New! Your Student Can Be a Math Maker

Posted on by Denise Gaskins

When children create their own math, they build a deep understanding of mathematical concepts and relationships.

And it’s fun!

So take a break from your normal math program to play with creative math. Students can:

Check Out the Gallery

We have a few entries already in the Student Math Makers Gallery.

Click Here To Visit the Gallery

Join the Student Math Makers

We’d love to add your students’ math to our collection and share it with viewers all around the world!

To submit a math creation, download a Math Makers Invitation and Submission Form below:

 
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This blog is reader-supported.

If you’d like to help fund the blog on an on-going basis, then please head to my Patreon page.

If you liked this post, and want to show your one-time appreciation, the place to do that is PayPal: paypal.me/DeniseGaskinsMath. If you go that route, please include your email address in the notes section, so I can say thank you.

Which I am going to say right now. Thank you!

“New! Your Student Can Be a Math Maker” copyright © 2021 by Denise Gaskins. “Creating Math Puzzles by Sian Zelbo, the author of Camp Logic, via NaturalMath.com.

Math Puzzle from the Ancient Kingdom of Cats

Posted on by Denise Gaskins

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.

 
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This blog is reader-supported.

If you’d like to help fund the blog on an on-going basis, then please head to my Patreon page.

If you liked this post, and want to show your one-time appreciation, the place to do that is PayPal: paypal.me/DeniseGaskinsMath. If you go that route, please include your email address in the notes section, so I can say thank you.

Which I am going to say right now. Thank you!

“Math Puzzle from the Ancient Kingdom of Cats” copyright © 2021by Denise Gaskins. Image at the top of the post copyright © Denise Gaskins.

Math Journals: Save the Cat!

Posted on by Denise Gaskins

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!

Math Journals and Creative Reasoning

Posted on by Denise Gaskins

Learning math requires more than mastering number facts and memorizing rules. At its heart, math is a way of thinking.

So more than anything else, we need to teach our kids to think mathematically. To make sense of math concepts and persevere in figuring things out. To notice the numbers, shapes, and patterns all around. To wonder about big ideas.

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.

Get started with creative math journaling today. Visit the Make 100 Math Rebels Kickstarter page to download the free “How To Be a Math Rebel” sampler pictured above, which contains one of my all-time favorite math prompts.

Make 100 Math Rebels

It doesn’t matter whether your students are homeschooled or in a classroom, distance learning or in person. Everyone can enjoy the experience of playing around with math.

Puzzle from the free Math Rebel Sampler.

Continue reading Math Journals and Creative Reasoning

A New Resource for Playful Math

Posted on by Denise Gaskins

Check out the Make 100 Math Rebels Kickstarter project, which just might transform your child’s experience of math.

What Is a Math Rebel?

Math rebels believe in Truth. We refuse to accept something just because the teacher or textbook says it. We want to see the connections between math concepts and to understand why things work.

Math rebels care about Justice. We resist society’s push for speed and conformity. We reject the cultural narrative that math has only One Right Answer.

Math rebels celebrate Creative Reasoning. We delight in finding new ways to look at math topics. We want to think deeply about ideas, and we are confident in our ability to figure things out.

Launch your family’s math rebellion today with my free printable PDF booklet, “How To Be a Math Rebel,” available only on the Make 100 Math Rebels Kickstarter page.

Here’s the link again:

Make 100 Math Rebels on Kickstarter

Math Journals for Kids and Adults

Posted on by Denise Gaskins

Journaling is a fantastic way to learn and remember any topic — including math. That’s why I created my dot grid journals for kids and adults.

But I just discovered that my printer hates journals and blank books. They refuse to publish them any more.

How frustrating!

So from now on, you can only get my math journals from Amazon. The largest-river-in-the-world store doesn’t mind dot grid pages (so far).

Silver Lining: Because the books aren’t available to regular bookstores, I don’t have to allow for the traditional bookstore discount. Which means I can cut the prices. By a LOT — the new prices are 30% off the original cost of the books!

Continue reading Math Journals for Kids and Adults

Journaling Pages

Posted on by Denise Gaskins

This afternoon, I’ve been working on the printable pdf math activity booklets I’ll be sending out as stretch goals to the backers of my Math You Can Play Kickstarter campaign.

Some of the booklets include dot grid pages for student journaling.

I love dot grid pages for writing because I can start a line anywhere on the page, and the dots help me keep things in line. (They’re also great for doodling.)

As students wrestle their thoughts into shape and create explanations, they do the same sort of work that mathematicians do every day. It’s difficult for children (or anyone) to pin down a thought and put it into words. But it’s great practice for life.

Journaling is a great practice for adult learners, too — and don’t we all want to be lifelong learners?

So I thought I’d share the journaling pages with you all, in case you’d like to get your children writing about math. There are three styles, ranging from plain to ornate parchment. Enjoy!

Download the Journaling Pages

UPDATE: The Kickstarter deals have ended, but my playful math books are still available through your favorite online store or by special order at your local bookshop. (Except for the Prealgebra & Geometry Games book, scheduled for publication in early 2021. Sign up for my email list to get the latest news.)

Math Journals for Elementary and Middle School

Posted on by Denise Gaskins

This fall, my homeschool co-op math class will play with math journaling.

But my earlier dot-grid notebooks were designed for adults. Too thick, too many pages. And the half-cm dot grid made lines too narrow for young writers.

So I created a new series of paperback dot-grid journals for my elementary and middle school students.

I hope you enjoy them, too!

Click here for more information

Math Journaling Prompts

So, what can your kids do with a math journal?

Here are a few ideas: 

I’m sure we’ll use several of these activities in my homeschool co-op math class this fall.

Noticing and Wondering

Learning math requires more than mastering number facts and memorizing rules. At its heart, math is a way of thinking.

So more than anything else, we need to teach our kids to think mathematically — to make sense of math problems and persevere in figuring them out.

Help your children learn to see with mathematical eyes, noticing and wondering about math problems.

Whenever your children need to learn a new idea in math, or whenever they get stuck on a tough homework problem, that’s a good time to step back and make sense of the math.

Kids can write their noticings and wonderings in the math journal. Or you can act as the scribe, writing down (without comment) everything child says.

For more tips on teaching students to brainstorm about math, check out these online resources from The Math Forum:

Problem-solving is a habit of mind that you and your children can learn and grow in. Help your kids practice slowing down and taking the time to fully understand a problem situation.

Puzzles Are Math Experiments

Almost anything your child notices or wonders can lead to a math experiment.

For example, one day my daughter played an online math game…

a math experiment
Click the image to read about my daughter’s math experiment.

A math journal can be like a science lab book. Not the pre-digested, fill-in-the-blank lab books that some curricula provide. But the real lab books that scientists write to keep track of their data, and what they’ve tried so far, and what went wrong, and what finally worked.

Here are a few open-ended math experiments you might try:

Explore Shapes
  • Pick out a 3×3 set of dots. How many different shapes can you make by connecting those dots? Which shapes have symmetry? Which ones do you like the best?
  • What if you make shapes on isometric grid paper? How many different ways can you connect those dots?
  • Limit your investigation to a specific type of shape. How many different triangles can you make on a 3×3 set of dots? How many different quadrilaterals? What if you used a bigger set of dots?
Explore Angles

  • On your grid paper, let one dot “hold hands” with two others. How many different angles can you make? Can you figure out their degree without measuring?
  • Are there any angles you can’t make on your dot grid? If your paper extended forever, would there be any angles you couldn’t make?
  • Does it make a difference whether you try the angle experiments on square or isometric grid paper?
Explore Squares
  • How many different squares can you draw on your grid paper? (Don’t forget the squares that sit on a slant!) How can you be sure that they are perfectly square?
  • Number the rows and columns of dots. Can you find a pattern in the corner positions for your squares? If someone drew a secret square, what’s the minimum information you would need to duplicate it?
  • Does it make a difference whether you try the square experiments on square or isometric grid paper?

Or Try Some Math Doodles

Create math art. Check out my math doodling collection on Pinterest and my Dot Grid Doodling blog post. Can you draw an impossible shape?

How Would YOU Use a Math Journal?

I’d love to hear your favorite math explorations or journaling tips!

Please share in the comments section below.

 
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P.S.: Do you have a blog? If you’d like to feature a math journal review and giveaway, I’ll provide the prize. Send a message through my contact form or leave a comment below, and we’ll work out the details.

This blog is reader-supported.

If you’d like to help fund the blog on an on-going basis, then please head to my Patreon page.

If you liked this post, and want to show your one-time appreciation, the place to do that is PayPal: paypal.me/DeniseGaskinsMath. If you go that route, please include your email address in the notes section, so I can say thank you.

Which I am going to say right now. Thank you!

“Math Journals for Elementary and Middle School” copyright © 2018 by Denise Gaskins. Photos of children © original artists / Pixabay.

Math Humor and Copywork

Posted on by Denise Gaskins

Homeschool Memories…

The more years we spent homeschooling, the more I appreciated Charlotte Mason’s work and tried to incorporate her ideas into our laid-back, eclectic, not-quite-unschooling program.

We never fit the typical Charlotte Mason mold. Mosquitos and natural laziness limited our nature walks, and our version of narration was much too informal.

But those are just techniques, methods.

What really interests me in Mason’s writing is the philosophy behind the methods. Two points resonated: That we must respect our children as persons in their own right. And that we must provide a generous, wide-ranging feast to their minds.

Striving to live out those principles had a profound influence on our day-to-day homeschooling.

Continue reading Math Humor and Copywork

How To Break In Your New Math Journal

Posted on by Denise Gaskins

I love my new paperback math journal series. The books are sturdy, inexpensive, and fit nicely in my purse.

But as with any paperback book, these have one problem. How do I use them without cracking the spine?

When we exercise, we need to warm up our bodies with a bit of stretching to prevent injury. In the same way, we need to warm up a new book to protect it. The process is called “breaking it in.”

It only takes a few minutes to break in a paperback book:

Step by Step

Never force the book but help it limber up gradually, and it will serve you well.

Because my journals are working books, I take the breaking-in process a bit further than shown in the video:

(1) Set the book on its back and follow the process above. Press down each cover, but not completely flat — let it bend at the fold line, about 1 cm from the actual spine. Then press a couple pages at a time, alternating front and back, down flat on each cover.

(2) Flip through the pages of the book forward and backward to limber them up.

(3) Repeat the steps of the video. This time, gently lean the main part of the book away from the part you are pressing down. Aim for a 130–140 degree angle.

(4) Flip through the pages again. For paperbacks, you can even roll the whole book back and forth a bit — gently curving the cover and pages almost as if you’re trying to fold the book in half — to encourage flexibility.

(5) Optional: Repeat the breaking-in process one more time. This time, fold each section back as close to 180 degrees as it will go.

And you’re done!

The pages will still curve in at the fold line, where they connect to the spine of the book. You want that because it makes the book strong. But now they’ll also open up to provide a nice, wide area for writing or math doodling.