I think of a number and add 6. My answer is negative 7, what number did I start with?

Sums and Things for Parents

Well done Lucie. How did you think that through?

Sums and Things for Parents

Negative 13

The story so far ……….

children’s recall of number facts has become more accurate and faster

children are more aware of the strategies they use to calculate

they use vocabulary correctly

they are more confident about maths

maths is more fun!

What can a numerate child do?

By the age of 11 they should :

have a sense of the size of number and where it fits into the number system

know by heart addition and subtraction facts to 20, multiplication and division facts to 10x10, doubles and halves, complements to 100, multiply and divide by 10 and 100

use what they know to figure out answers mentally

What can a numerate child do? (cont.)

calculate accurately and efficiently, both mentally and on paper, using a range of strategies

recognise when it is appropriate to use a calculator- and when it is not- and be able to use one effectively

explain their methods and reasoning using correct mathematical terms

judge whether their answers are reasonable and have strategies for checking them where necessary

The aim

The aim is for children to do mathematics in their heads, and if the numbers are too large, to use pencil and paper to avoid losing track. To do this children need to learn quick and efficient methods, including appropriate written methods.

Mathematics is foremost an activity of the mind, and written calculations are an aid to that mental activity.

The Numeracy Strategy aims to develop children’s mental strategies and then written methods that derive from and support mental methods.

Learning written methods is not the ultimate aim.

We want children to ask themselves:

Can I do this in my head?

Can I do this in my head using drawings or jottings?

Do I need to use an expanded/compact written method?

Do I need a calculator?

61 + 45 7800 – 5600

5735 + 3657 5735 + 3990

83 – 68 5002 – 4996

538 - 295 267 + 267

2.5 + 2.7 5.1 - 2.78

How do you add and subtract?

16

- 9

1

Mistakes children make:

643

+ 274

8117

803

- 526

187

…….and more:

6 10 13

76 + 47 =

76

Addition

11676

+ 40

123

+ 7

86

+10

96

+10

106

+10

116

+10

123

+7

358 + 473 =

Addition

358

+ 473

11120

700

831

358

+ 473

83111

100 + 70 + 6

+ 100 + 40 + 7

200 + 110 + 13

= 323

176 + 147 =

Addition

Subtraction

Imran has 43 conkers; he gives 24 away to his friends. How many does he have left?

43 – 24 =

4333

-10

23

-10

20

-3-1

19

19 conkers

Subtraction

Sam has saved 93p, Amy has 55p. How much more money does Sam have than Amy?

93 – 55 =

55 60

+5

93

+3

90

+30

38p more

Subtraction

8.23 – 4.55 =

3.68

8.23

8.00

5.00

4.55

+0.23

+3+0.45

Subtraction

A sports stadium holds 9010 spectators. 5643 people attend a football match. How many empty seats are there?

5643

5700

6000

9010

57

+300

+3010

3367

5643 5700 9010

+ 57 +300 +3010

3367 empty seats

6000

57 x 2 78 ÷ 2

43 x 50 742 ÷ 2

36 x 25 700 ÷ 4

18 x 15 65.5 10

8 x 19 17 ÷ 5

34 x 7 5.4 ÷ 6

How do you multiply and divide?

Mistakes children make:

76

x 8

5648

67

x 54

268

335

603 101 r 5

7 847

Multiplication

47 x 8 = x 40 78 320 56 376

37 x 46 =x 30 7

40 1200 280 14806 180 42 222

1702

……… leading to algebra at KS3

x a b

a a2 ab a

2 + ab

b ab b2

ab + b2

a2 + 2ab + b

2

(a + b)2 = (a + b) x (a + b)

(a + b)2 = a

2 + 2ab + b

2

Division

375 43 43 375

47 8 8 47

…or ‘chunking’

First on a number line 87 ÷ 7

17 873

subtract 7x10 or 7 ten times

We have subtracted seven 12 times and have 3 left

so… 87 ÷ 7 = 12 r 3

subtract 7x2 or 7 twice

-70

-14

A shop notice states that there are 87 shopping days to Christmas. How many weeks is that?

87

-70 (10 weeks)

17

-14 (2 weeks)

3

So it’s 12 weeks (and 3 days) of shopping to Christmas.

432 school children are going on an outing. If each bus takes 15 passengers, how many buses will be needed?

432 -300 (20 buses)

132

- 90 (6 buses)

42

So we need 29 buses or 28 buses and some cars!

-30 (2 buses)

12 (people left)

How can you help?

Talk about how you do maths

Give praise and encouragement

Be positive

Ask your child to explain

Make sure maths is fun!