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This unit has no problem-solving investigation.

- Kate knows that 136 × 31 = 4216. Explain how she can use this information to solve these calculations:

137 × 31

136 x 3.1

1.36 x 31

421.6 ÷ 136 - Steph saves £1.20 per week. How many weeks before she can buy a pair of trainers costing £48?
- Shopping for her birthday party, Amie buys a pack of 24 cans of lemonade for £10.80. What is the cost of each can?
- The height of an adult can be estimated by measuring their head length then multiplying that length by 8. Flo’s dad has a head length of 22.5cm. What is his approximate height?

Flo’s mum is 1.64m tall. What is her approximate head length? - The Blackpool Tower is 160 metres tall and 31 metres wide at its base. Ally makes a scale model of the tower. Her model is 32 centimetres tall. How wide is the base of her model?
- A square of side length
**a**has an area = 16cm². Another square, of side length**b**, has an area = 100cm². What is the ratio of their side lengths,**a**:**b**?

- The remaining area is planted with pears. What fraction is this
- Poppy calculates 3/4 + 2/5 = 5/9. Do you agree with her?
- Find the missing numbers in these calculations:

4/10 x 2 = ☐/5

9/6 ÷ ☐ = 1/2

3/4 - 2/5 = ☐

- 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 four 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 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.

- Write the correct symbol (<, > or =) in each box to make the statements correct:

12 x 12 ☐ 14 x 10

80 ÷ 20 ☐ 90 ÷ 30

240 ÷ 6 ☐ 270 ÷ 9

800 x 5 ☐ 70 x 50 - Sophia has the digit cards 6, 7 and 5. She makes a 2-digit number and a 1-digit number. She multiplies them together. Her answer is a multiple of 10. What could Sophia’s multiplication be?
- A farmer is packing eggs in boxes of 6. She has 980 eggs to pack. How many boxes can the farmer fill using 980 eggs? How many boxes will she need to hold all 980 eggs?
- Shaula calculates 1252 ÷ 14. She says, ‘There’s no remainder in the answer!’ Do you agree with her?

- Emilia scores 40 out of 70 in a test. Jay scores 55% in the same test. Who has the higher score? Explain how you know.
- Write these numbers in order, starting with the smallest:

0.43, 3/4, 34%, 4/3, 3.4