Sandwich Infant School Calculation Policy

Children begin to record in the context of play or practical activities and problems.

Children continue to explore mathematics practically progressing to formal recording and representation

ADDITION Year R Year 1 Year 2

Children look at numbers and how they can make those numbers using groups and amounts. Concrete, pictorial then abstract.

• Children to represent the cubes using dots or

crosses. They could put each part on a part whole model too.

• 4 + 3 = 7

Four is a part, 3 is a part and the whole is

seven.

Mental calculation

• Count on in 1s from a given 2-digit number

• Add two 1-digit numbers

• Add three 1-digit numbers, spotting doubles or pairs to 10

• Count on in 10s from any given 2-digit number

• Add 10 to any given 2-digit number

• Know number bonds (e.g. the’ story’ of 5)

Written calculation Children are taught to:

• Add by counting on, first in 1s then progressing to steps of different numbers

• Count on from the first number using fingers, objects, number lines

• Understand that addition can be done in any order and that it is more efficient to put the larger number first

• Count and combine sets of objects

• Understand the concept of equality before using the = sign. Calculations should be written either side of the equality sign so that the sign is not just interpreted as the ‘answer’. E.g. 2=1+1 and 2+3=4+1

• Begin to record addition number sentences using + and =.

• Find the missing numbers in a number sentence. The missing number needs to be placed in all possible places. Knowing the switcher and the rest

Mental calculation

• Count on in 1s and 10s from any given number

• Add two or three 1-digit numbers

• Add a 1-digit number to any 2-digit number using number

• facts, including bridging multiples of 10

• Add any pair of 2-digit numbers

• Number bonds – know all the pairs of numbers which make

• all the numbers to 12, and pairs with a total of 20

Written calculation Children are taught to:

• Count on in 10s and 1s on the number line e.g. 23 + 12 = 23 + 10 + 2 = 33 + 2 = 35

• Begin to use an empty number line for calculations

• Add 9 and 11 by adding 10 and adjusting by 1 35+9 = 44

• Add 2-digit numbers on the hundred square,

knowing the associated patterns.

• Round numbers up to the nearest multiple of ten.

23 33 35

+10 +2

35 44 45

+10

-1

Children begin to relate addition to combining two groups of objects. Activities might include:

• Using stories, games and songs to begin using

• language for addition

• Beginning to record in the context of play and

• practical activities

• Combining two parts to make a whole (concrete) use other resources too e.g. eggs, shells, teddy bears, cars.

• Practically combining two groups of objects

• Making a record in pictures, words or symbols of practical addition - pictorial

• Solving simple word problems using their fingers

• Constructing number sentences to go with practical activities – abstract

• Using the language of one more when adding one to a group

• Counting on using number lines using cubes or Numicon.

of the number family. 3 + 4 = = 3 + 4 3 + = 7 7 = + 4

• Know all the number bonds within 10

• Solve one-step word problems using concrete objects and pictorial representation. E.g. Peter had 12 apples. He bought 8 more at the greengrocers. How many apples did Peter have altogether?

• Know that subtraction is the inverse of addition and use known number facts to calculate mentally.

• Begin to add by bridging through 10 where necessary.

18 + 5 = 23

• Add larger 3-digit numbers by partitioning and recombining into 100’s, 10’s and 1’s.

• Solve one and two-step addition word problems. e.g.

• The Smith family left school and drove 12 miles to the library. They left the library and drove 14 miles home. How many miles did the Smith family drive?

18 20

23

+2 +3

10

7

3

Counting forwards along a number line.

• Use Dienes rods to partition numbers into 10’s and 1’s

Subtraction Year R Year 1 Year 2

- -

Children begin to record in the context of play or practical activities e.g. counting rhymes that count back. Activities might include: • Physically taking away and removing objects from a

whole (ten frames, Numicon, cubes and other items such as beanbags could be used).

• Removing objects from a group, i.e. ‘I have 5 apples and I take one away, how many are left?’ • Children to draw the concrete resources they are

using and cross out the correct amount. The bar model can also be used.

•

• Counting back (using number lines or number tracks) children start with 6 and count back 2.

6 – 2 = 4

Mental calculation

• Count back in 1s from a given 2-digit number

• Subtract one 1-digit number from another

• Count back in 10s from any given 2-digit number

• Subtract 10 from any given 2-digit number

• Know number bonds (e.g. the’ story’ of 5)

Written calculation Children are taught to:

• Understand that subtraction must start with the larger number and count back the smaller number.

• Subtract 1- digit and 2- digit numbers to 20 using concrete objects and pictorial representation.

13 - 2 = 11 Solve missing number problems 7 = - 9 15 – 9 = 20 - = 9 - = 11

• Begin to record subtraction number sentences using - and =.

• Use the hundred square to find 10 less by looking at the number above.

Mental calculation

• Count back in 1s, 2’s, 5’s and 10s from any given 2-digit number

• Subtract a 1-digit number from any 2-digit number using number facts, including bridging multiples of 10 e.g. 56 – 3 e.g. 53 – 5

• Subtract 10 and small multiples of 10 from any given 2-digit number

• Subtract any pair of 2-digit numbers by counting back in 10s and 1s or by counting up

Written calculation Children are taught to:

• Count back in 10s and 1s on the number line

• Subtract 9 and 11 by subtracting 10 and adjusting by 1 using the hundred square.

• Subtract 2- digit numbers on the hundred square by counting back in tens up the hundred square and then back in ones.

• Use an empty number line and draw how many jumps they are counting back. Progression would be to jump in 10s rather than in 1s.

• Solve missing number problems using larger numbers such as multiples of 10.

100 - = 20

• Use a number line to find the difference between two numbers.

• Solve one and two- step subtraction word problems e.g. Peter had 20 stamps. He used 5 on Christmas cards and 4 on birthday cards. How many stamps did he have left?

• Using stories and role play to encourage the language of subtraction e.g. ‘4 people were on the bus, one got off, how many were left?’

• Drawing a picture representation of a subtraction sentence. 5 take away 1 leaves 4

• Using the language of one less by taking one away from a group, e.g. tower of cubes.

• Using numbered floor tiles and number tracks to identify one less.

• Finding the difference (using cubes, Numicon or

Cuisenaire rods, other objects can also be used). Calculate the difference between 8 and 5.

• Understand subtraction as finding the difference

• The above model should be introduced with concrete objects that children can move (including cards with pictures) before progressing to pictorial representation.

• The use of other images is also valuable for modelling subtraction e.g. Numicon, bundles of straws, Dienes apparatus, multi-link cubes, bead strings.

• Begin to subtract to solve simple one-step word problems e.g Peter bought 5 apples. He gave 2 to his friends. How many did he have left?

• Begin to recognise that subtraction is the inverse of addition

• Know that subtraction is the inverse of addition and use known number facts to calculate mentally.

Multiplication Year R Year 1 Year 2

Children begin to count in groups of 2s, 5s and 10s using objects, songs and rhymes. Activities might include:

• Counting in groups of the same size in games and practical activities.

• Using practical resources to support counting such as Numicon, bead strings, counters, socks, shoes

• Using practical resources to support counting such as Numicon, bead strings, counters, socks, shoes

Mental calculation

• Begin to count in 2s, 5s and 10s

• Begin to say what three 5s are by counting in 5s, or what four 2s are by counting in 2s, etc.

• Double numbers to 10

Written calculation Children are taught to:

• Understand multiplication is related to doubling and combing groups of the same size.

• Group objects in 2s, 5s and 10s using concrete objects, pictorial representation and arrays.

Mental calculation

• Counts in 2’s, 3’s, 5’s, 10’s.

• Knows 2’s. 5’s, 10’s times tables by heart

• Knows doubles of numbers to 20.

Written calculation Children are taught to understand multiplication as:

• repeated addition eg 4+4+4=12

• grouping 4 x 2 = 8

• Arrays

• Begin to understand multiplication as repeated addition and represent this on a number line

2 + 2 + 2 + 2 + 2 = 10

• Solve simple one-step word problems involving multiplication e.g. 4 children had 2 pencils each. How many pencils did they have altogether?

• Solve simple one step word problems involving multiplication using greater amounts.

12 children have 5 pencils. How many pencils altogether.

Division

Year R Year 1 Year 2 Children begin to experience division as sharing objects into equal groups. Activities might include:

• Sharing out milk bottles and fruit at snack time

• Sharing practically in role play e.g. sharing biscuits in the home corner

• Sharing objects into two groups (halving)

• Sharing using a range of objects.

6 ÷ 2

Mental calculation

• Count in 2s, 5s and 10s

• Find half of even numbers to 12 and know it is hard to halve odd numbers

• Find half of even numbers by sharing

Written calculation Children are taught to:

• Group AND share small quantities- understanding the difference between the two concepts

• Share using concrete apparatus into equal groups

• Apply their counting skills to develop some understanding of grouping

Mental calculation

• Count in 2s, 5s and 10s

• Begin to count in 3s

• Relate division to grouping e.g. How many groups of 5 in 15? Halve numbers to 20

Written calculation Children are taught to:

• Continue to use grouping and sharing for division using practical apparatus, arrays, pictorial representations, number lines and bead strings.

• Use arrays as a pictorial representation for division

15 3 = 5 There are 5 groups of 3. 15 ÷ 5 = 3 There are 3 groups of 5.

• Find ½ and ¼ and simple fractions of a length, shape, set of objects and quantities.

• Solve simple one-step word problems involving division. e.g. There are 10 cakes and 5 children. How many cakes can they each have? Make sure it is fair!

• Partition larger numbers into 10’s and ones to share efficiently.

30÷3= 10

• Recognise, find, name and write ½, 1/3, ¼ and ¾ of a length, shape, set of objects and of amounts.

• Knows the names denominator and numerator

• Begin to relate division to fractions of numbers and shapes – e.g. ½ and ¼ is the same as dividing by 2 and dividing by 4.

• Continue to use grouping of objects practically and relate to real life situations. Progressing to grouping numbers into equal sets with a remainder.

• Begin to record their practical division as a written calculation using ÷ and = in a number sentence.

• Understand that division is the inverse of multiplication.

• Use the multiplication and division facts to work out missing numbers.

12 ÷ = 4

• Use division to solve more complex word problems: Use bar method and fraction walls