The folding problem
This problem solving activity has a geometry focus.
Can you fold your paper squares to make them look like each of these designs?
- Create squares, triangles and oblongs by folding paper.
- Identify and describe shapes.
- Devise and use problem solving strategies to explore situations mathematically (guess and check).
Although to an adult, this paper-folding problem is simple, to young students the approach to take to make each design is not so obvious. As the students solve this problem they are learning about shapes. It provides an opportunity for students to use their visual and spatial skills. This activity can also start forming understandings about fractional parts of regions.
- Copymaster of the problem (English)
- Copymaster of the problem (Māori)
- Paper squares (memo cube paper works well)
The Problem
Can you fold your paper squares to make them look like each of these designs?
Teaching Sequence
- Introduce the problem taking a piece of paper and folding it in half lengthways. Ask the students 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? - Draw the designs on the board or give the students the Copymaster of the problem.
- After the students 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? - If your class is ready, present more complex patterns for them to work out. Or ask the students to make their own folding problems to share with the class.
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?
The solutions to these problems is shown below.
Solution
Designs 1 and 3 involve a single fold. Designs 2 and 4 require 2 folds.