1. Review To introduce approaches to working out perimeter, area and volume of 2D and 3D shapes. 2

2. Outcomes the perimeter of regular and composite shapes the area of simple and composite shapes the volume of rectangular prisms. 3

3. Finding ‘missing’ perimeter dimensions 8 m 1 m If we know that the total length of the shape is 8 m... 4

4. 8 m 1 m... and that the two smaller rectangles are both 1 m long... 5

5. 8 m 1 m... then the length of the large middle rectangle must be... 6

6. 8 m 1 m 6 m 7

7. Now try this one: 20 m 5 m9 m ? 8

8. Now try this one: ? 12 m 16 m 9

9. Finding the area of composite shapes Divide the shape up into separate rectangles. Find the area of each separate rectangle. Add the areas together to find the total area of the shape. First, you may have to work out ‘missing’ dimensions of the perimeter. 16

10. This is a plan of a conference centre. There is a centre aisle two metres in width in the middle of the building. 20 m 22 m 20 m 15 m 10 m 17

11. Each seat takes up a space of one square metre. How many seats could be placed in the conference centre? 20 m 15 m 10 m 22 m 18

12. Think through ways of solving this task. 20 m 15 m 10 m 22 m 19

13. A starting point would be to work out the ‘missing dimensions’ of the perimeter. 20 m 15 m 10 m 22 m 20

14. Then you might begin to separate the room up into smaller rectangles. 20 m 15 m 10 m 22 m 21

15. 20 m 15 m 10 m 35 m 10 m 2 m 200 m 2 350 m 2 200 m 2 22 m 22

16. 20 m 15 m 10 m 35 m 10 m 2 m 200 m 2 350 m 2 22 m 23

17. 20 m 15 m 10 m 35 m 10 m 2 m 200 m 2 350 m 2 Total area = 200 + 350 + 350 + 200 m 2 = 1100 m 2 22 m 24

18. 20 m 15 m 10 m 35 m 10 m 2 m 200 m 2 350 m 2 Total area = 1100 m 2 22 m 25

19. 20 m 15 m 10 m 25 m 10 m 2 m 200 m 2 350 m 2 22 m This means 1100 chairs each taking an area of one metre square could fit in the centre. 26

20. Area of a triangle If the area of a rectangle is the length multiplied by the width (and it is!)... 2 cm 6 cm 27

21. Area of a triangle... then what do you think the area of a triangle might be? Use squared paper to test your theory, and write a formula to find the area of a triangle. 2 cm 6 cm 28

22. Finding the volume of rectangular prisms Height  Length  Width 29

23. Finding the volume of rectangular prisms 3 cm  8 cm  2 cm Volume = 48 cm 3 30

24. Summary: perimeter, area and volume Where possible, use real, everyday examples of 2D and 3D shapes when supporting learners to understand these concepts. Allow learners to understand through exploring ‘first principles’ to avoid ‘formulae panic’. Use visualisation ‘warm ups’ to develop 2D and 3D spatial awareness. Units, units, units! 35