Objectives Day 1 Find areas and perimeters. Day 2 Find volumes.

1. More Revision Understand and calculate areas, perimeters and volume Objectives Day 1 Find areas and perimeters. Day 2 Find volumes. Year 6

2. More Revision Understand and calculate areas, perimeters and volume Starters Day 1 Convert between mm, cm and metres (simmering skills) Day 2 Read Roman numerals (simmering skills) Year 6

3. More Revision Understand and calculate areas, perimeters and volume Starter Convert between mm, cm and metres Year 6

4. More Revision Understand and calculate areas, perimeters and volume Starter • Read Roman numerals Year 6

5. More Revision Understand and calculate areas, perimeters and volume Objectives Day 1 Find areas and perimeters. Year 6

6. Day 1: Find areas and perimeters. • It is hard to tell as they are different irregular shapes. • Here are two ponds. Which pond do you think covers the greater area? • Do the same for this pond. So, which pond covers the greater area? Each square represents a square metre. Write both areas in m2. • I'm going to count all the whole squares in this pond, then also count any squares that have half or more shaded. I'm going to ignore squares that have less than half shaded. Year 6

7. Day 1: Find areas and perimeters. • Look at the different rectangles. Remember that shapes can have the same area but different perimeters. • HINT! A rectilinear shape is one made out of rectangles, e.g. an ‘L’ or ‘T’ shape. • On cm2 paper, draw a rectangle with an area of 24cm2, then calculate its perimeter. • Now draw a rectilinear shape with an area of 24cm2, then calculate its perimeter. • Look at the different rectilinear shapes, all with the same area, but different perimeters. • Today’s‘Top Tip for Tests’is the strategy for quickly finding a rectangle’s perimeter: add two different sides and double. • What’s the strategy for finding the area? Year 6

8. Challenge Year 6

9. More Revision Understand and calculate areas, perimeters and volume Objectives Day 2 Find volumes. Year 6

10. Day 2: Find volumes. • Each of the cubes in my cuboid is 1cm3, so the volume is 36cm3. • How many are in the bottom layer? • How many layers are there? • So how many cubes altogether? Remember we can use a formula to describe this efficiently: length × width × height, or l × w × h for short. • Today’s‘Top Tip for Tests’is to use this formula to find the volume of cuboids.l × w × h • Volume is the amount of space taken up by the shape. • Look at the cuboid. Discuss in pairs how many cubes are in the cuboid. • We measure volume in centimetres cubed (cm3) or metres cubed (m3) or millimetres cubed (mm3) or even kilometres cubed (km3). • When volcano Mount St Helens erupted in 1980, it ejected around 4.2 km3 of rock and lava! Year 6

11. Day 2: Find volumes. 5m • Calculate the volume in m3. 4m 6m 5m x 4m x 6m = 120m3 Year 6

12. Sheet 1 Year 6

13. More Revision Understand and calculate areas, perimeters and volume Objectives Day 1 Find areas and perimeters. Day 2 Find volumes. Year 6

14. Problem solving and reasoning questions Nell says, If two rectangles have the same perimeter, they must have the same area. Do you agree? Explain your ideas. Draw two different quadrilaterals with an area of 20 cm2. Each side of an equilateral triangle measures 12cm. Each side of a regular hexagon is b cm. The perimeter of the hexagon is 6 centimetres less than the perimeter of the triangle. What number does b represent? A square of area 64cm2 is cut into quarters to create 4 smaller squares. What is the perimeter of one of the small squares? Ronnie has 36 centimetre cubes. She uses all 36 cubes to make a cuboid with dimensions 9cm, 2cm and 2cm. Write the dimensions of all the different cuboids she can make using all 36 cubes. A cuboid has a square base. It is three times as tall as it is wide. Its volume is 192 cubic centimetres. Calculate the width of the cuboid. Year 6

15. Problem solving and reasoning: Answers Nell says, If two rectangles have the same perimeter, they must have the same area. Do you agree? Explain your ideas. No. This is best negated by a counter-example. For example, a 3 by 4 cm and a 2 by 5 cm rectangle each have the same perimeter (14cm) but the first has an area of 12cm2 the second 10cm2 Draw two different quadrilaterals with an area of 20 cm2. 20cm by 1cm, 10cm by 2cm, 8cm by 2.5cm and 5cm by 4cm are all possibilities, check accuracy of drawings Each side of an equilateral triangle measures 12cm. Each side of a regular hexagon is b cm. The perimeter of the hexagon is 6 centimetres less than the perimeter of the triangle. What number does b represent? 5. The perimeter of the equilateral triangle is 36cm (3 x 12). The perimeter of the hexagon is 30cm (36 – 6); as it has 6 sides each must be 5cm (30 ÷ 6). Sketching the shapes will help children visualise the problem. A square of area 64cm2 is cut into quarters to create 4 smaller squares. What is the perimeter of one of the small squares? The area of each smaller square is 16cm2 (64 ÷ 4). The sides of the smaller square must be 4cm since 4cm x 4cm = 16 cm2. Ronnie has 36 centimetre cubes. She uses all 36 cubes to make a cuboid with dimensions 9cm, 2cm and 2cm. Write the dimensions of all the different cuboids she can make using all 36 cubes. 36cm, 1cm, 1cm. 18cm, 2cm, 1cm 12cm, 3cm, 1cm 9cm, 4cm, 1cm 6cm, 6cm, 1cm 9cm, 2cm, 2cm 6cm, 3cm, 2cm 4cm, 3cm, 3cm In each case multiplying the 3 lengths gives 36. A cuboid has a square base. It is three times as tall as it is wide. Its volume is 192 cubic centimetres. Calculate the width of the cuboid. 4cm. Imagine 3 cubes joined together to make the cuboid, each has a volume of 64 cubic centimetres (192 ÷ 3). Each length of the cube must be 4cm to give a volume of 64 cubic centimetres (4 x 4 x 4). Year 6