Celebrating Spring with Playful Math Carnival 172

Welcome to the 172nd edition of the Playful Math Blog Carnival, a buffet of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

The carnival went on hiatus for a couple of months due to unexpected life issues facing our volunteer hosts. But we’re back now, and ready to celebrate!

By tradition, we start the carnival with a puzzle in honor of our 172nd edition. But if you’d rather jump straight to our featured blog posts, click here for the Table of Contents.

Try This: Lazy Caterers and Clock-Binary Numbers

172 is a lazy caterer number: Imaging a caterer who brought a single large pie to serve the whole party. He needs to cut it into as many pieces as he can, using the fewest (straight) cuts he can get away with.

• If each guest gets one piece of pie, what sizes of parties (numbers of people) can the lazy caterer serve?
• Can you find a pattern in the lazy caterer sequence?

But for those of you who have followed the carnival for years, you may remember we played with the lazy caterer back in Playful Math 106. (That time, the caterer was serving pizza.) So here’s a bonus activity we’ve never done before…

The first several stages of a pattern are as follows:

• What do you notice about this pattern of shapes?
• What is the next shape in the sequence?
• Can you figure out how the shape below fits into the pattern?

This pattern sequence was named clock binary by its creator, noelements-setempty.

• What questions can you ask about this sequence?
• How are these shapes like the binary numbers?
• How are they different?

Contents

And now, on to the main attraction: the blog posts. If you’d like to skip directly to your area of interest, click one of these links.

• Exploring Elementary Arithmetic
• Adventuring into Algebra and Geometry
• Scaling the Slopes of High School Math
• Enjoying Recreational Puzzles and Math Art
• Teaching with Wisdom and Grace
• Giving Credit Where It’s Due

Many of the quotations below come from Amie Albrecht’s article, What does mathematical reasoning look like?

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Exploring Elementary Arithmetic

“Mathematics is often encountered as a curriculum of dry nouns. What would it mean to focus instead on the rich verbs? I think it could transform the very landscape of learning”

—Amie Albrecht, What does mathematical reasoning look like?

• Bethany Lake shares a free downloadable Multiply & Divide by Powers of Ten Game: Includes Exponents.

• Michael Minas and sons demonstrate two new games: Matchmaker for basic addition and subtraction, and Maths Grid for number properties and vocabulary.

• Tad Watanabe discusses the value of Seeing a number in relationship to other numbers.

• Your kids will enjoy these Slow Reveal bar graphs by Jenna Laib and Gail Standiford: Number of Baby Teeth Per Mammal for the younger set, and Box Office History for Star Wars Franchise for the rest.

• Jo Buijs explores Mathematics in a Spider’s Web and Mathematics and Bird Feathers.

• Jenna Laib talks with kids about A Third Grade Dilemma: Dividing by Zero and shares her Fraction Intervention: Sonata for Eighth Notes in E Flat Major.

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Adventuring into Algebra and Geometry

“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.”

—John Golden, Variable Kings — a Linear Equations Math Game

• Early geometry: Marilyn Burns plays around with Milk Cartons, Origami Paper, a Desmos Tool, and More.

• Sarah Carter explains the Silent Board Game for Finding Function Rules.

• 360 blog asks, How many digits of π should NASA use?

• John Golden shares Variable Kings — a Linear Equations Math Game.

• Henri Picciotto leads students through a Pythagorean inquiry with his story of The Three Triangles.

• Sarah Farrell offers a fun collection of Daily Maths Puzzles.

• For kids only: There’s still time to enter Amplify’s Polypad Art and Music Contest 2024.

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Scaling the Slopes of High School Math

“Are students merely encountering the ‘fossilised remains’ of mathematical reasoning, or are they embarking on a journey to unearth the full and vibrant landscape of mathematics for themselves?”

—Amie Albrecht, What does mathematical reasoning look like?

• Sarah Carter creates a Rational Exponents Puzzle to help students practice converting between radical form and rational exponent form.

• Students will also enjoy Sarah’s Semi-Log Plot Mystery Picture, and have fun making pictures of their own.

• Do you find math vocabulary confusing? Boss Maths Vocabulary makes words make sense.

• Instead of rushing ahead to calculus, how about taking a deeper dive into the math you thought you learned? James Tanton pulls it all together in College Algebra for Humans. (Still under construction: bookmark and return!)

• 360 blog reports on Math Mistakes that Make the News: Optimization.

• For more posts about creative math, check out the 226th Carnival of Mathematics and the Carnevale della Matematica 177: Matematica inesauribile.

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Enjoying Recreational Puzzles and Math Art

“Doing math properly is engaging in a kind of play: having fun with ideas that emerge when you explore patterns, and cultivating wonder about how things work.”

—Francis Su, quoted by Amie Albrecht in What does mathematical reasoning look like?

Puzzles

• Sarah Carter poses the Eights Challenge with a printable download.

• Maths Ed Ideas offers a set of card decks featuring problems, puzzles, teasers, provocations, jokes, quotes, and more: Random Acts of Math.

• Tanya Khovanova collects math jokes and puzzles. Check out her recent additions: Jokes from the Audience and Two Lovely Puzzles.

Books and Poetry

• Cindy West lists 10 Living Books for Middle School Math.

• Marlaina Cockcroft believes The Right Books Turn Math Haters into Math Lovers.

• Sue VanHattum shares a few of her favorite books: The Storytellers of Math.

• Chalkdust has been posting reviews of their Book of the Year nominees. Which is your favorite?

• JoAnne Growney is Enjoying Math-Poetry Connections and Celebrating Women who write Mathy Poems.

Miscellaneous

• Paula Beardell Krieg demonstrates Paper Toy: a Foldable Structure.

• The Four Sevens Podcast explores different ways to learn math through play.

• For your listening pleasure, Katie Steckles reviews a variety of Mathematics Podcasts.

• Play with physics and geometry with xkcd’s Machine.

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Teaching with Wisdom and Grace

“Students should expect mathematics to make sense, and as sense-making becomes the norm, something beautiful happens. They start building their own ideas, forming connections, developing insights that are uniquely theirs, and becoming empowered to be mathematical explorers.”

—Amie Albrecht, What does mathematical reasoning look like?

• Emily Souther relates her journey as a student and teacher in Math Magic.

• Dan Meyer opines that Authentic Tasks Have Failed Us.

• Sonya Post explores the Power of Noticing — and some of the problems that make it so hard.

• Gordon Hamilton talks about how to Teach Your Math Class Using Puzzles & Games.

• For homeschoolers, Pam Barnhill and I discuss How to Transform Math Lessons without Changing your Curriculum.

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Giving Credit Where It’s Due

Images are from Depositphotos, featured image of butterfly and dandelions by majaFOTO, and all photos are copyright of the various artists. The clock binary numbers were created by noelements-setempty, and quotations are from the blog posts listed.

And that rounds up this edition of the Playful Math Education Blog Carnival. I hope you enjoyed the ride.

The next installment of our carnival will open sometime during the month of May at Nature Study Australia. Visit our blog carnival information page for more details.

We need volunteers! Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math (even if the only person you “teach” is yourself) — if you would like to take a turn hosting the Playful Math Education Blog Carnival, please speak up!