Addition and Addition and SubtractionSubtraction

Calculating efficiently

and accurately

Objectives

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

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

Self-esteem

The Four RulesUnderstandinUnderstandin

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Mental Mental calculationcalculation

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Rapid Rapid recallrecall

Efficient Efficient written written

methodsmethods

Models, images & concrete materials

Stories / rhymesProblem solving and role play

Use of ICT

Progression in knowledge and understanding for + / -

• 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 counting

2. The one-to-one principle - understanding and ensuring that the next item in a count corresponds to the next number

3. The cardinal principle - knowing that the final number represents the size of the set

4. The abstraction principle - knowing that counting can be applied to any collection, real or imagined

5. 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

374 374

+ 248 + 248

12 622

110

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

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 awayTaking 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 taking awayaway 74 – 26 = 48

Number lines - counting on 74 – 26 = 48

0 26 30 70 74

+ 4 + 4

+ 40

3131 1414 2020 1616

2424 66 55 2525

3030 2929 1818 3636

1111 77 1313 11

14 20 21 34 39 45 50

Three 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.

Subtraction by decomposition

No breaking down needed:

563 − 241

500 + 60 + 3 − 200 + 40 + 1

300 + 20 + 2

Leading to:563

− 241322

Using red alerts:

563 − 248

500 and 60 and 3 − 200 and 40 and 8

Re-written as:

500 and 50 and 13 − 200 and 40 and 8

300 and 10 and 5

Leading to: 5 6 3 − 2 4 8

3 1 5

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