written calculation strategies key stage 1 & 2 · 2014. 11. 30. · related counting/mental...
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Written Calculation Strategies
Key Stage 1 & 2
Crosland Moor Junior School Dryclough Road, Crosland Moor
Huddersfield HD4 5HX
Addition Related Counting/Mental Maths Objectives
(This list is not indicative of all mental maths objectives) F
S
Read and write numbers from 1-20 in numerals
1 more (numbers up to 20)
Number bonds to 10
Y1
add and subtract one-
digit and two-digit
numbers to 20,
including zero
Count to and across 100 (forwards and backwards from 0
or 1)
Given a number identify 1 more or 1 less
Count read and write numbers to 100 in numerals
Count in multiples of 2, 5 and 10
Represent and use number bonds and related subtraction
facts up to 20
Recall addition facts up to 20
Y2
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
Recognise the place value of each digit in a two-digit
number (tens, ones)
Count in steps of 2, 3, and 5 from 0, and in tens from any
number, forward and backward
Fluently recall number bonds to 20
Fluent recall addition and subtraction facts to 20
Derive and use related facts up to 100 e.g. pairs (multiples
of ten) that add to make 100.
Addition Related Counting/Mental Maths Objectives
(This list is not indicative of all mental maths objectives) Y
3
add and subtract
numbers with up to
three digits, using
formal written
methods of columnar
addition and
subtraction
Recognise the place value of each digit in a three-digit
number (hundreds, tens, ones)
Read and write numbers up to 1000 in numerals
Pairs of 2 digit multiples of 5 that add to make 100
Pairs of multiples of 50 that total 1000
Find 1, 10 or 100 more or less than a given number
Add and subtract numbers mentally, including:
a three-digit number and ones
a three-digit number and tens
a three-digit number and hundreds
Y4
add and subtract
numbers with up to 4
digits using the formal
written methods of
columnar addition and
subtraction where
appropriate
solve simple measure
and money problems
involving fractions and
decimals to two
decimal places.
Recognise the place value of each digit in a four-digit
number (thousands, hundreds, tens, and ones)
Find 1000 more or less than a given number
Recognise the value of each digit in decimal numbers with
the same amount of decimal places (up to two decimal
places)
Addition Related Counting/Mental Maths Objectives
(This list is not indicative of all mental maths objectives) Y
5
add and subtract whole
numbers with more
than 4 digits, including
using formal written
methods (columnar
addition and
subtraction)
solve problems
involving number up to
three decimal places
Read, write, order and compare numbers to at least
1 000 000 and determine the value of each digit
Count forwards or backwards in steps of powers of 10 for
any given number up to 1 000 000
Add and subtract numbers mentally with increasingly large
numbers
Derive number bonds up to 1 (2dp)
Derive number bonds up to 10 (1dp)
Mentally add two decimal numbers e.g. 19.7 + 3.4
Y6
Read and write numbers up to 10 000 000 and determine
the value of each digit
Perform mental calculations, including with mixed
operations and large numbers
Subtraction
Related Counting/Mental Maths Objectives (This list is not indicative of all mental maths objectives)
FS
Read and write numbers from 1-20 in numerals
Counting forwards and backwards to 20
1 less (numbers up to 20)
Number bonds to 10
Y1
add and subtract one-
digit and two-digit
numbers to 20,
including zero
Count to and across 100 (forwards and backwards from 0
or 1)
Count read and write numbers to 100 in numerals
Given a number identify 1 more or 1 less, 10 more /10 less.
Represent and use number bonds and related subtraction
facts up to 20
Recall subtraction facts up to 20.
Y2
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
Recognise the place value of each digit in a two-digit
number (tens, ones)
Count in steps of 1, 2, 3, and 5 from 0, and in tens from any
number, forwards and backwards
Fluently recall number bonds to 20
Fluently recall subtraction facts to 20
Derive and use related facts up to 100 e.g. pairs (multiples
of ten) that add to make 100.
Show that addition of two numbers can be done in any
order (commutative) and subtraction of one number from
another cannot
Subtraction
Related Counting/Mental Maths Objectives (This list is not indicative of all mental maths objectives)
Y3
add and subtract
numbers with up to
three digits, using
formal written
methods of columnar
addition and
subtraction
Recognise the place value of each digit in a three-digit
number (hundreds, tens, ones)
Read and write numbers up to 1000 in numerals
Find 1, 10 or 100 more or less than a given number up to
1000
Recall pairs of 2 digit multiples of 5 that add to make 100
Recall pairs of multiples of 50 that total 1000
Mentally subtract 2 digit numbers e.g. TU-TU
Count from 0 in multiples of 4, 8, 50 and 100;
Y4
add and subtract
numbers with up to 4
digits using the formal
written methods of
columnar addition and
subtraction where
appropriate
solve simple measure
and money problems
involving fractions and
decimals to two
decimal places.
Recognise the place value of each digit in a four-digit
number (thousands, hundreds, tens, and ones)
Find 1000 more or less than a given number
Count in multiples of 6, 7, 9, 25 and 1000
Subtraction
Related Counting/Mental Maths Objectives (This list is not indicative of all mental maths objectives)
Y5
add and subtract whole
numbers with more
than 4 digits, including
using formal written
methods (columnar
addition and
subtraction)
solve problems
involving number up to
three decimal places
Read, write, order and compare numbers to at least
1 000 000 and determine the value of each digit
Count forwards or backwards in steps of powers of 10 for
any given number up to 1 000 000
Add and subtract numbers mentally with increasingly large
numbers
Derive number bonds up to 1 (2dp)
Derive number bonds up to 10 (1dp)
Mentally subtract using two decimal numbers e.g. 19.5 - 3.6
Y6
Extend to a wider range of problem solving tasks.
Read, write, order and compare numbers up to 10 000 000
and determine the value of each digit
round any whole number to a required degree of accuracy
Perform mental calculations, including with mixed
operations and large numbers
Multiplication Related Counting/Mental Maths Objectives
(This list is not indicative of all mental maths objectives) F
S
Through grouping and
sharing small
quantities, pupils begin
to understand:
multiplication and
division;
Count on an back in 1s and 2s to 20
Y1
doubling numbers and
quantities; and finding
simple fractions of
objects, numbers and
quantities.
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.
Count on and back in steps of 1, 2, 5 and 10, moving onto
multiplication facts for the 2 and 10 times table.
Recall doubles of numbers to 10 e.g. 9+9
Y2
solve problems
involving multiplication
and division, using
materials, arrays,
repeated addition,
mental methods, and
multiplication and
division facts, including
problems in contexts.
Fluently recall and use multiplication facts for the 2, 5 and
10 multiplication tables
Recall doubles of numbers to 15 e.g. 14 + 14
Count on and back in steps of 3, leading to multiplication
facts for the 3 times table.
Y3
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 and progressing
to formal written
methods
Fluently recall and use multiplication facts for the 3, 4 and
8 multiplication tables
Mentally double multiples of 10 and 100
Mentally double 2 digit numbers up to 30 e.g. Double 26
Multiply whole numbers by 10 and 100
Y4
multiply two-digit and
three-digit numbers by
a one-digit number
using formal written
layout
Fluently recall facts for multiplication tables up to 12 × 12
Use facts to mentally multiply higher multiples e.g. 6x7 =
42 so 60 x 7 = 420
Mentally multiply by using knowledge of factors e.g 4 x 8 =
4 (x2 x2 x2)
Understand multiplying by 0 and 1; dividing by 1
Mentally multiply together three numbers
Recognise and use factor pairs and commutativity in mental
calculations
Multiply whole numbers by 10, 100 and 1000
Y5
multiply numbers up to
4 digits by a one- or
two-digit number using
a formal written
method, including long
multiplication for two-
digit numbers
U x U.t
Fluently multiply mentally drawing upon known facts:
3 x 4 = 12 so 300 x 40 = 12 000
8 x 7 = 56 so 0.8 x 7 = 5.6
Recall doubles of decimals (1dp) to 10 e.g. Double 8.7
Identify multiples and factors, including finding all factor
pairs of a number, and common factors of two numbers
Multiply and divide whole numbers and those involving
decimals by 10, 100 and 1000
Y6
multiply multi-digit
numbers up to 4 digits
by a two-digit whole
number using the
formal written method
of long multiplication
multiply one-digit
numbers with up to two
decimal places by
whole numbers
Perform mental calculations, including with mixed
operations and large numbers
Mentally multiply whole numbers and decimals by
10/100/1000
Division Related Counting/Mental Maths Objectives (This list is not indicative of all mental maths objectives)
FS
Through grouping and
sharing small
quantities, pupils begin
to understand:
multiplication and
division;
Count on and back in 1 and 2 to 20
Y1
solve one-step
problems involving
division, by calculating
the answer using
concrete objects,
pictorial
representations and
arrays with the
support of the
teacher.
Count on and back in steps of 1, 2, 5 and 10, moving onto
division facts for the 2 and 10 times table.
Recall halves of numbers to 20 e.g. Half of 18 = 9
Y2
As above with strong
focus on:
using multiplication and
division facts for the
2, 5 and 10
multiplication tables
Fluently recall and use division facts for the 2, 5 and 10
multiplication tables
Recall halves of even numbers to 30 e.g. Half of 28 =14
Count on and back in steps of 3, moving onto division facts
for the 3 times table.
Show that multiplication of two numbers can be done in any
order (commutative) and division of one number by another
cannot
Y3
use multiplication and
division facts for the
3, 4 and 8
multiplication tables
Fluently recall and use division facts for the 3, 4 and 8
multiplication tables
Mentally calculate halves of multiples of 10 and 100 moving
onto halves of 2 and 3 digit even numbers.
Divide whole numbers by 10 and 100
Y4
Divide numbers up to 3
digits by 1 digit using
the formal written
method of long division
Fluently recall and use division facts for multiplication
tables up to 12 × 12
Use facts to mentally divide higher multiples e.g. 42 ÷ 7 =6
so 420 ÷ 7 = 60
Mentally divide by using knowledge of factors e.g 32 ÷ 4 =
32 ÷ 2 ÷ 2
Understand multiplying by 0 and 1; dividing by 1
Divide whole numbers by 10, 100 and 1000
Y5
divide numbers up to 4
digits by a one-digit
number using the
formal written method
of short division and
interpret remainders
appropriately for the
context
Recall halves of decimals (1dp) to 10 e.g. Half of 7.4
Identify multiples and factors, including finding all factor
pairs of a number, and common factors of two numbers
Divide whole numbers and those involving decimals by 10,
100 and 1000
Divide numbers mentally drawing upon known facts e.g. 42
÷ 7 =6 so 420 ÷ 70 = 6
Identify multiples and factors, including finding all factor
pairs of a number, and common factors of two numbers
Y6
divide numbers up to 4
digits by a two-digit
whole number using the
formal written method
of long division
Divide decimals by a 1
digit number
Perform mental calculations, including with mixed
operations and large numbers
Identify the value of each digit in numbers given to three
decimal places and multiply and divide numbers by 10, 100
and 1000 giving answers up to three decimal places
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