Explain how to make different shapes with the same area | Maths

Starter quiz

Which of the following shapes is rectilinear?

a

b

c ✓

d
This shape has an area of ______ square units.

'8' ✓
This shape has an area of ______ square units. Count squares efficiently.

'20' ✓
Which of the following methods would help to work out the area of this rectilinear shape? Select all that apply.

Count all the coloured squares. ✓

Count the columns: 5 + 3 + 3 + 5 ✓

Count the rows: 4 + 4 + 2 + 2 + 4 ✓

Count 5 four times

Subtract 4 from 20 ✓
What is the area of this shape in square units?

9 ✓

13

15
What is the area of this shape in square units? ______

'12' ✓

Exit quiz

Complete the definition: Rectilinear shapes are 2D polygons composed of one or more __________.

lines

rectangles ✓

shapes

square units

squares
Look at Shape A and Shape B. Which of the following statements is true?

a has a greater area than b.

b has a greater area than a.

a and b have the same area. ✓

a and b have unequal areas.
How can these shapes be made equal? Select all options that apply.

Remove a square unit from Shape A.

Add a square unit to Shape B. ✓

Remove a square unit from Shape A and from Shape C. ✓

Add two square units to Shape B.
Tick all of the statements that are true about the two shapes shown in the image.

Each of the two shapes has been made by combining two pentominoes. ✓

The two shapes have the same area as each other. ✓

The two shapes have a different area to each other.

Each of the shapes has an area of ten square units. ✓

If the two pentominoes in each shape were re-positioned, the area would change.
Tick all of the statements that are true.

The two shapes have an equal area.

The two shapes have different areas. ✓

If two more half-squares were added to b, the two shapes would be equal. ✓

If a square unit was added to b, the two shapes would be equal. ✓

If two square units were removed from a, the two shapes would be equal.
Which of these combinations would combine to create a non-rectilinear shape with an area of 6 square units? Select all that apply.

4 full squares, 2 half-squares.

4 full squares, 4 half-squares. ✓

5 full squares, 1 half-square.

5 full squares, 2 half-squares. ✓

6 full squares.

Worksheet

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Presentation

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Video

Lesson Details

Key learning points

If you have the same number of squares, the area will be the same however they are arranged.
There must be no gaps or overlaps between the shapes for the area to be the same.

Common misconception

Two shapes cannot have the same area if they look different.

Use square sticky notes. Pupils can then move the shapes around to prove that two shapes can have the same area but look different.

Keywords

Area - The measurement of a flat surface. It measures a 2D space.
Rectilinear - Rectilnear shapes are 2D polygons composed of one or more rectangles.