Compose and decompose shapes

What you will learn

• Compose and decompose shapes

Models used: number sentences, stories, diagrams.

Before you start

• Recognise rectangles, squares, triangles, circles, half-circles and quarter-circles

Two triangles can make one rectangle

Can we fit two matching triangles together to make a rectangle?

1. Here is one triangle. The pale outline shows the rectangle we want to fill.

   The pieces must cover exactly the required region. Turning a piece changes its position, not its size.

2. Turn a matching triangle to fill the space. Its long edge meets the first triangle’s long edge.

3. Together the triangles cover the rectangle exactly. There is no gap or overlap.

   2 matching triangles → 1 rectangle

4. We can reverse this: cut the rectangle along that diagonal to get the two triangles back.

Worked example: A new example, together

How many equal quarter-circle pieces make a semicircle?

1. Follow the joining edges and check the region that the pieces cover together.

   Equal parts can be composed into a larger shape without gaps or overlap.

2. A quarter is one of four equal parts of a circle.

   How many equal quarter-circle pieces make a semicircle?

   2

3. A quarter is one of four equal parts of a circle.

4. A half-circle uses two of those parts.

5. 2 quarter-circle pieces make the requested shape.

6. Check the result against the question we started with.

   Two quarters are one half.

   We found 2. Equal parts can be composed into a larger shape without gaps or overlap.

Common mistakes to discuss

• Leaving gaps or overlaps. Shapes fit together only when they cover the space exactly, without overlapping.

Check your understanding

• Compose and decompose shapes
• explain a shape by composing or separating its parts
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.