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Level One > Geometry and Measurement

# The Folding Problem

Achievement Objectives:

Achievement Objective: Sort objects by their appearance.

Specific Learning Outcomes:

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).

Description of mathematics:

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.

Required Resource Materials:
Paper squares (memo cube paper works well)
Copymaster of the problem (English)
Copymaster of the problem (Māori)
Activity:

### Problem

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

### Teaching sequence

1. 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?
2. Draw the designs on the board or give the students the Copymaster of the problem.
3. 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?
4. 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.

#### 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

AttachmentSize
The Folding Paper Maori.pdf45.34 KB
The Folding Problem.pdf36.8 KB

## Sandwiches

Divide a region into two equal parts through folding or cutting

Demonstrate that the two parts are equal and describe these parts as halves

## Flip's Flag

apply the angle properties of squares, rectangles and triangles

use fractions to express the relationships between the areas of rectangles, squares and triangles

devise and use problem solving strategies to explore situations mathematically (be systematic).

## Round Robins

These are level 3 number and statistics problems and level 5 number problems from the Figure It Out series.