Birk Hill Infant & Nursery School

POLICY NAME: Maths Calculations

Approval & Authorisation

NAME JOB TITLE DATE

Elizabeth Warhurst Chair of TLC 16.10.17

Change History

VERSION DATE REASON NAME

1 16.10.17 Cover Sheet Added David Bell

Birk Hill Infant School

Policy for Calculations in Maths

Introduction

At Birk Hill we believe that children should be introduced to the processes of calculation through practical, pictorial, oral and mental activities. As children begin to understand the underlying ideas they:

develop ways of recording to support their thinking and calculations learn to interpret mathematical signs and symbols use particular methods that apply in special cases.

Over time children learn how to use models and images, such as empty number lines, to support their mental and informal calculations.

As children’s mental methods are strengthened and refined, so too are their informal written methods. When they are ready, children will learn a range of efficient written calculation methods that can be applied generally.

Mental methods of calculation

Oral and mental calculation practice is essential in developing a strong understanding of number. Early practical learning should be part of all children’s experience in Foundation Stage and Key Stage 1.

Progression in

Calculations

Addition

Objective and Strategies

Concrete Pictorial Abstract

Combining two parts to make a whole: part- whole model

4 + 3 = 7

10= 6 + 4

Use cubes to add two

numbers together as a

group or in a bar.

8 1

Use pictures to add two numbers together as a group or in a bar.

Use the part - part

whole diagram as

shown above to

move into the

abstract. Use Numicon to

add together 2

numbers.

5

3

8

Starting at the bigger number and counting

on

Adding on in tens and multiples of ten

Start with the larger number on the bead string and then count on to the smaller number 1 by 1 to find the answer.

Start with the number then use practical equipment Dienes to count on in tens.

12 + 5 = 17

Start at the larger number on the number line and count on in ones or in one jump to find the answer. Use the 100 square to add on 10 or multiples of 10 to any number. 16 + 10 = 26

5 + 12 = 17 Place the larger number in your head and count on the smaller number to find your answer. Add on 10 or a multiple of 10 mentally using jottings to support where necessary. 26 + 30 =

26 36

46 56

Regrouping to

make 10.

6 + 5 = 11

Start with the bigger number and use the smaller number to make 10.

Use pictures or a number line. Regroup or partition the smaller number to make 10.

7 + 4= 11 If I am at seven, how many more do I need to make 10. How many more do I add on now?

Adding three single digits

4 + 7 + 6= 17 Put 4 and 6 together to make 10. Add on 7.

Following on from making 10, make 10 with 2 of the digits (if possible) then add on the third digit.

Progress to using sticks for counting.

IIIII + IIIII + III Cross and count to find the total.

Combine the two numbers that make 10 and then add on the remainder.

Column method- no regrouping

Column method with

24 + 15= Add together the ones first then add the tens. Dienes or similar base 10 equipment should be used.

After practically using the base 10 blocks and one cubes children can progress to drawing 10s and 1s below the numbers in the linear calculation.

The tens should be added together and then the ones should be added together. The tens and ones should be recombined.

26 + 58 = 84 10 11 10 11

A bank is used for intrducing vertical addition. T O To combine the tens and ones they are ‘saved’ in a ‘bank’ and added vertically. T O 5 0 6 5 6

32 + 24 = 10 11 10 11

10 10 11

10

regrouping

28 + 15= Add together the ones first.

When 10 is reached the ones cubes should be exchanged for a 10 stick. The 10 stick should be put into the tens column. Next, add the tens. Dienes or similar base 10 equipment should be used.

10 11 10 11

11 10 11

10 11

10

BANK

T O

7 0

1 0

4

8 4

The tens total should be banked first. Then the ones

should be counted and banked at 10. Remaining ones

should be counted and banked. Adding the ones together

and the tens together will give the final total.

When numbers are in the bank they should be added

ones first!

Subtraction

Objective and Strategies

Concrete Pictorial Abstract

Taking away ones

Use physical objects, counters, cubes etc to show how objects can be taken away.

6 – 2 = 4

Cross out drawn objects to show what has been taken away.

Children should progress to drawing sticks as jottings instead of pictures. 9 – 3 = 6

I I I I I I I I I

18 – 3 = 15

8 – 2 = 6

Taking away tens

42 – 10 = 32

To be able to subtract 10 from any number up to 100 using a 100 square. 34-10=24 79-40=39

79 – 40 = 39 Subtract mentally by counting backwards in multiples of 10. Jottings/fingers may be used to support.

Counting back Make the larger number in your subtraction. Move the beads along your bead string as you count backwards in ones. 13 – 4 Use counters and move them away from the group as you take them away counting backwards as you go.

Count back on a number line or number track

Start at the bigger number and count back the smaller number showing the jumps on the number line.

This can progress all the way to counting back using two 2 digit numbers.

Put 13 in your head, count back 4. What number are you at? Use your fingers to help.

Find the difference

Compare amounts and objects to find the difference.

Use cubes to build towers or make bars to find the difference

Use basic bar models with items to find the difference

Count on to find the difference.

Draw bars to find the difference between 2 numbers.

Hannah has 23 sandwiches, Helen has 15 sandwiches. Find the difference between the number of sandwiches.

Find the difference between any number and a two digit number (with or without regrouping)

This could be done practically using counting equipment. Dienes or any base 10 equipment would make the process quicker and more accurate. Where the ones to be subtracted are greater than the ones being subtracted from a ten stick would need to be exchanged for ten ones.

65 – 23 = 42

7 30 5

23 30 60 65

1111111 10 10 10 11111

23 30 60 65

The tally should be added using a bank as shown in the addition section, ie when ten ones have been counted they should be banked as 1 ten.

Bank T O 3 0

1 0 2

4 2

Part Part

Whole Model

Link to addition- use the part whole model to help explain the inverse between addition and subtraction.

If 10 is the whole and 6 is one of the parts. What is the other part?

10 - 6 =

Use a pictorial representation of objects to show the part part whole model.

Move to using numbers within the part whole model.

10

5

Multiplication

Objective and Strategies

Concrete Pictorial Abstract

Doubling Use practical activities to show how to

double a number.

Draw pictures to show how to double a number.

The number to be doubled is put into a doubling hoop.

It is written again in the other half of the hoop, ie doubled, and the 2 numbers are added together.

Counting in multiples

Count in multiples supported by concrete objects in equal groups.

Use a number line or pictures to continue support in counting in multiples.

Count in multiples of a number aloud. Write sequences with multiples of numbers. 2, 4, 6, 8, 10 5, 10, 15, 20, 25 , 30

12

Repeated

addition

Children progress to using jotting sticks in hoops. I I + I I + I I

Write addition sentences to describe objects and pictures.

Arrays- showing

commutative multiplication

Create arrays using counters/ cubes to show multiplication sentences.

Draw arrays in different rotations to find commutative multiplication sentences.

Link arrays to area of rectangles.

Use an array to write multiplication sentences and reinforce repeated addition.

Use different objects to add equal groups.

Multiplication of 2 digit numbers using ‘groups of’

22 x 4 = 88 Children use their understanding of commutative nature of multiplication to read this as 4 x 22 which is much simpler to set out and count.

32 x 3 = 96 Children are able to use their understanding of the commutative nature of multiplication to read this as 3 x 32. They will draw 3 groups and use tens and ones jottings to put 32 into each. The numbers in the hoops are then added to find the total.

10 10

10 1 1

10 10 10

1 1

10 10 10

1 1

Division

Objective and Strategies

Concrete Pictorial Abstract

Sharing objects into groups

I have 10 cubes, can you share them equally in 2 groups?

Children use pictures or shapes to share quantities.

15 ÷ 5 = 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Share 9 buns between three people.

9 ÷ 3 = 3

8 ÷

2 = 4

Division as grouping

Divide quantities into equal groups. Use cubes, counters, objects or place value counters to aid understanding.

96 ÷ 3 = 32

Use a number line to show jumps in groups. The number of jumps equals the number of groups.

Think of the bar as a whole. Split it into the number of groups you are dividing by and work out how many would be within each group.

28 ÷ 7 = 4 Divide 28 into 7 groups. How many are in each group?

Division within arrays

Link

division to multiplication by creating an array and thinking

about the number sentences that can be created. Eg 15 ÷ 3 = 5 5 x 3 = 15 15 ÷ 5 = 3 3 x 5 = 15

Draw an array and use lines to split the array into groups to make multiplication and division sentences.

Find the inverse of multiplication and division sentences by creating four linking number sentences. 7 x 4 = 28 4 x 7 = 28 28 ÷ 7 = 4 28 ÷ 4 = 7

Division with a remainder

14 ÷ 3 = Divide objects between groups and see how much is left over

Jump forward in equal jumps on a number line then see how many more you need to jump to find a remainder.

Draw people and jottings sticks in a neat pattern so that ‘extras’ (remainders can be seen clearly. 14 ÷ 4 = 3 R 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Complete written divisions and show the remainder using r.