Skip to content
Oak National Academy
Oak National Academy
Teachers
Pupils
New
New
Year 7

Problem solving with transformations

I can use my knowledge of transformations to solve problems.

Download all resources
arrow-right
Share activities with pupils
arrow-right
New
New
Year 7

Problem solving with transformations

I can use my knowledge of transformations to solve problems.

Download all resources
arrow-right
Share activities with pupils
arrow-right
warning

These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.
View new resources
arrow-right

Lesson details

Key learning points

  1. By understanding what changes and what is invariant, you can determine whether a transformation has occurred.
  2. Sometimes you might need to persevere in order to find the right transformation.
  3. You may be able to check your deductions by carrying out the transformation.

Keywords

  • Transformation - A transformation is a process that may change the size, orientation or position of a shape.

  • 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.

Common misconception

When completing an inverse translation, students may believe they need to flip the vector.

Ask students to say in words how you would return to the starting point, to highlight the direction needed and then link to the vector.

This lessons draws on perimeter and area, coordinates and algebra, so you may need to support or add extra examples.
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

Skip lesson video

Loading...

Starter quiz

Download starter quiz

6 Questions

Q1.
The is the distance around a 2D shape.
Correct Answer: perimeter
Q2.
Match the inverse operations.
Correct Answer:$$+$$,$$-$$

$$-$$

Correct Answer:$$\times$$,$$\div$$

$$\div$$

Correct Answer:$$-$$,$$+$$

$$+$$

Correct Answer:$$\div$$,$$\times$$

$$\times$$

Q3.
Complete the descriptions below by matching the transformation with the detail needed to describe it fully.
Correct Answer:A rotation ,by $${90^{\circ}}$$ clockwise about (3,4)

by $${90^{\circ}}$$ clockwise about (3,4)

Correct Answer:A reflection,in the y-axis.

in the y-axis.

Correct Answer:A translation,by $${-1 \choose 5}$$

by $${-1 \choose 5}$$

Correct Answer:An enlargement,by scale factor 0.25 from (0, 0)

by scale factor 0.25 from (0, 0)

Q4.
What is the area of a triangle with a base length of 6 cm and perpendicular height of 8 cm?
48 cm$${^{2}}$$
Correct answer: 24 cm$${^{2}}$$
48 cm
24 cm
Q5.
Which transformation does this property table belong to?
An image in a quiz
translation
rotation
reflection
Correct answer: enlargement
Q6.
The point (3, 5) is reflected in the -axis to become (-3, 5).
Correct Answer: y

Exit quiz

Download exit quiz

6 Questions

Q1.
The perimeter and area are the same after a translation, rotation or reflection because the object and image are .
Correct Answer: congruent
Q2.
A shape is rotated $${90^{\circ}}$$ anti-clockwise about $$(2,7)$$. Which of the following rotations would result in the image being moved to the same position as the original object?
Correct answer: Rotation $${90^{\circ}}$$ clockwise about $$(2,7)$$
Rotation $${90^{\circ}}$$ clockwise about $$(7,2)$$
Correct answer: Rotation $${270^{\circ}}$$ anti-clockwise about $$(2,7)$$
Q3.
The coordinate $$(a, b)$$ has been translated by $${4 \choose 3}$$. The image of this point will have the coordinate __________.
$$(4a, 3b)$$
$$(a4, b3)$$
Correct answer: $$(a + 4, b + 3)$$
$$ (a - 4, b - 3)$$
Q4.
Shape A is reflected in the $$x$$-axis to create shape B. Shape B is then reflected in the $$y$$-axis to create shape C. Which transformations would map shape C onto shape A?
An image in a quiz
Correct answer: A rotation $${180^{\circ}}$$ about the origin.
Correct answer: A reflection in the line that passes through $$(-4, 4)$$ and $$(3, -3)$$
A translation by $${4 \choose 4}$$
A reflection in the line that passes through (4, 4) and (-2, -2)
Q5.
A shape with perimeter 16 cm is enlarged by scale factor 3. The perimeter of the image is cm.
Correct Answer: 48 cm, 48cm, 48
Q6.
The point A(p + 3, q + 5) has the image $$A^{\prime}$$(p + 1, q + 8). Which vector has it been translated by?
$${2 \choose 3}$$
Correct answer: $${-2 \choose 3}$$
$${2 \choose -3}$$
$${-2p \choose 3q}$$