1. Two way tables There are 125 children in Year 6. 52% of them are girls. 20% of girls do not play football. Five times as many boys play as do not play football. Fill in the table. GirlsBoys Play football Do not play football You pick a boy at random from the whole group of boys. What is the probability of picking one that likes football?

2. Solving problems with averages (1) There are four numbers in a set of data. The mean is 7 and the range is 4. What could the numbers be? Hint: What must the four numbers add up to? Hint: What must the four numbers add up to? Hint: What must the difference between the biggest and the smallest be? Hint: What must the difference between the biggest and the smallest be?

3. Solving problems with averages (7) 3 A, B and C stand for three different numbers. The mean of A and B is 40. The mean of B and C is 35. A + B + C = 100. Calculate the values of A, B and C.

4. “Estimate the area of a circle when r = 5 cm” says Shamila. “What’s the formula again?” asked Beth. “πr 2 ” Shamila suggests, looking at her book. “Well, π x 5 is roughly 15” mumbled Abdul. “And 15 squared is 225!” called Beth triumphantly. Challenge: Explain why Abdul and Beth are wrong and work out a better estimate. Challenge: Explain why Abdul and Beth are wrong and work out a better estimate.

5. How numbers behave When you are adding, you can swap the numbers round. When you are subtracting, you can’t swap the numbers round. When you are multiplying, you can swap the numbers round. When you are dividing, you can’t swap the numbers round. So a + b b + a So a - b b - a So a x b b x a So a ÷ b b ÷ a ≠ means “is not equal to”. ≠ ≠ = =

6. 10 split into 4 equal parts 10 + 4 10 - 4 10 x 4 10 ÷ 4 4 + 10 4 - 10 4 ÷ 10 4 x 10

7. 10 split into 4 equal parts 10 + 4 10 - 4 10 x 4 10 ÷ 4 4 + 10 4 - 10 4 ÷ 10 4 x 10

8. Dice Games 1 d = the number on the dice

9. 5 more than the dice number 4 less than the dice number 4 multiplied by the dice number 5 multiplied by the dice number 5 less than the dice number 4 more than the dice number 4 take away the dice number Subtract the dice number from 5

10. 7 divided by the dice number The dice number multiplied by itself, then subtract 7 The dice number plus the dice number plus the dice number plus the dice number plus the dice number plus the dice number plus the dice number 7 multiplied by 2 more than the dice number 7 less than double the dice number 2 more than the dice number, all divided by 7 7 lots of the square of the dice number Subtract half the dice number from 7

11. dd x 2 ÷ 7÷ 7÷ 7÷ 7 ÷ 7÷ 7÷ 7÷ 7 + 3 - 5 + 4 + 4 + 1 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 x 12 - 1 ÷2 ÷ 2 ÷2 ÷ 2 ÷2 ÷ 2 ÷2 ÷ 2 dd dd dd dd

12. Harder Expressions d 2dd2d2 d3d3 1 2 3 4 5 10 0 d 64 25 144 400 0 1

13. Think of a number I think of a number. I multiply it by 3. I add 4. I multiply it by 2. I subtract 2. I divide it by 3. I subtract 2. I divide by 2. What number have I got? x 3x 3x + 4 6x + 8 6x + 6 2x + 2 2x x

14. Find two different ways to complete these equations. 1. ………… + 6 = ……. - 9 2. ………… x ………. = ……. - 3 3. ……… ÷ 5 = ……… + 9 4. ………. x 3 = ……… + 5 In an equation, the left hand side must equal the right hand side. Equations

15. How many solutions? x + 5 = y + 6 x 2 = 25 2x + 3 = x + 1 x + y = 10 x + 5 = x - 1 How many different numbers can you find for the letters to make the two sides of the equations equal?

16. Solving Simultaneous Equations Find a, b and c: a + b = 21 ac = 30 a + c = 17 Find x and y: 2x + y = 11 x + y = 7

17. The number I was thinking of is …….. I think of a number. I multiply it by 5 and subtract 1. My answer is 39. What number was I thinking of? Forming and solving equations Form an equation using the letter m to stand for the unknown value and solve it.

18. Finding 100% 15% of a number is 33. What is the number? 15% = 33 5% = 11 100% = 220 ÷ 3 x 20 ÷ 3 x 20