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

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

Column addition Extend to: £ £ km 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 away 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 taking away Number lines - taking away 74 – 26 = 48

Number lines - counting on 74 – 26 =

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 − − Leading to: 563 − Using red alerts: 563 − and 60 and 3 −200 and 40 and 8 Re-written as: 500 and 50 and 13 −200 and 40 and and 10 and 5 Leading to:5 6 3 −