calculation 2017-18 - reedswood e-act primary academy · 2017-11-24 · read, interpret and...

Calculation 2017-18

Calculation objectives years 1-6, for the four number operations – Addition (+),

Subtraction (-), Division () and Multiplication (x)

Year 1

Addition and subtraction Pupils should be taught to:

read, interpret and practise writing mathematical statements involving addition (+),

subtraction (-) and equals (=) signs accurately. add and subtract 1-digit and 2-digit numbers to 20 (9 + 9, 18 - 9), including zero.

add three 1-digit numbers. recall and use number bonds and related subtraction facts within 20.

solve simple word problems that involve addition and subtraction. Multiplication and division

Pupils should be taught to:

recognise and write the multiplication symbol (x) and the division symbol (÷) in mathematical statements, calculating the answer with the teacher using concrete objects.

solve word problems involving simple multiplication and division, with teacher support.

Year 2


rapidly recall and use addition and subtraction facts to 20. add and subtract numbers with up to two 2-digits including using column addition without

carrying and column subtraction without borrowing. add and subtract numbers mentally including:

- a 2-digit number and ones

- a 2-digit number and tens

- two 2-digit numbers

- use subtraction in ‘take away’ and ‘find the difference’ problems.

recognise and show that addition can be done in any order (commutative) and subtraction

cannot. recognise and use addition and subtraction as inverse operations including to check

calculations. solve word problems with addition and subtraction of numbers with up to 2-digits.

Multiplication and division


recall multiplication and division facts for the 2, 5 and 10 multiplication tables. use the multiplication (x), division (÷) and equals (=) signs to read and write mathematical

statements.

write and calculate mathematical statements for multiplication and division within the multiplication tables.

recognise and use the inverse relationship between multiplication and division to check calculations.

ensure pupils can recognise and show that multiplication can be done in any order (commutative) and division cannot.

solve word problems involving multiplication and division.

Year 3


add and subtract numbers with up to 3 digits, including using columnar addition and

subtraction.

accurately add and subtract numbers mentally including: pairs of one- and 2-digit numbers; 3-digit numbers and ones; 3-digit numbers and tens; 3-digit numbers and hundreds.

solve word problems including missing number problems, using number facts, place value, and more complex addition and subtraction.

Multiplication and division Pupils should be taught to:

recall and use multiplication and division facts for the 2, 3, 4, 5, 8 and 10 multiplication

tables. write and calculate mathematical statements for multiplication and division within the

multiplication tables; and for 2-digit numbers x 1-digit numbers, using mental and written methods.

solve word problems involving the four operations, including missing number problems.

Year 4


add and subtract numbers using formal written methods with up to 4 digits. accurately add and subtract numbers mentally including two 2-digit numbers.

estimate, within a range, the answer to a calculation and use inverse operations to check answers.

Multiplication and division


recall multiplication and division facts for multiplication tables up to 12 x 12. mentally perform multiplication and division calculations quickly and accurately, including

multiplying by 0 and dividing by 1. multiply or divide 2-digit and 3-digit numbers by a 1-digit number using formal written

methods; interpret remainders appropriately as integers. recognise and use factor pairs within 144. solve word problems involving the four operations.

find the effect of dividing a 2-digit number by 10 and 100, identifying the value of the digits in the answer as units, tenths and hundredths.

Year 5

Addition and subtraction


add and subtract whole numbers with up to 5 digits, including using formal written methods. add and subtract numbers mentally with increasingly large numbers.

add and subtract numbers with up to three decimal places. Multiplication and division


identify multiples including common multiples, and factors including common factors. know and use the vocabulary of prime numbers, prime factors and composite (non-prime)

numbers. establish whether a number up to 100 is prime and recall the prime numbers up to 19.

multiply numbers up to 4-digits by a 1 or 2-digit number using a formal written method, including long multiplication.

accurately multiply and divide numbers mentally drawing upon known facts.

divide numbers up to 4 digits by a 1-digit number and 10 and interpret remainders appropriately.

multiply and divide numbers by 10, 100 and 1000. recognise and use square numbers and square roots and the notation for square (2) and

square root (√) solve word problems involving addition and subtraction, multiplication and division.

Year 6

Addition, subtraction, multiplication and division


add and subtract negative integers.

multiply numbers with at least 4-digits by 2-digits of whole number using long multiplication. divide numbers up to 4-digits by a 2-digit whole number using long division, and interpret

remainders as whole number remainders, fractions, decimals or by rounding. perform mental calculations, including with mixed operations and large numbers.

use estimation to check answers to calculations and determine in the context of a problem whether an answer should be rounded, or written as a fraction or a decimal.

carry out combined operations involving the four operations accurately and state the order

of operations. solve word problems involving addition, subtraction, multiplication and division.

identify the value of each digit to three decimal places and multiply and divide numbers up to three decimal place by 10, 100 and 1000.

multiply and divide numbers with up to two decimal places by 1-digit and 2-digit whole numbers

recognise and use division in the context of fractions, percentages and ratio. solve linear missing number problems, including those involving decimals and fractions, and

find pairs of number that satisfy number sentences involving two unknowns.

The following pages show our schools’ written calculation methods for maths. They are

organised by number operations – Addition (+), Subtraction (-), Division () and Multiplication (x). Each section shows the written calculation methods for each operation starting from simple methods progressing to more advance ones.

Addition (+)

Number line

Counting on using a number line

Using a number line counting on in multiples of 100, 10 or 1.

Partitioning

Column method

Extending to decimal numbers

Using a number line to calculate time

Developing conceptual understanding and written methods for addition

Year 1 U+U developing to TU+U

Adding the most significant digits first 3+5=5+1+1+1=8

Using cubes/counters to work out a simple number sentence 4+3= ? 6+ ? =16

Counting on using a number line Count on in ones, e.g. 11+2= 7+4=

Counting on in tens, e.g. 45+20 as 45,55,65 Using number facts - Knowing 7= 7+0 or 6+1 or

5+2 or 4+3 Using number bonds - Patterns using know facts, e.g. 4+3= 7 so we know 24+3, 44+3, 74+3 etc.

Year 2 U+U, TU+U developing to TU+TU

Using Place value Know 1 more or 10 more than any number, e.g. 1

more than 67 or 10 more than 85.

Counting on using a number line Partitioning

Column method Children will be introduced to a formal written

method. No carrying is involved at this early stage.

Year 3 TU + TU, developing to HTU+TU or HTU+HTU

Using a number line counting on in multiples of

100, 10 or 1. Adding the most significant digits first

Partitioning Develop formal written method (column

method)

Year 4 HTU+TU or HTU+HTU, developing to THTU+THTU

Add whole numbers up to 4 digits. Children can

use partitioning method to add smaller numbers quickly. They will develop the column method as

their formal written and a number line for an informal method for addition.

Year 5 Add whole numbers up to 5 digits. Decimals

numbers will be introduced this year. They can use partitioning method to add smaller numbers quickly. Children will secure column method as

their formal written and a number line for an informal method for addition.

Year 6 Solve addition multi-step problems in contexts,

deciding which operations and methods to use and why.

Year 6 will use the column method and add larger numbers and decimals up to 3 places. In

order to keep the place value the children may add 0s in the empty decimal columns.

They are also secure in using the partitioning method to add smaller numbers quickly. And can use a number line to find totals, add

measurements and time.

Year Foundations

for addition 1 1 more

Number

bonds: 5, 6 Largest

number first. Number

bonds: 7, 8 Add 10. Number

bonds: 9, 10 Ten plus ones.

Doubles up to 10

Use number bonds of 10 to

derive bonds of 11

2 10 more Number

bonds: 20, 12, 13

Number bonds: 14,15

Add 1 digit to 2 digit by

bridging. Partition second

number, add tens then

ones Add 10 and

multiples. Number

bonds: 16 and 17

Doubles up to

20 and multiples of 5

Add near multiples of

10. Number

bonds: 18, 19 Partition and

recombine 3 Add multiples

of 10, 100

Add single digit bridging

through

boundaries Partition

second number to add

Pairs of 100 Use near

doubles to

add Add near

multiples of 10 and 100 by

rounding and adjusting

Partition and recombine

4 Add multiples

of 10s , 100s, 1000s

Fluency of 2

digit + 2 digit Partition


Decimal pairs of 10 and 1 Use near

doubles to add

Adjust both numbers

before adding Add near

multiples Partition and

recombine

5 Add multiples of 10s , 100s,

1000s, tenths, Fluency of 2 digit + 2 digit

including with decimals

Partition second

number to add Use number

facts,

bridging and place value

Adjust numbers to

add Partition and

recombine 6 Add multiples

of 10s , 100s,

1000s, tenths, hundredths Fluency of 2

digit + 2 digit including with

decimals Partition


Use number

facts, bridging and

place value Adjust

numbers to add

Partition and recombine

Mental addition yearly targets

Year Mental addition (with jottings if required)

1 Solve one-step problems that involve addition and subtraction, using

concrete objects and pictorial representations, and missing number

problems such as 7 = ? – 9

2 Add numbers using concrete objects, pictorial representations, and

mentally, including:

a two-digit number and ones

a two-digit number and tens

two two-digit numbers

adding three one-digit

3 Add numbers mentally, including:

a three-digit number and ones

a three-digit number and tens

a three-digit number and hundreds

4 Solve addition two-step problems in contexts, deciding which operations and

methods to use and why.

5 Add numbers mentally with increasingly large numbers

6 Perform mental calculations, including with mixed operations and large

numbers

Subtraction (-)

Number line

Counting back

Counting up

Column methods

Developing conceptual understanding and written methods for subtraction

Year 1 U-U developing to TU-U

Use an informal and jottings to support, record or explain calculations and achieving consistent

accuracy. Building on existing mental strategies.

Use a number line to count back (when taking

away a small amount).

Use a number line to count up from the smaller to the larger number.

Use practical resources like cubes or counters to work out simple number sentences.

Year 2 U-U, TU-U developing to TU-TU

Use an informal and jottings to support, record or explain calculations and achieving consistent

accuracy. Building on existing mental strategies.

Use a number line to count back (when taking away a small amount).

Use a number line to count up from the smaller

to the larger number. Use practical resources like cubes or counters

to work out simple number sentences.

Year 3

TU-TU, developing to HTU-TU and HTU- HTU

Use an informal and formal method to support, record and building on existing mental

strategies. Discuss and compare methods and explain orally how they work.

Use a number line to count up from the smaller

to the larger number. Also use this informal method for measures, money and time.

Subtract numbers with up to three digits, using

a formal written method, compact decomposition (column method).

Year 4

Subtract numbers with up to 4 digits.

Use an informal and formal method to support, record or explain calculations, achieving consistent accuracy. Discuss, explain and

compare methods.

Use a number line to count up from the smaller to the larger number. Also use this informal

method for measures, money and time.

Subtract numbers with up to four digits, using a formal written method, compact decomposition (column method), where appropriate.

Extend to decimals, using both informal and

formal methods. Ensure children know that the decimal point should line up under each other/

one square for the decimal point.

Year 5 Subtract whole numbers with more than 4

digits. Solve subtraction problems in contexts, deciding which methods to use and why.

Use an informal and formal method to support,

record or explain calculations, achieving consistent accuracy. Discuss, explain and

compare methods. Use a number line to count up from the smaller


Subtract numbers with more than four digits,

using a formal written method, compact decomposition (column method), where

appropriate. Extend to decimals. Using the chosen method to

find the difference between two decimal fractions, time, money or measurements. Know

that decimal point should line up under each other.

Year 6 Subtract whole numbers with more than 5

digits. Solve subtraction multi-step problems in contexts, deciding which methods to use and why.

Use an informal and formal method to support,

record or explain calculations, achieving consistent accuracy. Discuss, explain and

compare methods. Use a number line to count up from the smaller


Subtract numbers with more than four digits,

using a formal written method, compact decomposition (column method), where

appropriate. Extend to decimals. Using the chosen method to

subtract two or more between decimal fractions with up to three digits, time, money or

measurements. Know that decimal point should line up under each other.

Year Foundations for subtraction 1 1 less

Number bonds, subtraction: 5, 6, 7,8,9,10

Count back

Subtract 10.

Teens subtract 10.

Difference between 2 10 less

Number bonds, subtraction: 20, 12, 13

Number bonds, subtraction: 14, 15 Subtract 1 digit from 2 digit by bridging

Partition second number, count back in 10s then 1s

Subtract 10 and multiples of 10 Number bonds, subtraction: 16, 17

Subtract near multiples of 10

Difference between Number bonds, subtraction: 18, 19 3 Subtract multiples of 10 and 100

Subtract single digit by bridging through boundaries

Partition second number to subtract

Difference between

Subtract near multiples of 10 and 100 by rounding and adjusting 4 Subtract multiples of 10s, 100s, 1000s

Fluency of 2 digit subtract 2 digit


Decimal subtraction from 10 or 1

Difference between

Subtract near multiples by rounding and adjusting 5 Subtract multiples of 10s, 100s, 1000s,, tenths,

Fluency of 2 digit- 2 digit including with decimals.


Difference between

Adjust numbers to subtract 6 Subtract multiples of 10s, 100s, 1000s, tenths, hundredths.

Fluency of 2 digit - 2 digit including with decimals


Use number facts bridging and place value

Adjust numbers to subtract

Difference between

Mental subtraction yearly targets

Year Mental subtraction (with jottings if required)

1 Solve one-step problems that involve addition and subtraction, using

concrete objects and pictorial representations, and missing number

problems such as 7 = – 9

2 Add and subtract numbers using concrete objects, pictorial

representations, and mentally, including:

* a two-digit number and ones

* a two-digit number and tens

* two two-digit numbers

* adding three one-digit numbers

3 Add and subtract numbers mentally, including:

* a three-digit number and ones

* a three-digit number and tens

* a three-digit number and hundreds

4 Solve addition and subtraction two-step problems in contexts, deciding

which operations and methods to use and why.

5 Add and subtract numbers mentally with increasingly large numbers.


numbers.

Multiplication (x)

Describing an array (set)

Using a number line

Multiplication

Written'Methods'

'

2

1 5 1

Developing'conceptual'

understanding''

2 frogs on each lily pad.! 5 frogs on each lily pad 5 x 3 = 15 5 x 2 = 2 x 5 Build tables on counting stick

!! Link to repeated addition

!

If I know 10 x 8 = 80 then … So 13 x 4 = 10 x 4 + 3 x 4

Build tables on counting stick

43 x 6 by partitioning If I know 4 x 6 = 24 then 40 x 6 is ten times bigger, 40 x 60 is one hundred times bigger. 13 x 16 by partitioning 10 3 10 6 100 + 30 + 60 + 18 = 208 Build tables on counting stick

Grid method linked to formal written method If I know 4 x 6 then 0.4 x 6 is ten times smaller 0.4 x 0.6 is ten times smaller again.

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Foundations

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12 40

18 240 6

3 40 X

40 x 6 = 240 3 x 6 = 18 43 x 6 = 258

!

= 7290

= 1458 +

8748

1 5 1

2

1

Multiplication

Written'

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Multiplication

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3 40 X

40 x 6 = 240 3 x 6 = 18 43 x 6 = 258

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= 7290

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1 5 1

2

1

Partitioning

Grid method

Column method - short multiplication

Column method – long multiplication

Developing conceptual understanding and written methods for

multiplication

Year 1 Focusing on multiplication facts 2x, 5x, and

10x


Using a number line

Year 2 Focusing on multiplication facts 2x, 3x, 4x,

5x,and 10x


Using a number line

Introduce the partitioning method

Year 3 Focusing on multiplication facts 2x,3x,4x, 5x,

6x, 8x and 10x

Using a number line

Partitioning TUxU

Introduce grid method and short

multiplication (column method) TUxU

Year 4 Multiplication facts up to 12 x 12

Partitioning TUxU/HTUxU

Grid method

Short multiplication (column method)

TUxU/HTUxU

Year 5

Consolidate all multiplication facts up to 12 x 12 Use all methods to support, record or explain

calculations, achieving consistent accuracy. Discuss, explain and compare methods.

Approximate first. Explain orally how method works.


Grid method TUxU/HTUxU/TUxTU

Short multiplication (column method) TUxU/HTUxU

Long multiplication (column method) TUxTU

Extend to simple decimals (2dp)

Year 6

Consolidate multiplication facts up to 12 x 12 Use all methods to support, record or explain

calculations, achieving consistent accuracy. Discuss, explain and compare methods.

Approximate first. Explain orally how method works.


Grid method TUxU/HTUxU/TUxTU

Short multiplication (column method) TUxU/HTUxU

Long multiplication (column method) TUxTU

Extend to decimals

Year Foundations

for

multiplicati

on 1 Count in

multiples of

2, 5 and

10’s.

Know

doubles up

to 10.

Double

multiples of

10. 2 Recall and

use x and ÷

facts for

the 2, 3, 5

and 10x

times,

including

recognising

odd and

even

numbers.

Doubles up

to 20 and

multiples of

5. 3 Recall and

use x and ÷

facts for

2,3,4,5,8

and 10.

Double two

digit

numbers. 4 Recall x and

÷ facts for

x tables up

to 12x12.

10 times

bigger.

Double

larger

numbers

and

decimals. 5 Recall x and

÷ facts for

x tables up

to 12x12.

Recall

prime

numbers up

to 19

know and

use the

vocabulary

of prime

numbers,

prime

factors and

composite

(non-‐

prime)

numbers

Recognise

and use

square

numbers

and cube

numbers,

and the

notation

for squared

(2) and

cubed (3).

10, 100,

1000 times

bigger.

10, 100,

1000 times

smaller.

Double

larger

numbers

and

decimals.

Partition to

multiply

mentally. 6 Recall x and

÷ facts for

x tables up

to 12x12.

Recall

prime

numbers up

to 19

know and

use the

vocabulary

of prime

numbers,

prime

factors and

composite

(non-‐

prime)

numbers

Recognise

and use

square

numbers

and cube

numbers,

and the

notation

for squared

(2) and

cubed (3).

10, 100,

1000 times

bigger.

10, 100,

1000 times

smaller.

Double

larger

numbers

and

decimals.

Partition to

multiply

mentally.

Mental multiplication yearly targets

Year Mental multiplication (with jottings if required)

1 Solve one-step problems involving multiplication and division, by calculating

the answer using concrete objects, pictorial representations and arrays

with the support of the teacher

2 Show that multiplication of two numbers can be done in any order

(commutative) and division of one number by another cannot

Solve problems involving multiplication and division, using materials, arrays,

repeated addition, mental methods, and multiplication and division facts,

including problems in contexts.

3 Write and calculate mathematical statements for multiplication and division

using the multiplication tables that they know, including for two-digit

numbers times one-digit numbers, using mental methods.

4 Use place value, known and derived facts to multiply and divide mentally,

including: multiplying by 0 and 1; dividing by 1; multiplying together three

numbers.

Recognise and use factor pairs and commutatively in mental calculations.

5 Multiply and divide numbers mentally drawing upon known facts

Multiply and divide whole numbers and those involving decimals by 10, 100

and 1000.

Identify multiples and factors, including finding all factor pairs of a

number, and common factors of two numbers establish whether a number up

to 100 is prime.


numbers.

Division ( )

Grouping and sharing

Division

Written'Methods'

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6 ÷2 = 3 by sharing into 2 groups and by grabbing groups of 2 How many 2s?

15 ÷ 3 = 5 in each group (sharing)

!! Link to fractions 15 ÷ 3 = 5 groups of 3 (grouping)!!!10 ÷2 = 5

!! Use language of division linked to tables How many 2s?

!

Grouping using partitioning 43 ÷ 3 If I know 10 x 3 … Use language of division linked to tables How many 3s?

Grouping using partitioning 196 ÷ 6 If I know 3 x 6 … then 30 x 6… ‘Chunking up’ on a number line 196 ÷ 6 = 32 r 4 Use language of division linked to tables.

192 ÷ 6 using place value counters to support written method Exchange 100 for ten 10s 19 tens into groups of 6 3 groups so that is 30 x 6, exchange remaining 10 for ten 1s So 192 ÷ 6 = 32

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Using a number line – using knowledge of times tables

Using a number line – introducing a remainder

Standard compact method

Long division

Remainder as a decimal and fraction

Developing conceptual understanding and written methods for division

Year 1

Know the related division facts for x2, x5 and x10 tables

Use multiplication facts as: groups and sharing

equally.

Start to use a number line

Year 2

Know the related division facts for facts 2x, 3x, 4x, 5x,and 10x.


equally.

Use a number line

Year 3

Know the related division facts for 2x, 3x, 4x, 5x, 6x, 8x and 10x


equally.

Use a number line including remainders Introduce standard compact method TU÷U

Year 4

To use the related division facts for x2, x3, x4, x5, x6, x8, x10 and introduce x7 and x9.

Use a number line including remainders

Standard compact method TU÷U including remainders

Year 5 To use the related division facts up to 12x12.

Develop and refine written methods for division.


Standard compact method TU÷U/HTU÷U

including remainders Introduce compact long division TU÷TU

Represent remainders as a fraction and a

decimal

Extend to decimals including money

Year 6 To use the related division facts up to 12x12.

Develop and refine written methods for division. Use all methods to support, record

or explain calculations, achieving consistent accuracy.


Standard compact method TU÷U/HTU÷U/ThHTU÷U including remainders

Compact long division TU÷TU/HTU÷TU

Represent remainders as a fraction and a

decimal Extend to decimals including money

Year Foundations for division 1 Counting in multiples of twos, fives and tens.

Halves up to 10

Counting back in 5s

Halve multiples of 10

How many 2s? 5s? 10s? 2 Recall and use x and ÷ facts for the 2, 5 and 10 x times, including recognising

odd and even numbers.

Halves up to 20

Count back in 3s 3 Recall and use x and ÷ facts for the 3, 4, 6 and 8 times tables.

Review division facts (2x, 5x, 10x table)

Halve two digit numbers 4 Recall x and ÷ facts for x tables up to 12 x 12.

10 times smaller.

Halve larger numbers and decimals. 5 Recall x and ÷ facts for x tables up to 12 x 12.

Recall prime numbers up to 19.

Know and use the vocabulary of prime numbers, prime factors and composite

(non-prime) numbers.

10, 100, 1000 times small/bigger

Partition to divide mentally

Halve larger numbers and decimals 6 Recall x and ÷ facts for x tables up to 12 x 12.

Recall prime numbers up to 19.

Know and use the vocabulary of prime numbers, prime factors and composite

(non-prime) numbers.

10, 100, 1000 times small/bigger

Partition to divide mentally

Halve larger numbers and decimals

Mental division yearly targets

Year Mental multiplication (with jottings if required)

1 Solve one-step problems involving multiplication and division, by calculating

the answer using concrete objects, pictorial representations and arrays

with the support of the teacher.

2 Show that multiplication of two numbers can be done in any order

(commutative) and division of one number by another cannot

Solve problems involving multiplication and division, using materials, arrays,

repeated addition, mental methods, and multiplication and division facts,

including problems in contexts.

3 Write and calculate mathematical statements for multiplication and division

using the multiplication tables that they know, including for two-digit

numbers times one-digit numbers, using mental methods.

4 Use place value, known and derived facts to multiply and divide mentally,

including: multiplying by 0 and 1; dividing by 1; multiplying together three

numbers Recognise and use factor pairs and commutativity in mental

calculations.

5 Multiply and divide numbers mentally drawing upon known facts

Multiply and divide whole numbers and those involving decimals by 10, 100

and 1000.


numbers.

calculation 2017-18 - reedswood e-act primary academy · 2017-11-24 · read, interpret and...

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