Hogarth Primary

School

Introduction

Current teaching methods for maths and even the way that sums are

recorded appear very different from those used twenty years ago. As

a result, parents are sometimes reluctant to help their children with

maths homework for fear of doing things in the wrong way. However,

children do really benefit when parents take a keen interest in their

mathematical learning.

The aim now is for children to do calculations in their heads and, if the

numbers are too large, to use a variety of ways of writing them down

that helps their thinking. You can help your child to gain confidence

and develop a positive attitude towards mathematics by talking about

what has been taught at school and helping them to notice and use

mathematics in an everyday context.

Within this booklet we have tried, as simply as possible, to help you to

help your children. We take you through how numeracy is now taught

from the earliest counting and mental skills to their recording of

calculations to support thinking.

Counting

Counting is important so that children learn the order of

numbers and where numbers are in relation to each other. It is

important for children to know how close 10 is to 7 and how far

away 10 is from 97. We use number lines & 100 squares to help

children to recognise this.

Counting forward and backwards, from zero and then starting

from other numbers, sets the foundation for addition and

subtraction. Counting in steps, such as twos, fives and tens sets

the foundation for multiplication and division.

Help your child practice counting by:

Counting the number of steps to bed, pages in a

storybook, buttons on their coat, motorbikes on a car

journey.

Play games that involve counting items or using a dice,

such as snakes & ladders, dominos or cards.

Make mistakes when counting to see if your child notices

what was missing.

+ Addition +

Early addition begins with finding one or two more than a number,

using a number line or 100 square.

Children will then learn to read number sentences and worded

problems and use a number line or objects to solve them.

As the numbers increase children draw a number line to calculate

the steps they have taken to find the answer.

Example: 7 + 4 = ? or 7 people are on a bus, 4 more get on, how many

are on the bus now?

Children may find the number 7 on a number line and count on 4 or

count 7 cubes/pictures/tally marks and then add 4 more to find the

answer.

Example: 47 + 25 = ? or A sunflower is 47cm tall, it grows another

25cm, how tall is it now?

They start the number line at 47 then add multiples of numbers that

they know. As children confidence increases the number of jumps

will reduce.

72 47 57

+ 10 + 10 + 3 + 2

67 70 47 67 72

+ 20 + 5

Or

│││││││ + ││││

Example: Make the bee fly 5 spaces on the number line, now fly four

more, what number have you got to?

+ Addition +

Children will then be taught written methods for calculations,

starting with partitioning using the expanded method.

As children become more confident the expanded method can be

‘squashed’ into the traditional compact method.

Example: 487 + 546 = ? or There are 487 boys and 546 boys in a

school, how many children are there altogether?

546 + 487

13 (6+7) 120 (40+80) 900 (500+400)

1033

546 = ( 500 + 40 + 6 ) + 487 = ( 400 + 80 + 7 )

1033 = ( 900 + 120 + 13)

Or

Example: 12786 + 2568 = ? or 12786 people visited the museum

last year, the numbers increased by 2568 this year, how many people

visited altogether?

12786 + 2568 15354 1 1 1

The number is partitioned into its place value

amounts, i.e. units (6+7), tens (40+80) and

hundreds (500+400). The results of each

partition are then added together to find the

answer.

- Subtraction -

Early subtraction begins with finding one or two less than a number,

using a number line or 100 square.

Children will then learn to read number sentences and worded

problems and use a number line or objects to solve them.

.

Example: Find the number 47 and take away 2, what number do you

have?

Example: 7 – 3 = ? or Mum baked 7 biscuits, I ate 3, how many

were left?

Children may count 7 biscuits then take away 2, or draw 7 dots and

3 dots and find the difference between the two numbers

Taking away

Or ●●●●●●● ●●● Finding the difference

- Subtraction -

As the numbers increase children draw a number line to calculate

the steps they have taken to find the answer.

Children will then be taught how to record these steps vertically.

Example: 84 - 27 = ? or I cut 27cm off a ribbon measuring

84cm, how much is left?

They start the number line at the smaller number and count up, in

multiples they know, to the larger number to find the difference. As

childrens confidence increases the number of jumps will reduce.

30 80 84

+ 50 + 4 + 3

27

Example: 834 – 378 = ? or The library owns 834 books, 378 are out

on loan, how many books are on the shelves?

834

- 378 22 ( to 400) 400 ( to 800)

34 (to 834 ) 456

400 800 834

+ 400 + 34 + 22

378

x Multiplication x

Children are taught to understand multiplication as repeated

addition, beginning with learning to count in twos, fives and tens,

then progressing to threes and fours, before learning all times

tables. To solve multiplication number sentences and worded

problems children begin using pictures, dots or tally marks drawn in

groups.

Children will then progress to drawing an array to give an image of

the answer. This helps children develop the understanding that 4x3

is the same as 4x3.

Children could draw an empty number line and count on in equal

steps, recording each jump.

Example: 2 x 3 = ? or There are 2 cakes in a pack, how many in 3

packs?

+ +

Example: 4 x 3 = ? or A chew costs 4p, how much do 3 chews cost?

●●●● Or ●●● ●●●● ●●● ●●●● ●●● ●●●

Example: 6 x 4 = ? or There are 4 cats, each has 6 kittens, how many

are there altogether?

+ 6

24 18 12 6 0

+ 6 + 6 + 6

x Multiplication x

As the numbers increase larger jumps can be made on a number

line using partitioning.

Children will finally advance to using partitioning with the grid

method.

Example: 13 x 7 = ? or There are 13 biscuits in a packet, how

many biscuits in 7 packets?

The number is partitioned into its place value amounts, i.e. units (3)

and tens (10). Each value is multiplied by 7, which is a times table

they would have learnt, to give two jumps on the number line. The

results of each partition (70+21) are then added together to find

the answer (91).

0 70 91

+ 70 + 21

3 x 7 10 x 7

Example: 72 x 34 = ? or A cat is 72cm long, a tiger is 34 times

longer, how long is the tiger?

Each number is partitioned and placed on a grid, then each part is

multiplied. When calculating 70 x 30 children can break the sum

further into units (7 x 3) then make the answer 100 times bigger (as

each number is 10 times bigger than the unit). The numbers are then

added across the rows, then those two numbers added together to

find the answer.

70 2

30 2100 60 = 2160 + = 2448 4 280 8 = 288

÷ Division ÷

Children begin to learn division as sharing equally.

Children are then taught to understand grouping.

Children then progress to using a number line to calculate the

number of jumps from.

Example: 6 ÷ 2 = ? or 6 easter eggs are shared between 2

children, how many do they get each?

Example: 12 ÷ 4 = ? or 4 apples can fit in a basket, how many

baskets can you fill with 12 apples?

//// //// //// Basket 1 Basket 2 Basket 3

Example: 28 ÷ 7 = ? or A sweet costs 7p, how many can I buy with

28p?

As children knowledge of times tables increases they can use it to

help with division. For instance, children may know 4 x 7 = 28 so will

realise there are four 7’s in 28.

+ 7

28 21 14 7 0

+ 7 + 7 + 7

÷ Division ÷

Knowledge of times tables also helps as the numbers get larger, as

they can they can jump in bigger groups.

Children then progress to the method of ‘chunking’.

Example: 84 ÷ 6 = ? or I need 6 drawing pins to put up a pictures,

how many pictures can I put up with 84 pins?

Children can jump in bigger groups as they know that 10 groups of 6

takes you to 60 and then you need another 4 groups of 6 to reach 84,

so altogether they need 14 groups of 6.

0 60 84

+ 60 + 24

6x10 6x4

Example: 184 ÷ 7 = ? or I need 184 chairs for a concert

arranged in rows of 7, how many rows do I need?

Fact Box

1 x 7 = 7 2 x 7 = 14 5 x 7 = 35

10 x 7 = 70 20 x 7 = 140

184 - 140 (7 x 20) 44

42 (7 x 6) 2 = 26 r2

Children start at 184 and subtract 140

(20 groups of 7). Then subtract 42 (6

groups of 7). So the answer is 20+6=26

with a remainder of 2. Children are

encouraged to use a fact box from their

knowledge of times tables to assist them

in subtracting the correct groups.

Practice at Home

Help your child practice addition, subtraction, multiplication and

division by:

Asking your child to add up the shopping and calculate what

money they need and what change they may get.

Encourage them to count their pocket money to calculate how

much more they need to buy what they would like.

Throw 2 dice ask your child to find the total of the numbers (+),

the difference (-) and the product (x) and see if they can do it

without counting.

Practicing which number facts they are currently learning at

school (times tables/doubles/number bonds).

Using a set of playing cards turn over two cards ask your child to

add or multiply the numbers. If they answer correctly they keep

the card, see how many cards they can collect in one minute

Give your child an answer and ask them to write as many number

sentences as they can.

Give your child a number fact (e.g. 5+3 = 8) and ask them to

write what else they know from this fact (e.g. 3+5=8, 8-5=3, 8-

3=5, 50+30=80, 15+3=18).

Shapes & Measure

Help your child practice shapes and measure by:

Ask your child to find and describe different shapes (i.e. cube,

cuboid, cylinder, sphere etc) and describe its properties (i.e.

vertices, faces, edges).

Play guess the shape by you describing the shape and your child

guesses what it is.

Look for symmetrical objects. Help your child to draw

symmetrical pictures.

Practice measuring lengths and heights in metres or

centimetres. Ask your child to estimate before your measure.

Practice measuring weights and volumes by your child helping

with the cooking.

Find items around the home and ask your child to put them in

order of weight by feel alone, then check by measuring them.

Useful Links:

School learning platform ‘DB Primary’

BBC Website –

Maths for KS1 - www.bbc.co.uk/schools/ks1bitesize

Maths for KS2 – www.bbc.co.uk/schools/ks2bitesize

Overview – www.bbc.co.uk/skillswise