st swithun wells catholic primary school maths calculations we all know the importance of being able...

St Swithun Wells Catholic Primary School

Maths Calculations

We all know the importance of being able to confidently carry out simple mathematical calculations and how often we do this throughout our day. In school we frequently hear from parents that they are struggling to help their child complete their homework because the way ‘we do things’ is so different from how they ‘did’ maths at school.

In response to this we have put together a simple guide explaining the main way we teach mathematical calculations and how these build up and progress through the school. Our main emphasis is on developing children’s understanding of calculations and encouraging children to use practical equipment, visual images and mental strategies. As their understanding develops children begin to record. This guide will show you the ways children use to record.

The progression of calculation strategies for addition, subtraction, multiplication and division.

Children are introduced to the processes of calculation through practical, oral and mental activities. As they begin to understand the underlying ideas, they develop ways of recording to support their thinking and calculation methods and learn to use the appropriate signs and mathematical language.

The overall aim is that by the time they leave primary school they:

have a secure knowledge of number facts and a good understanding of the four operations;

are able to use this knowledge and understanding to carry out calculations mentally;

can use diagrams and informal jottings to help record steps and part answers;

have an efficient method of calculation for each operation that they can use with confidence;

use a calculator effectively, check the steps involved and decide if the numbers displayed make sense.

When teaching addition, subtraction, multiplication or division we plan for the

following;

First experiences need to be practical activities with concrete equipment.

Children then need to be allowed to record in their own ways through drawing pictures and making jottings.

They can then move onto recording in more standard ways such as those demonstrated by the teacher.

Children will need to see number lines used so they can form visual images for the number operations and eventually being able to draw own number lines to solve addition, subtraction, multiplication and division problems.

Connections need to be made between different strategies.

Strategies for addition:

1. Count on in ones – use practical apparatus2. Count on in ones from the biggest number – fingers to nose3. Adding tens, then ones – use structured number line and blank

number line4. Partitioning single digits: 9 (5 + 4)5. Partitioning larger numbers 6. Compact method such as column addition.

1. Count on in ones, using practical apparatus

2. Count on in ones from the biggest number

9 +1 +1 +1 +1 +1

10 11 12 13 14

9 + 5 = 14

Strategies for Addition

3. Adding tens, then ones.

37 + 15


+1+1+1037 +1

5247

+1 +1

4. Partitioning single digits

+5+4

11 + 9 (4 + 5)

1115 20

364 + 258

5. Partitioning larger numbers


+200364

564 614

+ 50 + 8

622

+3081

111 116

+ 5

81 + 35

6. Compact method such as column addition

300 + 60 + 4

301 + 50 + 8

500 + 110 + 12

30 + 7

31 + 5

40 + 12 = 52


364+258

622

Strategies for subtraction

1. Counting back in ones2. Counting back in tens, then ones.3. Finding the difference by counting on4. Partitioning and recombining without decomposition5. Partitioning and recombining with decomposition

1. Count back in ones, using practical apparatus

2 3 4 5 6 7 8

9

9 - 2

3 4 5 6

Counting back in ones, using a number line

1 2 7 8 9 10

1

Strategies for Subtraction

2. Counting back in tens and then ones.

27 - 13

-1 -1 -10

14

-1

16

17

15

27

3. Finding the difference by counting on

in tens and then ones.

+10 +1 +1 +1

23 27

13

+1


4. Partitioning and recombining without decomposition – using a number line.

- 9 - 20 - 100

57 86186

66

5. Using an expanded column subtraction.

753 - 231

700 + 50 + 3

200 + 30 + 1

500 + 20 + 2 = 522

-


6. Partitioning and recombining with decomposition.

741 - 367

700 + 40 + 1

701 + 60 + 7

301 + 70 + 4 = 374

11130600 741

367

374

11136

--


Strategies for multiplication

1. Repeated addition starting with pictures, then moving on to a number line.

2. Simple arrays (what do you see?)3. Arrays involving partitioning4. Grid method5. Grid method using 2 and 3 digit numbers.

1. Repeated addition, starting

with objects or pictures

Repeated addition, using a number line

0 5 1510 20

+ 5 + 5 + 5 + 5

Strategies for Multiplication

2. Simple arrays (what do you see?)


Describe what you see.

4 rows of 3 teddy bears.

5 + 5 + 5 + 5

3. Arrays involving partitioning

2

30 5


35 x 2

4. Grid method

10

10 3

1

10 x 10 = 100

10 x 3 = 30

1 x 10 = 10

1 x 3 = 3

143


11 x 13

5. Grid method up to using 2 and 3 digit numbers

x 10 10 5

10 100 100 50

8 80 80 40

250

200

25 partitioned into 2 tens and 5 ones

18 X 25 = 450


x 30 7

100 3000 700 3700

20 600 140 740

5 150 35 185

4625

125 X 37 = 4,625

Strategies for division

1. Doubling/halving, making sets2. Count in multiples of 2, 5 and 103. Sharing and grouping4. Using arrays to explain partitioning5. Use inverse to link multiplication and division problems6. Simple chunking7. Chunking with larger numbers

Strategies for Division

half of 8 is 4

8 ÷ 2 = 4

double 4 is 8

4 x 2 = 8

1. Doubling and halving, making sets.


2. Count in multiples of 2, 5 and 10

2

4 6 8

10 10 ÷ 2 = 5

How many 2s in 10?


3. Sharing and grouping


4. Using arrays to explain partitioning

There are 95 parents coming to a school production.

The school hall is wide enough for 17 chairs in a row.

The caretaker has set out 6 rows.

Are there enough chairs for all the parents?

How could you calculate the answer?

5. Using inverse operation (multiplication used to solve division)

20 x 5 = 100

100 ÷ 5 = 20

100 ÷ 20 = 5



6. Simple chunking

198 ÷ 6

6 √198

60 x 10

138

60 x 10

78

60 x 10

18

18 x 3

0

Answer = 33


7. Chunking with larger numbers

In Barton zoo a week’s supply of 1256 apples is to be shared equally between 6 elephants. How many apples will each elephant get?

6√1256

600 x 100

656

600 x 100

56

54 x 9

2

209

Answer is 209 remainder 2

The compact short division is:

6√1 2 5 6

209 rem 2

In this example, the digits need to be carefully aligned in the appropriate columns. An advantage of a strategy based on repeated subtraction of ‘chunks’ is that the same method can be extended to work with two-digit divisors.

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