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 Rules Understanding Mental calculations Rapid recall Efficient written methods Models, images & concrete materials Stories / rhymes Problem 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 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

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 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) =

(+ 2) (+ 3) (+ 30) = = 77 + (3 + 2) = = 82 No number line

Addition by partitioning = = =

1 Column addition Extend to: £ £ km km

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.

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 =

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

− 2 − 4 − 20 Number lines - taking away 74 – 26 = 48

Number lines - counting on 74 – 26 =

Subtraction by partitioning – 100 = – 80 = – 6 = 568

Subtraction by decomposition