Aim To explain some of the strategies that we use to teach +, -, x and ÷.

Concrete/practical/objects Pictorial Abstract (‘writing it down’)

We always try to relate calculations to real-life and to solving problems Mental as well as pencil-and-paper methods Develop rapid, confident recall of number facts and Times Tables

Addition Add Add Plus Plus More than More than Count on Count on

Laying the foundations…… Number lines Practical equipment Multilink cubes Real life contexts Number bonds Patterns

= Use of a 100 square = Use of a number line

Partitioning…….. Place value Partitioning Recombining

Children use their knowledge to move towards the ‘standard’ written method: Continue to use partitioning = 101

Column addition…. The final step, when the children have a sound grasp of place value & of the whole process…

Subtraction

3-2= Taking away practically.

Use of a number line/100 square 12-6=

Written methods for Subtraction Partitioning Subtraction can be recorded using partitioning to write equivalent calculations that are easier to carry out mentally. For this involves partitioning the 28 into 20 and 8, then subtracting 20 and 8 in turn. 74 – 28 is the same as 74 – 20 – 8 74 – 20 = – 8 = 46

Written methods for Subtraction Stage 4: Column method The expanded method is eventually reduced to:

Multiplication

Multiplication- repeated addition xx x 3x5= (3 groups of 5) xx x xx x = 15

Arrays Children should be able to model a multiplication calculation using an array. This knowledge will support with the development of the grid method. 3 x 5 5 x 3

Grid Method Using partitioning, we can look at 8 x 13 = 104 as 8 x 10 plus 8x3: = 104

Standard Written Method

Division ÷

Written methods for Division Initially division is introduced as ‘sharing’ using real objects or pictures. Share 10 apples equally between 2 children which eventually becomes 10 ÷ 2 = 5

Remainders:

Written Methods for Division ‘Short’ division

Written methods for Division Long division for HTU ÷ TU The next step is to tackle HTU ÷ TU. This is the 'long division' method. The 20, or 2 tens, and the 3 ones forming the answer are recorded above the line, as in the second version.