Early El Math Games

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. 

Number Sense

In our class we discuss these as: 

• one-to-one correspondence - as learners count, they have one (and only one!) number assigned to each object being counted.
• hierarchical inclusion - (worst name candidate) the idea that a number contains smaller numbers. If you have 6 you also have 5, etc.
• 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.
• 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.
• magnitude/comparison - both being able to directly compare quantities, and identify relative size - like locating where 7 is between 5 and 15.

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.)

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.

General Educational Game Advice

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.

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.

Divvy Up (Counting, Hierarchical Inclusion) Materials: Number Cards

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.

Optional, arrange the 10 objects in two rows of five to sneak in some 5s structure and complements of 10.

Variation: if there are not enough to take, you have to pass. Encourages comparison, but can make the end take a while.

More or Less (Comparison, Strategy)

Materials: Number Cards

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.

More Together (Counting on, addition, hiearchical inclusion, decomposition)

Materials: Number cards mixed up in four piles.

Two teams: each turn over a card. Who has more? Then the teams turn over their 2nd card. Who has more together?

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.

A tie? Flip over one more. No need for an overall winner, just who wins each turn.

Staircase  (Counting, counting on, hiearchical inclusion)

Materials: optional gameboard, a lot of stacking cubes and a die.

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…

How many behind? (Decomposing, hiearchical inclusion, part part whole stories) Materials: 10 (or 12!) unifix cubes.

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.

Big Three (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!

(Riff on Rat-a-Tat-Cat, a great commercial math game.)

Moving to Story & Operation

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.

• Join. One quantity, increasing over the story. Unknown could be the start, the change or the result.
• Separate. One quantity, decreasing over the story. Unknown could be the start, the change or the result.
• Comparison. Two quantities, related by the difference between them. Unknown could be the referent, the difference or the compared quantity.
• Part Part Whole. Two quantities that are part of a group. Unknown could be either part or the whole.
• 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.

Comparison Game

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.

Making a Difference 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.

Facts

I feel like this is a place where games have made an inroad. But still, there's plenty of fun to be had.

10s Go Fish and Concentration Make 10

Pretty self explanatory. Remember to not let kids take extra turns. Both games I like to have kids score by counting their 10s.

Double Time (Doubles and counting on)

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.

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.

Ten Penny Game (Fives structure, sums to 10)

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.

Cover All (Addition, decomposing)

This is the classic math game Shut the Box.

Cover All gameboard, but really all students need is a track from 1 to 10.

Play: roll two dice, and cover up any combination of numbers that add to the same amount.

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?

Dice Squares (adapted from Illustrative Math)

Materials: Gameboard, 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. 

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.

Make Your Own

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.

Give Me More

Just two resources to end.

• One of my favorite YouTube channels is Michael Minas, 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.
• Jenna Laib has a few easy, high leverage games. She writes about making games and then shares her favorites. We've used Number Boxes 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.)

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!

Game on!

Playful Math Education 151

Welcome to the 151st edition of Denise Gaskin's Playful Math Education Carnival 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.

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 quadratic form primes (not sure why those are of interest). It's a lucky number 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 Polypad, which has new features to play with each month, seemingly.)

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?

Make

To get things started, maybe give Steve Phelp's fractal snowflake maker a try. If paper is your thing, try Paula Beardell Krieg's directions.

Paula also had a great post reviewing her month of making Johnson Solids. She's been doing Saturday half hour folding sessions that are the epitome of playful math making.

Jenna Laib shared a tweet thread about a quick drawing game that got kids thinking. Update: she wrote a blog post about it!

Can't have one of these without a Simon Gregg post. Here his learners are building Number Blocks, a show he's already converted me to.

Vincent Pantaloni shared a Set game (a Set set?) with just geometric symbols. I think it could be really challenging.

Just shortly before publishing, Jonathan pushed send on a post about haikus and magic from having a typewriter 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 32,518,460. He added two more on Twitter:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11. That's enough.

2.71 8281828 45 and so on

Play, Game & Puzzle

Back from May, but spot on theme, Peter Rowlett writes about Math Play with Young Children.

Annie Forest shared a place value, low materials math game called Draw 10 that she first wrote about a few years ago.

Adrienne Burns tweets about making a math Bingo game better, for addition and representation.

Michael Minas and family share multiple games a month on YouTube. Mostly number and operations. If I had to pick one from Nov/Dec, it would be Strawberry vs Dinosaur, a sweet little numberline game (named after their counters).

Jenna Laib, who would be my nominee for blogger of the year, despite some stout competition, shared her all purpose number boxes game in May, as a part of her high leverage games collection. Mark Chubb wrote a post about how he plays it, with multiple different operations and a units of measurement context.

James Cleveland Tran tweeted an integral calculus version of one of my favorite simple but high leverage games.

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. 

They also raise a lot of mathematical questions, such as the one Howie Hua is solving here for Magic the Gathering. Howie's TikTok is full of amazing nuggets, strategies and math.

There was a fun Global Math Department meeting about Beast Academy Playground games, and Erick Lee shared some of his favorites. Troll hole is one I love to share on a whiteboard or paper if there's an opportunity.

Celeste Bancos revisited the Secret Number Game.

Pam's addressing that you can learn math through play in homeschool, too.

Iva Sallay crosses Sarah Carter and Joseph Nebus and makes a puzzle!

Colleen Young connects to a bunch of math puzzle resources.

Patrick Vennebush is working out a better multiple choice test in his Mathy Jokes blog.

Content

Bumba Stories has a short history of why we have 12 months.

The Quiet Pond has a review of what looks like a good picture book, Danny Chung Sums It Up. 

Christopher Danielson share's one perfect page from The Last Marshmallow.

Speaking of counting, Early Math Counts has some early math winter counting opportunities.

Dave Taylor started a Twitter thread about historical numerals by starting with the Cistercian numbers.

Brian Bushart shared one of his favorite resources, a free collection of math interventions, Pirate Math Equation Quest. It is not all pirate themed, but lots of great supporting materials.

One-Fifty-One is a hard rock band... not my taste, but if it's yours, rock on.

Jenna Laib had a great geometry post about the half triangle. If you listen closely, you can hear the learners progressing van Hiele levels.

If you're looking to stretch your brain, try Jim Propp's monthly essay, this time on numbers from games. Bonus John Conway stories.

Katie Steckles wrote a sweet piece for the Aperiodical about  Spirograph Math.

I should be blogging more... and if I did, I would definitely write about the interesting responses to this tweet about dividing polynomials with partial quotients. 

Teaching

Dylan Kane, always challenging, provocative and brief, takes on productive struggle.

David Sladkey wrote about implementing some of the Thinking Classroom ideas with his learners. Practical and productive.

Margie Pearse wrote a post for Heinemann on using literature to address social justice in math.

Dan Finkel's reflecting on a big question "Am I a Mathematician?"

In Memoriam

We'll close with Math Ed Podcast's interview of Dr. Liz Fennema, one of the founders of  Cognitively Guided Instruction. She passed away this month in hospice. She received the NCTM lifetime achievement award 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.

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 Twitter or via the Playful Math Education Carnival homepage. Denise is hosting January, but then there are lots of opportunities ahead. Ask me and I'll happily add some suggestions for posts!

Cheers to a mathy new year! I know champagne is more typical, but where's the 151 in that?

Game Promotion

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.

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 course page.

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.

Caleb Anderson - Safe or Sorry

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.

Original post: Safe or Sorry

Heather Anderson - Bad Calculators

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 https://www.badcalculators.com/

Arianna Ayers - Make and Take

Arianna Ayers made this video for an upper elementary/middle school math game on mixed operations. (It's the first of several games from Nicholas Smith 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!"

Original blogpost: Make and Take

Danielle Jurcich - Card Catch

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: Card Catch Handout

Cameron Morgan - Treasure Hunt

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."

Gameboard is here: Treasure Hunt Gameboard (but it is easily played with pen and paper)

Olivia Sassanelli - Tug of War

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!"

Original game: Tug of War (original) (Has a bit more interaction and back and forth.)

Kayla Shirah - Honeycomb

Kayla Shirah demonstrates Honeycomb, another 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: Honeycomb Gameboard and Rules. 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."

Playful Math Carnival 145

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 144th Anniversary Edition, as night doth follow gentle day, and by that we were blown away.  

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 fun number site.) And 145 shows up in Matt Parker's melancoil. 145 degrees (F) makes something medium rare...  maybe that should be the goal for this edition?

Volvo 145. Ove approved.

Hop in the 145 and let's go! 

Books & Essays

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 Public Math website, which has more besides. Also see the mathszine hashtag on Twitter.

That was my introduction to Ayliean, who had some thoughts on STEMinism.

Some of those zines inspired Sophia Wood for her first Fractal Kitty zine, on the Cantor Set.

Jim Propp was musing on division by zero. History, what ifs, new possible numbers...

Edmund Harriss has a new children's book out, HELLO NUMBERS! What Can You Do? and has been out supporting the release. Read more at Chalkdust's Math Book of the Year series. Also super curious about Eugenia Cheng's Molly and the Mathematical Mystery.

Speaking of playful math authors, RIP to Norton Juster, author of The Phantom Tollbooth and The Dot and the Line.

Games

Sarah Carter reviewed the mathgame Proof positively.

James Cleveland posted his new linear graphing mathgame. Played it with my games seminar students and I think there's a lot of potential.

Simon Gregg and his learners were making variations on Snakes and Ladders.

Henry Segerman suggests this negatively curved sliding puzzle.

Excellent post at Play and PK on Listening.  Guest appearance from the always welcome Max Ray Riek in that post.

I've been making some GeoGebra for remote learning play. There's a measure division game, a fraction comparison game, a fraction addition/iteration/equivalence game and the classic Shut the Box.

Art

Dana Ernst shared quilts his student Michelle Reagan made on the 5 groups of order 8.

Practically a quilt, Master of the Pattern Blocks, Hana Murray, made this amazing tiling replete with dodecagons. 

Robert Fathauer was interviewed on Math, Art and Tessellations. His new book is a masterwork.

Sophia is also in the middle of a 101 days of coding challenge, and shared her ecliptic ripples.

Paula Beardell Krieg had some practical advice for cutting curves by cutting straight.

I got to work on a fun project with my son studying art education, Yemeni squares. 

Wait There's More

I found this perusing old NCTM practitioner journals for fraction tasks and it sparked some interesting conversation. Like just how many solutions are there?

And it wasn't the only time 1/3 appeared in this third month, as I saw a nifty Roger Nelson proof with out words of an odd identity.

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 Egg Puzzles, for example), and found several possibilities for this edition!

• a mousey Bedtime math problem set
• Catriona Agg appearing at 538's the Riddler
• a math chapter book from Peggy Chambers

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 Denise know.

NPR made a comic of this teacher's pandemic teaching story. (Less helpful, probably, McSweeney's suggestions for teacher self-care.) Hope you are taking care of you and yours, and getting vaccinated!

So long 145! Hope it was 5x5.

Escape Dr. Latham's Laboratory

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 .

GUEST POST by Ashly Latham

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!

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. 

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. 

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.

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! 

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. 

Ashly's extensive materials and instructions, including for her supper cool solution wheel are here.

In addition, each capstone student picked a good math game to promote with a video. Ashly picked Michael Pershan's Baldermath.

Fractions vs Decimals

 From the things you forgot you wrote file...

Fractions vs. Decimals

The Battle of the Century

Ringside Announcer (RA): Welcome ladies and gentlemen to the Battle of the Century:  Fractions vs. Decimals!

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.

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.

>ding<

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.

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.

RA:  Not really, Howard, but I’m used to it.  Oh!  Decimal made a rounding error and Fractions lands an uppercut.  

CC:  That’s exactly the answer, Kid Decimals!

RA:  The traditionalists are out of their seats, cheering on Fractions.  Even the French are into it!

CC:  He’s certainly got that je ne sais quoi, eh, Jim?

RA:  Huh?  Back to the action, Fractions is pressing his advantage.  But decimals sees an opportunity and – oh! The referee calls time!

CC:  I don’t think it was intentional, but that was definitely below the vinculum.

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.  

CC:  Invert and multiply that!  Whew!

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.

CC:  Decimals looks like he doesn’t know if his point is going left or right, Jim.

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.  

CC:  That’s half of something, alright.  

RA:  Then Decimals comes right back with a repeating combination!  Oh, and a non-terminating, non-repeating wallop!  Fractions has no answer for that.

CC:  Right in the Pi hole!  Practically transcendental ring work, Jim.

RA:  They’re really taking a beating out there.  Howard, I think the crowd’s getting confused about what’s important here.

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!

>Ding<

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?

CC:  Did you double check your answer, Jim?  Nothing would surprise me –

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!

CC:  The judges have called them equivalent!  Oh the equality!  Looks like we’re in for a rematch.