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?

3

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.

A Classic Mistake

Challenge: Explain why Abdul and Beth are wrong and work out a better estimate.

How numbers behaveWhen 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”.

≠

≠

=

=

10 split into 4 equal parts

10 + 4 10 - 4

10 x 4

10 ÷ 4

4 + 10

4 - 10

4 ÷ 104 x 10

10 split into 4 equal parts

10 + 4 10 - 4

10 x 4

10 ÷ 4

4 + 10

4 - 10

4 ÷ 104 x 10

Dice Games 1

d - 3 3d

Total Total

d + 7 20 - d

Total Total

d = the number on the dice

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

7 divided by the dice

numberThe dice number multiplie

d 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

d x 2

÷ 7

+ 3

- 5

+ 4

+ 1

- 5

x 12

- 1

÷ 2

d

d

d

d

Forming expressions 2

Harder Expressions

d 2d d2 d3

1

2

3

4

5

10

0

d

642514440001-1

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?

x3x3x + 46x + 86x + 62x + 22xx

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

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 a, b and c:

a + b = 21ac = 30a + c = 17

Find x and y:

2x + y = 11 x + y = 7

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.

Finding 100%

15% of a number is 33. What is the number?

15% = 33

5% = 11

100% = 220

÷ 3

x 20

÷ 3

x 20