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

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

Enlargement is a transformation that causes a change of size.

A scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.

Volume is the amount of space occupied by a closed 3D shape.

The effect of enlargement on the volume of a 3D shape

Maths

Checking and securing understanding of direct proportion in context

The effect of enlargement on the perimeter of a shape

The effect of enlargement on the area of a shape

Using the scale factor for enlarging an area

Using the scale factor for enlarging a volume

Checking and securing understanding of congruent triangles (SSS)

Checking and securing understanding of congruent triangles (SAS)

Checking and securing understanding of congruent triangles (ASA)

Checking and securing understanding of congruent triangles (RHS)

Problem solving with advanced similarity knowledge

In the prior unit, pupils enhanced their understanding of enlargement. In this unit, pupils investigate the effect of an enlargement on the perimeter and area of a 2-D shape and the volume of a 3-D shape.

In this unit, pupils investigate the effect of an enlargement on the perimeter and area of a 2-D shape and the volume of a 3-D shape.

Similarity

__________ is the amount of space occupied by a closed 3D shape.

A cuboid of dimensions 2 cm by 3 cm by 10 cm is enlarged by a scale factor of 3. Work out the volume of the enlarged cuboid.

Shape A is a 3D shape. Shape A is enlarged by scale factor 3 to give shape B. What is the volume scale factor from A to B?

Match each linear scale factor to correct the volume scale factor.

Prism S and prism T are similar. What is the scale factor of enlargement from prism S to prism T?

Prism A and prism B are similar. The end face of prism A has an area of 15 cm². The volume of prism B is {{ }} cm³.

The transformation that causes a change in {{}} of the object is enlargement.

Rectangles A and B are similar. What is the area scale factor from A to B?

Shapes P and Q are similar. The perimeter of shape P is 18 cm and the perimeter of shape Q is 72 cm. The area scale factor from P to Q is {{}}.

Sectors E and F are similar. The area of sector E is 30π cm². What is the area of sector F?

Sectors E and F are similar. The area of shape E is 24π cm² and the area of sector F is 150π cm². The radius of sector F is {{}} cm.

Triangles L and M are similar. The area of triangle M is 54 cm². What is the perimeter of triangle M?

The effect of enlargement on the volume of a 3D shape

Lesson outcome