The word “puzzle” can mean a lot of things: peg puzzles, number games, and jigsaws with squiggly pieces. But our favorite at Bedtime Math is the “tangram.” This ancient Chinese puzzle uses 7 shapes that you move around to match a picture. The picture gives no clues about where the shapes go — you have to figure that out! Here we’ve made this turtle by lining up the shapes as shown. The 7 shapes fit with each other in a special way: the medium triangle is the same size as 2 tiny triangles put together, and a big triangle is the same as 2 medium ones. The square and parallelogram also each equal 2 tiny triangles. Check out this page to print and cut out your own tangrams, and to match some puzzles yourself!

*Wee ones:* Point to all the triangles in the picture. What colors are they?

*Little kids:* If 2 tiny triangles make a medium triangle, and 2 medium triangles make a big triangle, how many tiny triangles do you need to make a big triangle? *Bonus:* The 2 tiny triangles against the green square make a shape called a “trapezoid.” Imagine that shape is all one color. How many sides does it have?

*Big kids:* How many tiny triangles can you fit in the whole big square that holds all the shapes? (*Hint: *the whole big square can fit 4 big triangles.) *Bonus:* If a giant tangram square covers 128 square inches, how much area does each tiny triangle cover? Can you figure out a handy way to divide by that number?

Answers:

*Wee ones:* Red, purple, pink, blue, and orange.

*Little kids:* 4 tiny triangles, since it takes 2 pairs. *Bonus:* 4 sides. It’s a “quadrilateral” just like squares and rectangles!

*Big kids:* 16 tiny triangles. *Bonus:* 8 square inches. To divide by 16, you’re just cutting in half 4 times in a row, since 16 is 2 x 2 x 2 x 2.

Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking before she could walk, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.