“Insect Math” is an excerpt from Task Cards Book #4, available as a digital printable activity guide at my bookstore. Read more about my playful math books here.

Do you want your children to develop the ability to reason creatively and figure out things on their own?

Help kids practice slowing down and taking the time to fully comprehend a math topic or problem-solving situation with these classic tools of learning: See. Wonder. Create.

See: Look carefully at the details of the numbers, shapes, or patterns you see. What are their attributes? How do they relate to each other? Also notice the details of your own mathematical thinking. How do you respond to a tough problem? Which responses are most helpful? Where did you get confused, or what makes you feel discouraged?

Wonder: Ask the journalist’s questions: who, what, where, when, why, and how? Who might need to know about this topic? Where might we see it in the real world? When would things happen this way? What other way might they happen? Why? What if we changed the situation? How might we change it? What would happen then? How might we figure it out?

Create: Create a description, summary, or explanation of what you learned. Make your own related math puzzle, problem, art, poetry, story, game, etc. Or create something totally unrelated, whatever idea may have sparked in your mind.

Math journaling may seem to focus on this third tool, creation. But even with artistic design prompts, we need the first two tools because they lay a solid groundwork to support the child’s imagination.

So I thought this week, I’d share some of my favorites with you. First up: Problem Solving Tips from James Tanton.

You may know Tanton from the popular Exploding Dots and other activities at the Global Math Project website. But he’s been busy for decades sharing the delight and the beauty of the subject. He currently serves as the Mathematician-at-Large for the Mathematical Association of America.

Read on to discover several of Tanton’s best problem-solving tips for middle school and older students.

Have fun exploring math with your kids!

How to Think like a School Math Genius

In this 4-video series, Tanton presents five key principles for brilliant mathematical thinking, along with loads and loads of examples to explain what he means by each of them. A call for parents and teachers to be mindful of the life thinking we should foster, encourage, promote, embrace and reward — even in a math class!

Two Key — but Ignored —Steps to Solving Any Math Problem

Every challenge or problem we encounter in mathematics (or life!) elicits a human response. The dryness of textbooks and worksheets in the school world might suggest otherwise, but connecting with one’s emotions is fundamental and vital for success — and of course, joy — in doing mathematics.

Essays and videos showing how to approach math puzzles in a way that a) is relevant and connected to the curriculum, and b) revels in deep, joyous, mulling and flailing, reflection, intellectual play and extension, insight, and grand mathematical delight.

Scroll down and start with the Ten Problem-Solving Strategies.

“The true joy in mathematics, the true hook that compels mathematicians to devote their careers to the subject, comes from a sense of boundless wonder induced by the subject.

“There is transcendental beauty, there are deep and intriguing connections, there are surprises and rewards, and there is play and creativity.

“Mathematics has very little to do with crunching numbers. Mathematics is a landscape of ideas and wonders.”

—James Tanton

CREDITS: Feature photo (top) by Ian Stauffer via Unsplash.com.

Welcome to the 152nd 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!

We didn’t have a volunteer host for January, so I’m squeezing this in between other commitments. This is my third no-host-emergency carnival in the last year, which is NOT sustainable. If you’d like to help keep the Playful Math Carnival alive, we desperately need hosts for 2022!

By tradition, we start the carnival with a puzzle or activity in honor of our 152nd edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

Math Journaling with Prime Numbers

Cool facts about 152: The eighth prime number is 19, and 8 × 19 = 152. When you square 152, you get a number that contains all the digits from 0–4. You can make 152 as the sum of eight consecutive even numbers, or as the sum of four consecutive prime numbers.

But 152 has two real claims to fame:

It’s the smallest number that is the sum of the cubes of two distinct odd primes.

And it’s the largest known even number you can write as the sum of two primes in exactly four ways.

So here’s your math investigation prompt:

Play around with prime numbers. Explore their powers, their sums, and anything else about them you like.

What do you notice? What do you wonder?

What’s the most interesting number relationship you can find?

As queen of the house, Cimorene insists on being involved in anything that happens in her domain. This includes promoting the Playful Math Journaling Kickstarter.

So she created a cat math journaling prompt to help your children experience the fun of playing around with math.

But first, she encourages you to visit the Kickstarter page and download the free 16-page printable Math Journaling Sampler file. Your kids will love solving Cimorene’s puzzle on one of the parchment-style pages!

[The free download will always be there, even after the Kickstarter project ends.] Visit the Kickstarter

Here is Cimorene’s Puzzle

“The Princess of Cats has a luxuriously soft tail about 12 inches (30 cm) long. Her tail is three times the length of her noble head. Her beautiful, furry body is as long as head and tail together. How long is the Princess from her delicate nose to the tip of her majestic tail?”

So, how does math journaling work? What do children do with a problem like this?

They may want to make a list of the things they know from the story. Perhaps they will draw a picture of the cat and label the proportions. Each will take their own approach to figure it out.

And then the best part of any math journal prompt is when kids make their own math.

Can they write a new puzzle about their own pet?

Or about their favorite animal?

Encourage your children to share their math creations with their friends and family.

Cimorene would love to read it, too! If you share your story in the comments section below, I will be sure to show it to her.

Are you looking for new ways to explore math with your kids?

Would you like an easy, no-prep resource for creative problem-solving, number play, math art, word problems, mini-essays, math poetry, geometry investigations, research projects, and much more?

I’ve just launched a Kickstarter project for people to preorder my new book, 312 Things To Do with a Math Journal. It just might transform your child’s experience of math.

In a math journal, children explore their own ideas about numbers, shapes, and patterns through drawing or writing in response to a question. Journaling teaches them to see with mathematical eyes. Not just to remember what we adults tell them, but to create their own math.

Scroll down the Kickstarter project page to download the free 16-page printable “Math Journaling Sampler” file. It includes one of my all-time favorite math activities.

If you like what you see, I’d love to have your support. The more people we can get to share the project in the early days, the more likely Kickstarter will join in and promote it to new readers.

Puck is concerned that some people don’t understand the idea behind the Math Rebel journals. He decided to create a journaling prompt so your children can experience the joy of creative reasoning (and save cats from their mortal enemy!)

Journaling is a great way to help children learn to see with mathematical eyes. Not just to remember what we tell them, but to create their own math.

Many people know it’s important for students to do hands-on experiments in science. But Puck realized that most adults don’t know how to do a math experiment.