Tricky Triangles

Tricky Triangles

May 21, 2020

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?




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.

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About the Author

Laura Overdeck

Laura Overdeck

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.

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