Thinking Thursday: Insect Math

“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.

Problem Solving with James Tanton

At the back of my new Word Problems from Literature book, I’ve included an appendix with links to recommended online resources.

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.

MAA AMC Curriculum Inspirations

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.

Think Puzzles and Think Cool Math

Here are some essays illustrating astounding tidbits of mathematical delight. And here are some purely visual puzzles to surprise.

“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.

Playful Math #152: Auld Lang Syne Edition

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?

Playful Math Journaling with a Cat

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.]

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.

And remember to back the Playful Math Journaling Kickstarter so your whole family can enjoy the adventure of playing with math!

Playful Math Journaling: Preorder on Kickstarter

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.

Have fun playing math with your kids!

Math Journals: Save the Cat!

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.

So Puck created this Cat Escape puzzle…

Make Sense of Math

So, I decided to rewrite the Standards for Mathematical Practice into student-friendly language.

Here’s the final installment…

Math Tip #8: Make Sense of Math.

• Don’t get lost in the details of a problem. Look for general truths.
• Apply common sense to math situations.
• Think about how different things are similar.
• Think about how similar things are different.
• Pay attention to your thinking process. What patterns do you find there?

Discern Patterns

I’m almost done rewriting the Standards for Mathematical Practice into student-friendly language.

They say mathematics is the science of patterns. So here’s…

Math Tip #7: Discern Patterns.

• Look for patterns in numbers, shapes, and algebra equations.
• Notice how numbers can break apart to make a calculation easier.
• Number patterns morph into algebra rules.
• Adapt math situations to make the structure clear. (For example, by adding new lines to a geometry diagram.)
• Step back from a situation to see it from a new perspective.
• Try to find simpler patterns within complex equations or diagrams.
• Not all patterns continue forever. Test your patterns. Can you trust them?

Say What You Mean

Continuing my project of rewriting the Standards for Mathematical Practice into student-friendly language.

Here’s my version of SMP6…

Math Tip #6: Say What You Mean.

• Words can be tricky, so watch your language.
• Label drawings and graphs to make them clear.
• If you use a variable, tell what it means.
• Care about definitions and units.
• Pay attention to rules (like the order of operations).
• Use symbols properly (like the equal sign).
• Understand precision. Never copy down all the digits on a calculator.

As I’ve mentioned before, I decided to try my hand at rewriting the Standards for Mathematical Practice into student-friendly language.

Here’s my version of SMP5…

Math Tip #5: Master Your Tools.

• Collect problem-solving tools.
• Practice until you can use them with confidence.
• Classic math tools: pencil and paper, ruler, protractor, compass.
• Modern tools: calculator, spreadsheet, computer software, online resources.
• Physical items: dice, counters, special math manipulatives.
• Tools for organizing data: graphs, charts, lists, diagrams.
• Your most important weapon is your own mind. Be eager to explore ideas that deepen your understanding of math concepts.