FreeStanding Mathematics Activity Perimeter and area Nuffield Foundation

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Free-Standing Mathematics Activity Perimeter and area © Nuffield Foundation 2011

Free-Standing Mathematics Activity Perimeter and area © Nuffield Foundation 2011

How much lawn feed do I need? How much edging do I need to

How much lawn feed do I need? How much edging do I need to go around the lawn? © Nuffield Foundation 2011 The gardener needs to work out the perimeter and the area of the lawn

The perimeter of a shape is the total length of its sides Perimeter of

The perimeter of a shape is the total length of its sides Perimeter of a rectangle = length + width + length + width length 5 m lawn length 3 m Perimeter of this lawn = 5 + 3 + 5 + 3 = 16 m Think about Is there another way to find the perimeter? © Nuffield Foundation 2011

Area measures the surface of something 1 metre 1 m 2 1 square metre

Area measures the surface of something 1 metre 1 m 2 1 square metre © Nuffield Foundation 2011 1 cm 2 1 mm 2

Area of a rectangular lawn 5 metres long 3 metres wide The area is

Area of a rectangular lawn 5 metres long 3 metres wide The area is 15 square metres = 15 m 2 Area of a rectangle = length × width © Nuffield Foundation 2011

Area of rectangle = length × width 65 m 32 m field Area of

Area of rectangle = length × width 65 m 32 m field Area of field = 65 × 32 = 2080 m 2 21 cm page © Nuffield Foundation 2011 30 cm Area of the page = 30 × 21 = 630 cm 2

To find the perimeter of this L-shaped room Think about What else is needed?

To find the perimeter of this L-shaped room Think about What else is needed? 3 m 1. 5 m 4. 5 m 2. 2 m 3 m 5. 2 m © Nuffield Foundation 2011 Perimeter 3 + 1. 5 + 2. 2 + 3 + 5. 2 + 4. 5 = 19. 4 m

To find the area of this L-shaped room Think about How can we do

To find the area of this L-shaped room Think about How can we do this? 3 m 1. 5 m 4. 5 m 2. 2 m A B 5. 2 m 3 m Area of A = 4. 5 × 3 = 13. 5 m 2 Area of B = 3 × 2. 2 = 6. 6 m 2 Total area = 13. 5 + 6. 6 = 20. 1 m 2 © Nuffield Foundation 2011

To find the area of this L-shaped room Another way 3 m A 4.

To find the area of this L-shaped room Another way 3 m A 4. 5 m B 1. 5 m Area of A = 3 × 1. 5 2. 2 m = 4. 5 m 2 3 m Area of B = 5. 2 × 3 5. 2 m Total area = 4. 5 + 15. 6 = 20. 1 m 2 © Nuffield Foundation 2011 = 15. 6 m 2

To find the area of this L-shaped room Yet another way! 3 m Area

To find the area of this L-shaped room Yet another way! 3 m Area of large rectangle = 5. 2 × 4. 5 1. 5 m 4. 5 m 2. 2 m 3 m = 23. 4 m 2 Area of small rectangle = 2. 2 × 1. 5 5. 2 m Total area =23. 4 − 3. 3 = 20. 1 m 2 © Nuffield Foundation 2011 = 3. 3 m 2 Think about Which way was best?

At the end of the activity • • • What does the word ‘perimeter’

At the end of the activity • • • What does the word ‘perimeter’ mean? How do you find the perimeter of a shape? What units are used for perimeters? How do you find the area of a shape? What units are used for areas? • How would you find the area of this shape? © Nuffield Foundation 2011 Car park Play area Carpet Mirror surround