In Year 3 your child will be:

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Helping Your Child With Maths

We know that the way in which we teach calculation always seems to be changing. Parents often comment “We didn’t do it like that when I was at school!” We hope that through this booklet you will feel more comfortable when helping and supporting your child with their numeracy work.

In Year 3 your child will be taught: Addition – using number lines to add one and two digit numbers 8 + 7 = 15

We are adding 7 to 8, by starting at the biggest number and counting on 2, which took us to 10, then we added another 5 so we have added 7 altogether. When the children become more confident, we count on from the biggest number to the next multiple of 10, before adding on the remainder. 48 + 36 =

Addition – using partitioning and recombining to add two and three digit numbers in a column method (one number above another) Towards the end of year 3 we begin to partition to add. This means we split up numbers into tens and units in order to add. Partitioned numbers are then written under one another:

47  40  7  76 70  6 110  13  123 When we add the tens and units back together, we call this recombining.

In Year 3 your child will be taught: Subtraction – using number lines to subtract 2 and 3 digit numbers A good way of subtracting is to start with the smallest number (the number being taken away) and count on to the target number (the number being taken from). This is called “finding the difference.”

This number line solves the problem 74 – 27, by counting on. To get from 27 to 74 we have added on 3, 40 and 4 giving us a total of 47. So 74 – 27 = 47

This number line solves the problem 326 – 178 by counting on. So 326 – 178 = 148 Subtraction – using partitioning and recombining to subtract two and three digit numbers Towards the end of year 3 we begin to partition to subtract. We are still counting on to find the difference but are beginning to introduce a more formal written method.

74  27 3 40 4 47

 30  70  74

We have started at 27 and have counted on 3, to take use to the next multiple of 10 which is 30. We have then added on 40 taking us to 70, then 4 to take us to the target number of 74. Altogether we have added on 47.

In Year 3 your child will be taught: Multiplication – using number lines to times 1 and 2 digit numbers. Children will be using beads or cubes for support, so to calculate they will take 3 groups of 4 cubes and then count how many they have altogether. Children will then move on to using a number. 3 x 4 = 12 can be shown as follows. 1x4 2x4 3x4

4

8

12

Towards the end of year 3 we begin to partition to multiply. So that 52 x 3 = 50 x 3 and 2 x 3 = which is the same as 150 + 6 = 156. This can be shown on a number line as follows. 1x50 2x50 3x50 2x3=6

50

100

150

156

Children will be learning to times a number by 10 by moving the digits one place to the left. 6 x 10 = 60 H

T 6

78 x10 = 780 U 6 0

H 7

T 7 8

U 8 0

We do not say that we “add a zero or nought” because this will make multiplying decimals harder in year 5.

In Year 3 your child will be taught: Division Children will be using cubes or beads to support division. So to divide 16 by 4, they will take 16 cubes and group them into 4 piles, before counting each pile. Children will also learn to round up or down depending on a problem. Word problem – 5 people fit into a car. If there are 16 people how many cars do we need to transport these people?

Division – using number lines to divide 2 digit numbers by 1 digit. So, to calculate 16 divided by 4, the children will start at 0 and count up in steps of 4 until they arrive at 16. They will be able to see that there are 4 lots of 4 in 16.

0

4

8

12

16

In Year 4 your child will be taught: Addition – using an expanded column method to add 2 and 3 digit numbers

47  76 13 110 123

Here we have added the units and tens separately, and then recombined to get our answer. This method is also used to tackle money problems using decimals.

Towards the end of year 4 they will begin to add 2 and 3 digit numbers using a formal column method.

47  76 123

258  87 345

366  458 824

11

11

11

This method may look easier than the expanded method used in year 3, but before attempting it, it is essential that the children understand the value of each of the digits being used. So we say “carry a ten” or “carry a hundred” not “carry a one. “

In Year 4 your child will be taught: Subtraction – of 2 digit numbers on a number line including numbers to 1 decimal place. A good way of subtracting is to start with the smallest number (the number being taken away) and count on to the target number (the number being taken from). This is called “finding the difference.”

To calculate 22.4 – 17.8 we start at 17.8 add 0.2 which take us to 18, we then add 4 taking us to 22 then we add 0.4 taking to our target number of 22.4 So altogether we have added 4.6 Subtraction – using an expanded column method to subtract 2 and 3 digit numbers including decimals We then encourage children to move to a more formal written method.

22.4 17.8 0.2  18 4.0  22 0.4  22.4 4.6 Again we are 22.4 – 17.8 we start at 17.8 add 0.2 which take us to 18, we then add 4 taking us to 22 then we add 0.4 taking to our target number of 22.4 So altogether we have added 4.6 this time we have recorded it in a different way. In Year 4 your child will be taught: Multiplication – using a grid method of multiple TU by U and HTU by U The grid method involves partitioning numbers, splitting them into T and U or H T U, before multiplying these separately by the U. 323 x 3 =

X 3

H T 300 20 900 60 900 + 60 + 9 = 969

U 3 9

Children will be learning to times a number by 1000 by moving the digits move three places to the left. 72 x 1000 = 72,000 TTH

Th

H

T 7

U 2

7

2

0

0

0

We do not say that we “add zero or nought” because this will make multiplying decimals harder in year 5. In Year 4 your child will be taught: Division – Using a bus stop method to divide T U by U. This involves partitioning the number to be divided into smaller numbers which are easier to work with. So to divide 73 by 3, we firstly split the 73 into 60 and 13, then calculate how many 3s are in 60 and 13. We use this method to record it.

20 + 4 r 1 3 60 13 Children will be learning to divide numbers by 10, 100 and 1000. This involves moving digits 1, 2 or 3 places to the right. 230 ÷ 10 Th

H 2

230 ÷ 100 T 3 2

U 0 3

H 2

T 3

U 0 2

. . .

t 3 3

In Year 5 your child will be taught: Addition – Expanded column method to add 3 and 4 digit numbers So to add 3422 and 4624 3422 +4624 6 40 1000 7000 8046

2+4 20 + 20 400 + 600 3000 + 4000

Here we have added the units, tens, hundreds and thousands separately, and then recombined to get our answer. This method is also used to tackle money problems using decimals. For example £153.27 + £ 241.68 As the children become more confident they will move towards using a more formal written methods when handling larger numbers. It is essential that the children understand the value of each of the digits being used. So we say “carry a ten” or “carry a hundred” not “carry a one.“ In Year 5 your child will be taught: Subtraction – Expanded column method to subtract 3 digit numbers If we were subtracting 278 from 563 we first partition the number into HTU

-

500 200

60 70

3 8

We know that 8 cannot be taken from 3 so we exchange 1 ten for 10 units

-

500 200

50 70

13 8 5

Now we can see that 70 cannot be taken from 50 so we exchange 1 hundred to 10 lots of 10

-

400 200

150 70 80

13 8 5

Finally we can take 200 from 400

-

400 200 200

150 70 80

13 8 5

When we recombine 200 80 and 5 we get our answer of 285 This seems a long process but it helps to reinforce the value of the digits that are being used. Towards the end of year 5 children will be introduced to a more compact column method using exchange.

-

4 5 2 2

15 6 7 8

13 3 8 5

In Year 5 your child will be taught: Multiplication – using a grid method of multiple HTU by TU, TU by TU and U. t by U The grid method involves partitioning numbers, splitting them up before multiplying them. 23 x 34 T U X 20 3 30 600 90 4 80 12 600 + 90 + 80 + 12 = 782 To find the answer we have recombined the totals in the grid.

This method is also used to multiply units and tenths 6 x 1.8 U . tenth X 1 0.8 6 6 4.8 6 + 4.8 = 10.8 To find the answer we have recombined the totals in the grid. Children will be learning to times a number with a decimal place by 10, 100 and 1000 by moving 1, 2 or 3 places to the left. 4.2 x 10 Th

H

T 4

4.2 x 100 Th

H 4

T 2

U 4 2

. t . 2

U 4 0

. t . 2

We do not say that we “add zero or nought” because this does not work when multiplying decimals. In Year 5 your child will be taught: Division – Using a bus stop method to divide H T U by U. This involves partitioning the number to be divided into smaller numbers which are easier to work with. So to 196 ÷ 6 we would firstly split the 196 into 60, 60, 60 and 16, because we know that 10 x 6 = 60 and that 3 x 60 = 180 We would put this into a bus stop

Eg. What is 196 divided by 6?

6

10 + 10 + 10 + 2 r 4 60 60 60 16

Children will be learning to divide whole numbers and decimals by 10, 100 and 1000. This involves moving digits 1, 2 or 3 places to the right.

230 ÷ 100 H 2

6.2 ÷ 100 H

T 3

T

U 0 2

.

U 6 0

. .

t

.

3

.

t h tth 2 0 6 2

We make sure that we put in the 0 in the units column which makes the number clearer to read, we would not just write .062

In Year 6 your child will be taught: Addition – By Year 6 the children should have developed their addition skills and should now be practising. They should be able to use partitioning to split numbers into thousands, hundreds, tens, units and decimals before recombining (adding back together). These skills were taught in year 5 and involve the following method : Year 5 method : Addition – Expanded column method to add 3 and 4 digit numbers So to add 3422 and 4624 3422 +4624 6 40 1000 7000 8046

2+4 20 + 20 400 + 600 3000 + 4000

Here we have added the units, tens, hundreds and thousands separately, and then recombined to get our answer. This method is also used to tackle money problems using decimals. For example £153.27 + £ 241.68 As the children become more confident they will move towards using a more formal written methods when handling larger numbers. It is essential that the children understand the value of each of the digits being used. So we say “carry a ten” or “carry a hundred” not “carry a one.“

In Year 6 your child will be taught : Subtraction –

700  40  1  300  60  7

600

130

11

700  40  1  300  60  7 300  70  4

6 13 11

741  3 67 374

We can see that 1 cannot be taken from 7, so we exchange (swap / borrow!) 1 ten for 10 units so that the 1 becomes 11. This leaves what was the 40 as 30. We have also exchanged 100 for 10 tens, this means the 700 becomes a 600 and the 30 becomes 130. In Year 6 your child will will be taught: Multiplication The children will use the same grid method as they used in Year 5 but with larger numbers. X 30 4

H 300 9000 1200 10500

T 20 600 80 700

U 3 90 12 105

10500 + 700 + 105 =11305

The children will also be expected to solve problems using more than one operation (+ - x ÷). The following problem uses both subtraction and multiplication. Three children each win £5.60 If they go to the cinema and it cost £9.30 How much change do they have altogether? First the children will times the £5.60 by 3 using the grid method, or mentally if able. Then subtract £9.30 from the answer using partitioning and recombining (see above) to get the answer. In Year 6 your child will be taught: Division Year 6 should also be able to divide whole numbers or simple numbers with one decimal place by halves, fifths and tenths.

Eg. What is 3.5 divided by 0.5? WORD PROBLEM ‘I need 3.5kg of sugar. Sugar is sold in bags which weigh 0.5 kg. How many bags do I need to buy?’ 0.5 1.0 1.5 2.0 2.5 3.0 3.5 There are 7 lots of 0.5 in 3.5 so I need 7 bags of sugar.

All other division is revision of the methods used in Year 5, these methods are shown below : Y5 method – also used in Y6 : Division – Using a bus stop method to divide H T U by U. This involves partitioning the number to be divided into smaller numbers which are easier to work with. So to calculate 196 ÷ 6 we would firstly split the 196 into 60, 60, 60 and 16, because we know that 10 x 6 = 60 and that 3 x 60 = 180 We would put this into a bus stop

Eg. What is 196 divided by 6?

10 + 10 + 10 + 2 r 4

Children be learning divide16 whole numbers a 6 will60 60 to60

Children will be learning to divide whole numbers and decimals by 10, 100 and 1000. This involves moving digits 1, 2 or 3 places to the right 230 ÷ 100

H 2

6.2 ÷ 100 H

T 3

T

U 0 2

.

U 6 0

. .

t

.

3

.

t h tth 2 0 6 2

We make sure that we put in the 0 in the units column which makes the number clearer to read, we would not just write .062

Glossary Column Method

Organising numbers on top of each other to help solve calculations.

Decimal Number

A number including parts less than a whole unit

Difference

The gap between two numbers, another word used for taking away or subtraction

Divide

To share between

Exchange

To swap

Expanded Method Split up numbers into more manageable chunks to help solve calculations Mentally

In your head, without using fingers / paper

Multistep

Problems needing more than one calculation

Number Line

A line drawn to help organise calculations

Operation

addition + , subtraction - , multiply x , divide ÷

Partition

Splitting a number up

Recombine

Adding all parts of a calculation back together to get answer

Remainder

The number left over after dividing

Target Number

The number you are aiming for

2 Digit Number

A number which has a ten and a unit e.g. 34