At Stoke Park Junior School the children receive a daily
maths lesson. As a basis for planning, the staff use the
National Curriculum for mathematics. This outlines what
is expected of each child for each year group.
This leaflet outlines the expectations of the National
Curriculum and the methods used by the staff to aid the
teaching and learning of written calculations.
The aim is that children use mental methods when
appropriate, but for calculations that they cannot do in
their heads they use an efficient written method accurately
and with confidence. It is important to remember that
sometimes a mental strategy will solve a problem quicker
than writing down a standard method. The children will
use the methods taught, and apply them to a wide variety
of problem solving situations.
The aim is that the children find an efficient written method
to solve calculations with all numbers and not race
through to a formal written calculation method.
1
To add successfully, children need to be able to:
• recall all addition pairs to 9 + 9 and complements in 10;
• add mentally a series of one-digit numbers, such as 5 + 8 + 4;
• add multiples of 10 (such as 60 + 70) or of 100 (such as
600 + 700) using the related addition fact, 6 + 7, and their
knowledge of place value;
• partition two-digit and three-digit numbers into multiples of 100,
10 and 1 in different ways.
2
My Targets for Addition
Can I add Ones + Ones using objects?
Can I add Ones + Ones using objects on a number line?
Can I add Ones + Ones on a number line starting on the
biggest number and counting on?
5+ 3= 8
3+2=5
I have 3 apples and 2 apples, I have 5 apples altogether.
3+2=5
If I have 3 apples and 2 apples, I have 5 apples altogether.
Prove it:
Prove it:
Prove it:
Can I add TO + Ones on a structured number line?
Can I add TO + Ones on an unstructured number line?
This means there are no numbers on the line and you
have to write them on.
13+8=21
14+5=19
Can I add a multiple of 10 to a number on an
unstructured number line?
20+10=30
13+10=23
13+20=33
Prove it:
Prove it:
Can I use an unstructured number line to add TO + TO
by counting on in Tens and Ones, not crossing the 10’s
boundary?
Can I use an unstructured number line to add TO + TO
by counting on in Tens and Ones, crossing the 10’s
boundary?
24+23=47
36+28=64
I have 36p and my mum gives me 28p pocket money. How much
money do I have altogether?
Prove it:
Prove it:
Prove it:
Can I add TO+TO using partitioning?
67+24=91
60+20=80
7+4=11
80+11=91
Prove it:
3
Can I add TO+TO on an unstructured number line
crossing a 100’s boundary?
Can I add TO+TO using partitioning crossing the 100’s
boundary?
76 +57 =133
58+67=125
50+60= 110
8+7=15
110+15=125
Prove it:
Can I add HTO + TO using the expanded method of addition, adding
the ones first crossing boundaries of 10s and then 100s?
625
+ 48
13
60
600
673
Prove it:
783
+ 42
5
120
700
825
367
+ 85
12
140
300
452
45+24=69
45
+24
9 (5+4)
60 (40+20)
69
45+28=73
45
+28
13 (5+8)
60 (40+20)
73
Prove it:
Prove it:
Can I HTO + HTO using the expanded method of addition, adding the
ones first crossing boundaries of 10s, 100s and 1000s?
Can I add HTO +TO using carrying?
a) Carrying ones
b) Carrying tens
c) Carrying ones and tens
625
783
367
+ 48
+ 42
+ 85
673
825
452
1
1
11
205
+176
11(5+6)
70 (70+0)
300 (200+100)
381
587
+475
12 (7+5)
150 (80+70)
900 (500+400)
1062
Prove it:
Can I add HTO + HTO using carrying?
Can I add TO +TO using the expanded column method
of addition, adding the ones first, firstly crossing no
boundaries then crossing the boundary of 10s?
Prove it:
Can I add several numbers with different numbers of
digits in columns?
257
39
+386
682
587
+475
1062
11
Can I add numbers in the 1000s using carrying?
3587
+ 675
4262
111
7648
+1486
9134
111
6584
+ 5848
12432
111
12
Prove it:
Prove it:
Can I add numbers involving decimals using columns?
Can I add several decimals numbers using the standard
column method?
£5.75
+ £3.18
£8.93
1
Prove it:
Prove it:
78.3
6.85
+326.04
411.19
121
Prove it:
4
To subtract successfully, children need to be able to:
• recall all addition and subtraction facts to 20;
• subtract multiples of 10 (such as 160 – 70) using the related
subtraction fact, 16 – 7, and their knowledge of place value;
• partition two-digit and three-digit numbers into multiples of one
hundred, ten and one in different ways (e.g. partition 74 into
70 + 4 or 60 + 14).
5
My Targets for Subtraction
Can I subtract Ones-Ones using objects?
Can I subtract using objects on a number line?
(Ones-Ones)
If I have 6 apples and I eat 2, I have 4 apples left.
5-3= 2
Can I subtract in ones on a number line using some
objects? (Ones-Ones)
6-2=4
6-2=4
Prove it:
Prove it:
Can I subtract TO-O counting back in ones using a
number line?
If a farmer has 18 apples on a tree and he picks
3. How many apples will be left?
Prove it:
Can I count back in tens on a number line using a
structured number line and then an unstructured
number line? (TO-T)
Can I subtract tens and ones on an unstructured
number line, counting back in 10s then ones? (TO-TO)
Start with subtracting teen numbers then other 2-digit
numbers (as below)
I have 36p, I spend 28p. How much do I have left?
34-30=4
Counting back
36-28=8
18-3=15
Counting on
Prove it:
Prove it:
Prove it:
Can I use an unstructured number line to subtract TOTO, counting back in bigger multiple of 10?
There were 72 books in the library. Children borrowed
24 of them. How many books were left in the library?
Can I subtract HTO – TO on an unstructured number
line?
There were 132 marbles in a jar. Sarah took 48 out of
the jar. How many marble were left?
Can I subtract HTO-HTO on an unstructured number
line?
172-124=48
Counting back
Counting back
72-24=48
132-48=84
Counting on
Counting on
Prove it:
Prove it:
Prove it:
6
3
1
Can I subtract using two digits in a column?
(TO-TO)
Can I subtract HTO-TO numbers using columns?
Carrying a hundred
72-24=48
72
-24
70 + 2
20 + 4
132-41=91
132-48=84
explained by
explained by
132
- 41
60 +12
20 + 4
40 + 8 = 48
100+30+2
40+1
132
- 48
0 12 12
132
- 48
84
132
- 41
91
72
-24
48
100+30+2 100 +20+12 0+ 120 +12
40+8
40+ 8
40+ 8
0+ 80+ 4 = 84
leading to
0 13
6 12
Prove it:
Can I subtract HTO – TO numbers using columns?
Dealing with zeros when adjusting
Prove it:
102-48=54
102
100+ 0+2
- 48
40+8
563-271=292
Can I subtract HTO-HTO by making adjustment from
hundreds to tens?
0 +100+ 2
40+
4008
0+ 90+12
40 + 8
160
4 16
500500
 600+
3
400

150

50+
4=
54
60  3
5 13
63
400  160  3
 70  8  200  70  8
 200leading
 to70  1  200
 200
 70  1
 2 71
200  80  5
200 10 290  2
200  90  2
2 92
03
70  8
0 +130+ 2
40 +1
90 + 1
Leading to
leading to
Can I subtract HTO –TO numbers using columns?
Carrying a ten and hundred (HTO-TO)
9
0 10 12
Prove it:
Can I subtract HTO-HTO by making adjustment from
hundreds to tens and tens to ones?
563-278=285
400
500
150
50
13
13
500  60  3
 200  70  8
200  80  5
4 15 13
5 6 3
 278
285
- 48
54
Prove it:
Prove it:
Can I subtract numbers in the 1000s using carrying?
6467-2684= 3783
5 13 16
6467
400
 90  13
 200
 70  8
-2684
200
 20  5
3783
Prove it:
Prove it:
Can I subtract HTO-HTO dealing with zeros when
adjusting?
503-278=225
400
400
90
100
13
3
500  0  3
 200  70  8
200  20  5
4
Can I subtract decimals?
562.3- 174.6=387.7
9
10
9 13
5 0 3
 278
2 25
Prove it:
Then subtracting different
decimals:
14.24-8.7=5.54
347.9-7.25=340.65
Prove it:
7
To multiply successfully, children need to be able to:
• recall all multiplication facts to 12 × 12;
• partition numbers into multiples of 100, 10 and 1;
• work out products such as 70 × 5, 70 × 50, 700 × 5 or 700 × 50
using the related fact 7 × 5 and their knowledge of place value;
• add two or more single-digit numbers mentally;
• add multiples of 10 (such as 60 + 70) or of 100 (such as
600 + 700) using the related addition fact, 6 + 7, and their
knowledge of place value;
• add combinations of whole numbers using the column method.
8
Times-table Mountain Challenge
Structure- from September 2014
Foothills1 2x table in order
Foothills 2 2x table random order
Foothills 3 5 x table in order
Foothills 4 5 x table random order
Foothills 5 10 x table in order
Pupils are given 2 ½ minutes
every week to take the
challenge. They can not take
the actual test away with them
but any additional work at
home with their focus tables
will certainly help them pass
the challenge.
Foothills 6 10 x table random order
Stage 1
2, 5 & 10 times-tables
Stage 2
Division facts corresponding to the 2, 5 & 10 times tables
Stage 3
2,3,4,5 & 10 times tables
Stage 4
Division facts corresponding to the 2,3,4,5 & 10 times tables
Stage 5
Multiplication and division of numbers by 10 or 100
Stage 6
6, 7, 8 & 10 times tables
Stage 7
Division facts corresponding to the 6, 7, 8 times tables
Stage 8
times tables up to 10 x12
Stage 9
times table and division facts for 11 and 12s
Stage 10a Multiplying 2-digit multiples of 10 or multiples of 100
Stage 10b Multiplying decimals by a single digit number
Stage 10c
Multiplying and dividing decimals by 10 or 100
Member of the x club!
Deadly 60 challenges
9
My Targets for Multiplication
Can I describe an array including
the language ‘rows and columns’?
Can I recognise an array as
repeated addition sentences?
Can I describe an array using
multiplication calculations?
5 x 4= 20
4 x 5= 20
Can I solve simple Ones x Ones
number problems on a structured
number line, using pictures?
Can I solve simple Ones x Ones
number problems on an
unstructured number line?
There are 5 cakes in one box. How
many cakes in 4 boxes?
4x5=20
5x 4= 20
Prove it:
Prove it:
Can I multiply TO x Ones using the
grid method?
5+5+5+5 or 4+4+4+4+4
Prove it:
Prove it:
Can I use a number line and
partitioning to calculate Teens x
Ones ?
Can I work out a Teens x Ones
calculation through partitioning?
3 friends each baked 14 cakes. How
many cakes were there altogether?
14x3=42
14 x 3 = (10 x 3) + (4 x 3)
30 +
12 = 42
Can I multiply a number by 10 and
100?
Can I use my times table
knowledge to calculate related
facts?
3 x 10= 30
30 x 10= 300
3 x 100= 300
30 x 100= 3000
6x4=24
60x4=240
40X6=240
60x40=2400
Prove it:
Prove it:
Prove it:
23x8=184
Prove it:
10
Can I multiply HTO X Ones using
the grid method?
346x9=3114
Can I multiply TO x TO using the
grid method?
72 x 38=2736
2160
+ 576
=2736
Prove it:
Prove it:
Can I multiply HTO X Ones using
partitioning in columns, leading to
without partitioning?
short multiplication
346x9=3114
346
Leading to
x 9
346
54 (6 x9)
X 9
360 (40 x 9)
3114
45
2700 (300 x9)
3114
Can I multiply ThHTO X O using
partitioning in columns, leading to
without partitioning?
short multiplication
4346x8=34768
4346
Leading to
x
8
4346
48 (6 x 8)
X 8
320 (40 x 8)
34768
2400 (300 x 8)
234
32000 (4000 x 8)
34768
Prove it:
Prove it:
CONTINUE WITH THIS METHOD FOR
BIGGER NUMBERS IF YOU ARE
CONFIDENT.
Can I multiply decimals X O using
knowledge of place value?
short multiplication
4.92x3=14.76
Can I use long multiplication for
TO x TO?
72x38=2736
1
Leading to
4.92
X 3___
14.76
2
72
x 38
576
2160
2736
Can I use long multiplication for
HTO x TO?
Can I use long multiplication for
bigger numbers?
352x27=9504
3 1
352
x 27
2464
7040
9504
Progressing to using their place value
knowledge when multiplying decimals (4.92x
100= 492, 492 x 3= 1476, 1476 ÷100=14.76)
Explained by
8x2= 16, record 6 and carry the 1 (10)
8x70=560 +10= 570
570+6= 576
30X2=60
30X70=2100
2100+60=2160
then 2160+576=2736
1
Explained by
7x2= 14, record the 4 and carry the 1(10)
7X50=350+10=360, record the 6 for 60 and carry 3 (300)
7x300=2100+300=2400
2400+60+4= 2464
20X2=40
20X50=1000
20x300=6000
6000+1000+40=7040
then 2464+7040=9504
Prove it:
Prove it:
Prove it:
1
Can I use long multiplication,
making use of place value
knowledge, to multiply decimals?
3.77x2.8=
6
5
3 .7 7 (2 decimal places)
1
1
x
2 . 8 (1 decimal place)
3 0 1 6
7 5 4 0
1 0. 5 5 6 (3 decimal places)
Multiply the numbers just as if they were whole
numbers.
Place the decimal point in the answer by
starting at the right and moving a number of
places equal to the sum of the decimal places in
both numbers multiplied.
Prove it:
11
To carry out written methods of division successfully,
children need to be able to:
• understand division as repeated subtraction;
• estimate how many times one number divides into another – for
example, how many sixes there are in 47, or how many 23s
there are in 92;
• multiply a two-digit number by a single-digit number mentally;
• subtract numbers using the column method.
12
My Targets for Division
Can I share objects between people and
things?
( one for me, one for you)
Can I group objects between people
and things?
(a group of)
Can I record a TO ÷O calculation using
a structured number line?
Can I record a TO ÷O calculation using
an unstructured number line?
20÷5=4
Sharing 6 objects equally between 3
people means there are 2 objects each.
8 apples into groups of 2
Prove it:
Can I use objects to work out the
remainders when one number is
divided by another?
I have 20 cakes; I can fit 5 cakes in a
box. How many boxes will I need?
4 boxes
Prove it:
Prove it:
Can I use a number line to work out the
remainders when one number is
divided by another?
Can I work out whether I need to
round up or round down when finding
a remainder?
20÷3=6r2
7÷2=3r1
There are 7 bones to share with 2 pups.
But 7 cannot be divided exactly into 2
groups, so each pup gets 3 bones, but
there will be 1 left over.
Prove it:
Prove it:
48÷6=8
I have 48 cakes; I can fit 6 cakes in a box.
How many boxes will I need?
8 boxes
Prove it:
Can I divide TO÷O using known
multiples (2, 5 or 10) to chunk on an
empty number line?
68÷4=17
I have 20 Smarties to put on my cakes.
Each cake needs 3 Smarties. How many
cakes can I make?
6 cakes as you haven’t got enough
Smarties for another cake.
I have 20 cakes. I can fit 3 cakes in a
box. How many boxes will I need?
7 boxes as you need to have another
box for the other 2 cakes.
Prove it:
Prove it:
13
Can I divide TO÷O through chunking
using known multiples (2, 5 or 10)?
70÷5= 14
70
- 50
20
- 10
10
-10
0
= 14
256÷7= 36r4
10 x 5
10x5=50
5x5=25
2x5=10
1x5=5
2x5
Can I use short division to divide
decimals?
Prove it:
256
- 70 10 x 7
186
-140 20 x7
46
- 42 6 x 7
4
2x5
Prove it:
132.3÷3= 44.1
Can I divide HTO÷O using known
multiples when chunking in a column?
Can I divide HTO÷O using short
division?
128÷5=25r3
10x7=70
5x7=35
2x7=14
1x7=7
Can I present the quotient as a fraction
or decimal?
short division (HTO÷O)
134÷4=33.5
0 2 5 r3
5 1 1228
Decimal (as shown above)=33.5
Fraction=33 2/4
=36 r 4
Prove it:
Can I divide HTO÷TO using long
division?
Prove it:
Prove it:
Can I present the quotient as a fraction
or decimal?
long division
432÷15=28 r 12
432÷15
Prove it:
Prove it:
14
Glossary of terms
Terminology
Definition
O= one T= ten H= hundred Th=thousand TTh= ten thousand
HTh= hundred thousand M= Million
th= tenths hth=hundredth thth=thousandth
Array
An arrangement of objects, usually in rows and columns to aid in
quickly multiplying.
Bridge
Bridging to the nearest 5 or 10 (when using a number line or
mentally, knowing how much more or less is needed to get to the
next multiple of 5 or 10 e.g. if you are on 34 you need a jump of 6 to
get to 40.)
Cardinal number
Cardinal numbers (or cardinals) are numbers that say how many of
something there are, such as one, two, three, four, five.
Answers the question "How Many?"
Carry
Describe the action involved in a written calculation when digits are
added up and give rise to a number that is more than the given
digits, thus requiring the larger part to be ‘moved’ over to the next
place value.
E.g. 5 + 7 = 12, so the 2 of the twelve remains in the ones and the
ten part of the number has to ‘move’ over to the Tens.
Chunking
Term used to describe a written method for division
Chunking refers to the ability to ‘group’ together larger amounts
when dividing.
Consecutive
Following in order.
Consecutive numbers are adjacent in a count
For example: 5, 6, 7 are consecutive numbers. 25, 30, 35 are
consecutive multiples of 5.
Commutativity
For addition and multiplication, the numbers in calculation can be in
any order and will result in the same answer. E.g. 3 x 4 = 12 and 4
x 3 = 12 or 3 + 4 = 7 and 4 + 3 = 7. Addition and multiplication are
commutative.
Subtraction and Division are not commutative. However children
must understand that the numbers in a calculation can also be any
order but will result in a different answer. E.g. 7 – 5 = 2 and 5 – 7 =
-2.
Decimal Numbers Numbers with a value less than 1 – tenths (ten of these make one
whole number), hundredths (one hundred of these make one whole
number, ten make a tenth).
Decimal Point
Refers to the ‘dot’ put between digits in a number to distinguish
between the ones and the decimal part of a number.
Diennes
Useful apparatus which is used to support the understanding of
Apparatus
Place Value.
Digit
One of the symbols of a number system, most commonly the
symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. For example, the number 29
is two-digit number; 5 is a one-digit number
Dividend
The quantity which is to be divided. E.g. in the calculation, 12 ÷3,
the dividend is 12.
Divisor
The quantity by which another quantity is to be divided.
E.g. for the calculation 12 / 3, the divisor is 3.
Estimate
Verb: To arrive at a rough or approximate answer
Noun: A rough or approximate answer
15
Exchange
Factor
Fewer
Grid Method
Grouping/Group
Inverse
Inverse of
multiplication (as
a method of
division)
Less
Long
Multiplication
Jottings
Least Significant
Digit
Multiple
Number bonds
Number Line
Refers to moving digits from different place values e.g. moving 10
to the units to be able to subtract (used to be referred to as
‘borrowing’, but we don’t use this term now as it never gets given
back!)
Factors are numbers you can multiply together to get another
number:
Example: 2 and 3 are factors of 6, because 2 × 3 = 6.
A number can have MANY factors!
Used to compare two or more sets of countable (discrete) objects.
For example, ‘There are fewer biscuits on this plate than on that
plate’, or ‘There are two fewer apples in this bag’.
A written method for solving multiplications, see calculations page.
This term is used in division and relates to times table facts. For
instance for 15÷3 the 15 is divided into groups of 3 (so the 3 times
table is used to solve the problem and you can get 5 groups of 3
from 15).
This refers to the opposite calculation relationship, such as
multiplication being the inverse of division and addition being the
inverse of subtraction. For instance the inverse of 1+2=3 is 3-2=1.
Counting up from 0 in multiples to reach a number in order to solve
division calculation. Inverse of multiplication is used to see how
many amounts make a given number. E.g. starting at 0 and
counting up in steps of 3 until 12 is reached. Some children find
counting on in the multiples from 0 easier than repeated subtraction
and this is fine so long as they understand they are using the
inverse of multiplication rather than repeated subtraction.
Used to compare ‘uncountable’ (continuous) quantities including
measures.
For example, ‘This bottle has less water in than that one’.
A formal calculation strategy that builds on the understanding of the
grid method into a compact column method. The multiplier is larger
than 12 and therefore is partitioned during the process to aid
calculation. Long Multiplication is a multi-stage calculation which
requires final stage addition calculation in order to reach the final
outcomes.
Jottings are essentially notes/pictures/number sentences or number
lines. Any form of written workings made to help solve a
mathematical problem.
Describes the smallest part of a given number
(most commonly refers to the units, although if working with
decimals will refer to the smallest decimal part).
A multiple is a number that is part of a particular times table e.g.
multiples of 10 are any number ending in a zero: 10, 20, 30, 40 etc.
The numbers that when added make multiples of ten, one hundred,
one thousand etc. For instance 7+3=10, therefore 17+3=20, so
27+3=30 etc and 70+30=100.
A line on which numbers are represented by points.
Division marks are numbered, rather than spaces.
They can begin at any number and extend into negative numbers.
They can show any number sequence.
012345678910
16
Number Sentence
Numeral
Ordinal numbers
Partition
Pattern
Place Holder
Place Value
Product
Quotient
Ratio
Recombine
Remainder
Sequence
Short
Multiplication
Zero
Using mathematical symbols to explain a calculation e.g. 3 + 2 = 5.
A symbol used to denote a number. For example, 5, 23 and the
Roman V are all numbers written in numerals.
A term that describes a position within an ordered set. For example,
first, second, third, fourth … twentieth.
1.To separate a set into subsets
2.To split a number into component parts. For example, the twodigit number 38 can be partitioned into 30 + 8 or 19 + 19.
A systematic arrangement of numbers, shapes or other elements
according to a rule.
Term used to describe a zero in a number, for instance in 302 the
zero holds the place of the Tens and shows the number has no
Tens. Without it the number written would read as thirty-two
Understanding for instance; Hundreds, Tens and Ones
– Knowing ten ones makes one ten, knowing ten tens is one
hundred. Knowing you can’t have 11 ones.
In mathematics, a product is the result of multiplying, or an
expression that identifies factors to be multiplied. Thus, for
instance, 6 is the product of 2 and 3 (the result of multiplication).
The result of a division calculation. E.g. In the calculation of 12 ÷ 3,
the quotient is 4.
The comparison of two properties 2:3
All ratio relationships are proportional.
Term often used alongside partitioning. It refers to the ‘putting back
together’ of numbers that have been partitioned. E.g. 20 + 4
recombined is 24.
Term used to describe the amount left over from dividing (sharing
or grouping).
An ordered set of numbers or shapes arranged according to a rule.
A formal calculation strategy that builds on the understanding of the
grid method into a compact column method. The multiplier is 12 or
less and therefore not partitioned during the process as the
calculations should rely on knowledge of key multiplication facts up
to 12 x 12.
An expanded short multiplication method details each stage in
brackets and shows clear connections to the grid method. This will
be used as a vital stage in bridging understanding from the grid
method to short multiplication.
1. Nought or nothing
2. In a place-value system, a place-holder. For example, 105
3. The cardinal number of an empty set.
Useful Maths Vocabulary
Addition – add, plus, total, and, altogether
Subtraction – find the difference, take away, minus, less than,
Division – grouping, sharing, quotient, divide, halve
Multiplication – repeated addition, grouping, product, times, lots of, double
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Useful Websites
http://www.bbc.co.uk/bitesize/ks2/maths/ - aimed at supporting 10-11 year
olds as they prepare for their Key Stage 2 National Curriculum Tests
http://www.bbc.co.uk/skillswise/numbers - a BBC site with a range of
activities, facts sheets and games covering all areas of maths
www.counton.org/games - a range of interactive games
www.mathszone.co.uk – a range of interactive games and activities covering
all areas of maths
www.primarygames.co.uk – a range of interactive games covering all areas
of maths
www.teachingtables.co.uk – practise multiplication tables through fun games
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Stoke Park Junior School
Underwood Road,
Bishopstoke,
Eastleigh SO50 6GR
Tel: 023 80612789
Fax: 023 80653212
E-mail:adminoffice@stokepark-jun.hants.sch.uk
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