Addition and Subtraction

Calculating efficiently and accurately

[KS1]

Objectives

To explore the knowledge, skills and understanding required for children to add, subtract, multiply and divide efficiently and accurately

To explore the progression in recording and (some of) the teaching approaches used

The Four RulesUnderstanding Mental

calculations

Rapid recall

Efficient written methods

Models, images & concrete materials

Stories / rhymesProblem solving and role play

Use of ICT

Progression for addition and subtraction

• Counting

• One more / less

• Addition as combining two groups, then counting on

• Subtraction as take away or difference (eg how many more is … than …?)

• Ten more/less

• Recall of addition/subtraction facts to 10, 20 and beyond

• Understand that subtraction and addition are inverses

Counting and estimation

There are 5 principles of counting:1. The stable order principle - understanding that the number

names must be used in that particular order when counting2. The one-to-one principle - understanding and ensuring that

the next item in a count corresponds to the next number3. The cardinal principle - knowing that the final number

represents the size of the set4. The abstraction principle - knowing that counting can be

applied to any collection, real or imagined5. The order irrelevance principle - knowing that the order in

which the items are counted is not relevant to the total value

94 65 48 30 71

28 36 56 97 32

12 24 51 82 19

77 63 44 53 28

60 96 75 17 43

2 + 3 =I buy 2 cakes and my friend buys 3 cakes.How many cakes did we buy altogether?

(Children could draw a picture to help them work out the answer)

8 + 5 = 8 people are on the bus. 5 more get on at the next stop. How many people are on the bus now?

(Children could use dots or tally marks to represent objects – quicker than drawing a picture)

Addition

pictures

symbols

Counting on – jumps of 1(modelled using bead strings) 18 + 5 = 23

18 19 20 21 22 23 24

+1 +1 +1 +1 +1

47 77 80 82

(+ 2)(+ 3)(+ 30)

35 + 47 = 47 + 30 + 5= 77 + (3 + 2)

= 82

35 + 47 = 82

No number line

374 + 248

Addition by partitioning

70 + 40 = 110 4 + 8 = 12

300 + 200 = 500

622

1

Column addition

Extend to:

1247 + 367 £2.36 + £6.48 3.5 + 4.8 7.48 + 2.6 12.5 km + 6.08 km

1

+ 248374

622

31 14 20 1624 6 5 2530 29 18 3611 7 13 1

14 20 21 34 39 45 50Three in a row

Choose two numbers from the row of numbers above the grid.

Find the difference between these numbers.

If the answer is on the grid, cover that number with a counter.

5 – 2 =I have five cakes. I eat two of them. How many do I have left?

A teddy bear costs £5 and a doll costs £2. How much more does the bear cost?

(Take away)

(Find the difference)

13 – 5 =Mum baked 13 biscuits. I ate 5. How many were left?

Lisa has 13 felt tip pens and Tom has 5. How many more does Lisa have?

Drawing a picture helps children to visualise the problem

Using dots or tally marks is quicker than drawing a detailed picture

(Take away)

(Find the difference)

Subtraction

Taking away – jumps of 1(modelled using bead strings) 13 – 5 = 8

8 9 10 11 12 13

-1 -1 -1 -1 -1

Counting on – jumps of 1(modelled using bead strings) 11 – 8 = 3

0 1 2 3 4 5 6 7 8 9 10 11

+1 +1 +1

74 48 50 54

− 2− 4

− 20

Number lines - taking away

74 – 26 = 48

Number lines - counting on

74 – 26 = 48

0 26 30 70 74

+ 4 + 4

+ 40

Subtraction by partitioning

754 - 186

754 – 100 = 654654 – 80 = 574574 – 6 = 568

Subtraction by decomposition