Egerton’s
Calculation
Policy
ADDITION
Reception to Year 7 Expected Progression.
Step 1
Counting On
LO: Record in the context of play or practical activities.
Success Criteria
1. I will add by counting objects.
2. I will use number bonds to count on.
2+3=
COMMENTARY AND LINKS FOR
PARENTS
Begin to relate addition to combining
two groups of objects
Add
At a party, I eat 5 cakes and my friend
eats 3.
How many cakes did we eat altogether?
7 people are on the bus. 4 more get on
at the next stop. How many people are
on the bus now?
• Make a record in pictures, words or
symbols of addition activities already
carried out.
• Construct number sentences to go
with practical activities
• Use of games, songs and practical
activities to begin using vocabulary
 Solve simple word problems using
their fingers
Step 2
Number Lines
LO: I will add using a number line or by partioning.
Success Criteria:
1. I can circle the largest number in the number sentence.
2. I can draw a straight line using a ruler.
3. I can put the largest number on the left hand side of the line.
4. I can break the smallest number up into tens and units.
5. I can start on the left hand side.
6. I can jump along the line using the tens then the units.
7. I can put the tens I have jumped in then the units on top of the jump.
8. I can circle the answer.
9. I can check to make sure my answer is reasonable.
COMMENTARY AND LINKS FOR
PARENTS
8 + 3 = 11
+1
+1
8
9
+1
10
11
Counting forwards.
Your child will know pairs of numbers
that add to 10. They will know how to
move these on in steps.
What is 32 + 24?
+ 10
32
+ 10
42
+1
52
53
+1
54
+1
+1
55 56
Partioning
56 + 41 =
5 6
+
50
+ 40
90
+
9 7
Children partion numbers so that
56+41 becomes 50+40 and 6+1.
4 1
7
+
6
6
+
1
KS2 examples
The train leaves at 2 o’clock in the
afternoon and arrives at 5:30pm.
How long is the journey?
+3h
+ 30m
2pm
5:30pm
5pm
The journey takes 3 hours 30 minutes
23.7 + 4.4
+4
23.7
+ 0.3
27.7
+ 0.1
28
28.1
Step 3:
Standard Written Method.
I will add using the standard written method.
Success Criteria:
1. I can put the headings for each column at the top.
2. I can put the question into columns (one digit in each box).
3. I can put my addition sign on the right hand side.
4. I can put the decimal point in my answer if needed.
5. I can start adding from the right hand column. (E. g. ones or decimals)
6. I can put any carries under the next column.
7. I can check to see if there are any carries you need to add.
COMMENTARY AND LINKS FOR
PARENTS
HTU
546 +
487
1033
1 1
Addition with Decimals
36.7 + 214 =
2 1 4 .0 +
3 6 .7
___________
2 5 0 .7
The standard written method is the
most efficient of all the methods;
however for a lot of children it does not
promote understanding. It is important
that they have the understanding before
they are consistently using this method
and have shown they are secure using
the other methods.
Add a 0 to 214
as a place
holder
e.g. 214.0
____________
1
Addition with Decimals (conversion
is necessary)
3.4 L + 250 mL =
3.400 +
0.250
_________
3.650
_________
Progression beyond year 7 will rely upon consistent and
accurate use of the final method.
SUBTRACTION
Reception to Year 7 Expected Progression.
Step 1
Object Removal
Children begin to record in the context of play or practical activities and problems.
LO: I will subtract by taking objects away.
COMMENTARY AND LINKS FOR
PARENTS
5–1=4
I had five balloons. One burst. How
many did I have left?
Take away
A teddy bear costs £5 and a doll costs
£1. How much more does the bear cost?
Find the difference
Lisa has 5 felt tip pens and Tim has 1.
How many more does Lisa have?
Begin to relate subtraction to ‘taking
away’
• Make a record in pictures, words or
symbols of subtraction
activities already carried out
• Use of games, songs and practical
activities to begin using vocabulary
• Construct number sentences to go
with practical activities
• Relate subtraction to taking away and
counting how many objects are left.


Step 2
Number Lines
LO: I will subtract using a number line.
Success Criteria:
1. I can circle the largest number in the number sentence.
2. I can put the largest number on the right hand side of the line.
3. I can break the smallest number up into tens and ones.
4. I can decide whether or not to count up from the smallest number to the
largest or count back from the largest number.
5. I can jump along the line using the tens and then the ones.
6. I can put the tens I have jumped in then the ones on top of the jump.
7. I can circle the answer.
8. I can check to make sure my answer is reasonable.
COMMENTARY AND LINKS FOR
The baker makes 54 loaves and sells 28.
How many has he left?
PARENTS
54 - 28 = 26
- 20
-4
-4
34
30
26
26 loaves are left
87 - 35 =
8 7
-
54
3 5
80
- 30
7
5
50
2
5 2
Find the difference between 152 and 94.
152 - 94 = 58
-52
-6
100
94
152
KS2 examples
The train leaves at 12.18 and arrives at 15.46.
How long is the journey?
The journey takes 3h 28min
- 3h
- 12min
- 16min
12.18
6.1 – 2.4
12.30
- 0.6
2.4
3
3.1 + 0.6 = 3.7
15.30
- 3.1
6.1
15.46
Step 3
Standard Written Method
LO: I will subtract using the standard written method.
Success Criteria:
1. I can put the question into columns (one digit in one box).
2. I can put my subtraction sign on the right hand side.
3. I can start subtracting from the right hand column. (E. g ones or decimals.)
4. I can put the decimal point in my answer if needed.
5. I can subtract the bottom number from the top number.
6. I can check to see if you need to borrow.
5 13 1
6431 358
285
COMMENTARY AND LINKS FOR
PARENTS
Subtraction including Decimals
264 – 61.9 =
2 6 ³4 .¹0 6 1 .9
_____________________
20 2 . 1
_____________________
Progression beyond year 7 will rely upon consistent and
accurate use of the final method.
MULTIPLICATION
Reception to Year 7 Expected Progression.
Step 1
LO: I will be able to count in repeated groups of the same size:
Success Criteria:
• Count in twos; fives; tens
 Chant in 2s, 5s and 10s.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
COMMENTARY AND LINKS FOR
PARENTS
2x4
Each child has two feet. How many feet
do four children have?
2
+
2
+
2
+
2
Step 2
Number Lines
LO: I will multiply using a number line with a repeated addition.
1.
2.
3.
4.
I can draw an empty number line.
I can put my start number on the number line (0).
I can circle the number I am multiplying by.
I can count up in the number I am multiplying by writing the number of
jumps as I go.
5. I can write where I get to after each jump under the number line.
6. I can circle the answer at the end.
7. I can check to make sure my answer is reasonable.
4 x4
There are 4 cats. Each cat has 4 kittens.
How many kittens are there altogether?
+4
+4
+4
+4
4
8
0
4x3
3x4
0



COMMENTARY AND LINKS FOR
PARENTS
12
16




Step 3
Number Lines
LO: I will multiply using a number line by chunking.
Success Criteria:
1. I can draw an empty number line.
2. I can put my start number on the number line (0).
3. I can circle the number I am going to count up in (the number I am
multiplying by).
4. I can choose the chunks I am going to use.
5. I can jump in the chunk.
6. I can circle the answer at the end.
7. I can check to make sure my answer is reasonable.
COMMENTARY AND LINKS FOR
PARENTS
16 x 4
10 x 4 = 40
0
6 x4 = 24
40
64
Step 3b
Grid Method
LO: I will multiply using the Grid method.
Success Criteria:
1. I can write the partitioned numbers down.
2. I can draw the correct grid.
3. I can put the numbers into the correct place on the grid.
4. I can multiply the numbers together (check for any easy steps).
5. I can make my addition question using the answers (look at the success
criteria to help make the addition).
6. I can add my numbers together.
7. I can check to make sure my answer is reasonable.
14x7=
10
COMMENTARY AND LINKS FOR
PARENTS
4
7
7
10
4
70
28
70 +
28
98
17 x 14
10
10
4
7
100
70
40
28
268 x 53
200
50
3
10 000
600
100 +
70
40
28
238
60
3 000
180
8
400
24
10000 +
3000
400
600
180
24
14204
Step 3c
Formal method
LO: I will multiply decimals using the column method.


The Column Method
15.8 × 6.7
COMMENTARY AND LINKS FOR
PARENTS
Ignore the decimal in the first instance
First, multiply each of 1 5 and 8 by 7
(ones), don’t forget you may have to
carry!
158
x 67
1106
45






158
x 67
1106
9480
158
x 67
1106 x 7
9480 x60
10586
Adjust back place value = 105.86
7x8= 56 then 7x5 = 35 but plus the 5
makes 40.
Finally, 7x1 = 7. We add the carried 4 to
make 11.
Now we need to multiply by 60. We add
a zero on the right-hand side of the next
row. This is because we want to multiply
by 60 (6 tens), which is the same as
multiplying by 10 and by 6. Once you
have done this you can multiply by 6
Now add your two rows together, and
write your answer.
Now we must add in the decimal. We
altered the question by two place value
and so we adjust the answer back.
Progression beyond year 7 will rely upon consistent and
accurate use of the final methods.
DIVISION
Reception to Year 7 Expected Progression.
Step 1
Sharing in Groups
LO: I will share an amount into a given group size.
Success Criteria
1. I can draw halve numbers up to 10 (even numbers).
2. I can use counters to share amounts.
There are 12 sweets and 2 children. They COMMENTARY AND LINKS FOR
share the sweets equally, how many
PARENTS
sweets does each child have?
Share objects into equal groups
Use related vocabulary
Sharing between two
Activities might include:
 Sharing of milk at break time
 Sharing sweets on a child’s
birthday
 Sharing activities in the home
corner
 Count in tens/twos
 Separate a given number of
objects into two groups (addition
and subtraction objective in
Each child has 6 sweets
reception being preliminary to
multiplication and division)
Grouping in threes
There are 12 sweets and each party bag
needs three sweets.
How many party bags can be made?
There are 4 party bags
4 apples are packed in a basket. How
many baskets can you fill with 12 apples?
  
Count in twos, tens
How many times?
How many are left/left over?
Group
Answer
Right, wrong
What could we try next?
How did you work it out?
Share out
Half, halve
Step 2
Number Lines
LO: I will divide using a number line using repeated subtraction.
Success Criteria
1. I can draw an empty number line.
2. I can put my start number on the number line at the right hand side.
3. I can circle the number I am going to count down in (the number I am
dividing by).
4. I can count up or down in the number I am dividing by, by writing the jumps
as I go and writing where I get to.
5. I can count how many jumps I have made to get to 0.
6. I can check to make sure my answer is reasonable.
28÷7 = 4
COMMENTARY AND LINKS FOR
PARENTS
A chew bar costs 7p. How many can I
buy with 28p?
-7
-7
-7
-7
________________________________
0
7
14
21 28
Step 3
Number Lines
LO: I will divide by chunking using a number line.
Success Criteria
1. I can draw an empty number line.
2. I can put my start number on the number line at the right hand side.
3. I can circle the number I am going to count down in (the number I am
dividing by).
4. I can choose the chunks I am going to use.
5. I can jump in the chunk.
6. I can count how many jumps I have made to find the answer.
7. I can check to make sure my answer is reasonable.
64 children need to be seated in groups
of 4. How many tables will be needed to
seat all the children?
COMMENTARY AND LINKS FOR
PARENTS
64 ÷ 4 = 16
10 x 4
0
5x4
40
1x4
60
64
0
16 tables will be needed to seat all the
children.
Step 3b
Standard Written Method
LO: I will divide using the standard written method known as the ‘Bus Stop’.
Success Criteria:
1. I can identify what is the divisor and what is the dividend.
2. I can put my divisor outside the ‘shelter’ and the dividend under the ‘shelter.’
3. I can start dividing from the left hand column.
4. I can carry remainders over to the next column
5. I can jot down the times table to support my working.
6. I can put the decimal point in my answer if needed.
7. I can check to make sure my answer is reasonable.
Short Division
COMMENTARY AND LINKS FOR
PARENTS
Short Division with 2 digit numbers
𝟓𝟕𝟖 ÷ 𝟏𝟕 =
𝟑 𝟒
𝟏𝟕|𝟓 𝟓𝟕 𝟔𝟖
Jot down 17 times table to
support calculation
17
34
51
68
Short Division with remainders
𝟑𝟖 ÷ 𝟔 =
𝟔𝒓𝟐
𝟔|𝟑 𝟑𝟖
Short Division with decimals (answers
to 1 decimal place)
𝟏𝟐𝟖 ÷ 𝟓 =
𝟐 𝟓 . 𝟔
𝟓|𝟏 𝟏𝟐 𝟐𝟖 . 𝟑𝟎
Rounded to 1 d.p. 42.7
Long division with remainders,
fractions and decimals
A.R.E: By Year 5 all students are expected
to be able to completed short division
with a remainder
Progression beyond year 7 will rely upon consistent and
accurate use of the final method.
It is expected that students will continue to use the same method in Year 7 and
Year 8. They will adjust the dividend and divisor by a common factor before the
division so that no further adjustment is needed after the calculation
e.g.
361.6 ÷ 0.8 is equivalent to 3616 ÷ 8
REASONS FOR USING WRITTEN METHODS
 To aid mental calculation by writing down some of the numbers and answers
involved
 To make clear a mental procedure for the pupil
 To help communicate methods and solutions
 To provide a record of work to be done
 To aid calculation when the problem is too difficult to be done mentally
 To develop and refine a set of rules for calculations
WHEN ARE CHILDREN READY FOR WRITTEN CALCULATIONS?
Addition and subtraction
 Do they know addition and subtraction facts to 20?
 Do they understand place value and can they partition numbers?
 Can they add three single digit numbers mentally?
 Can they add and subtract any pair of two digit numbers mentally?
 Can they explain their mental strategies orally and record them using
informal jottings?
Multiplication and division
 Do they know all the multiplication facts including the 12 times table?
 Do they know the result of multiplying by 0 and 1?
 Do they understand 0 as a place holder?
 Can they multiply two and three digit numbers by 10 and 100?
 Can they double and halve two digit numbers mentally?
 Can they use multiplication facts they know to derive mentally other
multiplication facts that they do not know?
 Can they explain their mental strategies orally and record them using
informal jottings?
The above lists are not exhaustive but are a guide for the teacher to judge when a
child is ready to move from informal to formal methods of calculation. These
should be linked with Age Related Expectations. (A.R.E)
The core strands of the new curriculum
 become fluent in the fundamentals of mathematics, including through varied
and frequent practice with increasingly complex problems over time, so that
pupils develop conceptual understanding and the ability to recall and apply
knowledge rapidly and accurately.
 reason mathematically by following a line of enquiry, conjecturing
relationships and generalisations, and developing an argument, justification
or proof using mathematical language
 can solve problems by applying their mathematics to a variety of routine and
non-routine problems with increasing sophistication, including breaking
down problems into a series of simpler steps and persevering in seeking
solutions.
PROBLEM SOLVING
LO: I will solve problems.
Success Criteria:
1. I can read the question.
2. I can underline key information.
3. I can write down the operation I need to use.
4. I can write the number sentence.
5. I can do my working out.
6. I can check my answer to make sure it’s reasonable.
7. I can write my answer into a sentence.