Short Blocks

Maths Year 6 Spring Multiplication and Division (A)

Each unit has everything you need to teach a set of related skills and concepts.

Scale factor problems concerning area (suggested as 2 days)

Planning and Activities

Day 1 Teaching
Children sketch a right-angle triangle where the sides along the right angle are 4cm and 7cm long. They measure the longest side, compare, and find the area. Draw a similar triangle with each side next to the right angle twice the length. Compare the longest sides. Define similar triangles and model the scaling effect. Remind children how to find the area of a parallelogram (see below plan), multiplying the base by the height.
Group Activities
-- Scale up rectangles, triangles and parallelograms by a factor of 2 and 3 and see what happens to the area.

Day 2 Teaching
Define similar shapes as identical in shape, but not in size. Show ‘Similar shapes’ (see resources). Ask children to find 2 rectangles which look similar. Measure the sides of each. Ask children to work out the scale factor (1½). Repeat for triangles (scale factor is 3).
Group Activities
Use the ‘Geometry genius’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Identify pairs of similar rectangles and triangles. Use the scale factor to work out side lengths.
-- Draw similar shapes, using a scale factor of 2 or 3 or 1.5. Identify pairs of similar shapes drawn by others and find the scale factor?

You Will Need

  • Mini-whiteboards and pens
  • Rulers
  • ‘Scaling up’ activity sheet (see resources)
  • cm2 paper
  • Similar shapes (see resources)
  • Similar shapes - triangles and rectangles sheets (see resources)
  • ITP: Function Blocks


Day 1
Calculate the dimensions of toys, given scale factors.

Day 2
Identify pairs of similar rectangles and triangles. Use a scale factor to calculate the lengths of sides.

Mastery: Reasoning and Problem-Solving

  • True or false?
    If one triangle is scaled up to have sides 3 times as long as another, the area is also 3 times as large.
    If two rectangles are similar and the scale factor is 4, then the area of the larger rectangle is 16 times that of the smaller rectangle.
  • Calculate the area of the triangle whose sides are half the length of this one (see download). Compare the two areas. What do you notice?
    Explain why the area of the smaller has this relation to the area of the larger.

In-depth Investigation: Geometry Genius
Children use what they know about how to find the areas of triangles and parallelograms to find the areas of rhombi, kites and trapezia.

Extra Support

Function Blocks
Tables knowledge is an important pre-requisite for scaling. Use Function Blocks ITP to generate multiplication by 3. Can children work out the function? Repeat with other single-step x and ÷ functions.