Addition
Suggested Year 5
Prior learning
Mental
strategies
Informal
written
methods
Check that children can already:
 Count from any given number in whole number steps
 Use positive and negative numbers in practical contexts;
position them on a number line
 Add mentally pairs of 2 digit whole numbers e.g: 47 + 58
 Use efficient written methods to add t 2 and 3 digit whole
numbers and £p
 Use decimal notation for tenths and hundredths in the
context of money and measurement.
 Use decimal notation for tenths and hundredths and
partition decimals; position 1 and 2 place decimals on a
number line
 Order decimals to 2 places and position them on a number
line
 Use a calculator to carry out 1 and 2 step calculations
involving all 4 operations; interpret the display correctly in
the context of money
 Use the relationship between mm, cm and m
 Double 2 digit numbers
 Decimals/fractions that total 1
 Counting up through multiples of 10, 100, 1000 using empty
number line
 Partitioning adding most significant digits first
 Add several numbers
 Respond rapidly to oral or written questions, explaining the
strategy used e.g. add or subtract three-digit multiples of
10
 Where calculations are set out in columns, know that units
should line up under units and so on: by adding the most
significant digits first or by compensation.
 Use of number lines
 Partitioning
 Pictorial
Formal
written
methods
expanded &
compact plus
examples
Model and
images
examples
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Written methods HTU+HTU, ThHTU+HTU with carrying
Extend to decimals (up to 3 digits, not just money)
Continue to develop an efficient standard method that can
be applied generally – using carrying
Extend to decimals
587
+475
1062
¹¹
500 + 400 = 900
80 + 70 = 150
7 + 5 = 12
900 + 150 + 12 = 1062
Carrying
Partition adding most significant first
Which three numbers could have a total of 450? How many
altogether are 121 and 345? Use a calculator to find all the
different totals you can make by using three of these five
numbers: 8, 4008, 562, 3103, 95.
Key questions
Tim has saved £86 for an electronic player costing
£119. Which number sentence could Tim use to find how much more
he needs to save?
A 119 + 86 = ?
B ? – 86 = 119
Opportunities
for using and
applying
Problem Solving – word problems
Puzzles
Practical problems
Creative links with topic planned work
Investigations such as “Lunar Maths”
problem, solution, calculate, calculation, equation, operation,
answer, method, explain, predict, reason, reasoning, pattern,
relationship, rule, sequence
place value, partition, thousands, digit, four-digit number, decimal
point, decimal place, tenths, hundredths 1000 more
Vocabulary
positive, negative, above/below zero, compare, order, greater than
( ), less than ( ), equal to ( ), round, estimate, approximately
add, sum, total, difference, plus,
calculator, display, key, enter, clear, constant
pound ( ), penny/pence (p), units of measurement and abbreviations,
degrees Celsius ( C)
Subtraction
Suggested Year 5
Check that children can already:
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Prior learning
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Count from any given number in whole number steps
Use positive and negative numbers in practical contexts; position them on a
number line
Subtract mentally pairs of 2 digit whole numbers eg. 91-35
Use efficient written methods to subtract 2 and 3 digit whole numbers and
£p
Use decimal notation for tenths and hundredths in the context of money
and measurement.
Use decimal notation for tenths and hundredths and partition decimals;
position 1 and 2 place decimals on a number line
Order decimals to 2 places and position them on a number line
Use a calculator to carry out 1 and 2 step calculations involving all 4
operations; interpret the display correctly in the context of money
Use the relationship between mm, cm and m
Mental
strategies
Informal
written
methods
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Blank number lines
100 square
Jottings
Use informal pencil and paper jottings
to answer:
? + 756 = 924; ? + ? = 1;
? − 256 = 424; ? − ? = 1.2
Pictorial jottings
Place value of numbers especially in columns

Formal
written
methods
expanded &
compact plus
examples
Find differences by counting up through next multiple of 10, 100, 1000;
Partition into H, T and U, adding the most significant digits first;
Identify near doubles;
Add several numbers, making multiples of 10s, 100s etc.
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Decomposition using partitioning to support which then leads onto a more
compact method;
Extend to decimals with up to 3 digits and the same number of decimals
places.
Use a written method to answer:
o 14 136 + 3258 + 487 =?;
o 141.36 32.58
Number lines (for larger numbers than these examples e.g HTU – TU, HTU –
HTU)
When counting on or back jump to the nearest multiple of 10 first as in above
examples.
Decomposition:
754
= 700 + 50 + 4
- 286
200 + 80 + 6
------------------------Model and
images
examples
700 + 40 + 14
- 200 + 80 + 6
Short method:
6 14
7 514
-286
468
600 + 140 + 14
- 200 + 80 + 6
---------------------400 + 60 + 8 = 468
Respond rapidly to oral or written questions, explaining the strategy used.
Subtract 50 from 225
What is the difference between 155 and 390?
Decrease 650 by 25.
570 add a number is 590.
Use known facts to answer:
? + 62 = 189;
? − 62 = 189; 7.6 − 5.8 = ?
Use a calculator to:
Find all the differences you can make by using two of the numbers.
Key questions
Opportunities
for using and
applying
Which of these subtractions can you do without writing anything down?
Why is it possible to solve this one mentally? What clues did you look for? What is
the answer to the one that can be solved mentally?
How did you find the difference? Talk me through your method. [If the child
explains a method of counting backwards, ask:] Is it possible to count up as well?
Why will this give the same result?
Which is easier?
If 2003 is the answer to a similar question, what could the question be?
Roughly, what will the answer to this calculation be?
How do you know that this calculation is probably right?
Could you check it a different way?
Word problems
Practical problems
Puzzles
Creative links with topic planned work
problem, solution, calculate, calculation, equation, operation, answer, method,
explain, reasoning, reason, predict, relationship, rule, formula, pattern, sequence,
term, consecutive, discount
Vocabulary
place value, digit, numeral, partition, decimal point, decimal place, thousands, ten
thousands, hundred thousands, millions, tenths, hundredths, positive, negative,
above/below zero, compare, order, ascending, descending, greater than ( ), less
than ( ), round, estimate, approximately
calculator, display, key, enter, clear, constant
Multiplication
Suggested Year 5
Prior learning
Mental
strategies
Informal
written
methods
Check that children can already:
 Count from any given number in whole number steps
 Use positive and negative numbers in practical contexts; position them on
a number line
 Recall multiplication facts to 10 x 10
 Multiply 1000 by 10 and then 100 (whole number answers)
 Use written methods to multiply TU x U
 Use decimal notation for tenths and hundredths in the context of money
and measurement.
 Use decimal notation for tenths and hundredths and partition decimals;
position 1 and 2 place decimals on a number line
 Order decimals to 2 places and position them on a number line
 Use a calculator to carry out 1 and 2 step calculations involving all 4
operations; interpret the display correctly in the context of money
 Use the relationship between mm, cm and m
 Use diagrams to identify equivalent fractions eg 6/8 and ¾ or 7/100 and
7/10; interpret mixed numbers and position them on a number line eg 3
1/2
 Know the equivalence between decimal and fraction forms of one half,
one quarter, tenths and hundredths
 Double 2 digit numbers
 Use written methods to record, support and explain multiplication of 2
digit numbers by a 1 digit number including division with remainders eg 15
x9
 Use the vocabulary of ratio and proportion
 Calculate all multiplication tables.
 Using mental and pen and paper methods to answer missing number
questions
 Use division as the inverse of multiplication
 Mentally, supported by jottings.
 Approximation.
Formal
written
methods
expanded &
compact plus
examples
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Grid method HTUxU, TUxTU, Partitioning
Short multiplication HTUxU
Long multiplication TUxTU
Model and
images
examples
Grid Method
Key questions
Opportunities
for using and
applying
Vocabulary
If someone had forgotten the 8 times-table, what tips would you give them to
help them to work it out?
What links between multiplication tables are useful?
How many nines are there in 63?
Write in the missing numbers.
5 70 600 4 4
200
What is 50 times 90?
This calculator display shows 0.1. Tell me what will happen when I multiply by
100. What will the display show? What number is ten times as big as 0.01? How
do you know that it is ten times 0.01?
How would you explain to someone how to multiply a decimal by 10?
What is a quick way to multiply by 1000?
One sticker book costs £1.35. How much would five sticker books cost? How did
you work it out? Could you do it differently?
Estimate; approximate; approximately; brackets, inverse, product, times,
multiply, multiplied by, once, twice, three times, four times, five times, …. ten
times,
times as (big, long, wide and so on)
repeated addition
array
row, column
times table
DIVISION
Suggested Year 5
Prior learning
Mental
strategies
See Year 4
Check that children can already:
 Count from any given number in whole number steps
 Use positive and negative numbers in practical contexts;
position them on a number line
 Add or subtract mentally pairs of 2 digit whole numbers eg
47 + 58, 91-35
 Use efficient written methods to add and subtract 2 and 3
digit whole numbers and £p
 Recall multiplication and division facts to 10 x 10
 Multiply or divide numbers to 1000 by 10 and then 100
(whole number answers)
 Use written methods to multiply and divide TU x U, TU÷U
 Use decimal notation for tenths and hundredths in the
context of money and measurement.
 Use decimal notation for tenths and hundredths and
partition decimals; position 1 and 2 place decimals on a
number line
 Order decimals to 2 places and position them on a number
line
 Use a calculator to carry out 1 and 2 step calculations
involving all 4 operations; interpret the display correctly in
the context of money
 Use the relationship between mm, cm and m
 Use diagrams to identify equivalent fractions eg 6/8 and ¾
or 7/100 and 7/10; interpret mixed numbers and position
them on a number line eg 3 1/2
 Know the equivalence between decimal and fraction forms of
one half, one quarter, tenths and hundredths
 Double and half 2 digit numbers
 Use written methods to record, support and explain
multiplication and division of 2 digit numbers by a 1 digit
number including division with remainders eg 15 x 9, 98 ÷6
 Use the vocabulary of ratio and proportion
 Rapid recall of tables facts and related division facts
 Tables Facts and corresponding division facts and links to
fractions
Informal
written
methods
Formal
written
methods
expanded &
compact plus
examples
Model and
images
examples
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Knowing ÷ 0 is not possible
Is there a remainder after HTU÷U?
Relate division to fractions – practical problems
Knowing ÷ is not commutative
Divided whole numbers by 10,100,1000
Division facts up to 10 x 10
Chunking method for HTU÷U
Bus stop method
Chunking method
Bus stop method
540 ÷ 6 =
0 90
6 )5 54 0
6 x 50 = 300
6 x 40 = 240
So, 6 x 90 = 540
Therefore, 540 ÷ 6 = 90
Key questions
Opportunities
for using and
applying
__
How many 6s in 5?
0, carry the 5.
How many 6s in 54? 9
How many 6s in 0? 0
Look at Y5 Resources/ Pitch and Expectations to give levelled
word problems from past NCT papers to support learning,
teaching and plenaries.
 Find fractions of amounts using division and multiplication.
 Find fractions using division e.g 1/100 of 5KG
 Solve problems using fractions
 Use % of numbers for quantities e.g 15% of £80.00
 Solve problems using percentages
 Use a calculator to solve problems involving decimals
Vocabulary
problem, solution, calculator, calculate, calculation, equation,
operation, symbol, inverse, answer, method, explain, predict, reason,
reasoning, pattern, relationship, divide, product, quotient, remainder,
multiple, common multiple, factor, divisor, divisible by
decimal fraction, decimal place, decimal point, percentage, per cent
(%)
discount e.g: 20% of £5.00 =