### Anna Grossnickle HinesHomeGuide

Quilts in the Classroom

Let's Do Math to PIECES!
using the book, PIECES: A YEAR IN POEMS AND QUILTS

Designing With Half-square Triangles

Let's play with lines!

• Take a square. Draw a line to divide it half diagonally.
• What happens?
• Quilters call these triangles half-square triangles.  They use them a lot.
• In PIECES three quilts use half-square triangles.
• Can you find them?
• Two use just a few half-square triangles, but one uses lots of them.
• It was fun to design with half-square triangles.
• There are so many possibilities! Want to try a few?
• Take two squares. Draw the lines to divide them in half diagonally.
• How many different ways can you put them together?
• Take four squares and divide them in half diagonally.
•  Now how many ways can you put them together?
• Try this with 16 squares.
• How many different designs can you make?
• Try 25 squares.
• What happens?  Do you run into any difficulties or limitations?
• Why?
• Try 36 squares.
• Now what happens?
• Isn't that interesting?
• Do you know about symmetry?
• When something is symmetrical, you can put a line through the center and both halves will be just the same.
• Actually the two halves will be exact opposites, or mirror images of one another.
• Can you think of anything else that is symmetrical?
• Nature uses lots of symmetry. Keep an eye open for examples.
• Can you make a symmetrical design with 8 half square triangle blocks?
• Can you make a square design?
• Can you make a symmetrical design with 9 half-square triangle blocks?
• Can you make a square design?
• What's the next number of half-square triangle blocks you need to make a symmetrical design?
• What's the next number you need to make a square design?
• Are designs using half-square triangles always symmetrical?
• Are symmetrical designs always square?
• What does it take to make a design that is both square and symmetrical?
• What happens if you use plain squares instead of triangle-squares?
• When a design is not symmetrical we call it asymmetrical.
• Can you make an asymmetrical design with 9 half-square triangle blocks?
• Can you do it with 4?  ....16?  ....36?
Want to try some more symmetrical and asymmetrical designs?  Let's add color!