Calculation ProgressionCalculation Progression

AshfieldAshfield

Numbers all around you!Numbers all around you!

Mental Maths progression overviewMental Maths progression overviewYEAR 1YEAR 1• Derive and recall all pairs of numbers with a total of Derive and recall all pairs of numbers with a total of

10 and addition facts for totals to at least 5; work 10 and addition facts for totals to at least 5; work out the corresponding subtraction facts.out the corresponding subtraction facts.

YEAR 2YEAR 2• Derive and recall all addition and subtraction facts Derive and recall all addition and subtraction facts

for each number to at least 10, all pairs with totals for each number to at least 10, all pairs with totals to 20 and all pairs of multiples of 10 with totals up to 20 and all pairs of multiples of 10 with totals up to 100.to 100.

• Derive and recall multiplication facts for the 2, 5 and Derive and recall multiplication facts for the 2, 5 and 10 times-tables and the related division facts; 10 times-tables and the related division facts; recognise multiples of 2, 5 and 10.recognise multiples of 2, 5 and 10.

YEAR 3YEAR 3• Derive and recall all addition and subtraction facts Derive and recall all addition and subtraction facts

for each number to 20, sums and differences of for each number to 20, sums and differences of multiples of 10 and number pairs that total 100.multiples of 10 and number pairs that total 100.

• Derive and recall multiplication facts for the 2, 3, 4, Derive and recall multiplication facts for the 2, 3, 4, 5, 6 and 10 times-tables and the corresponding 5, 6 and 10 times-tables and the corresponding division facts; recognise multiples of 2, 5 or 10 up division facts; recognise multiples of 2, 5 or 10 up to 1000. to 1000.

YEAR 4YEAR 4• Use knowledge of addition and subtraction facts Use knowledge of addition and subtraction facts

and place value to derive sums and differences of and place value to derive sums and differences of pairs of multiples of 10, 100 or 1000.pairs of multiples of 10, 100 or 1000.

• Derive and recall multiplication facts up to 10 x 10, Derive and recall multiplication facts up to 10 x 10, the corresponding division facts and multiples of the corresponding division facts and multiples of numbers to 10 up to the tenth multiple.numbers to 10 up to the tenth multiple.

YEAR 5YEAR 5• Use knowledge of place value and addition and Use knowledge of place value and addition and

subtraction of two-digit numbers to derive sums subtraction of two-digit numbers to derive sums and differences and doubles and halves of and differences and doubles and halves of decimals (e.g. 6.5 decimals (e.g. 6.5 2.7, half of 5.6, double 2.7, half of 5.6, double 0.34)0.34)

• Recall multiplication facts up to 10x10 and use Recall multiplication facts up to 10x10 and use them to multiply pairs of multiples of 10 and 100; them to multiply pairs of multiples of 10 and 100; derive quickly corresponding division factsderive quickly corresponding division facts

YEAR 6YEAR 6• Use knowledge of place value and multiplication Use knowledge of place value and multiplication

facts to 10x10 to derive related multiplication facts to 10x10 to derive related multiplication and division facts involving decimals (e.g. 0.8x7, and division facts involving decimals (e.g. 0.8x7, 4.8 4.8 6) 6)

• Use knowledge of multiplication facts to derive Use knowledge of multiplication facts to derive quickly squares of numbers to 12x12 and the quickly squares of numbers to 12x12 and the corresponding squares of multiples of 10.corresponding squares of multiples of 10.

Y1Y1• U ± UU ± U• TU + U (bridging 20)TU + U (bridging 20)• TU (up to 20) – UTU (up to 20) – U• U + 9U + 9• Mult of 10 ± mult of 10Mult of 10 ± mult of 10• Finding the difference Finding the difference

(numbers up to 20)(numbers up to 20)• Combinations of groups of Combinations of groups of

equal numbers of objects (U x equal numbers of objects (U x U)U)

• Sharing objects into equal Sharing objects into equal groups (U/TU ÷ U)groups (U/TU ÷ U)

• Use bead strings / number Use bead strings / number lines to calculatelines to calculate

Y2Y2• U + U + UU + U + U• TU ± UTU ± U• TU ± multiple of 10TU ± multiple of 10• TU – TU (small TU – TU (small

difference)difference)• Use inverse operations Use inverse operations

to check calculations to check calculations (+/-)(+/-)

• U x UU x U• U / TU ÷ U (including U / TU ÷ U (including

remainders)remainders)• Use number lines and Use number lines and

jottings to help them jottings to help them carry out calculationscarry out calculations

Progression in Progression in MentalMental CalculationsCalculations

Y3• TU ± U• TU ± near

multiple of 10• HTU – HTU (small

difference)• U / TU x 10 / 100• TU x U (partition)• TU ÷ U (linked to

recall facts)• Fractions of

amounts (eg ¼ of £24)

• Rounding for estimation

Progression in Progression in MentalMental CalculationsCalculationsY5Y5

• +/–+/– decimals: apply decimals: apply known facts & bridge known facts & bridge through landmarksthrough landmarks

• ThHTU – ThHTU (eg ThHTU – ThHTU (eg 7012 – 3984)7012 – 3984)

• x / ÷ whole nos. & x / ÷ whole nos. & decimals by 10 / 100 / decimals by 10 / 100 / 10001000

• Rounding for estimation Rounding for estimation (integers & decimals) (integers & decimals)

• Integers x / ÷ UIntegers x / ÷ U• Fractions of amounts Fractions of amounts

(eg ¾ of £220) (eg ¾ of £220)

Y4• TU ± TU• +/– multiples of 10 / 100• ThHTU – ThHTU (small

difference)• x / ÷ by 10 / 100 (whole

no. answer)• M of 10 x U (including

near multiples)• Divide using factors

(eg 2400 ÷ 20)• Solve problems involving

money, measures & time• Fractions of quantities

(eg 2/3 of 24 cm)

Y6

• Mental multiplication and division with decimals (U.t x / U)• Efficient written methods: - add and subtract whole numbers and decimals;- multiply and divide whole numbers and decimals by a one-digit number, TU x TU and HTU x TU

Which methods to support mental Which methods to support mental calculation ?calculation ?

Number linesNumber lines100 squares100 squares

JottingsJottingsPartitioningPartitioning

Tables and division facts ( trios)Tables and division facts ( trios)AdjustingAdjustingEstimatingEstimatingRoundingRounding

Inverse operationsInverse operationsCuisenaireCuisenaire

Dienes – base 10Dienes – base 10

Key Resources : Piece of string, bead strings, RulerKey Resources : Piece of string, bead strings, Ruler Number LinesNumber Lines

GamesGames

Follow the leaderFollow the leader

LettersLetters

Number line Number line

Ways to support times tables at Ways to support times tables at homehome

• Dot to dotsDot to dots

• Loop cards – dominoesLoop cards – dominoes

• Match the answer Match the answer

• TriosTrios10

5 2

1x2

2

Written calculation progression Written calculation progression overviewoverview

YEAR 1YEAR 1• use practical and informal written methods to support use practical and informal written methods to support

the subtraction of a one-digit number from a one digit the subtraction of a one-digit number from a one digit or two-digit number and a multiple of 10 from a two-or two-digit number and a multiple of 10 from a two-digit numberdigit number

YEAR 2YEAR 2• use practical and informal written methods to add and use practical and informal written methods to add and

subtract two-digit numbers subtract two-digit numbers • Represent repeated addition and arrays as Represent repeated addition and arrays as

multiplication, and sharing and repeated subtraction multiplication, and sharing and repeated subtraction (grouping) as division; use practical and informal (grouping) as division; use practical and informal written methods and related vocabulary to support written methods and related vocabulary to support multiplication and division, including calculations with multiplication and division, including calculations with remainders remainders

YEAR 3YEAR 3• Develop and use written methods to record, support or Develop and use written methods to record, support or

explain addition and subtraction of two-digit and three-explain addition and subtraction of two-digit and three-digit numbersdigit numbers

• Use practical and informal written methods to multiply Use practical and informal written methods to multiply and divide two-digit numbers (e.g. 13 3, 50 4); round and divide two-digit numbers (e.g. 13 3, 50 4); round remainders up or down, depending on the contextremainders up or down, depending on the context

YEAR 4YEAR 4• Refine and use efficient written methods to add and Refine and use efficient written methods to add and

subtract two-digit and three-digit whole numbers subtract two-digit and three-digit whole numbers and .pand .p

• Develop and use written methods to record, support Develop and use written methods to record, support and explain multiplication and division of two-digit and explain multiplication and division of two-digit numbers by a one-digit number, including division with numbers by a one-digit number, including division with remainders (e.g. 15 9, 98 6) remainders (e.g. 15 9, 98 6)

YEAR 5YEAR 5• Use efficient written methods to add and Use efficient written methods to add and

subtract whole numbers and decimals with up subtract whole numbers and decimals with up to two places to two places

• Refine and use efficient written methods to Refine and use efficient written methods to multiply and divide HTU U, TU TU, U.t U and multiply and divide HTU U, TU TU, U.t U and HTU U HTU U

YEAR 6YEAR 6• Use efficient written methods to add and Use efficient written methods to add and

subtract integers and decimals, to multiply and subtract integers and decimals, to multiply and divide integers and decimals by a one-digit divide integers and decimals by a one-digit integer, and to multiply two-digit and three-integer, and to multiply two-digit and three-digit integers by a two-digit integer digit integers by a two-digit integer

YEAR 7YEAR 7• Use standard column procedures to add and Use standard column procedures to add and

subtract integers and decimals, and to multiply subtract integers and decimals, and to multiply two-digit and three-digit integers by a one-digit two-digit and three-digit integers by a one-digit or two-digit integer; extend division to dividing or two-digit integer; extend division to dividing three-digit integers by a two-digit integerthree-digit integers by a two-digit integer

Addition Addition andand Subtraction Subtraction

MultiplicationMultiplication and Division and Division

Resources we useResources we use

• Fingers!Fingers!

• NumiconNumicon

• NumberlinesNumberlines• 100 squares100 squares• Multiplication gridsMultiplication grids• Counters/cubesCounters/cubes• Base 10 Base 10

Lessons – what do they look like ?Lessons – what do they look like ?

Y1-Y6 – children have a daily numeracy Y1-Y6 – children have a daily numeracy lesson ( mental/oral, main input, group lesson ( mental/oral, main input, group work or independent task, plenary)work or independent task, plenary)

Rec – maths is throughout the day, Rec – maths is throughout the day, children explore maths through a range children explore maths through a range of child initiated and adult led activitiesof child initiated and adult led activities

What you will see today!!What you will see today!!

A range of activities where children will A range of activities where children will be using a range of strategies and be using a range of strategies and skills….have fun and enjoy!skills….have fun and enjoy!

Please feel free to leave any questions on Please feel free to leave any questions on the question board so we can support the question board so we can support you in any way we can.you in any way we can.

Number line gameNumber line game

6+4=106+4=10

10 take away 9 = 110 take away 9 = 1

1 add 17 = 181 add 17 = 18

18 . . . . 18 . . . .