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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. Girls Boys 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? 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 difference between the biggest and the smallest be? Solving problems with averages (7) 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. “Estimate the area of a circle when r = 5 cm” says Shamila. “What’s the formula again?” asked Beth. “πr2” 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. How numbers behave ≠ means “is not equal to”. When you are adding, you can swap the numbers round. So a + b = b + a When you are subtracting, you can’t swap the numbers round. So a - b ≠ b - a When you are multiplying, you can swap the numbers round. So a x b = bxa When you are dividing, you can’t swap the numbers round. So a ÷ b ≠ b ÷ a 10 split into 4 equal parts 10 - 4 10 + 4 4 + 10 10 x 4 4 - 10 10 ÷ 4 4 ÷ 10 4 x 10 10 split into 4 equal parts 10 - 4 10 + 4 4 + 10 10 x 4 4 - 10 10 ÷ 4 4 ÷ 10 4 x 10 Dice Games 1 d = the number on the dice d-3 Total 3d Total d+7 Total 20 - d Total 5 more than the dice number 4 more than the dice number 5 less than the dice number 4 multiplied by the dice number Subtract the dice number from 5 4 less than the dice number 4 take away the dice number 5 multiplied by the dice number 7 divided by the dice number 7 less than double the dice number 2 more than the dice number, all divided by 7 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 lots of the square of the dice number Subtract half the dice number from 7 7 multiplied by 2 more than the dice number d x2 +1 ÷7 -5 +3 x 12 +4 -5 -1 ÷2 Harder Expressions d 1 2 3 4 5 10 0 2d d2 d3 d 64 25 144 400 0 1 -1 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 Equations 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. How many solutions? x+5=y+6 x2 = 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? Solving Simultaneous Equations Find x and y: Find a, b and c: 2x + y = 11 x+y=7 a + b = 21 ac = 30 a + c = 17 Forming and solving equations I think of a number. I multiply it by 5 and subtract 1. My answer is 39. What number was I thinking of? Form an equation using the letter m to stand for the unknown value and solve it. The number I was thinking of is …….. Finding 100% 15% of a number is 33. What is the number? ÷3 15% = 33 ÷3 5% = 11 x 20 x 20 100% = 220