Playful Math Carnival 177

Interesting time to be hosting this carnival! I feel like there's a small resurgence with blogging, and I want to be part of it. I've really missed writing informally professionally. I've been a part-time host since Math Teachers at Play 22, 14 years ago!, and a big part of the original purpose of the blog was to collect, curate and share things that delighted and supported me. If you're interested in hosting, contact Denise Gaskins, the founder of this here carnival. The January carnival will be at her blog, but I think February is open!

177 is semiprime, for which two primes? 

177 is the ninth Leyland number, of the form x^y+y^x. What are x & y for 177? They're both prime, which should be a special kind of Leyland I think.

177 is the first "non-trivial" 60-gonal number. (1 and 60 are too easy.) What is the next 60-gonal number? (Pictured) What does the sequence of the first non-trivial n-gonal numbers look like? (6, 9, ...)

177 is a Leonardo number, so named by Edsgard Dijkstra for their relation to the Fibonacci numbers. The first five are 1, 1, 3, 5, 9... can you determine the pattern?

But the coolest thing to me is that it's the magic constant of the smallest magic square of distinct primes! I'll get you started...

Supposedly the 2nd highest dart score is 177 - but I need someone to explain that to me. Supposedly I used to play darts!

177 is getting too big for many interesting images on Google image search. So I tried AI. Give me 177 ants marching! 75 at most. Give me a stack of 177 balls. Hmm... I don't think so. That set me off to GeoGebra to make a visualization tool.

Things are hopping over on Bluesky. Most of these links are from there. Here's a math teacher starter pack, or a mathsky star pack part 1 or part 2 or an #elemmathchat starter pack. Other good tags to check are #mathsky, #iteachmath or #mathstoday. So far it's been positive and energetic.

Gamey

Denise shares a math game every Monday, like Area Block or Coin Chain.

Sara Van Der Werf reshared her amazing 5x5 game, for adding, multiplying and a bit of strategy.

Erick Lee and his son invented a sweet exponents game that I'm dying to try.

Some fine mathematicians seem to have proved that Henry Dudeney's famous equilateral to square dissection is minimal. I made a GeoGebra puzzle out of it to celebrate. That dissection is hinged and Manuel Sada made GeoGebra for that! Denise shared a Dudeney game I had never seen before.

I've really been enjoying the Celtix puzzle by Andrew Taylor. Great UI. Multiple solutions to each, but took me awhile to get the hang of just focusing on one color at a time. Here's two solutions to Puzzle 177. HT Ayliean.

Sarah Carter, queen of math puzzles, shared some winter themed Sudoku puzzles, also available in Christmas flavor.

Catriona Agg continues to invent the sweetest geometry puzzles. This one with four equilateral triangles was really neat.

I've always thought a card sort was an activity that invited play. Marilyn Burns continues to amaze me, like here when she tried her first card sort!

David Flynn shared a puzzle he made for 3rd graders. Get from start to finish using only right angles.

Artsy

Xavier Golden (full relation) found the classic Eames math shorts (plus more) in a single YouTube playlist.

Ben Orlin's math with Bad Drawings is a constant delight, but I especially loved his musings on Edgar Degas and math.

Erick also shared an old Bree Pickford-Murray post making posters for missing hexagons (after first inventing hexagon types).

Min Min shared an old post of Sarah's making slope-keyed nameplates. 

Paula Beardell Krieg has a bunch of upcoming workshops, but still found time to share this open and close pop up.

Grant Snider drew a sweet math fable. (Is it a rhombus, though?)

Sue Van Hattum's super cool Althea series is continuing. Here she shares a problem with a problem.

Lucie Rose mathematically constructs medieval geometry.

Teachy

Nat Banting blogged about an essential teaching reminder.

Dan Wekselgreene shared a routine that my preservice secondary teachers tried and liked, Correct, Incorrect, Incomplete.

Jenna Laib writes about students writing silly story problems.

Glenn Waddell did a whole series of quadratics this fall, wrapping up with the mystery of the b coefficient.

Dylan Kane never lost the beat, still the most consistent math teacher writer. Here he's thinking about Ben Orlin's book and Hemingway and Negative Numbers.

Extry

Maybe you're looking for last minute mathy gifts? Thanks, Aperiodical. Who wouldn't want a handmade zine? How you could wrap them from this post.

Ali Almossawi shares some math history about a few great mathematicians who were famously slow.

I didn't get many math comics made this #mathtober  but this was definitely the biggest hit.

That's it for me! See you next year. Coming soon, Xavier's and my math graphic novel, AL, Logical!

What? Are you still here? Then enjoy one of Howie Hua's many riffs on a holiday meme.

Just Sitting Down

I had an elementary ed class canceled for low enrollment and got a calculus course instead. It's really been a teaching challenge, which is always good for a teacher educator. Usually when I teach calculus, I start with integration. It's more intuitive than derivatives, and a lot of our calc I students have had some calculus before and think they know it because they can take derivatives of polynomials. But I have the good fortune to be in a department with Matt Boelkins, who's written a terrific calculus book, free to students, so I'm trying to be more of a team player.

I have not been able to establish a good culture of collaboration, and say at least 20 times a class to talk to their tablemates as they work on activities. I'm using random grouping daily, and by now most have worked with most others. I'm disappointed in myself that I have not made more tasks into complex instruction tasks, which would help with interaction A LOT. But time is what it is.

The heart of the differential calculus part of the course to me is the optimization and related rates sections. Making sense of rate of change in context for optimization. And the power of the derivative idea in related rates. We can take the derivative with respect to time even when time is not a variable! Astounding!

After two days on optimization and two days on related rates I had not gotten a lot of the in class assessment options back, and I thought they were intimidated by the problems. So I took an extra day to do one more of each. Both pretty standard problems which I added some small wrinkles.

They all set to work, parallel play as always. I encouraged talk, which as usual got a minute of conversation, then back to themselves. I paused class to get some shared thinking on the whiteboard.

Finally I just started sitting down with the groups. Asked where they were, found out from each member, and asked questions that got them explaining to each other what they thought. Table by table, sat with everyone. I know, on some level, that if you want learners to do something you have to model it, but do I do it? The rest of the class conversation was pretty good.

The next class we started integration thinking, and discourse was better than average. So I think I'm going to continue sitting down on the job. As opportunity allows.

Variable Kings - a Linear Equations Math Game

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 YouTube playlist. Many of the games completed in my seminar are in this playlist. 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 Desmos escape room and Math Heads, a number mystery game this year), and they develop a game of their own.

Ryan Brummel made a video for Math Heads, our group game as mentioned above, a game he tested extensively with his algebra students.

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.

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.

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.

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.

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.

Why Play Math Games?

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.

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.

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.

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!

Multiplication Mazes - a puzzle for fact practice

 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 YouTube playlist. Many of the games completed in my seminar are in this playlist. 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 Desmos escape room and Math Heads, a number mystery game this year), and they develop a game of their own.

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 Math for Love.)

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 Google doc here. What follows is Keri's story of making the game, and her ideas on why we should play games in math class.

Story of my Game

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. 

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. 

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. 

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. 

Why Play Games in the Math Classroom?

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. 

Building Mathematical Knowledge

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. 

Collaboration with Peers

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. 

Student Engagement

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. 

Critical Thinking Skills

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. 

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 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. 

Coordistroy - Classroom Graphing Game

 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 YouTube playlist. Many of the games completed in my seminar are in this playlist. 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 Desmos escape room and Math Heads, a number mystery game this year), and they develop a game of their own.

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 high school/college focused video for it, and Jordan Burnham made a game built on that structure, Boxzee.

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.

Coordistroy Development

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.

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. 

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!

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! 

Why Play Games in Math Class?

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. 

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. 

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. 

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! 

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?)

Algebra Spoons - an Algebra Representations Math Game

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 YouTube playlist. Many of the games completed in my seminar are in this playlist. 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 Desmos escape room and Math Heads, a number mystery game), and they develop a game of their own.

This post is sharing Corrina Campau's games - she was also the lead Desmos engineer on the escape room!

Her first video was for Jenna Laib's Number Boxes. Really an all time great classroom math game, it was extra influential to this year's seminar. Like Jordan Burnham's game Boxzee.

Corrina's original game has an original deck of cards, which would have multiple uses, but is great in her Math Spoons (Cards and Rules). 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.

The Story of Algebra Spoons

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.  

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.

Why Play Games in the Math Classroom and What Makes a Game Effective?

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?  

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.  

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.  

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.  

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.

Reference

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

Boxzee - Flexible Computation Game

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 YouTube playlist. Many of the games completed in my seminar are in this playlist. 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 Desmos escape room and Math Heads, a number mystery game), and they develop a game of their own.

Jordan Burnham selected Close to Zero, and integer addition game for her first video. Handout and original blogpost.

Jordan's original game Boxzee crosses one of my favorite classroom games, Number Boxes by Jenna Laib, with the classic Yahtzee. What follows is Jordan's explanation of the game and thoughts on why play games in math class.

Boxzee

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.

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. 

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. 

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. 

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.

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. 

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.

Why Play Math Games?

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.

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.

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. 

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.

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. 

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. 

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.

GEO - Middle School Geometry Game

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 YouTube playlist. Many of the games completed in my seminar are in this playlist. 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 Desmos escape room and Math Heads, a number mystery game), and they develop a game of their own.

Leah Barber selected Greater Than for her first video, an integer multiplication game. (Handout)

Leah's original math game is a great spin on Uno called Geo. Cards & Handout. What follows is Leah's explanation of the game and thoughts on why play games in math class.

How Geo Came To Be

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. 

Why Teachers Should Play GEO:

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. 

Other Uses: 

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. 

Why Play Math Games? 

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.

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. 

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. 

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.