## Math Game Monday: Fraction Catch

“Fraction Catch” is free on this website for one week only. It’s an excerpt from Multiplication & Fractions: Math Games for Tough Topics, available as an ebook at my bookstore (Thank you for cutting out the middleman!) and in ebook or paperback through many online retailers. Read more about my playful math books here.

Many parents remember struggling to learn math. We hope to provide a better experience for our children.

And one of the best ways for children to enjoy learning is through hands-on play.

This game builds number sense with fractions on an invisible number line.

## Fraction Catch

Math Concepts: proper and improper fractions, comparing fractions, equivalent fractions, number line, numerical order.

Players: any number.

Equipment: one set of double-six or double-nine dominoes.

## Thinking Thursday: Pixel Graphics

“Prompt #65 Pixel Graphics” is an excerpt from 312 Things To Do with a Math Journal, available as an ebook at my bookstore (Thank you for cutting out the middleman!) and in ebook or paperback through many online retailers. 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.

## Math Game Monday: Chomp

“Chomp” is free on this website for one week only. It’s an excerpt from 312 Things To Do with a Math Journal, available as an ebook at my bookstore (Thank you for cutting out the middleman!) and in ebook or paperback through many online retailers. Read more about my playful math books here.

Many parents remember struggling to learn math. We hope to provide a better experience for our children.

And one of the best ways for children to enjoy learning is through hands-on play.

This game pushes students to think ahead and deduce their opponent’s strategy.

## Chomp

Math Concepts: logic and strategic thinking.

Players: two players.

Equipment: pencil and paper.

## Celebrating Math with Pi Day

Are your students doing anything special for Pi Day?

Back when we were homeschooling, my kids and I always felt stir-crazy after two months with no significant break. We needed a day off — and what better way could we spend it than to play math all afternoon?

I love any excuse to celebrate math!

Pi Day is March 14. If you write dates in the month/date format, then 3/14 at 1:59 is about as close as the calendar can get to 3.14159etc.

(Otherwise, you can celebrate Pi Approximation Day on July 22, or 22/7.)

Unfortunately, most of the activities on teacher blogs and Pinterest focus on the pi/pie wordplay or on memorizing the digits. With a bit of digging, however, I found a few puzzles that let us sink our metaphorical teeth into real mathematical meat.

### What’s the Big Deal? Why Pi?

In math, symmetry is beautiful, and the most completely symmetric object in the (Euclidean) mathematical plane is the circle. No matter how you turn it, expand it, or shrink it, the circle remains essentially the same.

Every circle you can imagine is the exact image of every other circle there is.

This is not true of other shapes. A rectangle may be short or tall. An ellipse may be fat or slim. A triangle may be squat, or stand upright, or lean off at a drunken angle. But circles are all the same, except for magnification. A circle three inches across is a perfect, point-for-point copy of a circle three miles across, or three millimeters.

What makes a circle so special and beautiful? Any child will tell you, what makes a circle is its roundness. Perfectly smooth and plump, but not too fat.

The definition of a circle is “all the points at a certain distance from the center.” Can you see why this definition forces absolute symmetry, with no pointy sides or bumped-out curves?

One way to express that perfect roundness in numbers is to compare it to the distance across. How many times would you have to walk back and forth across the middle of the circle to make the same distance as one trip around?

The ratio is the same for every circle, no matter which direction you walk.

That’s pi!

### Puzzles with Pi

For all ages:

Sarah Carter created this fun variation on the classic Four 4s puzzle for Pi Day:

Using only the digits 3, 1, 4 once in each calculation, how many numbers can you make?

You can use any math you know: add, subtract, multiply, square roots, factorials, etc. You can concatenate the digits, putting them together to make a two-digit or three-digit number.

For older students:

1. Imagine the Earth as a perfect sphere with a long rope tightly wrapped around the equator. Then increase the length of the rope by 10 feet, and magically lift it off the Earth to float above the equator. Will an ant be able to squeeze under the rope without touching it? What about a cat? A person?

2. If you ride a bicycle over a puddle of water, the wheels will leave wet marks on the road. Obviously, each wheel leaves a periodic pattern. How the two patterns are related? Do they overlap? Does their relative position depend on the length of the puddle? The bicycle? The size of the wheels?

3. Draw a semicircle. Along its diameter draw smaller semicircles (not necessarily the same size) that touch each other. Because there are no spaces in between, the sum of the diameters of the small semicircles must equal the diameter of the large one. What about their perimeter, the sum of their arc lengths?

4. Choose any smallish number N. How can you cut a circular shape into N parts of equal area with lines of equal lengths, using only a straight-edge and compass? Hint: The lines don’t have to be straight.

[Solutions at Alexander Bogomolny’s Pi Page. Scroll down to “Extras.”]

It can be of no practical use to know that Pi is irrational, but if we can know, it surely would be intolerable not to know.

— Edward Titchmarsh

Here are a few pi-related links you may find interesting:

Or for pure silliness:

Have fun playing math with your kids!

## Thinking Thursday: Colored Paper and Metal Disks

“Prompt #26 Colored Paper and Metal Disks” is an excerpt from Math Journal Task Cards Mega-Bundle: 312 Ways To Play with Math, 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.

## Math Game Monday: Hide-and-Seek Zoo

“Hide-and-Seek Zoo” is free on this website for one week only. It’s an excerpt from 70+ Things To Do with a Hundred Chart, available as an ebook at my bookstore (Thank you for cutting out the middleman!) and in ebook or paperback through many online retailers. Read more about my playful math books here.

Many parents remember struggling to learn math. We hope to provide a better experience for our children.

And one of the best ways for children to enjoy learning is through hands-on play.

This game builds familiarity with the patterns in 2-digit numbers as players search for the secret squares on a hundred chart.

## Hide-and-Seek Zoo

Math Concepts: hundred chart, strategy.

Players: two players.

Equipment: printed gameboard, pencils or felt-tip markers.

## Thinking Thursday: Two Truths and a Lie

“Prompt #48 Two Truths and a Lie” is an excerpt from 312 Things To Do with a Math Journal, available as an ebook at my bookstore (Thank you for cutting out the middleman!) and in ebook or paperback through many online retailers. 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.