Learning Math with Puzzles

Learning mathematics begins with puzzles. As stories are to history or science, puzzles are to math.

In ancient times, math began with puzzles like:

• How can we keep track of our herds, or predict the cycles of the moon, or figure out how much to pay for taxes?

• How can we draw perfect right angles, or make beautifully symmetric designs?

• What are the ratios of harp strings that create the most beautiful sounds?

Math puzzles touch every area of life. Puzzles inspire curiosity and solving them brings joy.

And we can enrich any homeschool math program with puzzles that invite children to think about mathematical concepts.

Even those monster topics that often bring homeschooling families to tears, such as fractions.

Fractions Example 1: A Puzzle Story

How can we split 3 cookies between 4 people? What is your share?

Assume these are bakery-style cookies, large enough to cut in pieces. I like to model them by handing out three index cards and a pair of scissors to each student.

One child might imagine cutting each cookie into 4 pieces, giving one piece to each person.

Another might cut all the cookies into halves, give each person a half, and then cut the remaining pieces into half-halves.

Do you get the same amount of cookie either way? How do you know?

Is one solution better than another? Why?

What if the cookies are all different flavors? Does that change the answer? Or what if one person is allergic to peanuts, and one of the cookies is peanut-butter? Then how could you share fairly?

What if the cookies were 3 different flavors (maybe call them Almond, Blueberry, Chocolate –– A, B, and C), and we cut each cookie into 4 pieces, but then we handed out the pieces at random? What different combinations of flavors might you get?

Notice how much richness we can find in what might have been a single line on a math worksheet: 3 ÷ 4 = ?

Can you make up your own puzzle about sharing cookies?

Fractions Example 2: Math Art

Math art can be a wonderful source of creative thinking puzzles. For example:

Draw a square. Color exactly one-half of it.

How many different ways can you think of to do this?

How can you be sure you’ve colored exactly one-half?

What is your favorite of the designs you made? Why?

Make a math quilt: Divide your paper into squares, and color each square with a different one-half pattern. (Or cut out your earlier designs and paste them on a colored paper background.)

Can you pose a coloring-pattern challenge of your own?

To Be Continued…

This series began with the post, Homeschooling: The Rhythm of a Math Lesson. Watch for the remaining two posts in this series:

• The Rhythm of Math Puzzles
• The Rhythm of Math Games