Problem
Can you fold your paper squares to make them look like each of these designs?






What is this problem about?
Although to an adult, this paper-folding problem is simple, to young children the approach to take to make each design is not so obvious. As the children solve this problem they are learning about shapes. It provides an opportunity for children to use their visual and spatial skills. This activity can also start forming understandings about fractional parts of regions.

Achievement Objectives
Geometry (Level 1)
- identify, and describe in their own language, two-dimensional shapes

Mathematical Processes
- devise and use problem solving strategies to explore situations mathematically (guess and check).

Resources
Paper squares (memo cube paper works well)
Blackline master of the problem

Specific learning outcomes
The children will be able to:
- create squares, triangles and oblongs by folding paper
- identify and describe shapes

1. Introduce the problem taking a piece of paper and folding it in half lengthways. Ask the children to predict what they will see when you open out the paper.
   What shapes can you see?
   Are they the same size? How do you know?
2. Draw the designs on the board or give the children the blackline master of the problem.
3. After the children have worked on their own for a while, stop them and discuss:
   Who was able to make folds to look like this design? Tell us how you did it?
   Which one was the hardest? Why?
   What kind of shapes do you notice in the papers that you have made?
4. If your class is ready, present more complex patterns for them to work out. Or ask the children to make their own folding problems to share with the class.

Solution
Designs 1 and 3 involve a single fold. Designs 2 and 4 require 2 folds.

Extension
Can you fold a square so that it shows 3 rectangles?
Can you fold a square so that it shows 3 triangles?
Can you fold a square so that it shows both triangles and rectangles