A 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.
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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:
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.
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.
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.
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?
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.
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!"
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."
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."
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.
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!
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!
