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.]
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.

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

Math Puzzle from the Ancient Kingdom of Cats

It may look like Cimorene has lain down on the job, but don’t be fooled! She’s hard at work, creating a math investigation for your students to explore.

Cats know how important it can be for students to experiment with math and try new things. Playing with ideas is how kittens (and humans!) learn.

Cimorene wants you to know that the Make 100 Math Rebels Kickstarter offers a great way for human children to learn math through play. She encourages you to go watch the video and read all about the project.

Too often, school math can seem stiff and rigid. To children, it can feel like “Do what I say, whether it makes sense or not.” But cats know that kids are like kittens — they can make sense of ideas just fine if we give them time to play around.

So Cimorene says you should download the free sample journaling pages from the Math Rebels Kickstarter page. The beautiful parchment design makes doing math an adventure.


[The free download will always be there, even after the Kickstarter project ends.]
Make 100 Math Rebels Kickstarter

Cimorene’s Puzzle Challenge

Cimorene’s math puzzle is a classic geometry problem from the ancient Kingdom of Cats: Squaring the Circle.

Draw a circle on your journal page. Can you draw a square (or rectangle) that has the same area?

How would you even begin such a task?

Notice Cimorene’s hint in the photo above: Try drawing the square that just touches the edges of your circle. (We call those just-touching lines “tangents” to the circle.)

  • What do you notice? Do the square and the circle have the same area? How close are they?

The tangent square sets an upper limit on the area of the circle. You can see that any square that exactly matches the circle would have to be smaller than the tangent square.

  • Can you find a square that sets a lower limit on the area of the circle? That is, a square that must have less area than the circle?
  • What’s the biggest square you can draw inside your circle? Can you find a square that has all four corners on the circle?

We call that biggest-inside square “inscribed” in the circle. Any polygon whose corners all sit on the circle is an inscribed polygon.

  • Play around with circles and squares. How close can you get to matching their size?

Further Exploration

After you have explored for awhile on your own, Cimorene has one more twist in her puzzle.

In the ancient Kingdom of Cats, the wise ones estimated the area of a circle this way:

Divide the width of the circle in thirds, and then in thirds again. (That is, cut the diameter into nine parts.) Draw a square with sides measured by eight such parts.

You can try this on your journaling page by drawing a circle that is nine squares wide. Then draw a square overlapping it, with sides that are eight squares in length.

  • How closely do the areas match?

Playing with Pi

Here’s a surprise: Cimorene’s puzzle isn’t really about squares, but about calculus.

The problem of Squaring the Circle is really a much bigger question: Finding the area of a square, rectangle, or other polygon is relatively easy, but how can we discover the area of a curved shape?

For a circle, the area is related to the number pi, which is the number of times you would have to walk across the circle to equal the distance of one time walking around it.

graphic by John Reid (cc by-sa 3.0)

graphic by John Reid (cc by-sa 3.0)
So the problem of Squaring the Circle is really the same as asking, “What is the value of pi?”

  • Can you figure out what approximate value for pi matches the 8/9 square used in the ancient Kingdom of Cats?

If you’d like to learn more about pi, get ready for a celebration: Pi Day is coming soon! Every year, millions of children celebrate math on March 14th, because if you write the date as 3/14, it’s the same as the first three digits of pi.

Find out more about playing with pi in my Pi Day Round-Up post.

You may also enjoy:

Share Your Stories

Cimorene would love to hear about your children’s experiences playing with math! Please share your story in the comments below.

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…

Continue reading Math Journals: Save the Cat!

Can You Do the Math Salute?

Did your device hide the video? Find it on YouTube here.

How Is This Math?

The idea that math is only about numbers, calculations, and textbook exercises is one of the greatest lies we learn in school. Of course, nobody ever comes straight out and actually says that. But the whole system teaches us every day what counts for math and what doesn’t.

James Tanton’s math salute is a physical puzzle.

How in the world did he do that?

Physical puzzles don’t fit into our cultural understanding of math. But the process of figuring out the puzzle is the same problem-solving process we use to figure out other puzzles — including the puzzles we call math.

In fact, real mathematics is all about figuring out puzzles without a teacher showing you what to do. Problem-solving is a universally useful skill.

As master teacher W. W. Sawyer said:

“Everyone knows that it is easy to do a puzzle if someone has told you the answer. That is simply a test of memory. You can claim to be a mathematician only if you can solve puzzles that you have never studied before. That is the test of reasoning.”

—W. W. Sawyer, Mathematician’s Delight

So tackle the puzzle of the math salute. Show it to your kids. (And don’t be surprised if they figure it out before you do!)

[THE FINE PRINT: I am an Amazon affiliate. If you follow the link and buy something, I’ll earn a small commission (at no cost to you). But this book is a well-known classic, so you should be able to order it through your local library.]

New Printable Puzzle Books: Diffy Inception

The best way to practice math is to play with it—to use the patterns and connections between math concepts in your pursuit of something fun or beautiful.

Diffy Inception puzzles have their own symmetric beauty, but mostly they are just plain fun. Students can practice subtraction and look for patterns in the difference layers.

I just published four new activity books to our online store:

Notes to the teacher include puzzle instructions, game variations, journaling prompts, and more. Plus answers for all puzzles.

Available with 8 1/2 by 11 (letter size) or A4 pages.

Click for a Preview

My publishing company runs this online store, so you can find all my playful math books there — including an exclusive pre-publication ebook edition of my newest title, Prealgebra & Geometry: Math Games for Middle School. Click here to browse the Tabletop Academy Press store.

The Value of Puzzles

I love puzzles. Don’t you?

Here are several examples of river-crossing puzzles you and your kids can try. They date back at least to the time of Alcuin, the famous scholar from the court of Charlemagne.

I wish someone would write a whole math curriculum devoted entirely to puzzles.

W.W. Sawyer on the Value of Puzzles

Master teacher W.W. Sawyer didn’t write a curriculum, but he often used puzzles in the classroom.

“It is quite possible to use simultaneous equations as an introduction to algebra. Within a single lesson, pupils who previously did not know what x meant can come not merely to see what simultaneous equtions are, but to have some competence in solving them.

“No rules need to be learnt; the work proceeds on a basis of common sense.

“The problems the pupils solve in such a first lesson will not be of any practical value. They will be in the nature of puzzles.

“Fortunately, nature has so arranged things that until the age of twelve years or so, children are more interested in puzzles than in realistic problems.”

—W. W. Sawyer, Vision in Elementary Mathematics

Then he gives this example:

“A man has two sons. The sons are twins; they are the same height. If we add the man’s height to the height of one son, we get 10 feet. The total height of the man and the two sons is 14 feet. What are the heights of the man and his sons?”

Try This at Home

Not only can children solve puzzles like this, but even better — they can make up story puzzles of their own. You could spend a whole week or more making up silly height puzzles for each other to solve. By the time you were done, your kids would have a great introduction to algebra!

Maybe I never grew up. Because I still prefer puzzles over “real world” math problems.

What are your favorite kinds of puzzles? Please share in the comments section.

CREDITS: “Boat puzzles” comic from xkcd.com.
[THE FINE PRINT: I am an Amazon affiliate. If you follow the book link and buy something, I’ll earn a small commission (at no cost to you). But this book is a well-known classic, so you should be able to order it through your local library.]

More Dover Samples

“Without mathematics you can’t do anything! Everything around you is mathematics. Everything around you is numbers.”

—Anna Claybourne, I Can Be a Math Magician


Dover Publications sent out a new email today with fun coloring and craft samples. And several puzzles from I Can Be a Math Magician: Fun STEM Activities for Kids by Anna Claybourne.

Enjoy!

If you’d like to receive future Dover Sampler emails, you can sign up here.

THE FINE PRINT: I am an Amazon affiliate. If you follow the book link above and buy something, I’ll earn a small commission (at no cost to you).

Free Number Sense Resources from Steve Wyborney

If you teach children in the primary grades, you’ll enjoy this new series from the wonderful Steve Wyborney. Every day for the rest of the school year, Steve will post a new estimation or number sense resource for grades K–8 (or any age!) at his blog:

“This is my way of providing support and encouragement – as well as bringing math joy to your classroom… I’m going to stick with you all year long.”

—Steve Wyborney

Click to visit Steve’s blog

Free Sample: The Bogotá Puzzles

“Mathematics, besides being beautiful and useful, is fun. I hope [my book] brings mathematical joy to many.”

—Bernardo Recamán, The Bogotá Puzzles


Dover Publications occasionally posts free samples from some of their wonderful collection of books. This month’s sampler includes several puzzles from The Bogotá Puzzles by Bernardo Recamán.

Inspired by such illustrious collections as The Canterbury Puzzles, The Moscow Puzzles, and The Tokyo Puzzles. Colombian mathematician and professor Bernardo Recamán assembled these 80 brainteasers, word problems, sudoku-style challenges, and other math-based diversions while living and working in Bogotá.

Enjoy!

If you’d like to receive future Dover Sampler emails, you can sign up here.

THE FINE PRINT: I am an Amazon affiliate. If you follow the book link above and buy something, I’ll earn a small commission (at no cost to you).

Kenken is Mathematical Play

It’s back-to-school time here in the States. And that means it’s time for the Kenken Classroom Newsletter. Yay for math puzzles!

KenKen arithmetic puzzles build mental math skills, logical reasoning, persistence, and mathematical confidence.

Free via email every Friday during the school year.

What a great way to prepare your children for success in math!

Sign up anytime:

Click Here for KenKen Classroom Newsletter

Continue reading Kenken is Mathematical Play