How we teach calculation at Gospel OakA guide for Parents and Carers

Aims

• To explain how we teach your children +, -, x and ÷.

• To explain why we use these methods.

• To give you some ideas as to how you can support your children at home.

Why is maths taught differently now?• When I was at school, maths lessons involved teaching rules of how

to do things. We didn't question and often we didn't understand why we were "carrying ten" or "borrowing one".

• This meant that I was fine as long as I remembered the rules and as long as the type of question didn’t change, but I had no clear understanding of what I was doing and why it worked.

• Activities like this were probably okay for the children who ‘got’ maths, but not for those who struggled or were uninspired by the work on offer.

By the end of Key Stage 2, we want your children to:• Recall key number facts e.g. all +/- facts for each

number to 10, times tables, number bonds etc.• Have a good understanding of the 4 operations (+

- x ÷).• Have an efficient, reliable method of calculation for

each operation.• Apply their understanding to problems and real life

situations.• Use a calculator effectively.

Children need:

• To be taught the specific skills needed for calculation.

• To understand what they are doing and why.• To understand why maths is important in a real

life context.• To leave education with a solid understanding of

maths in order to help them in adult life.• And most of all... to enjoy maths.

Our methods

• All our calculation methods are based on developing an understanding of the number system and building on existing mental strategies.

• We want children to develop a mathematical understanding, a feel for the value of number, NOT just to learn a mechanical method that is prone to error.

• Once they fully understand what they are doing, they can move to more compact methods.

Please remember that each child is an individual and all children develop their mathematical understanding at a different pace.

ADDITION

Addition vocabulary• Add/adding/addition• Plus• Sum• And• Altogether/together• Increase• More• Total

Mental strategies for addition

• Recall of number bonds.

• Using near doubles.

• Partitioning (splitting a number up) and recombining (putting it back together again).

• Counting on and counting back in steps of 1, 10, 100 or 1000.

• Adding the nearest multiple of 10, 100 or 1000 and adjusting e.g. add 10 then take away 1 in order to add 9 to a number.

• Using the relationship between addition and subtraction.

Overview of progression in addition• R/Y1 - children are encouraged to develop a mental picture of the

number system in their heads.

• Y2 - children use empty number lines to count on from the larger number.

• Y3 - children continue to use empty number lines with increasingly large numbers, and begin to use informal paper and pencil methods.

• Y4 - children begin to carry below the line.

• Y5 - children extend the carrying method to numbers with at least four digits.

• Y6 - children extend the carrying method to numbers with any number of digits.

SUBTRACTION

Subtraction vocabulary• Subtract/subtraction• Minus• Take away• Take from• Fewer• Decrease• Difference between• Reduce

Mental strategies for subtraction• Recall of addition and subtraction facts.

• Finding a small difference by counting up.

• Partitioning (splitting a number up) and recombining (putting it back together again).

• Counting on and counting back in steps of 1, 10, 100 or 1000.

• Subtracting the nearest multiple of 10, 100 or 1000 and adjusting e.g. take away 10 then add 1 in order to take away 9 from a number.

• Using the relationship between addition and subtraction.

Overview of progression in subtraction• R/Y1 - children are encouraged to develop a mental picture of the

number system in their heads.• Y2 - children use empty number lines to count on and count back. • Y3 - children continue to use empty number lines with increasingly

large numbers, and begin to use informal paper and pencil methods.

• Y4 - children extend their use of written methods.• Y5 - children extend the decomposition method to larger numbers

and to decimal numbers.• Y6 - children extend the decomposition method to more complex

numbers.

MULTIPLICATION

Multiplication vocabulary• Multiply/multiplication/multiplied by• Times• Times table• Product• Groups of• Lots of

Mental strategies for multiplication• Using knowledge of doubling and halving.

• Using recall of times tables facts.

• Using closely related facts e.g. 13 x 11 = (13 x 10) + (13 x 1).

• Multiplying by 10, 100 or 1000.

• Partitioning numbers e.g. 23 x 4 = (20 x 4) + (3 x 4).

• Using knowledge of factors.

Overview of progression in multiplication• R/Y1 - children will experience equal groups of objects and will

count in 2s and 10s and begin to count in 5s.• Y2 - children will extend their understanding of multiplication. • Y3 - children continue to use repeated addition, numberlines and

arrays, and begin to use informal paper and pencil methods.• Y4 - children will continue to use arrays, leading into the grid

method of multiplication.• Y5 - children extend their use of the grid method to larger numbers

and decimals.• Y6 - children extend their use of the grid method to larger numbers

and decimals.

DIVISION

Division vocabulary• Divide/division/divided by• Divisible by• Share/share equally• Group

Mental strategies for division

• Using knowledge of doubling and halving.

• Using times tables facts to find division facts e.g. 3 x 5 = 15 so 15 ÷ 5 = 3.

• Using closely related facts e.g. 21 ÷ 7 = 3 so 210 ÷ 7 = 30, 210 ÷ 70 = 3, 2.1 ÷ 7 = 0.3 etc.

• Dividing by 10, 100 or 1000.

• Using knowledge of factors.

Overview of progression in division• R/Y1 - children will understand equal groups and share items out in

play and problem solving.• Y2 - children will extend their understanding of division. • Y3 - children continue to use repeated subtraction and

numberlines.• Y4 - children will develop their use of repeated subtraction, and

begin to use informal paper and pencil methods.• Y5 - children will continue to use a written method to solve division

questions.• Y6 - children will continue to use a written method to solve division

questions.

How you can support your child• Look for and talk about numbers in the environment

• Play games

• Shopping

• Counting on/back

• Number bonds

• Doubles/halves

• Times tables

• Division facts