New
New
Year 5

# Explain how to make different shapes with the same area

I can create different shapes with the same area.

New
New
Year 5

# Explain how to make different shapes with the same area

I can create different shapes with the same area.

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## Lesson details

### Key learning points

1. If you have the same number of squares, the area will be the same however they are arranged.
2. 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.

Pupils who grasp the concept of non-rectilinear shapes which use triangles having the same area as others may be encouraged to consider more complex non-rectilinear shapes, such as those in Lesson 2.
Teacher tip

### Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Starter quiz

### 6 Questions

Q1.
Which of the following shapes is rectilinear?
a
b
d
Q2.
This shape has an area of square units.
Correct Answer: 8, eight , 8., Eight
Q3.
This shape has an area of square units. Count squares efficiently.
Correct Answer: 20, 20., twenty, Twenty
Q4.
Which of the following methods would help to work out the area of this rectilinear shape? Select all that apply.
Correct answer: Count all the coloured squares.
Correct answer: Count the columns: 5 + 3 + 3 + 5
Correct answer: Count the rows: 4 + 4 + 2 + 2 + 4
Count 5 four times
Correct answer: Subtract 4 from 20
Q5.
What is the area of this shape in square units?
13
15
Q6.
What is the area of this shape in square units?
Correct Answer: 12, 12., twelve, Twelve

## Exit quiz

### 6 Questions

Q1.
Complete the definition: Rectilinear shapes are 2D polygons composed of one or more __________.
lines
shapes
square units
squares
Q2.
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.
Correct answer: a and b have the same area.
a and b have unequal areas.
Q3.
How can these shapes be made equal? Select all options that apply.
Remove a square unit from Shape A.
Correct answer: Add a square unit to Shape B.
Correct answer: Remove a square unit from Shape A and from Shape C.
Add two square units to Shape B.
Q4.
Tick all of the statements that are true about the two shapes shown in the image.
Correct answer: Each of the two shapes has been made by combining two pentominoes.
Correct answer: The two shapes have the same area as each other.
The two shapes have a different area to each other.
Correct answer: 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.
Q5.
Tick all of the statements that are true.
The two shapes have an equal area.
Correct answer: The two shapes have different areas.
Correct answer: If two more half-squares were added to b, the two shapes would be equal.
Correct answer: 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.
Q6.
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.
Correct answer: 4 full squares, 4 half-squares.
5 full squares, 1 half-square.
Correct answer: 5 full squares, 2 half-squares.
6 full squares.