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.

The effect of enlargement on the perimeter of a shape

Maths

Checking and securing understanding of direct proportion in context

The effect of enlargement on the area of a shape

Using the scale factor for enlarging an area

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

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

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

This sector is enlarged by scale factor 2. The angle in the image is {{}}°.

Each square on this coordinate grid is 1 unit long. This object is enlarged by a scale factor of 3 to make its image. Calculate the perimeter of the image.

A pentagon has a perimeter of 60 cm. The pentagon is enlarged by scale factor 4. The perimeter of the image is {{}} cm.

The object is enlarged by a scale factor of $$\frac{1}{3}$$ to make the image. What is the perimeter of the image?

A shape is enlarged by a scale factor of $$\frac{2}{3}$$ to make its image. The perimeter of the image is 25 cm. The perimeter of the object is {{ }} cm.

Two variables are in direct proportion if they have a constant {{ }} relationship.

Alex: It shows direct proportion because it is increasing.

Jacob: It doesn't show direct proportion because it is not a straight line.

Laura: It shows direct proportion because it passes through the origin.

Sam: It doesn't show direct proportion because there is no scale.

Sofia: You can't tell because you don't know what the variables are.

Some Oak pupils are discussing this graph. Which pupils are correct?

The ratio table shows the conversion €7 (Euros) = £6 (Pounds Sterling).  €350 = £{{ }}

The perimeter of an octagon is 88 800 cm. Which calculation shows its perimeter in metres?

A circular sector with an angle of 60° has radius = 6 cm, arc length = 2π cm and area = 6π cm².  The radius of the sector is increased to 18 cm. Find the arc length and area of the new sector.

The area of a triangle is 3400 cm². The area of the triangle in metres squared is {{ }} m².

Starter Quiz

Two variables are in direct proportion if they have a constant relationship.