Progression in Calculation St James RC Primary School 31 st January 2013

Progression in CalculationProgression in Calculation

St James RC Primary SchoolSt James RC Primary School

3131stst January 2013 January 2013

400 30 2

1 32 4 125 11109876

ObjectivesObjectives

To demonstrate the need for clear To demonstrate the need for clear and appropriate progression in and appropriate progression in mathematics.mathematics.

To highlight the importance of To highlight the importance of mental strategies.mental strategies.

To know how best to support your To know how best to support your children at home.children at home.

What What mathematics mathematics have you done have you done today?today?

30

400 2

1 32 4 125 111098761 32 4 125 11109876

Our AimOur Aim

By the end of key Stage 2, all By the end of key Stage 2, all children should be able to use children should be able to use an efficient written method for an efficient written method for each operation with confidence each operation with confidence and understanding.and understanding.

Prior KnowledgePrior Knowledge

Oral and mental work in mathematics Oral and mental work in mathematics is essential, particularly so in is essential, particularly so in calculation. Early practical, oral and calculation. Early practical, oral and mental work must lay the mental work must lay the foundations by providing children foundations by providing children with a good understanding of how with a good understanding of how the four operations build on efficient the four operations build on efficient counting strategiescounting strategies and a secure and a secure knowledge of knowledge of place value place value and and number factsnumber facts. .

Number FactsNumber Facts

Learning times tablesLearning times tables

Say the multiples (just the answers)Say the multiples (just the answers) Chant the tables (the old fashioned Chant the tables (the old fashioned

way!)way!) Test children on times table facts (not Test children on times table facts (not

in order)in order) Learn the ‘fact family’. (two Learn the ‘fact family’. (two

multiplication and two division multiplication and two division calculations that use the same calculations that use the same numbers)numbers)

Place ValuePlace Value

Th H T U.th hthTh H T U.th hth

How to help your child at How to help your child at homehome

Dice MeasuringDice Measuring Playing cards Board games Playing cards Board games Car number plates Door numbersCar number plates Door numbers Money TimetablesMoney Timetables Cooking DominoesCooking Dominoes Multiplication and division factsMultiplication and division facts Countdown TimeCountdown Time Please don’t introduce your Please don’t introduce your

child to compact written child to compact written methods before they are ready!methods before they are ready!

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Progression towards a Progression towards a compact (formal) written compact (formal) written methodmethod11 Establish mental methods, based on a good Establish mental methods, based on a good

understanding of place value in numbers.understanding of place value in numbers.22 Solve calculations in a horizontal format.Solve calculations in a horizontal format.3 Children set out written calculations, 3 Children set out written calculations,

initially using expanded layouts that record initially using expanded layouts that record their mental methods.their mental methods.

44 As children become more confident, they As children become more confident, they refine the written record into a more refine the written record into a more compact and efficient method.compact and efficient method.

55 Extend to larger numbers and to decimals. Extend to larger numbers and to decimals. (Children may initially need to return to a (Children may initially need to return to a more expanded layout.)more expanded layout.)

1 32 4 125 11109876

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AdditionAddition

Stage 1 – numbered lines counting on in Stage 1 – numbered lines counting on in ones.ones.

Stage 2 – Empty number linesStage 2 – Empty number lines Bridging to tenBridging to ten PartitioningPartitioning Adding larger numbersAdding larger numbersStage 3 – Partitioning (‘exploding’ – Partitioning (‘exploding’

number sentences)number sentences)Stage 4 – expanded notation in columnsStage 4 – expanded notation in columnsStage 5 – compact column method Stage 5 – compact column method

SubtractionSubtraction

Stage 1 – Numbered lines counting back in Stage 1 – Numbered lines counting back in ones.ones.

Stage 2 – empty number linesStage 2 – empty number lines Bridging to tenBridging to ten PartitioningPartitioning Subtracting larger numbersSubtracting larger numbersStage 3 – Use number line to count up Stage 3 – Use number line to count up

(useful for ‘find the difference’ and (useful for ‘find the difference’ and finding change).finding change).

Stage 4 – Expanded partitioningStage 4 – Expanded partitioningStage 5 – compact decompositionStage 5 – compact decomposition

MultiplicationMultiplication

Stage 1 – Repeat addition on a Stage 1 – Repeat addition on a number line.number line.

Stage 2 – Partitioning using known Stage 2 – Partitioning using known facts.facts.

Stage 3 – Grid method.Stage 3 – Grid method.

Stage 4 – Expanded layout.Stage 4 – Expanded layout.

Stage 5 – compact method.Stage 5 – compact method.

DivisionDivision

Stage 1 – Repeat subtraction on a Stage 1 – Repeat subtraction on a number line.number line.

Stage 2 – repeat subtraction on a Stage 2 – repeat subtraction on a number line finding remainders.number line finding remainders.

Stage 3 – Partitioning into ‘known’ Stage 3 – Partitioning into ‘known’ facts.facts.

Stage 4 – Chunking.Stage 4 – Chunking.

Stage 5 – Bus stop.Stage 5 – Bus stop.

‘‘Build on what pupils already know, understandBuild on what pupils already know, understand

and can do. Pupils should not be taught to use aand can do. Pupils should not be taught to use a

compact method if their understanding and compact method if their understanding and recordingrecording

of mental methods is not secure. When a ‘taught’of mental methods is not secure. When a ‘taught’

method does not build on pupils’ previous method does not build on pupils’ previous

understanding, then the various stages of the understanding, then the various stages of the

calculation will be difficult to reproduce and errorscalculation will be difficult to reproduce and errors

will result’will result’

Key Stage 3 StrategyKey Stage 3 Strategy

Key MessagesKey Messages

Consistency of approach is crucial Consistency of approach is crucial to children’s understanding of to children’s understanding of written calculationswritten calculations

If children are introduced to If children are introduced to compact methods before their compact methods before their understanding is developed they understanding is developed they will not be successfulwill not be successful

Division is mathematics where Division is mathematics where you get two numbers then you you get two numbers then you put one of the numbers into the put one of the numbers into the other number and you write how other number and you write how many can go into that number. many can go into that number. Then you multiply the number on Then you multiply the number on top with the number on the side top with the number on the side and you get the answer. Put it on and you get the answer. Put it on the bottom and subtract it with the bottom and subtract it with the number in the middle. the number in the middle. However many is left you put a ‘r’ However many is left you put a ‘r’ on the top then the number by on the top then the number by the ‘r’ that stands the ‘r’ that stands

as the reminder.as the reminder. EmilyEmily