The Maths Factor Topic Guide
Year/
Stage
Topic
No.
Topic title
Topic description
Explorer: Key Stage 1
Year 1
1
Counting and
number lines
This topic is designed to improve confidence with place value of numbers up to 100.
Firstly, your child’s counting skills will be checked: with numbers up to 10, then 11-20,
followed by numbers up to 100. Tens and units are introduced, to enable more efficient
counting and number ordering. The final section teaches placing numbers on a number
line up to 100.
Year 1
2
Adding up
This topic allows children to establish good mental addition skills of
adding any 1-digit number to any other 1-digit number.
The topic works through adding each digit separately to numbers up to 9, using
resources such as number tracks, then practises all addition bonds of numbers 1 to 9.
The last few modules start to work with adding to numbers up to 30, working at this
stage with adding 1, 2 or 3 only.
Year 1
3
Subtracting
This topic allows children to establish good mental skills of subtracting
1-digit numbers.
The topic works through subtracting 1-digit numbers from any number up to 10, then
starts subtracting from bigger numbers up to 30, working at this stage with subtracting
1, 2 or 3 only.
Year 2
4
More adding up
This topic aims to develop good mental skills of adding any 1-digit number to
numbers up to 99.
The topic works through adding progressively bigger digits by using a 100 square as
support and by helping children to use strategies to make addition easier. The final
module provides an opportunity to practise adding any 1-digit number to any number
up to 99.
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Year/
Stage
Topic
No.
Topic title
Topic description
Year 2
5
More subtracting
This topic aims to establish good mental skills of subtracting any 1-digit
number from any number up to 100.
Children are expected to already be confident with subtracting 1, 2 or 3 from any
number up to 30, so the topic starts with subtracting 4 from numbers up to 30, working
through subtracting each digit up to 9. The later modules work on subtracting
numbers up to 10 from numbers up to 100, encouraging children to use mental
strategies to make it easier.
Year 2
6
The 1, 2, 5 and 10
times tables
This topic introduces children to addition using the column method.
The topic begins with a review of adding 1-digit numbers to numbers up to 99, then
introduces the column format for addition, firstly with 1-digit numbers, then progressing
to 2-digit numbers. The topic finishes with adding three 2-digit numbers, resulting in
carry digits bigger than 1.
Adventurer: Lower Key Stage 2
Year 3
7
Adding bigger
numbers
This topic introduces children to addition using the column method.
The topic begins with a review of adding 1-digit numbers to numbers up to 99, then
introduces the column format for addition, firstly with 1-digit numbers, then progressing
to 2-digit numbers. The topic finishes with adding three 2-digit numbers, resulting in carry
digits bigger than 1.
Year 3
8
The 3, 6 and 9 times
tables
This topic teaches the 3, 6 and 9 times tables with a concluding module
identifying patterns between them.
Year 3
9
Units, ten, hundreds
and thousands
This topic teaches rounding numbers to the nearest 10 and 100, as well as developing
an understanding of the place value of numbers up to 9999.
The topic begins with rounding to the nearest 10, then to the nearest 100. The final
module of the topic focuses on the place value of 4-digit numbers, including
partitioning.
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Year/
Stage
Topic
No.
Topic title
Topic description
Year 3
10
The 4 and 8 times
tables
This topic teaches the 4 and 8 times tables.
Children are expected to have already covered the 2, 3, 5 and 6 times tables and so the
later modules identify patterns between these and the 4 and 8 times tables.
Year 3
11
Subtracting bigger
numbers
This topic introduces children to subtraction using the column method.
The topic begins with a review of subtracting 1-digit numbers from numbers up to 100
then introduces the column format for subtraction, subtracting 1-digit numbers and
progressing to working with larger numbers. The concept of decomposition or
exchanging is taught, through explaining subtraction by partitioning numbers and
demonstrating exchanging pictorially. The final module involves the subtraction
of 3-digit numbers and requires a good understanding of exchanging repeatedly.
Year 3
12
Tens, hundreds and
thousands
This topic develops place-value skills by teaching tens, hundreds and thousands.
The topic begins by putting numbers in order of size, followed by adding and
subtracting ten and then multiples of ten by using efficient mental methods. The last
few modules teach multiplying by 10, 100 and 1000, working with increasingly larger
numbers and providing children with a clear understanding of what happens to place
value.
Year 4
13
The 7 times table
This topic teaches the 7 times table.
Children are expected to have already covered the 8, 9 and 10 times tables and so this
topic also identifies patterns between these and the 7 times tables. The final module
consolidates all times tables that children have learnt so far; the 1 to 10 times tables.
Year 4
14
Dividing by numbers
up to 10
This topic introduces division and aims to develop the instant recall of division facts,
as with times table facts.
The topic begins by revising the 1 to 10 times tables then introduces the concept of
division and its link with multiplication. After this, the topic works progressively through
the division of 2-digit numbers by numbers up to 10 in an order which takes into
account the relative difficulty and patterns that can be identified. At the end of each
group of divisions, mixed practice sessions are included, to further embed division facts.
Toddler
Year/
Stage
Topic
No.
Topic title
Topic description
Year 4
15
Dividing with
remainders
This topic introduces division with answers that include remainders.
The topic then progresses through the division of 2-digit numbers by numbers up to
10 in an order which takes into account the relative difficulty and patterns that can be
identified: dividing by 2, 5 and 10, then dividing by 3, 6 and 9, followed by dividing by 4,
8 and 7. At the end of each group of divisions, mixed practice sessions are included to
further embed knowledge of division with remainders.
Year 4
16
Numbers less than
zero
This topic teaches negative numbers using number lines.
It then moves on to teaching addition and subtraction involving negative
numbers, starting with 1-digit numbers and progressing to 2-digit numbers.
Year 4
17
Multiplying and
dividing by tens,
hundreds and
thousands
This topic works on further skills involving tens, hundreds and thousands.
The topic begins by revising multiplying by 10, 100 and 1000, progressing to dividing by
10, 100 and 1000, teaching children through place-value principles. The final modules
involve dividing and multiplying by 5, by using the skills of dividing and multiplying by
10 and encouraging efficient mental methods.
Year 4
18
The 11 and 12 times
tables
This topic teaches the 11 and 12 times tables.
All times tables which children have learnt so far are consolidated; the 1 to 12 times tables.
Year 4
19
Lovely fractions
This topic introduces fractions.
It begins by checking children’s understanding of what a fraction is, progressing to
working with halves and quarters and adding these by using equivalence. Proper and
improper fractions and mixed numbers are briefly explained. Eighths and sixteenths are
introduced and children’s understanding of equivalence is further developed through
adding a mixture of fractions and putting them in order of size. In the later modules,
children encounter fractions being divided to make the lowest form and equivalence
between tenths, hundredths and thousandths, as preparation for work with
decimals.
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Year/
Stage
Year 4
Topic
No.
20
Topic title
Lovely decimals
Topic description
This topic introduces decimal numbers.
It begins with teaching decimal place value, followed by writing tenths and hundredths
as decimal numbers and as equivalent fractions. It develops children’s understanding
of ordering numbers with up to two decimal places, as well as teaching key equivalent
fractions and decimals. The later modules consist of extensive practice at multiplying
and dividing decimals by 10 and 100, consolidating place-value knowledge.
Pioneer: Upper Key Stage 2
Year 5
21
Starting long
multiplication
This topic introduces formal written multiplication methods.
It begins by revising times table facts. These multiplications are then arranged in
column format, progressing gradually to 2-digit then 3-digit numbers multiplied by a
1-digit number, with carry digits introduced at each stage. During the teaching
sequence, multiplications are also explained in expanded form by partitioning the
number being multiplied.
Year 5
22
Starting long division
This topic introduces formal division methods, with and without remainders.
It begins by revising basic division facts, then moves on to teaching chunking, as a
division method. After this the topic progresses through dividing increasingly larger
numbers by 1-digit numbers, first using the draw down method, then using short division.
The final section of the topic focuses on remainders, enabling children to understand if
rounding up or down is required in the context of word problems.
Year 5
23
Starting percentages
This topic introduces percentages.
It begins with a review of writing tenths, hundredths and thousandths as decimal
numbers, progressing to writing hundredths as percentages. Key equivalent
fractions and percentages are taught, followed by key equivalent decimals
and percentages. The final module involves converting between key fractions,
decimals and percentages.
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Year/
Stage
Topic
No.
Topic title
Topic description
Year 5
24
More decimals
This topic develops children’s arithmetic skills with decimal numbers.
It covers writing money in decimal form and progresses through adding and
subtracting decimals and rounding decimals to up to 2-decimal places. The later
modules work on multiplying and dividing decimals by 1-digit numbers.
Year 5
25
More fractions
This topic develops children’s arithmetic skills with fractions.
The topic begins by reviewing basic equivalence of fractions and teaches cancelling
down to the simplest form, before moving onto finding the lowest common
denominator and using this to add and subtract fractions. The modules then progress
through to teaching improper fractions and mixed numbers, developing confidence
with conversions then carrying out addition and subtraction. After this, children are
taught to find proper and then improper fractions of amounts, including mixed number
answers. The final module teaches multiplication of fractions.
Year 6
26
Percentages and
money
This topic develops children’s arithmetic skills with percentages, including finding
percentages of amounts of money.
The topic reviews key equivalent fractions and percentages, before progressing to more
difficult percentages. The final modules introduce percentage increases and decreases,
using money examples.
Year 6
27
Squares, square roots
and cubes
This topic introduces square numbers, square roots and cube numbers.
The topic begins by teaching square numbers and allows children to practise finding
square numbers up to 12 x 12, as well as adding and subtracting square numbers.
Square roots are then explained with the final module covering cube numbers.
Year 6
28
Being brilliant at long This topic further develops written multiplication skills.
multiplication
The topic begins by reviewing the multiplication of a 3-digit number by a 1-digit
number then progresses to multiplying by 2-digit numbers, 3-digit numbers and
by 4-digit numbers, with carry digits introduced at each stage. During the
teaching sequence, some multiplications are shown in expanded form, including
the use of the grid method.
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Year/
Stage
Topic
No.
Topic title
Topic description
Year 6
29
Being brilliant at long This topic further develops written division skills.
division
The topic begins by introducing simple division of 2-digit numbers by 2-digit numbers,
progressing through the division of 3-digit numbers and 4-digit numbers, with and without
remainders. Children are taught to find answers with one decimal place and to divide
increasingly larger numbers, with up to three decimal places in the answers. The final
modules involve dividing 4-digit numbers or 5-digit numbers by 3-digit numbers. In the
teaching sequence, the division method used is generally draw down and short division
when appropriate. The chunking method is also shown at various points in the topic.
Year 6
30
Number patterns and
sequences
This topic familiarises children with important number patterns and sequences.
The topic begins by identifying patterns between odd and even numbers when used in
addition, subtraction, multiplication and division. The properties of prime numbers are
then explained, encouraging children to learn the early sequence of primes, followed
by a module on finding the prime factors of numbers. The last few modules work with
different sequences, with a focus on being able to identify any missing numbers: square
numbers, cube numbers, triangular numbers, the Fibonacci sequence. Finally, children
can further develop their familiarity with these different sequences by practising a
mixture of all of them.
Year 6
31
Ratio and proportion
This topic introduces children to ratio and proportion and enables them to solve
ratio and proportion problems.
The topic starts with defining ratio, proportion and fractions and moves on to
explaining how to scale ratios up or down, then dividing in proportion. All questions
involve real-life type problems. The later modules work on further problem solving in
real-life contexts, first with converting between different currencies, then
converting between imperial and metric units of measurement.
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Year/
Stage
Year 6
Topic
No.
32
Topic title
Estimating and
checking
Topic description
This topic introduces children to estimating and checking answers.
First, children work on why estimation and checking are important and on some basic
number knowledge that can help with these skills. Once children understand the
importance of estimating results and checking answers, they then work through practising
estimating and checking with addition, subtraction, multiplication and division, finishing
with using estimation for problem solving.
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