2

Addition

3

35+ 28=

Partitioning

35= 30 5 This method can also be used for HTU 28= 20 8 30+ 20= 50 5+8= 13 50+ 13= 63 4

Using a Number Line to Add Two Digit Numbers

Start by adding the tens number, then adding the units number. This is first introduced on number line with all the numbers shown. If you do not have one of these at home use a ruler. Once a child is confident with the method, there is no need to write out all the numbers on the line.

+ 10 + 2 22 32 34 22 + 12 = 34 5

Column Addition with Carrying from Units to Tens

2 3 4 + 3 5 7

It is important that numbers are lined up in columns carefully. We always work from right to left. Any carrying is placed below the bottom line.

5 9 1

1 6

Column Addition with 3 Digit Numbers, Carrying from all Columns

8 3 4 + 4 6 7 1 3

1 1

0 1

7

Column Addition with Numbers with One Decimal Place

8 3 ∙ 4 + 4 6 ∙ 7 1 3

1 1

0 ∙ 1

It is important to line up the decimal point in each number when setting out the sums. Remember to place a decimal answer.

Subtraction

9

Using a Number Line to Subtract 2 Digit Numbers

Start by subtracting the tens number, then subtract the units number. This is first introduced on a number line with all the numbers shown. If you do not have one of these at home use a ruler. Once a child is confident with the method, there is no need to write out all the numbers on the line.

-2 - 10 34-12 = 22 22 24 34 10

-

Column Subtraction with Exchange from Tens to Units Column

7

5 8 4

1

3 5 7 2 2 7

11

-

Column Subtraction with Exchange from all Columns

4 1 7

5 8 4

1

3 9 7 1 8 7

12

-

Column Subtraction with Decimal Numbers with One Decimal Place and Exchange from all Columns

4 1 7

5 8 ∙ 4

1

3 9 ∙ 7

It is important to line up the decimal points when setting up calculations with decimal numbers

∙ 1 8 7

13

Multiplication

14

Using the Grid Method to Multiply by a Single Digit

First draw out a grid. It is only really necessary to draw out the red lines below. The grid can be used for numbers with any amount of digits e.g. 23x7 x 20 3 7 140

+

21

=

161 15

Using the Grid Method to Multiply by Two Digits

First draw out a grid. It is only really necessary to draw out the red lines below. The grid can be used for numbers with any amount of digits e.g. 23x37 x 30 7

Your child may wish to use this standard way to multiply numbers with more than one digit once they understand how numbers are partitioned. Of course, they may prefer to continue using this grid method instead.

20 600 140 + + 3 90 21

= =

+ 690 161 851 16

Using Column Multiplication

3 4 6 X 5 1 7 2 3 3 0

Once confident and with an understanding of how numbers are partitioned when multiplying, your child will be encouraged to use this standard way to multiply single digit numbers

17

Using Column Multiplication when Multiplying by a Two Digit X 2 5

+

Number 3 4 6 1 7 6 9 2 1 8 6 3 2 3 5 0 0 0

Your child may wish to use this standard way to multiply numbers with more than one digit once they understand how numbers are partitioned. However, they may prefer to continue using this grid method instead.

1 18

Using Column Multiplication with Decimal numbers X 5 1 7 3 • 0 2 3 19

How many groups are in..?

Division

20

Sharing a Number

8 divided by 4 = 2

21

Chunking 72 divided by 3 0 10x3 10x3 3 3 3 3 72 22

Using Arrays An array is an arrangement of a number or counters represented as a rectangle. The number of rows and columns show the numbers it can be divided by. For example, let’s consider the number 12. It can be visually represented in an array like this: So, 12 ÷ 2 = 6 23

Interpreting Arrays By showing division in this way and by ringing columns rather than rows, it is very clear to see that 12 ÷ 6 = 2 By ringing columns instead of rows the introduction to thinking of division as grouping can be made 12 divided by 2= 6 24

12 11 10 9 6 7 8 5 2 3 4 1

Locating Division Facts from a

x

Multiplication Square

1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 2 3 4 4 6 8 6 9 12 8 12 16 10 15 20 12 18 24 14 21 28 16 24 32 18 27 36 20 30 40 22 33 44 24 36 48 5 10 15 20 25 30 35 40 45 50 55 60 To find the answer to 42 ÷ 7: 6 7 8 12 14 16 18 21 24 24 28 32 30 35 40 36 42 48 42 49 56 48 56 64 54 63 72 60 70 80 66 77 88 72 84 96 1. Look across the top for the 7 column 9 18 27 36 45 54 63 72 81 90 99 108 10 20 30 40 50 60 70 80 90 100 110 120 2. Go down the x7 column until you find 42 11 22 33 44 55 66 77 88 99 110 121 132 12 24 36 48 60 72 84 96 108 120 132 144 3. Read across to see how many groups of 7 made 42

25

2 Standard Division (no remainders) 2 3 2 4

We always work from left to right

4 6 4 8 26

Standard Division (with a remainder in the answer) 2 3 2 4 r 1 2 4 6 4 9

Place the remainder after the letter ‘r’ at the end of the answer

27