1. Multiplication and Division
Solve problems using a scale factor in areas of shapes
Objectives
Day 1
Solve problems involving similar shapes where the scale factor is known. Find areas of triangles, rectangles and parallelograms.
Day 2
Solve problems involving similar shapes where the scale factor can be found.
Before teaching, be aware that:
On Day 1 children will need mini-whiteboards, pens and rulers.
On Day 2 children will need the Similar shapes resource sheet (see resources) NB Please print on A4 and tick the ‘Actual Size’ box on your printer settings to ensure that the shapes are printed at the correct sizes.
Year 6

2. Multiplication and Division
Solve problems using a scale factor in areas of shapes
Starters
Day 1
Algebra: missing numbers (simmering skills)
Day 2
Algebra: list pairs of variables (simmering skills)
Choose starters that suit your class by dragging and dropping the relevant slide or slides below to the start of the teaching for each day.
Year 6

3. Multiplication and Division
Solve problems using a scale factor in areas of shapes
Starter
Algebra: missing numbers
Simmering skills – to use this starter, drag this slide to the start of Day 1
Ask children to work out the missing numbers in equations (see next slide or starters resources). If they finish, they make up their own equations with missing numbers, one at a time, for a partner to solve.
Year 6

4. Year 6

5. Multiplication and Division
Solve problems using a scale factor in areas of shapes
Starter
Algebra: list pairs of variables
Simmering skills – to use this starter, drag this slide to the start of Day 2
Children work in pairs to list possible values of a and b in a × b = 36 where each are whole numbers, then 2c + d = 10.
Year 6

6. Multiplication and Division
Solve problems using a scale factor in areas of shapes
Objectives
Day 1
Solve problems involving similar shapes where the scale factor is known. Find areas of triangles, rectangles and parallelograms.
Year 6

7. Day 1: Solve problems involving similar shapes where the scale factor is known; Find areas of triangles, rectangles and parallelograms.
Sketch a right-angle triangle with sides adjoining the right angle of lengths 4cm and 7cm.
Measure the longest side and compare with your neighbour.
How can we find the area of this triangle?
We can sketch a rectangle around the triangle like this.
Find the area of the rectangle and halve it to find the area of the triangle.
1/2 × b × h
Year 6

8. Is the longest side also twice the length?
Day 1: Solve problems involving similar shapes where the scale factor is known; Find areas of triangles, rectangles and parallelograms.
Draw a similar-looking triangle but with each side next to the right angle twice the length of the first one.
Is the longest side also twice the length?
We call these two triangles ‘similar’.
In maths, we use this word to describe shapes that might be different in size but have the same proportions.
The corresponding sides of similar shapes are a multiple of each other.
What do you think the area might be?
Work it out…
So, the lengths of the sides are double the original lengths, but the area is 4 times the original!
Year 6

9. Work out the area of this parallelogram.
Day 1: Solve problems involving similar shapes where the scale factor is known; Find areas of triangles, rectangles and parallelograms.
To find the area of a parallelogram, we can ‘slide’ the triangle to the right to create a rectangle.
8cm
6cm
Work out the area of this parallelogram.
Year 6

10. Whole class investigation You will need a ‘Scaling up’ activity sheet.
Day 1: Solve problems involving similar shapes where the scale factor is known; Find areas of triangles, rectangles and parallelograms.
Whole class investigation
You will need a ‘Scaling up’ activity sheet.
Draw a similar rectangle on cm2 paper, such that the length of each side is double the original, and then another with triple the original length sides.
Find what has happened to the area of the rectangle.
Repeat for the triangle and parallelogram.
Be ready to feedback what you have found out.
Today’s GROUP ACTIVITY is a whole class investigation. You can find more details in the unit’s TEACHING AND GROUP ACTIVITIES download.
WT: As above, but work with double size of shapes only.
GD: As for above, then investigate what happens to the volumes of cuboids when you double or triple the length of each side.
Year 6

11. The Practice Sheet on this slide is suitable for most children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE: Calculate the dimensions of toys, given scale factors.
GD: Children also attempt the challenge.
Challenge
Year 6

12. Multiplication and Division
Solve problems using a scale factor in areas of shapes
Objectives
Day 2
Solve problems involving similar shapes where the scale factor can be found.
Year 6

13. Find two rectangles which look similar. Measure the sides of each.
Day 2: Solve problems involving similar shapes where the scale factor can be found.
Similar shapes are identical in shape, but not in size.
So all circles, squares and other regular shapes are similar, but rectangles might not be.
Find two rectangles which look similar. Measure the sides of each.
Work out the scale factor, i.e. the number we need to multiply the side length of the first shape by to get the larger shape.
The scale factor of the similar rectangles is 2 and the scale factors of the similar triangles is 3.
Today would be a great day to use a problem-solving investigation – Geometry Genius – as the group activity, which you can find in this unit’s IN-DEPTH INVESTIGATION box on Hamilton’s website.
Alternatively, children can now go on to do differentiated GROUP ACTIVITIES. You can find Hamilton’s group activities in this unit’s TEACHING AND GROUP ACTIVITIES download.
WT/ARE: Identify pairs of similar rectangles and triangles. Use the scale factor to work out side lengths.
GD: 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.
Repeat for the triangles.
It is useful to use a scale factor when producing a scale drawing of plans for a building or a model. The drawing would have the same proportions as the real building or model.
Year 6

14. The Practice Sheets on this slide and the next are suitable for most children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE/GD: Identify pairs of similar rectangles. Use a scale factor to calculate the lengths of sides.
To print at correct size, please print on A4 and tick the ‘Actual Size’ box on your printer settings.
Year 6

15. The Practice Sheets on this slide and the previous one are suitable for most children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE/GD: Identify pairs of similar triangles. Use a scale factor to calculate the lengths of sides.
To print at correct size, please print on A4 and tick the ‘Actual Size’ box on your printer settings.
Year 6

16. Multiplication and Division
Solve problems using a scale factor in areas of shapes
Well Done! You’ve completed this unit.
Objectives
Day 1
Solve problems involving similar shapes where the scale factor is known. Find areas of triangles, rectangles and parallelograms.
Day 2
Solve problems involving similar shapes where the scale factor can be found.
You can now use the Mastery: Reasoning and Problem-Solving questions to assess children’s success across this unit. Go to the next slide.
Year 6

17. Problem solving and reasoning questions
True or false
• If one triangle is scaled up to have sides 3x as long as another, the area is also 3x as large.
• If two rectangles are similar and the scale factor is 4, then the area of the larger is 16 times that of the smaller.
Calculate the area of the triangle whose sides are ½ the length of this one.
Compare the two areas.
What do you notice?
Explain why the area of the smaller has this relation to the area of the larger.
6cm
8cm
Year 6