Calculation 2017-18 - Reedswood E-ACT Primary Academy · 2017-11-24 · read, interpret and...
Transcript of 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
Addition and subtraction Pupils should be taught to:
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
Pupils should be taught to:
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
Addition and subtraction Pupils should be taught to:
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
Addition and subtraction Pupils should be taught to:
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
Pupils should be taught to:
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
Pupils should be taught to:
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
Pupils should be taught to:
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
Pupils should be taught to:
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
second number to add
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
second number to add
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
Extending to decimal numbers
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
to the larger number. Also use this informal method for measures, money and time.
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
to the larger number. Also use this informal method for measures, money and time.
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
Partition second number to subtract
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.
Partition second number to subtract
Difference between
Adjust numbers to subtract 6 Subtract multiples of 10s, 100s, 1000s, tenths, hundredths.
Fluency of 2 digit - 2 digit including with decimals
Partition second number to subtract
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.
6 Perform mental calculations, including with mixed operations and large
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.
With'jottings''
…'or'in'your'head'….'
' '
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Just'know'it!' ''
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Year' 1 2 3 4 5 6
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'
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.
With'jottings''
…'or'in'your'
head'….'' '
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Just'know'it!' ''
'
Year' 1 2 3 4 5 6
Foundations
' ' '' '
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' ' ''
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'
' ' ' ' '
' ' ''
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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'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.
With'jottings''
…'or'in'your'head'….'
' '
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Just'know'it!' ''
'
Year' 1 2 3 4 5 6
Foundations
' ' '' '
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' ' ' ' '
' ' ''
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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
Partitioning
Grid method
Column method - short multiplication
Column method – long multiplication
Extending to decimal numbers
Developing conceptual understanding and written methods for
multiplication
Year 1 Focusing on multiplication facts 2x, 5x, and
10x
Describing an array (set)
Using a number line
Year 2 Focusing on multiplication facts 2x, 3x, 4x,
5x,and 10x
Describing an array (set)
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.
Partitioning TUxU/HTUxU
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.
Partitioning TUxU/HTUxU
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.
6 Perform mental calculations, including with mixed operations and large
numbers.

Division ( )
Grouping and sharing
Division
Written'Methods'
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Developing'conceptual'
understanding''
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
With'jottings'''
…'or'in'your'head'….'
Just'know'it!' ''
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Year' 1 2 3 4 5 6
'''
Foundations'
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1 13
2 26
Using 4 52
known 5 130
multiplication
facts
8 104
10 260
Division
Written'Methods'
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Developing'conceptual'
understanding''
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
With'jottings'''
…'or'in'your'head'….'
Just'know'it!' ''
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Year' 1 2 3 4 5 6
'''
Foundations'
' '' ' '
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' ' ''
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1 13
2 26
Using 4 52
known 5 130
multiplication
facts
8 104
10 260
Division
Written'Methods'
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Developing'conceptual'
understanding'
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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
With'jottings'''
…'or'in'your'head'….'
Just'know'it!' ''
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Year' 1 2 3 4 5 6
'''
Foundations'
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1 13
2 26
Using 4 52
known 5 130
multiplication
facts
8 104
10 260
Division
Written'Methods'
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Developing'conceptual'
understanding'
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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
With'jottings'''
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2 26
Using 4 52
known 5 130
multiplication
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8 104
10 260
Division
Written'Methods'
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Developing'conceptual'
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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
With'jottings'''
…'or'in'your'head'….'
Just'know'it!' ''
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Year' 1 2 3 4 5 6
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Foundations'
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1 13
2 26
Using 4 52
known 5 130
multiplication
facts
8 104
10 260
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.
Use multiplication facts as: groups and sharing
equally.
Use a number line
Year 3
Know the related division facts for 2x, 3x, 4x, 5x, 6x, 8x and 10x
Use multiplication facts as: groups and sharing
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.
Use a number line including remainders
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.
Use a number line including remainders
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.
6 Perform mental calculations, including with mixed operations and large
numbers.