxsGKIZq_IBsNcif7emrKbN6yIDi0MU7ddIg1u-plgnaebJqsW5qYqGxNtqaOZOeYgbRUOXACGcMX7U1ENvb69pBj-ROxheD8nNB6JT9boGGWa3Mn/s1214/I155.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="810" data-original-width="1214" height="214" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMDBa7Zzq5aS6f7J1_XPiGQdqm33s9LQbcdFL-W0wJj8uGQV1nQslsx4FCQvPeFzyGtoxCCoTVxsGKIZq_IBsNcif7emrKbN6yIDi0MU7ddIg1u-plgnaebJqsW5qYqGxNtqaOZOeYgbRUOXACGcMX7U1ENvb69pBj-ROxheD8nNB6JT9boGGWa3Mn/s320/I155.jpeg" width="320" /></a></div>Karen Campe reminded me to promote <a href="https://mathwithbaddrawings.com/2022/04/05/on-parents-children-and-a-newborn-book-of-mathematical-games/" target="_blank">Ben Orlin's new math game book</a>, the epitome of playful math. I am loving it. Somehow it's even better than I expected. Karen also pointed out a pretty <a href="https://twitter.com/KarenCampe/status/1520380381857562625?s=20&t=WK98de3_Frk4Du7WMOfhVg" target="_blank">sweet hexagon tessellation</a> at La Guardia of all places, so you know she has an eye for fun.</div><div><p>The previous <a href="https://www.geogebra.org/m/Pt87zyD5" target="_blank">Playful Math Carnival</a> was at Denise Gaskins' blog, the founder of the carnival. Be sure to check her site weekly for the Math Game Mondays which are only up one week! Other goodies, too, though. Next up is at<span style="font-family: inherit;"> <a href="https://naturestudyaustralia.com.au/" style="background-color: white; border-bottom-color: rgb(197, 197, 197); border-bottom-style: solid; border-image: initial; border-left-color: initial; border-left-style: initial; border-right-color: initial; border-right-style: initial; border-top-color: initial; border-top-style: initial; border-width: 0px 0px 1px; box-sizing: border-box; margin: 0px; outline: 0px; padding: 0px; text-decoration-line: none; vertical-align: baseline;"><span style="color: #2b00fe;">Nature Study Australia</span></a>. Contact Denise if you're interested or willing to host. It really impresses me every time I do just how much good stuff is out there.</span></p><p><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3KA11i83D3DjhsftZCYkJ5r1n2OPBYDQouIkP-1QHMPj0qGmJq9IiGPXPscSDAEdKYjhys8H5po3RVn_YQcrOFhTBH0FBO45deLQCXfcRRgz818YCed9-fZCSufuaQEGCH_VRnTjpGpBlHvzf8jdZj1eUJvHmrqr33kPtC-HcnpFltM11GOpsQIki/s2560/FRhRZmtXIAAbUxf.jpeg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="2560" data-original-width="1920" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3KA11i83D3DjhsftZCYkJ5r1n2OPBYDQouIkP-1QHMPj0qGmJq9IiGPXPscSDAEdKYjhys8H5po3RVn_YQcrOFhTBH0FBO45deLQCXfcRRgz818YCed9-fZCSufuaQEGCH_VRnTjpGpBlHvzf8jdZj1eUJvHmrqr33kPtC-HcnpFltM11GOpsQIki/w300-h400/FRhRZmtXIAAbUxf.jpeg" width="300" /></a></p><p><span style="font-family: inherit;"><br /></span></p><p><span style="font-family: inherit;"><br /></span></p><p><span style="font-family: inherit;"><br /></span></p><p><span style="font-family: inherit;"><br /></span></p><p><span style="font-family: inherit;"><br /></span></p><p><span style="font-family: inherit;"><br /></span></p><p><span style="font-family: inherit;">PS. I've been working all year with <a href="https://www.instagram.com/xavithegoldenboygolden/" target="_blank">Xavier Golden</a> (yes relation) a preservice art teacher on a math graphic novel. And we're starting to see some inked and colored pages... I'm so excited!</span></p><p><span style="font-family: inherit;"><br /></span></p><p><span style="font-family: inherit;"><br /></span></p><p><span style="font-family: inherit;"><br /></span></p><p></p><br /><p><br /></p><div class="separator" style="clear: both; text-align: center;"><br /></div></div>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com2tag:blogger.com,1999:blog-235276292454918436.post-63347871184813611922022-02-25T16:06:00.005-05:002022-02-25T19:27:36.921-05:00Early El Math Games<p><span style="font-family: inherit;">As my preservice teachers have had the opportunity to work with a K/1 classroom this year, I've been thinking a lot more about early math games. Mostly I'm trying to tie these to the components of number sense. </span></p><p style="text-align: center;"><span style="font-family: inherit; font-size: medium;"><b>Number Sense</b></span></p><p><span style="font-family: inherit;">In our class we discuss these as: </span></p><p></p><ul style="text-align: left;"><li><span id="docs-internal-guid-fdf7a711-7fff-8a97-7ff3-495406f4f50c"><span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">one-to-one correspondence - as learners count, they have one (and only one!) number assigned to each object being counted.</span></span></span></li><li><span><span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">hierarchical inclusion - (worst name candidate) the idea that a number contains smaller numbers. If you have 6 you also have 5, etc.</span></span></span></li><li><span><span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">subitizing - visual recognition of quantities. Perceptual subitizing is immediate recognition of quantities, most commonly up to 5 or 6. Conceptual subitizing is visual chunking of a collection into smaller groups that can be perceptually subitized.</span></span></span></li><li><span><span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">cardinality - the center and core. Recognition of numbers as quantities, a characteristic of a collection that doesn't change with rearrangement. Kids can have most of these other concepts but still not have assembled them into cardinality.</span></span></span></li><li><span><span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">magnitude/comparison - both being able to directly compare quantities, and identify relative size - like locating where 7 is between 5 and 15.</span></span></span></li></ul><div><span style="white-space: pre-wrap;"><span style="font-family: inherit;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiChoNPEN8Tg2B7PQzac36NKX-ARszOQPTaFbJTPL6jfjXWVno3e514f4nJkzgMNJBC9spzJiETrhannGBeHXAkDjtg6uSKwvPgGyDbjcZ3lSn11AFKABUwqgR-7sGwRnNvz-8Q0_45Vvlm13tKxkeRdplDcH5cinuxrdVbQpgzH61vglDx1QJIYLU7=s4032" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="4032" data-original-width="3024" height="320" src="https://blogger.googleusercontent.com/img/a/AVvXsEiChoNPEN8Tg2B7PQzac36NKX-ARszOQPTaFbJTPL6jfjXWVno3e514f4nJkzgMNJBC9spzJiETrhannGBeHXAkDjtg6uSKwvPgGyDbjcZ3lSn11AFKABUwqgR-7sGwRnNvz-8Q0_45Vvlm13tKxkeRdplDcH5cinuxrdVbQpgzH61vglDx1QJIYLU7=s320" width="240" /></a>If possible, my favorite thing for many of these games is for kids to have number cards which they have a hand in making. Similar to Tiny Polka Dot cards, which are a great commercial version. The idea is to make four suits, 0 or 1 to 10, where the suits are different representations of the numbers. Ten frames, symbols or shapes organized into patterns, randomly placed or groups of shapes to encourage subitizing, etc. You can have numerals or tally marks or number words if that's something you want your learners working on. I tend to prefer cards that involve counting and supportive structures. I used to have my own cards I'd print, but the opportunity for creativity, ownership and doing mathematics is strong with kids making the cards. (Not to mention some sneaky assessment.)</span></span></div><div><span style="white-space: pre-wrap;"><span style="font-family: inherit;"><br /></span></span></div><div><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjwAkkXoXjw9Cl94kIfge-bGF2HdWPQ1VIsp3bnvkfA3CYFKXvM00Jey5ShQl5zBOQNGTsp5Zfg4U_OEIlihSs8HirmeFpHFZtbPOJ4qK6XzyTprs0hsFLjsWVZGQ6Cw9dBMVexrezDXF2sYuqF-5hlDrKKHNy2SCTyJLVJro7GJWbnG2oqJEq5ZP4m=s4032" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center; white-space: normal;"><img border="0" data-original-height="4032" data-original-width="3024" height="320" src="https://blogger.googleusercontent.com/img/a/AVvXsEjwAkkXoXjw9Cl94kIfge-bGF2HdWPQ1VIsp3bnvkfA3CYFKXvM00Jey5ShQl5zBOQNGTsp5Zfg4U_OEIlihSs8HirmeFpHFZtbPOJ4qK6XzyTprs0hsFLjsWVZGQ6Cw9dBMVexrezDXF2sYuqF-5hlDrKKHNy2SCTyJLVJro7GJWbnG2oqJEq5ZP4m=s320" width="240" /></a><span style="white-space: pre-wrap;"><span style="font-family: inherit;"><br /></span></span></div><div><span style="white-space: pre-wrap;"><span style="font-family: inherit;"><br /></span></span></div><div><span style="white-space: pre-wrap;"><span style="font-family: inherit;"><br /></span></span></div><div><span style="white-space: pre-wrap;"><span style="font-family: inherit;"><br /></span></span></div><div><span style="white-space: pre-wrap;"><span style="font-family: inherit;"><br /></span></span></div><div><span style="white-space: pre-wrap;"><span style="font-family: inherit;">Once you have the cards, familiar games create terrific mathematical opportunities. Go Fish and Memory/Concentration create counting opportunities, and set up future games using those structures, like 10s or equation Go Fish or Concentration.</span></span></div><div><span style="white-space: pre-wrap;"><span style="font-family: inherit;"><br /></span></span></div><div><span style="white-space: pre-wrap;"><span style="font-family: inherit;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEibn0bwLbqAvZ0JFGl3UaBN2lxJaU01w-3MsVLkbgJS5ZZWLsgS1MELuHdMEF78UfQZ5fWt_IsOybGG8T4JjvOccVQOkeWkJzrs439g1qSGQWtuNXp7VAckWSUsoXygPx2yhGnyhyp6Ab9Dc5oAFdtudlOfBArgMWTuk4Xxjiji5Z62SsTcIOKrhGZz=s4032" style="clear: left; margin-bottom: 1em; margin-right: 1em; text-align: center; white-space: normal;"><img border="0" data-original-height="3024" data-original-width="4032" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEibn0bwLbqAvZ0JFGl3UaBN2lxJaU01w-3MsVLkbgJS5ZZWLsgS1MELuHdMEF78UfQZ5fWt_IsOybGG8T4JjvOccVQOkeWkJzrs439g1qSGQWtuNXp7VAckWSUsoXygPx2yhGnyhyp6Ab9Dc5oAFdtudlOfBArgMWTuk4Xxjiji5Z62SsTcIOKrhGZz=s320" width="320" /></a></span></span></div><div><span style="white-space: pre-wrap;"><span style="font-family: inherit;"><br /></span></span></div><div><span style="white-space: pre-wrap;"><span style="font-family: inherit;"><div style="white-space: normal;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjrxaUsW4UItYEWDHRksqeZPjNwZyx_G2hXli5S9GFRSu-UrHxNtBW9sYxo6spbP76L1_KV8yQI0DL_s4uqbowhdOkyJTSayX10Jtv5FqwDfoqX0alVS7IYUCgZXxQzJmExpjBi3pRyFnG8sJfKwxeiznoQSX9xGrRkMXWQu0HL3xgnFgM0E9J9cyuA=s4032" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="3024" data-original-width="4032" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEjrxaUsW4UItYEWDHRksqeZPjNwZyx_G2hXli5S9GFRSu-UrHxNtBW9sYxo6spbP76L1_KV8yQI0DL_s4uqbowhdOkyJTSayX10Jtv5FqwDfoqX0alVS7IYUCgZXxQzJmExpjBi3pRyFnG8sJfKwxeiznoQSX9xGrRkMXWQu0HL3xgnFgM0E9J9cyuA=s320" width="320" /></a></div><span style="white-space: pre-wrap;"><span style="font-family: inherit;"><i>General Educational Game Advice</i></span></span></div><div style="white-space: normal;"><span style="white-space: pre-wrap;"><span style="font-family: inherit;">Many traditional games have a rule that when you're successful, you go again. I recommend against this because it increases wait time for other players, works against catch up, and can discourage the kids we want most to engage. </span></span></div><div style="white-space: normal;"><span style="white-space: pre-wrap;"><span style="font-family: inherit;"><br /></span></span></div><div style="white-space: normal;"><span style="white-space: pre-wrap;"><span style="font-family: inherit;">Similarly, I try to avoid games that emphasize speed, or require correctness to score and advance. I love for games to be an opportunity for collaboration and discussion, not a stand in for a quiz.</span></span></div></span></span></div><div><span style="white-space: pre-wrap;"><span style="font-family: inherit;"><br /></span></span></div><div><span><span style="font-family: inherit; white-space: pre-wrap;"><b>Divvy Up </b>(Counting, Hierarchical Inclusion)
Materials: Number Cards</span></span></div><div><span><span style="font-family: inherit; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: inherit;"><span style="white-space: pre-wrap;">Put about ten objects in the middle for each player. Using your number cards or dice, a player flips over a card and takes that many objects from the pile. Then counts up how many they have total. If appropriate, can have a score sheet where they write down that number. Game has two winners - one who takes the last object, one who has the most things. </span></span></div><div><span style="font-family: inherit;"><span style="white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: inherit;"><span style="white-space: pre-wrap;">Optional, arrange the 10 objects in two rows of five to sneak in some 5s structure and complements of 10.</span><span style="white-space: pre-wrap;">
</span></span></div><div><span style="font-family: inherit;"><span style="white-space: pre-wrap;">Variation: if there are not enough to take, you have to pass. Encourages comparison, but can make the end take a while.</span></span></div><div><span style="font-family: inherit;"><span style="white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: inherit;"><span style="white-space: pre-wrap;"><b>More or Less </b>(Comparison, Strategy)</span></span></div><div><span style="font-family: inherit;"><span style="white-space: pre-wrap;">Materials: Number Cards</span></span></div><div><span style="font-family: inherit;"><span style="white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: inherit;"><span style="white-space: pre-wrap;">Idea: instead of War, which is not bad, in the math game sense, try this game. Draw 3 cards and teams take turns. The team whose turn it is chooses more or less. Both teams choose a card and hold it face down, then reveal. If more was chosen, the larger number wins, if less, the smaller. If it's a tie, you chose a 2nd card from your hand with the same rule.</span></span></div><div><b style="font-family: inherit; white-space: pre-wrap;"><br /></b></div><div><b style="font-family: inherit; white-space: pre-wrap;">More Together</b><span style="font-family: inherit; white-space: pre-wrap;"> (Counting on, addition, hiearchical inclusion, decomposition)</span></div><div style="text-align: left;"><span id="docs-internal-guid-ef7ebb85-7fff-0ad3-e10a-c5fdbe74bee5"><span style="font-family: inherit;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Materials: Number cards mixed up in four piles.<br /><br /></span></span></span></div><div style="text-align: left;"><span><span style="font-family: inherit;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Two teams: each turn over a card. Who has more? Then the teams turn over their 2nd card. Who has more together?<br /><br /></span></span></span></div><div style="text-align: left;"><span><span style="font-family: inherit;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">If learners are ready to count on, can just count from the first number. (6,5) Had 6, then 7, 8, 9, 10, 11 - pointing to pips on cards. If students would benefit from counting out blocks for how much (6 for this, 5 for that, count together), use blocks. Can introduce counting on here, too.<br /><br /></span></span></span></div><div style="text-align: left;"><span><span style="font-family: inherit;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">A tie? Flip over one more. No need for an overall winner, just who wins each turn.</span></span></span></div><div><span id="docs-internal-guid-f207b06f-7fff-209c-a06f-9e0bd2acd27b"><span><h4 dir="ltr" style="font-family: inherit; line-height: 1.38; margin-bottom: 4pt; margin-top: 14pt;"><span style="background-color: transparent; font-style: normal; font-variant: normal; text-decoration-skip-ink: none; vertical-align: baseline; white-space: pre-wrap;">Staircase</span><span style="background-color: transparent; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> <span style="font-weight: normal;"> (Counting, counting on, hiearchical inclusion)</span></span></h4><p dir="ltr" style="font-family: inherit; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span id="docs-internal-guid-38bbb7de-7fff-23d5-5ada-04d46b544922"></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;">Materials: optional <a href="https://docs.google.com/document/d/1mqKez2BzYqxCmIokAZuo3g5PemcLml8XOoVI6BDlInQ/edit?usp=sharing" target="_blank">gameboard</a>, a lot of stacking cubes and a die.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;">Play: roll a die, and build a stack of that many cubes, then roll another (or reroll) and add that many, with the two summands in different colors. Put them on your team’s track on the sum. If you already have that number, that’s okay, put it on the same space. Winner is the first to get three spaces in a row (make a staircase). Some students lay them down, some stand them up.
Variation 1: If the three step game is too short, play to four or five steps.
Variation 2: if you roll a sum you already have, you can choose to remove the same sum from your opponents’ board. (Increases interaction.)
Variation 3: Playing with number cards 1-10. If you get a 1 or a 2 first card, you must take another. Otherwise it’s your choice. Bigger than 12 is a bust, you lose your turn. Probably best with a four or five step win condition, and can be combined with variation 2 as well.
Lots of opportunity to notice and wonder. Notice the different ways to get the same sum, wonder how much you have together, notice that 2+5 is the same as 5+2, ask what you hope to get on that second die roll…</span></p><div style="font-family: inherit;"><span style="background-color: transparent; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><b>How many behind? </b>(Decomposing, hiearchical inclusion, part part whole stories)
Materials: 10 (or 12!) unifix cubes.
<br /></span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Show and count how many cubes in the stack. Now put the whole stack behind your back, and bring 1 cube out front. Ask: how many cubes behind my back?
Next time, keep 1 behind your back, then show the rest. (If your partner’s there, have them go.)
Learners and teachers take turns being the hider. If you want, you can always start with the same amount shown in front, or let people show a different number, then hide some behind. If the learners haven’t got the one less idea, try that one a few more times.</span><span style="background-color: transparent; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">
</span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><b>Big Three </b>(Magnitude)
Materials: deck of number cards.
Idea: Players start with 3 face down cards. On your turn, draw a card from the deck or the top card of the discard pile. Replace one of your face down cards with it. No peeking! The goal is to find the biggest cards you can. The card you replace is then discarded, even if it was a high card. When someone thinks they have the biggest cards, they call “Last Turn” and everyone else takes one more turn. Players add up their cards to see who has the Big Three.
Option: need more challenge? Play Big Four!</span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(Riff on <a href="https://boardgamegeek.com/boardgame/3837/rat-tat-cat" target="_blank">Rat-a-Tat-Cat</a>, a great commercial math game.)</span></div><div style="font-family: inherit;"><br /></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div><div style="font-family: inherit; text-align: center;"><span style="background-color: transparent; font-size: medium; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><b>Moving to Story & Operation</b></span></div><div style="font-family: inherit;"><span style="white-space: pre-wrap;">As kids have started to acquire number sense, we move into stories that provide the context for operations. The Cognitively Guided Instruction Framework, based on research analyzing how children acted out elemental math stories.</span></div><div style="font-family: inherit;"><ul style="text-align: left;"><li><span style="white-space: pre-wrap;">Join. One quantity, increasing over the story. Unknown could be the start, the change or the result.</span></li><li><span style="white-space: pre-wrap;">Separate. One quantity, decreasing over the story. </span>Unknown could be the start, the change or the result.</li><li>Comparison. Two quantities, related by the difference between them. Unknown could be the referent, the difference or the compared quantity.</li><li>Part Part Whole. Two quantities that are part of a group. Unknown could be either part or the whole.</li><li>Grouping. A number of groups, each group with a number of things, and a total. If the total is unknown, it's multiplication; if the number in the group is unknown, it's fair share/partative division; if the number of groups is unknown, it's measure/quotative division.</li></ul></div><div style="font-family: inherit;"><span style="white-space: pre-wrap;"><br /></span></div><div style="font-family: inherit;"><b style="white-space: pre-wrap;">Comparison Game</b></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Materials: number cards, especially if you have organized ones like dice face, hashmarks (if those are good for your kids), or ten frames. Plus 50-60 unifix cubes.
Both players flip a card and build a stack that tall. Compare the stacks. Count the difference and take it off the taller stack. The player with more scores the difference. First player to 20 scored cubes wins. If it’s a tie, no score. Afterwards be sure to describe the score as 8 is 3 more than 5, or 5 is 3 less than 8. You could write down 5+3=8 (or 8-5=3 if they seem familiar with subtraction and super-comfortable with addition number sentence already.) Transition to them writing the number sentences and saying which is how many more than the other.
If they are able to find the difference without counting blocks, make sure to have them describe their thinking. If they need challenge, don’t put the stacks together as they try to figure out how much more and less.</span><span style="background-color: transparent; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">
</span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><b>Making a Difference</b>
Materials: unifix cubes or counters about 30, number cards.
Play: Both players have three cards. Choose a card to play. The lower card scores how many blocks it takes to make it equal to the other card - let the learners know that low cards are better.. If students can do with just numbers, that’s fine. But at least the first couple plays, build both numbers and count up how many cubes to make the difference. The person with the lower card scores those blocks.
If it’s a tie, you have to play a second card from your hand. Draw back up to three cards. Winner is the first player or team to 12 cubes.</span><span style="background-color: transparent; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">
</span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div><div style="font-family: inherit; text-align: center;"><span style="background-color: transparent; font-size: medium; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><b>Facts</b></span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I feel like this is a place where games have made an inroad. But still, there's plenty of fun to be had.</span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><b>10s Go Fish and Concentration Make 10</b></span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Pretty self explanatory. Remember to not let kids take extra turns. Both games I like to have kids score by counting their 10s.</span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><b>Double Time </b>(Doubles and counting on)</span></div><div style="font-family: inherit;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg_uLzByKqlbODDQ9GZu16SyWKwbg0nL_UsdriELAjjPIG--N1_HgT0kcILYWGzgqkxzG4dXejruR9mPqVSkrnk13mzgqlfcU7V0I468Lwbc-mldMicrBB0n9BraeCcbbN00DSJbS4Qt3WW4VcnH-jVB0zoJR5x_Wn18txC59OwHD5SZC7ns47cLQkJ=s4032" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="3024" data-original-width="4032" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEg_uLzByKqlbODDQ9GZu16SyWKwbg0nL_UsdriELAjjPIG--N1_HgT0kcILYWGzgqkxzG4dXejruR9mPqVSkrnk13mzgqlfcU7V0I468Lwbc-mldMicrBB0n9BraeCcbbN00DSJbS4Qt3WW4VcnH-jVB0zoJR5x_Wn18txC59OwHD5SZC7ns47cLQkJ=s320" width="320" /></a></div><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Materials: a game track, which can be numbered. 1 to 40 or 50 makes a good length with number cards, 30 is okay with dice. Bonus if you color or design the track in alternating spaces, to hint at the counting by 2s connection.</span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Play: students roll one die and move that plus the same. First to the finish line wins. I like to have students write down what they rolled and how far they went. 3+3=6, etc. If the track is numbered, you can start sneaking in some questions like 'Oh, you're on 24 and moving 8? Where will you end up?' For students working on counting on, this game provides lots of practice, since you don't start with 24, 1 is 25. </span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div><b style="white-space: pre-wrap;">Ten Penny Game </b><span style="white-space: pre-wrap;">(Fives structure, sums to 10)</span><span style="white-space: pre-wrap;">
</span><div style="font-family: inherit;"><span style="font-family: inherit; white-space: pre-wrap;">Have two ten frames out, the blocks, and some pennies or chips for scoring. Put a penny on the tenth spot of each. Players take turns rolling a die, and adding that many blocks to one of the ten frames. If they fill up the last spot, you get the penny as a point. Clear all the blocks and put on a new penny. There will be lots of opportunities for counting, counting on, and using the fives structure. "How many on this ten frame? How many more to fill it?" Are good questions here.</span></div><div style="font-family: inherit;"><span style="font-family: inherit; white-space: pre-wrap;"><b><br /></b></span></div><div style="font-family: inherit;"><span style="font-family: inherit; white-space: pre-wrap;"><b>Cover All </b>(Addition, decomposing)</span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">This is the classic math game <a href="https://boardgamegeek.com/boardgame/9851/shut-box" target="_blank">Shut the Box</a>. </span></div><div style="font-family: inherit;"><br /></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><a href="https://drive.google.com/file/d/1sxTZ47sTu87GLL_eBPIc4NIQtgyMpf_w/view?usp=sharing" target="_blank"><span style="font-variant-east-asian: normal; font-variant-numeric: normal; text-decoration-skip-ink: none; vertical-align: baseline;">Cover All</span> gameboard</a>, but really all students need is a track from 1 to 10.</span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Play: roll two dice, and cover up any combination of numbers that add to the same amount.</span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><br /></span></span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;">With some kids, blocks help. If they set out how many they rolled, they can break them up in different ways. Consider questions to ask: what would be a good roll? What numbers might be harder to cover? What are different ways to split up our roll? (Helping them realize they have a choice.) What really makes this game a classic to me is that it really generates problems. Not how do you make 10, but how do you make 10 if I already used 7, 6 and 5. Is it even possible?</span></span></div><div style="font-family: inherit;"><span style="background-color: transparent; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div></span></span></div><div><div style="line-height: 1.38; margin-bottom: 4pt; margin-top: 14pt; text-align: left;"><span style="font-family: inherit;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal; text-decoration-skip-ink: none; vertical-align: baseline; white-space: pre-wrap;"><b>Dice Squares</b></span><span style="font-weight: normal;"> (adapted from Illustrative Math)</span></span></div><span style="white-space: pre-wrap;">Materials: <a href="https://docs.google.com/document/d/1ECrnaOqHvrWFQ_WgjgYHb4Qrms6CVnaKcIeGVQUVu-o/edit?usp=sharing" target="_blank">Gameboard</a>, dice.
This is a clever variation on dots and boxes. Roll two dice and fill in an edge next to that number. The player who puts the fourth edge on a box scores it! Mark with your symbol (X or O) or initials.</span> <p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Play with your students, thinking aloud at how you get your sums. For most of the kids, counting on would be a good strategy. 3 & 5, 5 -> 6,7,8. If students could benefit from using manipulatives to count, have them take as many as each roll, then find the total.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="font-family: inherit; font-size: medium; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><b>Make Your Own</b></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Notice how simple some of these are? Really, some of these tiny math games are just born from thinking what do I want learners experiencing, and then adding dice or cards. Competition is fine - and a reason to engage for some learners, but try to avoid rewarding speed and correctness. Add in a representation (cards or the gameboard or a manipulative) and you probably have a classic in the making. (Then send it to me!) The easy wrinkle to add to the strategy and thinking required is to add choice. Much like More or Less above is basically War - with two layers of choice added in. Instead of flip a card, have a hand of two or three and choose one. Try to make choices real choices though. In More or Less, the choice of more or less makes the choice of the card much more significant.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="white-space: pre-wrap;"><b><span style="font-size: medium;">Give Me More</span></b></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;">Just two resources to end. </span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"></p><ul style="text-align: left;"><li><span style="white-space: pre-wrap;">One of my favorite YouTube channels is <a href="https://www.youtube.com/channel/UC-F-4IIfKSd3mZCjs1zwukA/videos" target="_blank">Michael Minas</a>, who makes up tiny math games with his kids and then demonstrates them. A lot of good games, but what's better is the spirit of invention.</span></li><li>Jenna Laib has a few easy, high leverage games. She writes about <a href="https://jennalaib.wordpress.com/2019/05/28/the-simple-but-high-leverage-game-collection/" style="white-space: pre-wrap;" target="_blank">making games</a><span style="white-space: pre-wrap;"> and then shares her favorites. We've used </span><a href="https://jennalaib.wordpress.com/2019/05/29/one-of-my-favorite-games-number-boxes/" style="white-space: pre-wrap;" target="_blank">Number Boxes</a><span style="white-space: pre-wrap;"> a lot this year, from 1st to 5th grade, just altering for what content the kids are thinking about. (Really, just read everything she writes.)</span></li></ul><p></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;">Just this week we were using ___ x ___ – ___ with a trash can ___ with 3rd graders. I wanted it not to be just who gets the biggest numbers, so added in the subtraction. I like having a trash can because it adds some choice, which gives even kids who have all their facts something to think about. There is so much thinking you can see and assessing you can do even just watching kids play these, and if you get to play with them... forget about it!</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;">Game on!</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p></div><p></p>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com1tag:blogger.com,1999:blog-235276292454918436.post-11160195350032033492021-12-30T18:06:00.003-05:002022-01-02T13:33:27.454-05:00Playful Math Education 151<p>Welcome to the 151st edition of Denise Gaskin's <a href="https://denisegaskins.com/mtap/" target="_blank">Playful Math Education Carnival</a> for November/December 2021. That's a lot of good math that has been shared, but I'll try to narrow it down. Thanks especially to Iva Sallay and Denise herself who had good suggestions for links.</p><p><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhA13Hsmfud0xoypKkZ0n7mpmGA7C8uHpPt6ged5eNXicbzBTthxAHgVYcP6h9b5PayNPQ81FALqrgrwwxLi_YGpJSAqtYqNceGca-P9-jQtfDnL-hPGxV7bavZqummt2DcHGeakrcMHsJ866Rog7xaNfPAbIu6PaTzPJWyPf1nRJA2AhiMmEp01L9n=s834" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="828" data-original-width="834" height="199" src="https://blogger.googleusercontent.com/img/a/AVvXsEhA13Hsmfud0xoypKkZ0n7mpmGA7C8uHpPt6ged5eNXicbzBTthxAHgVYcP6h9b5PayNPQ81FALqrgrwwxLi_YGpJSAqtYqNceGca-P9-jQtfDnL-hPGxV7bavZqummt2DcHGeakrcMHsJ866Rog7xaNfPAbIu6PaTzPJWyPf1nRJA2AhiMmEp01L9n=w200-h199" width="200" /></a>It's always nice to have a prime edition! It's in a string of 4 primes separated by 12... does that happen very often? It's also the start of a string of four sexy primes... what number separates those? It's an older sibling twin prime, and a part of a string of <a href="https://oeis.org/A106856" target="_blank">quadratic form primes</a> (not sure why those are of interest). It's a <a href="https://mathworld.wolfram.com/LuckyNumber.html" target="_blank">lucky number</a> by Euler's count, and it turns out those share some asymptotic properties with the primes. It's a palindrome, and a natural ambigram in some fonts... so maybe a pambidrome? I think there's one more pambidrome prime before 200, but what's the first one after 200? It's the number of partitions of 17 into an odd number of parts. 17, [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]... and 149 others. (Image made in <a href="https://mathigon.org/polypad" target="_blank">Polypad</a>, which has new features to play with each month, seemingly.)<span style="white-space: pre;"> </span></p><p></p><p>Lagrange's theorem tells us that each positive integer can be written as a sum of four squares. But some of them can not be written as the sum of less than 4 squares, and 151 is like that. What are the four squares?</p><p><b>Make</b></p><p><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjOSu9lCxQRwBdVcV025iAYafO4GUOy_Sf0zFWD_gBVASXQpiZQOW4Pr61EKlflH2mD0-mclEYqjQ_1OcVs82lGiwPnajtA0nqk8JAeUtVSuN-7rEGH6-ZIzsK0qecX42JeZ7V5SYcZOc7vMd09t9rnW4fvI_GtPQSgM7-z4vhRq198MOIkoTxfb2mT=s1082" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="962" data-original-width="1082" height="178" src="https://blogger.googleusercontent.com/img/a/AVvXsEjOSu9lCxQRwBdVcV025iAYafO4GUOy_Sf0zFWD_gBVASXQpiZQOW4Pr61EKlflH2mD0-mclEYqjQ_1OcVs82lGiwPnajtA0nqk8JAeUtVSuN-7rEGH6-ZIzsK0qecX42JeZ7V5SYcZOc7vMd09t9rnW4fvI_GtPQSgM7-z4vhRq198MOIkoTxfb2mT=w200-h178" width="200" /></a>To get things started, maybe give Steve Phelp's <a href="https://www.geogebra.org/m/zqjazuvw" target="_blank">fractal snowflake maker</a> a try. If paper is your thing, try Paula Beardell Krieg's <a href="https://bookzoompa.wordpress.com/2016/12/10/its-paper-snowflake-time-again/" target="_blank">directions</a>.</p><p>Paula also had a great post reviewing her month of making <a href="https://bookzoompa.wordpress.com/2021/11/11/six-weeks-seven-shapes/" target="_blank">Johnson Solids</a>. She's been doing Saturday <a href="https://bookzoompa.wordpress.com/2021/12/22/upcoming/" target="_blank">half hour folding sessions</a> that are the epitome of playful math making.</p><p>Jenna Laib shared a <a href="https://twitter.com/jennalaib/status/1473377177714503682?s=20" target="_blank">tweet thread</a> about a quick drawing game that got kids thinking. Update: she wrote <a href="https://jennalaib.wordpress.com/2022/01/02/oops-i-forgot-small-beautiful-moments/" target="_blank">a blog post</a> about it!</p><p>Can't have one of these without a Simon Gregg post. Here his learners are <a href="https://followinglearning.blogspot.com/2021/12/building-mathematics.html" target="_blank">building Number Blocks</a>, <a href="https://www.youtube.com/c/Numberblocks" target="_blank">a show</a> he's already converted me to.</p><p>Vincent Pantaloni shared <a href="https://www.geogebra.org/m/d7qafd3r" target="_blank">a Set game</a> (a Set set?) with just geometric symbols. I think it could be really challenging.</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgM_jPb92F7FIZ9vmBxZvtdQFoQ-KzkqLrGKQKpsetngbMreNfaZO71C0-qhlc0Rq9UDVG3OxOxORZALV11O0tOqCIIVKMMv3WzMIQFXPzRnRJh60xMJ4tLzSvCJelUMFTOMKivpkPJ-opK41aYk-KQsZoM8lJHXrKVj1R703NP97KFGVMRVDlFbWje=s2048" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="2048" data-original-width="2048" height="200" src="https://blogger.googleusercontent.com/img/a/AVvXsEgM_jPb92F7FIZ9vmBxZvtdQFoQ-KzkqLrGKQKpsetngbMreNfaZO71C0-qhlc0Rq9UDVG3OxOxORZALV11O0tOqCIIVKMMv3WzMIQFXPzRnRJh60xMJ4tLzSvCJelUMFTOMKivpkPJ-opK41aYk-KQsZoM8lJHXrKVj1R703NP97KFGVMRVDlFbWje=w200-h200" width="200" /></a></div>Just shortly before publishing, Jonathan pushed send on a <a href="https://jd2718.org/2021/12/28/erika-and-sterling/" target="_blank">post about haikus and magic from having a typewriter</a> in his classroom. My favorite was this, which he admitted was his own! I shared that in grad school we loved numbers that could be haiku, like <span face="TwitterChirp, -apple-system, "system-ui", "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; white-space: pre-wrap;">32,518,460. </span>He added two more <a href="https://twitter.com/mathhombre/status/1476334805100941312?s=20" target="_blank">on Twitter</a>:<p></p><p><span face="TwitterChirp, -apple-system, "system-ui", "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; white-space: pre-wrap;">1, 2, 3, 4, 5,
6, 7, 8, 9, 10 and
11. That's enough.</span></p><p><span face="TwitterChirp, -apple-system, "system-ui", "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; white-space: pre-wrap;">2.71
8281828
45 and so on</span></p><p><b>Play, Game & Puzzle</b></p><p>Back from May, but spot on theme, Peter Rowlett writes about <a href="https://aperiodical.com/2020/05/mathematical-play-with-young-children/" target="_blank">Math Play with Young Children</a>.</p><p>Annie Forest shared a place value, low materials math game called <a href="http://showyourthinkingmath.blogspot.com/2016/12/week-before-winter-break-math-game.html" target="_blank">Draw 10</a> that she first wrote about a few years ago.</p><div>Adrienne Burns tweets about making a <a href="https://twitter.com/a_schindy/status/1469343212942864395?s=20" target="_blank">math Bingo game better</a>, for addition and representation.</div><div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEglK7N29ax0bVJzZ_xnszf84VDzDa2rwaADvSX_3bsO403I7JCDctfhZsEZZNmhYTeY8veMYLNRJ_cbS7ldjYfHsKnTm5bc6VV0L-pAK4GkfJKRd-b8C5SySormuvdMn_ayfCtDWzoB_Ulf15QNk-G6nrIWn-0TTZk18VUF4ixLRzhBWXfrvnD94foa=s1200" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="960" data-original-width="1200" height="160" src="https://blogger.googleusercontent.com/img/a/AVvXsEglK7N29ax0bVJzZ_xnszf84VDzDa2rwaADvSX_3bsO403I7JCDctfhZsEZZNmhYTeY8veMYLNRJ_cbS7ldjYfHsKnTm5bc6VV0L-pAK4GkfJKRd-b8C5SySormuvdMn_ayfCtDWzoB_Ulf15QNk-G6nrIWn-0TTZk18VUF4ixLRzhBWXfrvnD94foa=w200-h160" width="200" /></a></div></div>Michael Minas and family share multiple games a month <a href="https://www.youtube.com/channel/UC-F-4IIfKSd3mZCjs1zwukA/videos" target="_blank">on YouTube.</a> Mostly number and operations. If I had to pick one from Nov/Dec, it would be Strawberry vs Dinosaur, a sweet little <a href="https://www.youtube.com/watch?v=3qcndLnuEbE" target="_blank">numberline game</a> (named after their counters).<div><br /></div><div>Jenna Laib, who would be my nominee for blogger of the year, despite some stout competition, shared her all purpose <a href="https://jennalaib.wordpress.com/2019/05/29/one-of-my-favorite-games-number-boxes/" target="_blank">number boxes game</a> in May, as a part of her <a href="https://jennalaib.wordpress.com/2019/05/28/the-simple-but-high-leverage-game-collection/" target="_blank">high leverage games</a> collection. Mark Chubb wrote a post about <a href="https://buildingmathematicians.wordpress.com/2021/11/06/number-boxes/" target="_blank">how he plays it</a>, with multiple different operations and a units of measurement context.</div><div><br /></div><div>James Cleveland Tran tweeted <a href="https://twitter.com/jclevelandtran/status/1463166891959148551?s=20" target="_blank">an integral calculus version</a> of one of my favorite simple but high leverage games.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhVWarhpkIkdA6FCE2XJDmtd4nUzQFJwmxxtdHuv3LYfRZJ3GqsrJfaf_iJIoi8IgjXhXpAzXC_ziXEC8G4NUb0K3GidEPp69kDUCRb5hCf2MgzoyY6uKm-YeqE6HXbdBWleIOn5N4o5ht9uPNNVwzcXjQTMI0eOtaWJ5CjCs0bZDfZDfGjgcpt-QXs=s800" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="800" data-original-width="571" height="400" src="https://blogger.googleusercontent.com/img/a/AVvXsEhVWarhpkIkdA6FCE2XJDmtd4nUzQFJwmxxtdHuv3LYfRZJ3GqsrJfaf_iJIoi8IgjXhXpAzXC_ziXEC8G4NUb0K3GidEPp69kDUCRb5hCf2MgzoyY6uKm-YeqE6HXbdBWleIOn5N4o5ht9uPNNVwzcXjQTMI0eOtaWJ5CjCs0bZDfZDfGjgcpt-QXs=w285-h400" width="285" /></a></div>There were 151 original, or Kanto, Pokemon. (Mew is 151) I'm a big believer that strategy games of any type help develop problem solving, and sometimes number sense. Collectible card games add a lot to that, with deck construction and variety of situations adding more problem solving. </div><div><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiHgVZlcKn46e5WmzPQqOEc4RYH_jpZaxAYfPAXs34WuX6DtZyV_F1fOMP13ZZVNSImoJIXBFOtUjx6TD1mPbbQH45NfnUiHEGsOWnG15UVVe5qUnalOqCVhQs8o4Mm4yVXkMY6m3_zcMmQEqOepq8lKzuhGfrlg4J-n_6x-ed91jIraU2r44VTregV=s1280" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="720" data-original-width="1280" height="113" src="https://blogger.googleusercontent.com/img/a/AVvXsEiHgVZlcKn46e5WmzPQqOEc4RYH_jpZaxAYfPAXs34WuX6DtZyV_F1fOMP13ZZVNSImoJIXBFOtUjx6TD1mPbbQH45NfnUiHEGsOWnG15UVVe5qUnalOqCVhQs8o4Mm4yVXkMY6m3_zcMmQEqOepq8lKzuhGfrlg4J-n_6x-ed91jIraU2r44VTregV=w200-h113" width="200" /></a><br /></div><div>They also raise a lot of mathematical questions, such as the one <a href="https://www.tiktok.com/@howie_hua/video/7043228118248820014" target="_blank">Howie Hua is solving here</a> for Magic the Gathering. Howie's TikTok is full of amazing nuggets, strategies and math.</div><div><br /></div><div>There was a fun Global Math Department meeting about <a href="https://www.bigmarker.com/GlobalMathDept/Beast-Academy-Playground-Math-Games-and-Crafts-to-Foster-Curiosity-and-Build-Problem-Solving-Skills" target="_blank">Beast Academy Playground games</a>, and Erick Lee shared <a href="https://pbbmath.weebly.com/blog/math-play" target="_blank">some of his favorites</a>. Troll hole is one I love to share on a whiteboard or paper if there's an opportunity.</div><div><br /></div><div>Celeste Bancos revisited the <a href="https://bancosparenting.wordpress.com/2021/11/15/the-secret-number-game-revisited/" target="_blank">Secret Number Game</a>.</div><div><br /></div><div>Pam's addressing that you can <a href="https://pambarnhill.com/math-through-play-in-your-homeschool/" target="_blank">learn math through play</a> in homeschool, too.<br /><div><p>Iva Sallay crosses Sarah Carter and Joseph Nebus and <a href="https://findthefactors.com/2021/12/16/1702-a-puzzle-inspired-by-nebusj-and-mathequalslove/" target="_blank">makes a puzzle</a>!</p><p>Colleen Young connects to a bunch of <a href="https://colleenyoung.org/2021/12/27/puzzles-games/" target="_blank">math puzzle resources</a>.</p><p>Patrick Vennebush is working out a <a href="https://mathjokes4mathyfolks.wordpress.com/2021/12/01/better-multiple-choice/" target="_blank">better multiple choice test</a> in his Mathy Jokes blog.</p><p><b>Content</b></p><p>Bumba Stories has a short history of <a href="https://bumbastories.wordpress.com/2021/12/01/december-magazine-4/" target="_blank">why we have 12 month</a>s.</p><p>The Quiet Pond has a review of what looks like a good picture book, <a href="https://thequietpond.com/2021/11/12/five-reasons-to-read-danny-chung-sums-it-up-by-maisie-chan-maths-and-art-collide-in-this-sweet-story-about-grandmothers-language-barriers-and-kindness/" target="_blank">Danny Chung Sums It Up</a>. </p><p>Christopher Danielson share's <a href="https://talkingmathwithkids.com/blog/one-perfect-page/" target="_blank">one perfect page</a> from The Last Marshmallow.</p><p>Speaking of counting, Early Math Counts has some <a href="https://earlymathcounts.org/baby-its-cold-outside/" target="_blank">early math winter counting opportunities</a>.</p><p>Dave Taylor started <a href="https://twitter.com/taylorda01/status/1473224276891381763?s=20" target="_blank">a Twitter thread</a> about historical numerals by starting with the Cistercian numbers.</p><p>Brian Bushart shared one of his favorite resources, a free collection of math interventions, <a href="http://www.piratemathequationquest.com/" target="_blank">Pirate Math Equation Quest</a>. It is not all pirate themed, but lots of great supporting materials.</p><p><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgHhVEofP3Fyorn24w9VlHF6YpsyKhNjsy5a1rtyBMweThwVKGYNMrcSwJnP6qhV2vzEUctpqQkiL07VsVwj2HyO61IQl1dPd6M937Kw2jsUESyOj-HyFhwtHGvNo0JkRfo5K7g_bVQcf5rvvwF2eOkKWvI6LYrIEBeMz-Bs0mkmxPl3lK2M6wePHxz=s225" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="225" data-original-width="225" height="200" src="https://blogger.googleusercontent.com/img/a/AVvXsEgHhVEofP3Fyorn24w9VlHF6YpsyKhNjsy5a1rtyBMweThwVKGYNMrcSwJnP6qhV2vzEUctpqQkiL07VsVwj2HyO61IQl1dPd6M937Kw2jsUESyOj-HyFhwtHGvNo0JkRfo5K7g_bVQcf5rvvwF2eOkKWvI6LYrIEBeMz-Bs0mkmxPl3lK2M6wePHxz=w200-h200" width="200" /></a></p><p></p><p><a href="https://open.spotify.com/artist/0ucn7wKBWwL4EujQ8YywgW" target="_blank">One-Fifty-One</a> is a hard rock band... not my taste, but if it's yours, rock on.</p><p>Jenna Laib had a <a href="https://jennalaib.wordpress.com/2021/12/12/the-half-triangle-attending-to-precision-and-building-on-others-ideas/" target="_blank">great geometry post</a> about the half triangle. If you listen closely, you can hear the learners progressing van Hiele levels.</p><p>If you're looking to stretch your brain, try Jim Propp's monthly essay, this time on <a href="https://mathenchant.wordpress.com/2021/12/17/numbers-from-games/" target="_blank">numbers from games</a>. Bonus John Conway stories.</p><p>Katie Steckles wrote a sweet piece for the Aperiodical about <a href="https://aperiodical.com/2021/12/the-mathematics-of-spirograph/" target="_blank">Spirograph Math</a>.</p><p>I should be blogging more... and if I did, I would definitely write about the interesting responses to <a href="https://twitter.com/mathhombre/status/1472662668506980353" target="_blank">this tweet</a> about dividing polynomials with partial quotients. </p><b><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEibtTA9zE-1E_7P_9zmWjJsLOR2WXj5rKfl_I8Xa9-kSp9Rz5LYex-MM7Te8ahjLaVcmBDWp_gwL7oHwiOd8DhitbIhDEhKNXz4WBtvyfOG0WQHPAje6AVEIDyvJ0vfwIhrfAfLDOwqZTXJpyH-Lb2KokGdbyn2VyBSlzuc1Bfg_bhyl0yR9XfL8NDo=s727" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="452" data-original-width="727" height="199" src="https://blogger.googleusercontent.com/img/a/AVvXsEibtTA9zE-1E_7P_9zmWjJsLOR2WXj5rKfl_I8Xa9-kSp9Rz5LYex-MM7Te8ahjLaVcmBDWp_gwL7oHwiOd8DhitbIhDEhKNXz4WBtvyfOG0WQHPAje6AVEIDyvJ0vfwIhrfAfLDOwqZTXJpyH-Lb2KokGdbyn2VyBSlzuc1Bfg_bhyl0yR9XfL8NDo=s320" width="320" /></a></div><br /><b><br /></b></div>Teaching</b><p>Dylan Kane, always challenging, provocative and brief, takes on <a href="https://fivetwelvethirteen.wordpress.com/2021/12/14/what-is-productive-struggle-really/" target="_blank">productive struggle</a>.</p><p>David Sladkey wrote about implementing some of the <a href="https://teachhighschoolmath.blogspot.com/2021/12/the-magic-of-students-doing-challenging.html" target="_blank">Thinking Classroom ideas</a> with his learners. Practical and productive.</p><p>Margie Pearse wrote a post for Heinemann on <a href="https://blog.heinemann.com/linking-math-and-literature-to-explore-social-justice-and-global-issues" target="_blank">using literature to address social justice in math</a>.</p><p>Dan Finkel's reflecting on a big question "<a href="https://mathforlove.com/2021/11/am-i-a-mathematician/" target="_blank">Am I a Mathematician?</a>"</p><p><b>In Memoriam</b></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjv-QYPNhPqecwW_hgqYdP85h1le41-44gAT43jo0H2KjUPEhHoCe5aiy1TfaB5kBdNJW7wZl_s-Lma4Ovg9HNw3hIvnqG_zijUvjvC2lX_8ew7UmfvKWTumpbv-4C-neWVNZdxyhkWKef_-H3REum_-cm26ilP5-U3RZ3JRJFsMPNVDzAmp5yON_8b=s1151" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1151" data-original-width="1126" height="200" src="https://blogger.googleusercontent.com/img/a/AVvXsEjv-QYPNhPqecwW_hgqYdP85h1le41-44gAT43jo0H2KjUPEhHoCe5aiy1TfaB5kBdNJW7wZl_s-Lma4Ovg9HNw3hIvnqG_zijUvjvC2lX_8ew7UmfvKWTumpbv-4C-neWVNZdxyhkWKef_-H3REum_-cm26ilP5-U3RZ3JRJFsMPNVDzAmp5yON_8b=w196-h200" width="196" /></a></div>We'll close with Math Ed Podcast's <a href="https://www.podomatic.com/podcasts/mathed/episodes/2017-04-30T06_59_56-07_00" target="_blank">interview of Dr. Liz Fennema</a>, one of the founders of <a href="https://www.heinemann.com/cgimath/" target="_blank">Cognitively Guided Instruction.</a> She passed away this month in hospice. She received the <a href="https://www.nctm.org/Grants-and-Awards/Lifetime-Achievement-Award/Elizabeth-Fennema/">NCTM lifetime achievement award</a> this year, at least partially in response to a public campaign. CGI might not be playful in the same way as many of the resources shared here, but with their focus on improving learning for children, and listening to children's inherently playful approach to mathematical problem solving, they moved all of us forward. She also did significant work on gender in math education. Rest in peace, Dr. Fennema.<p></p><p><br /></p><p></p><p><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjQrzu6znISkaDglcRFzs4McKP84wilC3YuWbSOQyu7NRdJQ84PaHzkryGPI_qOsci1BKwjO6_5mmLSMbwYrldD98F7SshafgKS1j11yBr-Mvjcdxr4GaiT9My78R_aePIYop-KAJkz0FVjt2Mzt8jf-9DJR8qh-KfRZ9Ns8xzqWpClrn8JbINohfkm=s414" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="310" data-original-width="414" height="150" src="https://blogger.googleusercontent.com/img/a/AVvXsEjQrzu6znISkaDglcRFzs4McKP84wilC3YuWbSOQyu7NRdJQ84PaHzkryGPI_qOsci1BKwjO6_5mmLSMbwYrldD98F7SshafgKS1j11yBr-Mvjcdxr4GaiT9My78R_aePIYop-KAJkz0FVjt2Mzt8jf-9DJR8qh-KfRZ9Ns8xzqWpClrn8JbINohfkm=w200-h150" width="200" /></a></p>If you are interested in hosting this carnival, I highly recommend giving it a try. A little work, and a lot of fun. Contact Denise on <a href="https://twitter.com/letsplaymath" target="_blank">Twitter</a> or via the <a href="https://denisegaskins.com/mtap/" target="_blank">Playful Math Education Carnival</a> homepage. Denise is hosting January, but then there are lots of opportunities ahead. Ask me and I'll happily add some suggestions for posts!<p></p><p>Cheers to a mathy new year! I know champagne is more typical, but where's the 151 in that?</p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p></div></div>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com1tag:blogger.com,1999:blog-235276292454918436.post-75416005955652345692021-09-13T17:47:00.000-04:002021-09-13T17:47:14.522-04:00Game Promotion<p><span style="font-family: arial;">One of my treats the last few years has be to teach a section of a course originated by Char Beckman, a senior seminar to make classroom math games. We dig into examples, come up with criteria to evaluate them, design and playtest.</span></p><p><span style="font-family: arial;">One of the assignments is to make a video for an existing math game which has no video that they can find. Here are the videos from last Winter's designers - after too long a delay for which I apologize. If you're interested in the course, here's the <a href="https://bit.ly/496-W21" target="_blank">course page</a>.</span></p><p><span style="font-family: arial;">Upcoming posts will feature their original games - with a lot of amazing work. Are there games for which you would like to see a video? Leave a comment! I've got another group this fall.</span></p><p><b><span style="font-family: arial;">Caleb Anderson - Safe or Sorry</span></b></p><p></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/R9oiyuOltXo" width="320" youtube-src-id="R9oiyuOltXo"></iframe></span></div><span style="font-family: arial;"><br /><span style="background-color: #f9f9f9; color: #030303; letter-spacing: 0.2px; white-space: pre-wrap;">Safe or Sorry is a push your luck dice game that emphasizes multiples. He explains, "I would like people to know of this game because of the simplicity of the game and that this game requires no skill. I think teachers should use this game for those who need to learn how to skip count by 5’s and if teachers are using probability. Safe or sorry has little to no strategy, so students don’t have advantages. This way, one student cannot be particularly good at the game because it is all based on chance. I think this game would be beneficial to students for those struggling with addition and also skip counting. Plus, since there is no strategy the game is more fair." So there's *no* strategy? I also like how this can be adapted to other multiples.</span></span><p></p><p><span style="font-family: arial;"><span class="style-scope yt-formatted-string" dir="auto" style="background: rgb(249, 249, 249); border: 0px; color: #030303; letter-spacing: 0.2px; margin: 0px; padding: 0px; white-space: pre-wrap;">Original post: </span><a class="yt-simple-endpoint style-scope yt-formatted-string" dir="auto" href="https://www.youtube.com/redirect?event=video_description&redir_token=QUFFLUhqa25xSy1GcnhmOC1TTHlwMXM3czYyV3ZPSks1d3xBQ3Jtc0tublpPQ2dsUDVUWVk4Uzdud1VhVm5iOC1DY1VOX3NudEYxVkdfRVhqUjNwTDRjcWxHa0ZjaXE2Yk84QVQ5XzRMLUNkWXg4aE9jeWN0M3p1eWpaWk1aWXcyeFFIbmpsMkt2RVFKSmtoVUFfMTM4MUQ4UQ&q=http%3A%2F%2Fmathhombre.blogspot.com%2F2014%2F05%2Fsafe-or-sorry.html" rel="nofollow" spellcheck="false" style="background-color: #f9f9f9; cursor: pointer; display: var(--yt-endpoint-display, inline-block); letter-spacing: 0.2px; overflow-wrap: var(--yt-endpoint-word-wrap, none); text-decoration: var(--yt-endpoint-text-regular-decoration, none); white-space: pre-wrap; word-break: var(--yt-endpoint-word-break, none);" target="_blank">Safe or Sorry</a></span></p><p><b><span style="font-family: arial;">Heather Anderson - Bad Calculators</span></b></p><p></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/DMIQ6JK1o2c" width="320" youtube-src-id="DMIQ6JK1o2c"></iframe></span></div><span style="font-family: arial;"><br /><b><br /></b></span><p></p><p><span style="font-family: arial;"><span class="style-scope yt-formatted-string" dir="auto" style="background: rgb(249, 249, 249); border: 0px; color: #030303; letter-spacing: 0.2px; margin: 0px; padding: 0px; white-space: pre-wrap;">Heather Anderson made this video to explain the one person web-based math game Bad Calculators. She says, "‘Bad Calculators’ is a web game that is a really useful tool for developing arithmetic ability. Because the game uses specific operations and moves per level, players use arithmetic creatively which allows them to have unique practice with their skills. I feel this game is easily distinguishable from some other math games because it has obstacles players must work past, but also because it gets increasingly more difficult the longer a player plays. Another aspect of this game that caught my attention was the fact that players are able to use their possible moves in any combination and/or order they choose (for most levels) because there is no penalty for the number of steps it takes to complete a level. This game has a lot of factors that non-math games have, which makes it appealing to players. Yet, it includes a lot of crucial, foundational ideas in mathematics which makes it a very impactful math game as well."
Play the game at </span><a class="yt-simple-endpoint style-scope yt-formatted-string" dir="auto" href="https://www.youtube.com/redirect?event=video_description&redir_token=QUFFLUhqbW51LWRHMHY0ZWx2dVBodHJqdWVWcGtkajVFZ3xBQ3Jtc0tramlKbGlDbzFoSnJtY2M1NTNJY21WcnFvSUdjTEZJOF9tSVdQVWNwa29PLWRXY2tON1F6TkFGRmpRUEQxaldfVWNuZTJnc2o3bFpiU0c2TUwwbk5PN2pRd1NPNVNHSHNLTUdUZUxsSkNLRmQ5Q3QwZw&q=https%3A%2F%2Fwww.badcalculators.com%2F" rel="nofollow" spellcheck="false" style="background-color: #f9f9f9; cursor: pointer; display: var(--yt-endpoint-display, inline-block); letter-spacing: 0.2px; overflow-wrap: var(--yt-endpoint-word-wrap, none); text-decoration: var(--yt-endpoint-text-regular-decoration, none); white-space: pre-wrap; word-break: var(--yt-endpoint-word-break, none);" target="_blank">https://www.badcalculators.com/</a></span></p><p><b><span style="font-family: arial;">Arianna Ayers - Make and Take</span></b></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/4_g4qxSDd3M" width="320" youtube-src-id="4_g4qxSDd3M"></iframe></span></div><span style="font-family: arial;"><br /></span><p><span style="background-color: #f9f9f9; color: #030303; letter-spacing: 0.2px; white-space: pre-wrap;"><span style="font-family: arial;">Arianna Ayers made this video for an upper elementary/middle school math game on mixed operations. (It's the first of several games from <a href="https://twitter.com/smithnj" target="_blank">Nicholas Smith</a> on this list. He's a GVSU grad who was - and still is - always willing to make and playtest games.) She says, "Make and Take is a great game that incorporates using number operations to create combinations of playing cards. This game is fun, engaging, and requires strategy. There’s also an element of surprise because the players do not know which cards they will be dealt from the deck. In addition, the rules are simple and easy to understand. All you need is a deck of playing cards and at least two people, and you’ve got a recipe for a fun game night!" </span></span></p><p><span style="font-family: arial;"><span class="style-scope yt-formatted-string" dir="auto" style="background: rgb(249, 249, 249); border: 0px; color: #030303; letter-spacing: 0.2px; margin: 0px; padding: 0px; white-space: pre-wrap;">Original blogpost: </span><a class="yt-simple-endpoint style-scope yt-formatted-string" dir="auto" href="https://www.youtube.com/redirect?event=video_description&redir_token=QUFFLUhqbDVTREtTaHdlYm5tYUVsSzh0WERibXFpSGFRUXxBQ3Jtc0trS0pyLVgyRHlHWm9YTjJSQ2JEWVcwWlR1SElfeTRZQUlVaFJheTJGLW45YTNra25ERkhjbU9iWnZoVVo3N1RZLXNOQXgtLVdyWURUVGdFbmNiU290RU83MkRmZXdsb21DcExsSGZfZkJlamd4VVlTcw&q=https%3A%2F%2Fmathhombre.blogspot.com%2F2011%2F11%2Fmake-and-take.html" rel="nofollow" spellcheck="false" style="background-color: #f9f9f9; cursor: pointer; display: var(--yt-endpoint-display, inline-block); letter-spacing: 0.2px; overflow-wrap: var(--yt-endpoint-word-wrap, none); text-decoration: var(--yt-endpoint-text-regular-decoration, none); white-space: pre-wrap; word-break: var(--yt-endpoint-word-break, none);" target="_blank">Make and Take</a></span></p><p><b><span style="font-family: arial;">Danielle Jurcich - Card Catch</span></b></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/4_g4qxSDd3M" width="320" youtube-src-id="4_g4qxSDd3M"></iframe></span></div><span style="font-family: arial;"><br /></span><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><span class="style-scope yt-formatted-string" dir="auto" style="background: rgb(249, 249, 249); border: 0px; color: #030303; letter-spacing: 0.2px; margin: 0px; padding: 0px; white-space: pre-wrap;">Danielle Jurcich shows how to play Card Catch, a number and operation math game with playing cards, another made with Nicholas Smith. She says, "I chose to make a video about Card Catch because I really liked the idea that a teacher could simply have playing cards in their classroom and be able to play this game. The game can be played with between four and six people, so it is very interactive. Plus, the team aspect gets students to work together and even be able to devise a strategy for each card they lay down."
Rules handout: </span><a class="yt-simple-endpoint style-scope yt-formatted-string" dir="auto" href="https://www.youtube.com/redirect?event=video_description&redir_token=QUFFLUhqbkNHb1B3RW9BaFFpNFI0MkdxQzc4cGxza1ZiUXxBQ3Jtc0trQVk1UVM2b09OcWk5YW1Ha19HTFR2ekY5RXFicWw1XzBhcTFXSm9WM0VQczdrdFVjbE5aa2pvWm80NkE4NDdZeF9xUVZrY3pUelR6MFRFVnN4NTAtM1hXeDhYZDNRS0p2Zmg5SHdJa3I4aTVMSlp2WQ&q=http%3A%2F%2Fgvsu.edu%2Fs%2F1NT" rel="nofollow" spellcheck="false" style="background-color: #f9f9f9; cursor: pointer; display: var(--yt-endpoint-display, inline-block); letter-spacing: 0.2px; overflow-wrap: var(--yt-endpoint-word-wrap, none); text-decoration: var(--yt-endpoint-text-regular-decoration, none); white-space: pre-wrap; word-break: var(--yt-endpoint-word-break, none);" target="_blank">Card Catch Handout</a></span></p><p><b><span style="font-family: arial;">Cameron Morgan - Treasure Hunt</span></b></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/Ma-_NhdpPQk" width="320" youtube-src-id="Ma-_NhdpPQk"></iframe></span></div><span style="font-family: arial;"><br /></span><p><span style="background-color: #f9f9f9; color: #030303; font-family: arial; letter-spacing: 0.2px; white-space: pre-wrap;">Cameron Morgan demonstrates Treasure Hunt, a Battleship style math game for integers. She says, "Treasure hunt is a math game that only requires the downloadable game sheet. This game allows students to use addition and subtraction while also practicing the number line model. Treasure Hunt is a great game to play in the classroom because it has many aspects that make a good game some examples being good interaction, good rules, and inertia. There is plenty of interaction between player 1 and 2 such that their moves against each other affect the game. The rules are not too easy or hard and if one was to think they were too easy there is also an accelerated version. The game does not last two long and would make students want to keep playing to see if they can win the next time. Overall this is a great game that helps students with addition or subtraction without being super overwhelming or competitive for them."</span></p><p><span style="font-family: arial;"><span class="style-scope yt-formatted-string" dir="auto" style="background: rgb(249, 249, 249); border: 0px; color: #030303; letter-spacing: 0.2px; margin: 0px; padding: 0px; white-space: pre-wrap;">Gameboard is here: </span><a class="yt-simple-endpoint style-scope yt-formatted-string" dir="auto" href="https://www.youtube.com/redirect?event=video_description&redir_token=QUFFLUhqbFNuUjJJQ1U5UElmRFI0Vk52QzNhTHhZZjRBZ3xBQ3Jtc0traGdWZk1xcExqazZjSjNjRUxrNC1WOFBWZkxSazBYU2tKNnFpdW1QS1ZHVjlnRHR4ZW9ISnZJV2VYSUZjNVRHaE90QmxfWm9aR1lGSjBySTBtR084VUc3NDJweGI4ZFlqLW5fM2xTOGpRWEptM1R2aw&q=http%3A%2F%2Fgvsu.edu%2Fs%2F1NS" rel="nofollow" spellcheck="false" style="background-color: #f9f9f9; cursor: pointer; display: var(--yt-endpoint-display, inline-block); letter-spacing: 0.2px; overflow-wrap: var(--yt-endpoint-word-wrap, none); text-decoration: var(--yt-endpoint-text-regular-decoration, none); white-space: pre-wrap; word-break: var(--yt-endpoint-word-break, none);" target="_blank">Treasure Hunt Gameboard</a> (<span class="style-scope yt-formatted-string" dir="auto" style="background: rgb(249, 249, 249); border: 0px; color: #030303; letter-spacing: 0.2px; margin: 0px; padding: 0px; white-space: pre-wrap;">but it is easily played with pen and paper)</span></span></p><p><b><span style="font-family: arial;">Olivia Sassanelli - Tug of War</span></b></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/pvm_OEYItgg" width="320" youtube-src-id="pvm_OEYItgg"></iframe></span></div><span style="font-family: arial;"><br /></span><p><span style="background-color: #f9f9f9; color: #030303; font-family: arial; letter-spacing: 0.2px; white-space: pre-wrap;">Olivia Sassanelli started out making a video for a math game by me, but ended up making her own twist on it. She notes, "This game is a good game for younger students who are learning basic addition and subtraction of whole numbers (both positive and negative). For the content of this game, the students can focus on whether or not they want to add or subtract. This game also focuses on using strategy depending on which variation the students decide to play. This game is a super basic and simple game to play at the end of a lesson or to even play during class a few times. This game is quick to play so it works as a game students can play if there is time at the end of a lesson as well. The set up is very simple and the supplies are typically supplies you have laying around the classroom. Overall, this game has good content for the students with practicing basic addition and subtraction and also a super basic set up. I highly recommend this game because the feedback I received from students as well was very positive and the students generally enjoyed the game too!"</span></p><p><span style="font-family: arial;"><span class="style-scope yt-formatted-string" dir="auto" style="background: rgb(249, 249, 249); border: 0px; color: #030303; letter-spacing: 0.2px; margin: 0px; padding: 0px; white-space: pre-wrap;">Original game: </span><a class="yt-simple-endpoint style-scope yt-formatted-string" dir="auto" href="https://www.youtube.com/redirect?event=video_description&redir_token=QUFFLUhqbExqajJOeVo3a0tCdEVOY3Q3LTF0Z2ltMUcxUXxBQ3Jtc0tsbl9VWDhjYTBNN1M0dEdYXy1ROGd6TnZ3MnFNZ2w4djVMNWtQQld3OGNwUGVEWkNsc1drNlJuNzhHZTZTQzhsOFQ2cjJ4dU9uT01QTFNiYWNneU5HV2k2R005a1lCMVRoemFjcld1d3VrTkYwVV9Kbw&q=http%3A%2F%2Fgvsu.edu%2Fs%2F1NP" rel="nofollow" spellcheck="false" style="background-color: #f9f9f9; cursor: pointer; display: var(--yt-endpoint-display, inline-block); letter-spacing: 0.2px; overflow-wrap: var(--yt-endpoint-word-wrap, none); text-decoration: var(--yt-endpoint-text-regular-decoration, none); white-space: pre-wrap; word-break: var(--yt-endpoint-word-break, none);" target="_blank">Tug of War (original)</a> (Has a bit more interaction and back and forth.)</span></p><p><span style="font-family: arial;"><b>Kayla Shirah - Honeycomb</b></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/yLS9RfRo09s" width="320" youtube-src-id="yLS9RfRo09s"></iframe></span></div><span style="font-family: arial;"><br /></span><p><span style="font-family: arial;"><br /></span></p><p><span style="font-family: arial;"><span class="style-scope yt-formatted-string" dir="auto" style="background: rgb(249, 249, 249); border: 0px; color: #030303; letter-spacing: 0.2px; margin: 0px; padding: 0px; white-space: pre-wrap;">Kayla Shirah demonstrates Honeycomb, <i>another</i> Nick Smith math game collaboration on integer operations. She explains, "Honestly, reading the instructions I was a little confused. The visuals on the game instructions on what to do if you rolled a negative number was helpful but it was confusing to remember to flip the sign of the number you are multiplying by and by how ever many of the number you rolled. It made sense once I played the game with my fiance. With this being confusing at first to me as a college student, I thought well there isn’t a video on this game so I’ll make one. It had materials that I knew I had in my house, two different colored dice, a coin, the game board. Which this would be ideal for a student or teacher to play as well. I liked how the game wasn’t too long in playing time as well. I loved playing this game, it was fun and interactive for both players the whole time. It also had an element of catch up if a player rolls a high number due to chance. I thought it would be helpful to show an example of game play when you first start out because you can only add a number onto the board. As well as show an example of multiplying by an existing number on the board, since that is what I think the reader of the instructions needed clarity on. I also wanted to visually show that you can only multiply in a straight line if possible. This game is a great simple material math game that can be played many times by lots of students. This game gives students an opportunity to make choices during each turn even though they have the chance of rolling the dice as well. Overall, honeycomb is an awesome game to get students to remember how fun it is to use positive and negative numbers in addition and multiplication."
Handout with rules and gameboard: </span><a class="yt-simple-endpoint style-scope yt-formatted-string" dir="auto" href="https://www.youtube.com/redirect?event=video_description&redir_token=QUFFLUhqazBwcmU4QTVuNkV0T3N5bDg5RmI1RUlZX252Z3xBQ3Jtc0trZDk4aUtodUF0azVFTVRzNjZ6ejB0VzdEaXpCdkxLUEVjZ2pXTDVkdU1TeHVnYjFBZERYb05yaDRyNVZ6cEpueV9jTWNKSWZPR2lJcWtjNjdLYVhDbEVIczlzUmxEY2pONE42WU1JSkwtdHlQcTE2TQ&q=http%3A%2F%2Fgvsu.edu%2Fs%2F1NO" rel="nofollow" spellcheck="false" style="background-color: #f9f9f9; cursor: pointer; display: var(--yt-endpoint-display, inline-block); letter-spacing: 0.2px; overflow-wrap: var(--yt-endpoint-word-wrap, none); text-decoration: var(--yt-endpoint-text-regular-decoration, none); white-space: pre-wrap; word-break: var(--yt-endpoint-word-break, none);" target="_blank">Honeycomb Gameboard and Rules</a>. Nick says about this one - "This is the game I'm most proud of. I'd love to see this developed as an app. My original intent was to make it a 3d stacking game where the tiles flip black/white."</span></p><p><span style="background-color: #f9f9f9; color: #030303; letter-spacing: 0.2px; white-space: pre-wrap;"><span style="font-family: arial;"><br /></span></span></p><p><span style="background-color: #f9f9f9; color: #030303; letter-spacing: 0.2px; white-space: pre-wrap;"><span style="font-family: arial;"><br /></span></span></p><p><span style="background-color: #f9f9f9; color: #030303; letter-spacing: 0.2px; white-space: pre-wrap;"><span style="font-family: arial;"><br /></span></span></p><p><span style="background-color: #f9f9f9; color: #030303; letter-spacing: 0.2px; white-space: pre-wrap;"><span style="font-family: arial;"><br /></span></span></p><p><span style="background-color: #f9f9f9; color: #030303; font-family: Roboto, Arial, sans-serif; font-size: 14px; letter-spacing: 0.2px; white-space: pre-wrap;"><br /></span></p>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-89549278438947439572021-03-28T19:03:00.005-04:002021-03-28T19:03:57.869-04:00Playful Math Carnival 145<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGzJP2SO76V2Z8Q54SAY6jaTTN9FwOl6He2a4S1s6BRtO_RAPqjuaLrDFuPUWLnliYgfzAIXZEYYoDOwr2TYz5uO20NNUi3sgTdYsirK_Dgt_bL5uUaNCdffA4ie8v7uy9uLe8qqP7EOU/s1690/145.png" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1601" data-original-width="1690" height="271" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGzJP2SO76V2Z8Q54SAY6jaTTN9FwOl6He2a4S1s6BRtO_RAPqjuaLrDFuPUWLnliYgfzAIXZEYYoDOwr2TYz5uO20NNUi3sgTdYsirK_Dgt_bL5uUaNCdffA4ie8v7uy9uLe8qqP7EOU/w286-h271/145.png" width="286" /></a></div>Welcome to the 145th edition of the Playful Math Carnival. Once known as the Math Teachers at Play Carnival, this edition follows the Denise Gaskins' (founder of this here carnival) blowout <a href="https://denisegaskins.com/2021/02/22/playful-math-carnival-144-anniversary-edition/" target="_blank">144th Anniversary Edition</a>, as night doth follow gentle day, and by that we were blown away. <p></p><p></p>Sadly, there's nothing interesting about the pentagonal semiprime 145. Well, besides 145=1!+4!+5!. There are only four numbers for which that's true. And it's the fourth number that's a sum of squares in two different ways. And it's a Leyland number, because 3^4+4^3=145. (I wonder what the next Leyland numbers before and after are?) And the 145th prime number is 829 and 145829 is prime and the largest prime factor of 145 is 1+4+5+8+2+9 and that 145 is congruent to 1 in mod 8, mod 2, and mod 9. But besides that... there's practically nothing. (All these are from Pat Bellew's <a href="https://mathdaypballew.blogspot.com/2020/04/number-facts-for-every-year-date-121-150.html" target="_blank">fun number site</a>.) And 145 shows up in Matt Parker's <a href="https://www.youtube.com/watch?v=_DpzAvb3Vk4" target="_blank">melancoil</a>. 145 degrees (F) makes something medium rare... maybe that should be the goal for this edition?<p></p><p><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8IvG_Shah3m6QnRvlpPGtbBEKXgTwDNuFYTh7nocpsV57IpJtIu8n1zXbYnm6t1IS50t_abe8Y1jP6hv0e4BJgY0FPttQaDhM-GiOGnLaaMXvc7rIbP6-G-f5U8VID65EMwUFx-IWbC8/s500/v145.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto; text-align: center;"><img border="0" data-original-height="375" data-original-width="500" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8IvG_Shah3m6QnRvlpPGtbBEKXgTwDNuFYTh7nocpsV57IpJtIu8n1zXbYnm6t1IS50t_abe8Y1jP6hv0e4BJgY0FPttQaDhM-GiOGnLaaMXvc7rIbP6-G-f5U8VID65EMwUFx-IWbC8/w256-h192/v145.jpg" width="256" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Volvo 145. Ove approved.</td></tr></tbody></table></p><p>Hop in the 145 and let's go! </p><p><span style="color: red; font-size: medium;"><b>Books & Essays</b></span></p><p>Just before this month started I got to participate in a nifty mathzine fest from Becky Warren, Chris Nho and Ayliean. Technically February, it was after Denise's edition so I'm counting it. Several of the results are on the <a href="https://www.public-math.org/mzf2021" target="_blank">Public Math website</a>, which has <a href="https://www.public-math.org/zines" target="_blank">more besides</a>. Also see the <a href="https://twitter.com/hashtag/mathszine?src=hashtag_click&f=live" target="_blank">mathszine hashtag</a> on Twitter.</p><p>That was my introduction to Ayliean, who <a href="https://www.youtube.com/watch?v=vbTobNxFjmc" target="_blank">had some thoughts</a> on STEMinism.</p><p>Some of those zines inspired Sophia Wood for her first Fractal Kitty zine, on <a href="https://fractalkitty.com/2021/03/14/cantor-set-zine/" target="_blank">the Cantor Set</a>.</p><p></p><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUMqxZdnfmtw0kpzotifaVPKio-TRJEF__xlntpfClf9SajXjd1fu5eFEYSEz4hGFwutdortCV0Mc_MoGG7tYazLSp8sC1F1m8Hv0zp7UmrF0DwFkkMzipCfhzf4vhRmGOfH5HuTaGfgg/s225/P145.jpeg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="225" data-original-width="225" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUMqxZdnfmtw0kpzotifaVPKio-TRJEF__xlntpfClf9SajXjd1fu5eFEYSEz4hGFwutdortCV0Mc_MoGG7tYazLSp8sC1F1m8Hv0zp7UmrF0DwFkkMzipCfhzf4vhRmGOfH5HuTaGfgg/s0/P145.jpeg" /></a></div>Jim Propp was musing on <a href="https://mathenchant.wordpress.com/2021/03/16/dividing-by-zero/#more-3901" target="_blank">division by zero</a>. History, what ifs, new possible numbers...<p></p>Edmund Harriss has a new children's book out, <i><a href="https://chalkdustmagazine.com/blog/hello-numbers-what-can-you-do/" target="_blank">HELLO NUMBERS! What Can You Do?</a></i> and has been out supporting the release. Read more at Chalkdust's <a href="https://chalkdustmagazine.com/book-of-the-year/" target="_blank">Math Book of the Year</a> series. Also super curious about Eugenia Cheng's <i><a href="https://chalkdustmagazine.com/blog/molly-and-the-mathematical-mystery/" target="_blank">Molly and the Mathematical Mystery</a></i>.<div><br /></div><div>Speaking of playful math authors, <a href="https://deadline.com/2021/03/norton-juster-dead-obituary-the-phantom-tollbooth-the-dot-and-the-line-childrens-author-was-91-1234709849/">RIP to Norton Juster</a>, author of <a href="https://www.youtube.com/watch?v=pZ1ldmMzmvk" target="_blank">The Phantom Tollbooth</a> and <a href="https://www.youtube.com/watch?v=D_QhIVYlcmE" target="_blank">The Dot and the Line</a>.</div><div><br /></div><div><span style="color: red; font-size: medium;"><b>Games</b></span><br /><div><br /></div><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzfQMmYGVkBPVuhzU3u3KhZT1wVfRcy57j_7laljH1Pfo12dDDcMoF7PUFH4Bk_CU0wmWv4I7sYkIcQb_bsB2ZakXlGUgFOotm8DRUUJ8pQtiU0N4iDbMQnXdVnVgLlP6wbaYeB369tkQ/s225/cap145.jpeg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="225" data-original-width="225" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzfQMmYGVkBPVuhzU3u3KhZT1wVfRcy57j_7laljH1Pfo12dDDcMoF7PUFH4Bk_CU0wmWv4I7sYkIcQb_bsB2ZakXlGUgFOotm8DRUUJ8pQtiU0N4iDbMQnXdVnVgLlP6wbaYeB369tkQ/s0/cap145.jpeg" /></a>Sarah Carter <a href="https://mathequalslove.net/proof-math-game-review/" target="_blank">reviewed the mathgame Proof</a> positively.</div><div><br /></div><div>James Cleveland posted his new <a href="https://rootsoftheequation.wordpress.com/2021/03/11/slopes-and-lattices-game/" target="_blank">linear graphing mathgame</a>. Played it with my games seminar students and I think there's a lot of potential.</div><div><br /></div><div>Simon Gregg and his learners were making variations on <a href="https://twitter.com/Simon_Gregg/status/1367536522795311106?s=20" target="_blank">Snakes and Ladders</a>.</div><div><br /></div><div>Henry Segerman suggests this <a href="https://www.youtube.com/watch?v=Hc3yfuXiWe0" target="_blank">negatively curved sliding puzzle</a>.<br /><div><br /></div><div>Excellent post at Play and PK on <a href="https://playandpk.blogspot.com/2021/03/listening.html" target="_blank">Listening</a>. Guest appearance from the always welcome Max Ray Riek in that post.</div><div><p>I've been making some GeoGebra for remote learning play. There's a <a href="https://www.geogebra.org/m/kpuks7ywhttps://www.geogebra.org/m/kpuks7yw" target="_blank">measure division game</a>, a <a href="https://www.geogebra.org/m/xn4dmgac" target="_blank">fraction comparison game</a>, a <a href="https://www.geogebra.org/m/kxjdkd8q" target="_blank">fraction addition/iteration/equivalence game</a> and the classic <a href="https://www.geogebra.org/m/gbnwym84" target="_blank">Shut the Box</a>.</p><p><span style="color: red; font-size: medium;"><b>Art</b></span></p><p>Dana Ernst <a href="https://danaernst.com/the-5-groups-of-order-8/" target="_blank">shared quilts</a> his student Michelle Reagan made on the 5 groups of order 8.</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoqDPlrTP-sff80LiQlFy2hAPt0ZU51ceBgy8jP0TEPe6JHfqk5wLoV-pROCM3Vz4xX3ypcg60CdQnaP6YW8UhnnERLO5xs3tCuaseTDPcb-xaC280klQorDQhRWzvHfX_XmH6YA-0M3o/s1800/HanaMurrayTiling.jpeg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1800" data-original-width="1800" height="348" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoqDPlrTP-sff80LiQlFy2hAPt0ZU51ceBgy8jP0TEPe6JHfqk5wLoV-pROCM3Vz4xX3ypcg60CdQnaP6YW8UhnnERLO5xs3tCuaseTDPcb-xaC280klQorDQhRWzvHfX_XmH6YA-0M3o/w348-h348/HanaMurrayTiling.jpeg" width="348" /></a></div>Practically a quilt, Master of the Pattern Blocks, Hana Murray, made <a href="https://twitter.com/MurrayH83/status/1373354813837086721?s=20" target="_blank">this amazing tiling</a> replete with dodecagons. </div><div><br /></div><div>Robert Fathauer was interviewed on <a href="http://www.mathisintheair.com/eng/2021/03/14/math-art-tessellations-an-interview-with-robert-fathauer/" target="_blank">Math, Art and Tessellations</a>. His new book is a masterwork.</div><div><br /></div><div>Sophia is also in the middle of a 101 days of coding challenge, and shared her <a href="https://fractalkitty.com/101-days-of-creative-coding-docc/day-56-of-101-docc/" target="_blank">ecliptic ripples</a>.</div><div><br /></div><div>Paula Beardell Krieg had some practical advice for <a href="https://bookzoompa.wordpress.com/2021/03/15/cutting-curves-by-cutting-straight/" target="_blank">cutting curves by cutting straight</a>.</div><div><br /></div><div>I got to work on a fun project with my son studying art education, <a href="https://mathhombre.tumblr.com/post/644419249052483584/x-yemeni" target="_blank">Yemeni squares</a>. </div><div><br /></div><div><br /></div><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjntTZUVbtZmEPvnQwmd3t005zlTIFXGAcGySnLyajGVknWi7hfzqxlFX8C-tgrggn8K6RHJGeFI2uCbLmd9agiA4aGsm3xyIyxMhJg5GMkd34G2jWHaVMYu4M0daYVv-_yxCKfPbnozSc/s824/onethird.png" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="440" data-original-width="824" height="148" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjntTZUVbtZmEPvnQwmd3t005zlTIFXGAcGySnLyajGVknWi7hfzqxlFX8C-tgrggn8K6RHJGeFI2uCbLmd9agiA4aGsm3xyIyxMhJg5GMkd34G2jWHaVMYu4M0daYVv-_yxCKfPbnozSc/w278-h148/onethird.png" width="278" /></a><p><b><span style="color: red; font-size: medium;">Wait There's More</span></b></p><p>I found this perusing old NCTM practitioner journals for fraction tasks and it sparked some interesting conversation. Like just how many solutions are there?</p><p>And it wasn't the only time 1/3 appeared in this third month, as I saw a nifty <a href="https://www.geogebra.org/m/ux9zuv4d" target="_blank">Roger Nelson proof with out words</a> of an odd identity.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLGbaFZyAfLd-epCVi_h-fR-8taSoDqDPKgbqL7HatvMQ1lNA1HxXVHozUh4ZiI-Eb2ZS5qkPvDb8eE-7MwU7WvBZDxi7sAblFJtsEfKDR5LTwrQuoA3e9IXSnR6AFHsnXd4dLzZ-LQ6A/s480/OddThirds.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="467" data-original-width="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLGbaFZyAfLd-epCVi_h-fR-8taSoDqDPKgbqL7HatvMQ1lNA1HxXVHozUh4ZiI-Eb2ZS5qkPvDb8eE-7MwU7WvBZDxi7sAblFJtsEfKDR5LTwrQuoA3e9IXSnR6AFHsnXd4dLzZ-LQ6A/s320/OddThirds.gif" width="320" /></a></div><br /><p><br /></p><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiFGWRENZCTuU5xrWaK0U2lA1J1F3dnoT0bqI71BwQ5YzLVf8ump3XbfoAXSsTbiHVkEdKpVTonWNUKEqgbvRobm9ItJPQoWDZPvpCGBZn1qWSAL9lt6RJeYi-ekSpkSbZdZlD1L32WKQ/s1000/lt145.jpg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1000" data-original-width="1000" height="224" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiFGWRENZCTuU5xrWaK0U2lA1J1F3dnoT0bqI71BwQ5YzLVf8ump3XbfoAXSsTbiHVkEdKpVTonWNUKEqgbvRobm9ItJPQoWDZPvpCGBZn1qWSAL9lt6RJeYi-ekSpkSbZdZlD1L32WKQ/w224-h224/lt145.jpg" width="224" /></a></div>Iva Sallay is hosting the next Playful Math Carnival, 146. It's sure to be a treat, as she is a prodigious puzzle poster herself (take these Easter season <a href="https://findthefactors.com/2021/03/25/1622-a-blue-egg-for-your-easter-basket/" target="_blank">Egg Puzzles</a>, for example), and found several possibilities for this edition!</div><div><ul><li>a mousey <a href="http://bedtimemath.org/fun-math-house-cleaning-mouse/" target="_blank">Bedtime math problem set</a></li><li>Catriona Agg appearing at <a href="https://fivethirtyeight.com/features/can-you-find-an-extra-perfect-square/" target="_blank">538's the Riddler</a></li><li><a href="https://peggylchambers.com/2021/01/10/2020-expect-the-unexpected-math-magic/" target="_blank">a math chapter book</a> from Peggy Chambers</li></ul></div><p>I enjoy putting these together, even though I am not regularly blogging myself. (Despite my best intentions...) One of the reasons I started blogging was to share and curate some of the cool things I was seeing from the amazing MTBoS, and it's still a good thing. If you're interested in hosting, just let <a href="https://twitter.com/letsplaymath" target="_blank">Denise</a> know.</p><p>NPR made a comic of this teacher's <a href="https://www.npr.org/2021/03/23/978142942/comic-how-one-math-teacher-broke-through-to-her-virtual-students" target="_blank">pandemic teaching story</a>. (Less helpful, probably, McSweeney's suggestions for <a href="https://www.mcsweeneys.net/articles/march-is-teacher-self-care-month" target="_blank">teacher self-care</a>.) Hope you are taking care of you and yours, and getting vaccinated!</p><p>So long 145! Hope it was 5x5.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2NG6-HEiOadGAZpOaaBIN-VgTsvdhlQCb0SsW-UBcd9Xy3i4D-_tYmDmzsPZJX_NLtMDy-EiAVjquB_BwTQ1f6H9NIfS-x_PFUb-p_osdke-1boL1ZN-TBdV22O6NQkvDl0q000MSU7A/s832/Screen+Shot+2021-03-28+at+3.51.53+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="758" data-original-width="832" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2NG6-HEiOadGAZpOaaBIN-VgTsvdhlQCb0SsW-UBcd9Xy3i4D-_tYmDmzsPZJX_NLtMDy-EiAVjquB_BwTQ1f6H9NIfS-x_PFUb-p_osdke-1boL1ZN-TBdV22O6NQkvDl0q000MSU7A/s320/Screen+Shot+2021-03-28+at+3.51.53+PM.png" width="320" /></a></div><br /><p><br /></p><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /><div class="separator" style="clear: both; text-align: center;"><br /></div></div></div></div>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com2tag:blogger.com,1999:blog-235276292454918436.post-54155242907927662832020-12-13T12:33:00.000-05:002020-12-13T12:33:54.107-05:00Escape Dr. Latham's Laboratory<p><span style="font-family: inherit;">The final game from the 2020 math capstone GAMES class. Begun by Char Beckmann, I was thrilled to teach this course and will soon have my second group. Here's the final entry, an escape room. Ashly was committed early on to make an escape room and I am impressed at the work as well as the perseverance required to finish while student teaching during the pandemic under the conditions .</span></p><p><span style="font-family: inherit;">GUEST POST by Ashly Latham</span></p><p><span style="font-size: 11pt; white-space: pre-wrap;"><span style="font-family: inherit;">Escape Dr Latham’s Laboratory is a game I created for my capstone project for MTH 496. When I first heard that we were creating a game I thought of the escape room me and my friends played before the class where we sat down and started talking about creating our game. This inspired me to create an escape-room inspired math game that allowed students to have fun while also doing math!</span></span></p><p><span style="font-size: 11pt; white-space: pre-wrap;"><span style="font-family: inherit;">This game originally started as a fifth grade game but as I got into an accident and injured my hand, I had to postpone the idea. Finally, when I received enough function to get back to work I was a Teacher Assistant in a third grade class classroom. These third graders inspired me to adjust the game so they could play it. </span></span></p><p><span style="font-size: 11pt; white-space: pre-wrap;"><span style="font-family: inherit;">The puzzles students will complete in this game will focus mostly on multiplication skills as this is what my students were working on at the time I created this. There are ten different puzzles but some puzzles have two answers which allow students to only play six puzzles each play. </span></span></p><p><span style="font-size: 11pt; white-space: pre-wrap;"><span style="font-family: inherit;">To create this game I searched the internet for fun multiplication puzzles. This included literal puzzles but also some riddles. After I found enough puzzles for what I wanted, I began to construct the scene cards. These tell a story as students work from puzzle to puzzle. The hardest part was constructing the solution wheel so that it was hard for students to guess answers and each answer had a different code. This took me spending lots of time creating my own symbols.</span></span></p><p><span style="font-size: 11pt; white-space: pre-wrap;"><span style="font-family: inherit;">When I tried it out with my third grade students, they LOVED it. I tested out the first couple puzzles and the students were constantly asking where the rest were. After finishing it, I had those same students try it. It took two 30 minute sessions to complete but they sacrificed their recess time just to finish it! They even want to do it again to find the other solutions! </span></span></p><p><span style="font-size: 11pt; white-space: pre-wrap;"><span style="font-family: inherit;">In the attachment for the game, all of the topics and standards are explained along with how to begin the game and set everything up. Though it’s in color, you can absolutely print it out in black in white. I hope you give it a try as it’s very fun and rewarding! Though carving out an hours time of your classroom might be hard, you could have students do one puzzle a day for a morning or ending activity for the day. </span></span></p><p><span style="font-size: 11pt; white-space: pre-wrap;"></span></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="465" src="https://www.youtube.com/embed/7DCAAUJLCvM" width="560" youtube-src-id="7DCAAUJLCvM"></iframe></div><br /><span style="font-family: inherit;"><br /></span><p></p><p><span style="font-size: 14.6667px; white-space: pre-wrap;">Ashly's extensive materials and instructions, including for her supper cool solution wheel are <a href="https://drive.google.com/file/d/1L5EXpHbAUKBHlPcopNa9mo2F9dRI2dsa/view?usp=sharing" target="_blank">here</a>.</span></p><p><span style="font-size: 11pt; white-space: pre-wrap;"><span style="font-family: inherit;">In addition, each capstone student picked a good math game to promote with a video. Ashly picked Michael Pershan's <a href="http://mathmistakes.org/baldermath/" target="_blank">Baldermath</a>.</span></span></p><p><span style="font-size: 11pt; white-space: pre-wrap;"></span></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="473" src="https://www.youtube.com/embed/DK1fIIEeiac" width="569" youtube-src-id="DK1fIIEeiac"></iframe></div><br /><span style="font-family: inherit;"><br /></span><p></p><p><br /></p>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0tag:blogger.com,1999:blog-235276292454918436.post-18526595038647166052020-12-03T15:38:00.004-05:002020-12-03T15:38:26.875-05:00Fractions vs Decimals<p> From the things you forgot you wrote file...</p><p><b>Fractions vs. Decimals</b></p><p><i>The Battle of the Century</i></p><p><i></i></p><div class="separator" style="clear: both; text-align: center;"><i><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikzQAH8NEfRbzw4wWmyAYa_SEB2I8S3Yb2KYjRs2hbxtLrogFq48ItZ2-tQgeLDI9gBCoq1fkxL3iiTiorGaWK6PLqg6jPBfXibRWJSg5A0KFZ5oJJLVFAGY7Xr-dB7WCQpKswcs6zSY4//" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1431" data-original-width="2048" height="448" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikzQAH8NEfRbzw4wWmyAYa_SEB2I8S3Yb2KYjRs2hbxtLrogFq48ItZ2-tQgeLDI9gBCoq1fkxL3iiTiorGaWK6PLqg6jPBfXibRWJSg5A0KFZ5oJJLVFAGY7Xr-dB7WCQpKswcs6zSY4/w640-h448/image.png" width="640" /></a></i></div><i><br /><br /></i><p></p><p>Ringside Announcer (RA): Welcome ladies and gentlemen to the Battle of the Century: Fractions vs. Decimals!</p><p>Old Man Fractions has been king of the hill for so long he can remember the pharaohs. But relative new-comer decimals has been rocketing through the ranks past previous contenders like Mixed Numbers and Percents, buoyed by the rise of science and handheld technology. Tonight they settle the issue once and for all, mano a mano.</p><p>Color Commentator (CC): That’s right, Jim. And they have both clearly prepared. Fractions has developed his upper body so much he looks positively improper. Decimals has emphasized speed work, and is awfully quick to the point. Hey, looks like they’re ready to start.</p><p>>ding<</p><p>RA: They come out swinging! Fractions looks like his strategy is to corner decimals and work his weaker visual representations. Oh there’s a pie model and a fraction strip combo! Decimals finally lands a 100 grid haymaker and gets back out to the center of the ring.</p><p>CC: Looks like that speed work is paying off, Jim. Decimals is coldly calculating without having to hit any special menu buttons on the calc, if you know what I mean.</p><p>RA: Not really, Howard, but I’m used to it. Oh! Decimal made a rounding error and Fractions lands an uppercut. </p><p>CC: That’s exactly the answer, Kid Decimals!</p><p>RA: The traditionalists are out of their seats, cheering on Fractions. Even the French are into it!</p><p>CC: He’s certainly got that je ne sais quoi, eh, Jim?</p><p>RA: Huh? Back to the action, Fractions is pressing his advantage. But decimals sees an opportunity and – oh! The referee calls time!</p><p>CC: I don’t think it was intentional, but that was definitely below the vinculum.</p><p>RA: The referee gives Decimals a warning and they’re back in. Fractions still looks a little wobbly, and Decimals presses the advantage, really working over Fraction’s arcane and misunderstood algorithms. </p><p>CC: Invert and multiply that! Whew!</p><p>RA: Fractions gives a nice example of unit fraction multiplication and is back in the fight. Oh, and lands a nice left hand on a complicated long-division problem.</p><p>CC: Decimals looks like he doesn’t know if his point is going left or right, Jim.</p><p>RA: It’s back and forth at this point folks. Fractions simplifies nicely, and catches Decimals a good one. Decimals lands a nice easy comparison, but Fractions hits a unit confusion counter-punch. </p><p>CC: That’s half of something, alright. </p><p>RA: Then Decimals comes right back with a repeating combination! Oh, and a non-terminating, non-repeating wallop! Fractions has no answer for that.</p><p>CC: Right in the Pi hole! Practically transcendental ring work, Jim.</p><p>RA: They’re really taking a beating out there. Howard, I think the crowd’s getting confused about what’s important here.</p><p>CC: I think you’re right, Jim, there’s kind of a baffled silence. Not that unusual at a rational battle like this one, though!</p><p>>Ding<</p><p>RA: That’s time. The fighters move to their corners. The judges communicate their decision to the ref. It’s pretty close on my scorecard, Howard. What do you think?</p><p>CC: Did you double check your answer, Jim? Nothing would surprise me –</p><p>RA: The ref is ready and brings both fighter’s to the center of the ring.… he pulls up both fighter’s hands! It’s a draw!</p><p>CC: The judges have called them equivalent! Oh the equality! Looks like we’re in for a rematch.</p><div><br /></div><br /><br /><p></p>John Goldenhttp://www.blogger.com/profile/18212162438307044259noreply@blogger.com0