Playful Math Carnival #154: The Math Journaling Edition

Welcome to the 154th edition of the Playful Math Education Blog Carnival — a smorgasbord 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.

Bookmark this post, so you can take your time browsing.

There’s so much playful math to enjoy!

By tradition, we start the carnival with a puzzle/activity in honor of our 154th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

Try This Puzzle/Activity

Since 154 is a nonagonal number, I think you might enjoy visiting some of my old “Adventures of Alexandria Jones” posts about figurate numbers:

And then try this math journaling prompt: Build or draw your own nonagonal numbers — numbers built from 9-sided polygons.

How many nonagonal numbers can you find? What do you notice? Does it make you wonder?


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.

Would you like to help keep the Playful Math Carnival going? We need volunteer hosts! Find out more at the Playful Math Education Blog Carnival home page.

Note: The bonus math journaling prompts and images below are from my new book, 312 Things To Do with a Math Journal. Have fun playing math with your kids!

Talking Math with Kids

“Look at this one. It’s only this big. I thought it would be way bigger. Let’s make a bigger square, like twenty by twenty. Will that be a too-bigger pocket?”

—Celeste Bancos, Origami Pockets and a Paper Pickup Truck

  • Puzzles can be a wonderful prompt for math discussion. Can your children work together to find solutions to Sian Zelbo’s Same Sum Circles?

Bowling (solitaire game)

Draw circles in a bowling-pin pattern. Write the numbers 1–10 in the circles. Roll two dice and cross out any combination of circles that exactly matches that sum. Those are the pins you knocked down. Roll again, trying to hit more pins.

If all the numbers left are 6 or less, you may choose to roll only one die. Can you knock down all the pins? What is your strategy?

—Denise Gaskins, 312 Things To Do with a Math Journal

Bowling pins are arranged in a triangle and numbered from the shortest row to the longest. The triangle may point up or down, whichever you prefer.

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Exploring Elementary Arithmetic

“When interviewing students to learn how they reason, we’re often surprised, intrigued, and delighted. Their thinking stretches our own thinking and informs our instruction. Similarly, we think it’s also valuable for students to learn to listen to each other during class instruction. Understanding how their classmates reason can expand their own thinking.”

—Marilyn Burns, What Was Nathan Thinking?

  • Your children may enjoy these daily number challenge puzzles: Numble (find a 3-digit multiple of 3) and Nerdle (find a daily equation). Or create your own puzzles for each other with Michael Minas’s (@mminas8) new game Equationle.
  • Colleen Young (@ColleenYoung) organizes her Number Resources — including this Number Operations puzzle that builds understanding of multiplication, division, and place value. After they solve it, challenge your kids to create a similar puzzle of their own.

Triangular Numbers

You’ve heard of square numbers. Triangular numbers are their smaller cousins. Arrange dots in a bowling-pin pattern. Count the dots to find the triangular number: one dot in the first row (T1 = 1), two in the second row (T2 = 1 + 2), three in the third row (T3 = 1 + 2 + 3), etc.

Keep adding more dots. Each row is one dot longer than the previous row. How many triangular numbers can you find? Do you see any patterns? Can you think of any questions to ask?

—Denise Gaskins, 312 Things To Do with a Math Journal

The first four triangular numbers are 1, 3, 6, and 10.

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Adventuring into Algebra and Geometry

“As this had taken less time than I expected, I had to then think quick and come up with an extension…”

—Michael Jacobs, A Nice Algebra Puzzle

  • And you can always go explore Don’s blog for yourself. Here are a few puzzles he collected to help students understand slope (or gradient).

Everything Is a Rectangle

Draw any quadrilateral (four-sided shape) on your page. How can you convert it into a rectangle with the same area? For example, can you imagine cutting off one part and pasting it in a different place?

What if it’s an unusual shape like a kite or an arrowhead? Extra challenge: Can you convert shapes that are not quadrilaterals?

—Denise Gaskins, 312 Things To Do with a Math Journal

No matter how many times you cut and paste, the total area remains the same.

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Scaling the Slopes of High School Math

“Take a risk and find the guts to create something really personal, whether it’s funny or dark or thought-provoking or just mathematically beautiful. Just push yourself a bit out of your comfort zone and take a chance and have fun with it!”

—Julia Schanen, Share Math Like Strogatz: An Interview with Julia Schanen

Explain a Mistake

Describe a mistake you made in math, or a problem you missed on a quiz or test. What went wrong? How will you avoid this error the next time? Do you understand the problem now, or is there something more you need to learn about it?

—Denise Gaskins, 312 Things To Do with a Math Journal

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Enjoying Recreational Puzzles and Math Art

“The answers to both can be found with an online search, and the latter can be computed in milliseconds by writing some code, but you’ll have more fun if you find the answers using that big lump of gray matter in your skull.”

—Patrick Vennebush, The Great Puzzle Hunt

  • Patrick Vennebush (@pvennebush) drops a couple of math puzzles and an algebra joke — and links to an upcoming online math event — in The Great Puzzle Hunt.

Circle Pattern

Draw a circle. Draw another circle the same size, with its center at any point on the first circle’s circumference. At each point where the circles meet, draw another circle centered there. Continue drawing circles with their centers at each new intersection.

What do you see in this pattern? Can you think of any questions to ask?

—Denise Gaskins, 312 Things To Do with a Math Journal

This delightful, never-ending circle pattern can be the starting point for many math art projects. Try connecting the intersection points with straight lines to make other shapes and designs.

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Teaching with Wisdom and Grace

“Everyone deserves a chance to experience what makes people fall in love in mathematics.”

—Dan Finkel, 4 Reasons Play and Math Go Together

  • Anna Blinstein (@ablinstein) relates her experience implementing Consolidation — that is, wrapping up the big ideas at the end of class to help students make key connections.

Reinvent Your Homework

Find a page of calculations in your math book, or download a worksheet online. Choose two or three of the questions. Write a story problem to match each calculation.

For example, for the calculation 3/4 × 8, you might imagine a recipe that takes 3/4 cup of flour. But you are planning a party and need to make eight times that amount. How much flour will you need in all?

—Denise Gaskins, 312 Things To Do with a Math Journal

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Giving Credit Where It’s Due

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 take place at John Golden’s Math Hombre blog sometime during the month of April.

Would you like to take a turn hosting the Playful Math Carnival? Visit our blog carnival information page for more details.

Playful Math Carnival Home Page

Math journaling prompts and images (except as noted below) are from 312 Things To Do with a Math Journal.

Nonagonal-Number.gif: Referenced on Wolfram/Alpha: Nonagonal Number, CC BY-SA 4.0, via Wikimedia Commons.

Photos above: “Purple beach” photo by Nick Dunn on Unsplash. “Homework photo 1” by Anoushka P, and “Homework photo 2” by Antoine Dautry on Unsplash (license terms).

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