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Year 9

Checking understanding of similarity

I can enlarge a shape and can state what changes and what is invariant.

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New
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Year 9

Checking understanding of similarity

I can enlarge a shape and can state what changes and what is invariant.

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Share activities with pupils
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Lesson details

Key learning points

  1. An enlargement means a change in size.
  2. The lengths of the lines may change when enlarged.
  3. The angles inside an object do not change when enlarged.
  4. When an object is enlarged, the image is similar.

Keywords

  • Object - The object is the starting figure before a transformation has been applied.

  • Image - The image is the resulting figure after a transformation has been applied.

  • Similar - Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.

  • Scale factor - Scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.

  • Invariant - A property of a shape is invariant if that property has not changed after the shape is transformed.

Common misconception

When a pair of similar shapes are not in the same orientation, pupils may select an incorrect pair of lengths to calculate the scale factor.

Encourage pupils to take a systematic approach to locating pairs of corresponding lengths by looking for the longest edge in each shape, then the second longest, third longest, etc.

Computer software could be used to demonstrate changing the size of photographs. Look at examples what happens when the are stretched out of proportion and when it is enlarged while maintaining their proportions. If pupils have access to computers, they could try this themselves.
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).

Lesson video

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Starter quiz

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6 Questions

Q1.
Two shapes are if the only difference between them is their size. Their side lengths are in the same proportions.
Correct Answer: similar
Q2.
The __________ is the multiplier between similar shapes that describes how large one shape is compared to the other.
centre of enlargement
line of reflection
Correct answer: scale factor
vector
Q3.
Which rectangle is a correct enlargement of of rectangle R?
An image in a quiz
A
Correct answer: B
C
Q4.
Triangle A has been enlarged by a scale factor of 2 to get triangle B. Match each unknown length from triangle B with its size.
An image in a quiz
Correct Answer:$$a\text{ }$$ cm,6 cm

6 cm

Correct Answer:$$b\text{ }$$ cm,8 cm

8 cm

Correct Answer:$$c\text{ }$$ cm,10 cm

10 cm

Q5.
A square has length 8 cm. It is enlarged by a scale factor of $$1\over{2}$$. The side length of its image is cm.
Correct Answer: 4, four
Q6.
Each angle in an equilateral triangle is 60°. If an equilateral triangle is enlarged by a scale factor of 2, each of its angles will be °.
Correct Answer: 60, sixty

Exit quiz

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6 Questions

Q1.
A property of a shape is if that property has not changed after the shape is transformed.
Correct Answer: invariant
Q2.
A shape is being enlarged by a scale factor of 4. One vertex is 3 cm from the centre of enlargement. Its corresponding vertex on the image will be cm from the centre of enlargement.
An image in a quiz
Correct Answer: 12, twelve
Q3.
Sofia is enlarging the shape by a scale factor of 2. Which vertex has Sofia plotted incorrectly?
An image in a quiz
A
Correct answer: B
C
Q4.
A parallelogram is enlarged by a scale factor of 3. Which of the following measurements will remain invariant?
Correct answer: The angles.
The length of its base.
The length of its height.
The length of its slope.
Q5.
The two triangles are similar. The value of $$x$$ is .
An image in a quiz
Correct Answer: 18, eighteen, 18 cm, 18cm
Q6.
A triangle has a base of 6 m and height of 2 m. A similar triangle, in the same orientation, has a base of 15 feet. Its height is feet.
Correct Answer: 5, five, 5 feet, five feet