Muswell Hill Primary School
Mathematics Calculation Policy
MHPS Addition and Subtraction Calculation Policy
PLEASE NOTE: At MHPS we understand that it is important for children to develop conceptual understanding alongside procedural fluency.
“The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on
the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated
problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional
practice, before moving on. “ (from P1 of 2013 New Curriculum)
Year 1
Year 2
add and subtract one-digit and two-digit numbers to 20,
including zero
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
* add all pairs of multiples of 10 up to 100 (60 + 40)
* Find the difference by counting up
* Identify near doubles and add
* Add by adjusting ( 6 + 9 is 6 + 10 - 1, 11 - 8 is 10 - 8 + 1)
* Use partitioning
* Add doubles to 10 + 10, and then at least to 20 (17 + 17)
read, write and interpret mathematical statements
involving addition (+), subtraction (-) and equals (=) signs
show that addition of two numbers can be done in any order
(reorder when adding) and subtraction of one number from
another cannot
Year 3
Year 4
MENTAL CALCULATION
add and subtract numbers mentally, including:
* a three-digit number and ones
* a three-digit number and tens
* a three-digit number and hundreds
* sums and differences of multiples of 10, e.g. 50 + 80,
120 – 90
* pairs of two-digit numbers with a total of 100, e.g. 32
+ 68
* addition doubles of numbers 1 to 100, e.g. 38 + 38,
and the corresponding halves
* what must be added to any three-digit number to
make the next multiple of 100, e.g. 5
* add or subtract any pair of two-digit numbers,
including crossing the tens and 100 boundary, e.g. 47
+ 58, 91 – 35
* pairs of fractions that total 1
reorder numbers when adding
partition: add tens and ones separately, then recombine
partition: count on or back in tens and ones to find the
difference
partition: double and adjust
partition: count on or back in minutes and hours, bridging
through 60 (analogue and digital time )
Year 5
Year 6
add and subtract numbers mentally with increasingly large
numbers, decimals, and mixed numbers and measures
•sums and differences of decimals, e.g. 6.5 + 2.7, 7.8 – 1
•doubles and halves of decimals, e.g. half of 5.6, double 3.4
what must be added to any four-digit number to make the next
multiple of 1000, e.g
•add or subtract a pair of two- digit numbers or three-digit
multiples of 10, e.g. 38 + 86, 620 – 380, 350+ 360
add or subtract a near multiple of 10 or 100 to any two-digit or
three-digit number, e.g. 235 + 198
find the difference between near multiples of 100, e.g. 607 –
588, or of 1000, e.g. 6070 – 4087
partition: add hundreds, tens or ones separately, then
recombine
subtract by counting up from the smaller to the larger number
partition: double and adjust
use knowledge of place value and related calculations, e.g. 6.3
– 4.8 using 63 – 48
WRITTEN METHODS (WITH APPROPRIATE REPRESENTATIONS)
read, write and interpret mathematical statements involving addition
add and subtract numbers with up to three
(+), subtraction (-) and equals (=) signs
then four digits.
Represent number bonds and related subtraction facts within 20
Progress from using informal methods,
jottings and number lines to using formal
written methods of columnar addition and
subtraction appropriately.
INVERSE OPERATIONS, ESTIMATING AND CHECKING ANSWERS
recognise and use the inverse relationship between addition and
estimate the answer to a calculation and use
subtraction and use this to check calculations and solve missing
inverse operations to check answers
number problems.
use rounding to check reasonableness of
answers
solve one-step problems that involve addition and subtraction, using
concrete objects and pictorial representations, and missing number
problems such as 7 =  - 9
Progress to solve problems with addition and subtraction:
* using concrete objects and pictorial representations, including
those involving numbers, quantities and measures
* applying their increasing knowledge of mental and written methods
solve simple problems in a practical context involving addition and
subtraction of money of the same unit, including giving change
apply addition and subtraction skills to investigations, including finding
all possibilities, visual problems, logic problems and rules and patterns.
add and subtract whole numbers, including using
formal written methods, and including decimals
numbers, and more than two numbers.
(columnar addition and subtraction)
use rounding to check answers to calculations
and determine, in the context of a problem, levels
of accuracy
use estimation to check answers to calculations
and determine, in the context of a problem, levels
of accuracy.
PROBLEM SOLVING
solve problems, including missing number
problems, using number facts, place value,
two step problems, and more complex
addition and subtraction
solve addition and subtraction multi-step
problems in contexts, deciding which operations
and methods to use and why
decide operations and methods, and why
solve more complex problems which involve
decimals, fractions, percentages, mixed numbers,
measures and time.
apply addition and subtraction skills to
investigations, including finding all
possibilities, visual problems, logic problems
and rules and patterns.
apply addition and subtraction skills to
investigations, including finding all possibilities,
visual problems, logic problems and rules and
patterns.
MHPS Multiplication and Division Calculation Policy
PLEASE NOTE: At MHPS we understand that it is important for children to develop conceptual understanding alongside procedural fluency.
“The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the
security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems
before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before
moving on. “ (from P1 of 2013 New Curriculum)
Year 1
Year 2
count in multiples of twos, fives and tens use knowledge of
multiplication facts for the 2, 5 and 10 times-tables, and
corresponding division facts
find the total number of objects when they are organised into
groups of 2, 5 or 10 , e.g. recognise that there are 15 objects
altogether because there are three groups of five use patterns of
last digits, e.g. 0 and 5 when counting in fives
show that multiplication of two numbers can be done in any order
(commutative) and division of one number by another cannot
count in steps of 2, 3, and 5 from 0, and in tens from any number,
forward or backward
calculate mentally doubles of all numbers to 10, then 20 and
corresponding halves of even numbers
Year 3
Year 4
MENTAL CALCULATION
count in multiples of 25, 50 ,100 and 1 000
recall multiplication and division facts for multiplication
tables up to 12 × 12
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.
use understanding that when a number is multiplied or
divided by 10 or 100, its digits move one or two places to
the left or the right and zero is used as a place holder
use knowledge of multiplication facts and place value,
e.g. 7 x 8 = 56 to find 70 x 8, 7 x 80
use partitioning and the distributive law to multiply,
e.g.13 × 4 = (10 + 3) × 4 = (10 × 4) + (3 × 4)
multiply numbers to 20 by a single-digit, e.g. 17 × 3
Year 5
Year 6
count forwards or backwards in steps of powers of 10 for any
given number up to 1 000 000
multiply and divide numbers drawing upon known facts
multiply two digit numbers by 5, 20 , 25 and 50
multiply and divide whole numbers and those
involving decimals by 10, 100 and 1000
multiply and divide two-digit decimals such as 0.8 × 7, 4.8 ÷ 6
associate a fraction with division and calculate decimal fraction
equivalents (e.g. 0.375) for a simple fraction (e.g. 3/8)
know equivalent fractions, decimals and percentages.
Know percentage equivalent of one half, one quarter, three
quarters, tenths and hundredths
know odd and even numbers to 20, and then 100
Double multiples of 5 and 10
recognise and use factor pairs e.g identify that if 2 x 3 = 6
then 6 has the factor pair 2 and 3
know squares to 12 x12
know prime numbers less than 100
Halve any multiple of 10 up to 100, e.g. halve 90
know factor pairs to 100
doubles of multiples of 5 and 10 to 100, and doubles of
numbers 1 to 100, e.g. double 58, and corresponding
halves
use partitioning and recombining when halving and
doubling
use knowledge that halving and doubling are inverse
operations
Partition double the tens and ones separately, then recombine
Use knowledge that halving is the inverse of doubling and that
doubling is equivalent to multiplying by two
know division facts corresponding to tables up to 12 x 12 , and
the related unit fractions, e.g. 7 × 9 = 63 so one-ninth of 63 is 7
and one-seventh of 63 is 9
Simplify fractions by cancelling
Scale up and down using known facts, e.g. given that three
oranges cost 24p, find the cost of four oranges
know fraction and decimal equivalence
• identify numbers with odd and even numbers of factors and
no factor pairs other than 1 and themselves
WRITTEN METHODS
calculate mathematical statements for multiplication and division
within the multiplication tables and write them using the
multiplication (×), division (÷) and equals (=) signs
show that multiplication of two numbers can be done in any order
(commutative) and division of one number by another cannot
multiply two-digit and three-digit numbers by a one-digit
number progressing to formal written layout
multiply numbers up to 4 digits by a one- or two-digit
progressing to long multiplication
divide numbers up to 4 digits by a one-digit, then two-digit
number progressing to the formal written method of short
division, then long division and interpret remainders
appropriately for the context
use written division methods in cases where the answer has up
to two decimal places
Use their knowledge of the order of operations to carry out
calculations involving the four operations
INVERSE OPERATIONS, ESTIMATING AND CHECKING ANSWERS
estimate the answer to a calculation and use inverse
use estimation to check answers to calculations and determine,
operations to check answers
in the context of a problem, levels of accuracy
Properties of numbers: Mulitples, factors, primes, square and cubed numbers
Recognise and use factors
Identify multiples and factors, including finding all factor pairs
of a number and common factors of two numbers
Identify, know and use the vocabulary of prime numbers,
prime factors and composite (non-prime) numbers
use common factors to simplify fractions; use common
multiples to express fractions in the same denomination
calculate, estimate and compare volume of cubes and cuboids
3
using standard units, including centimetre cubed (cm ) and
3
cubic metres (m ), and extending to other units such as mm
3
3
and km
PROBLEM SOLVING
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
solve problems, including missing number problems,
involving multiplication and division, including positive
integer scaling problems
solve problems involving multiplication and division including
using their knowledge of factors and multiples, squares and
cubes
solve problems involving multiplication and division, using
materials, arrays, repeated addition, mental methods, and
multiplication and division facts, including problems in contexts
solve problems involving multiplying and adding, including
using the distributive law to multiply two digit numbers by
one digit, integer scaling problems
solve problems involving addition, subtraction, multiplication
and division and a combination of these, including understanding
the meaning of the equals sign
apply addition and subtraction skills to investigations, including
finding all possibilities, visual problems, logic problems and rules
and patterns.
apply addition and subtraction skills to investigations,
including finding all possibilities, visual problems, logic
problems and rules and patterns.
solve problems involving multiplication and division, including
scaling by simple fractions and problems involving simple rates
apply addition and subtraction skills to investigations, including
finding all possibilities, visual problems, logic problems and rules
and patterns.