1. Progression In Calculations.
Subtraction
Mathematical Calculations in East Worthing Schools.
This document has been discussed and agreed by all East Worthing Maths Leaders and is designed to help you to understand the calculation methods your child will be taught in school. When supporting your child at home with Maths work it would be helpful if you could reinforce these methods rather than teach them the way that you were taught. Your child’s teacher will be able to direct you to the appropriate method within this document to use at home.
Remember each child progresses at their own pace.

2. Understanding Subtraction.
Explanation
The physical act of counting out
a set number of objects and taking some away is an important step for children to explore. This is best done in a practical play based context as much as possible.
Count out a given number of objects and take away 1 of them... How many do you have now?
Understanding subtraction as taking away
Children need to experience counting out a set number of objects and then removing/taking away a certain number from that group. Initially this needs to be taking away 1 from a set.
Eg take away 1 leaves 6
Count out 7 objects. Then remove 1 from that set and count the objects that are left over.
Explore 1 less through simple songs and rhymes, for example ’10 green bottles’ or ‘5 little speckled frogs’.
Success criteria
I can use objects to take away 1 from any number up to 10.
I can work out how much I have left from an amount up to 10p when I buy a sweet costing 1p (using 1p coins to work practically).
Key Questions/Vocabulary
Less, less than, one less, before, take away, subtract, leaves, equals
What is the number before 5?
How many different ways can you show me that 8 subtract 1 is 7?
Can you show me how you worked out 1 less than.....?

3. Simple Jottings/Mark Making for Subtraction.=
Explanation
Simple mark making is the first stage of children’s
independent jottings to help them solve subtractions.
They draw the initial number of objects and then
cross off the number it says to take away and
count the ones left over. Children can also use
objects, such as counters, sweets, beads, to create
the initial group and then physically take away the
right number to find the answer to the subtraction.
At this level, children need to see that when doing subtraction the biggest number needs to be first and you take away the smaller number.
Success criteria
I can use simple jottings to support the subtraction of two numbers starting from numbers up to 10, then 20.
I can begin to select appropriate apparatus to support subtraction.
Key Question/Vocabulary
Count, count back, subtract, take away, cross off
Difference between, leaves, equals
How many are left over?
Find the number that is 6 less than...?
Count back 5 from 16, what number do you get to?

4. Using a Number Track for Subtraction.
Three less than nine is six
Explanation
Number tracks can be used for children to locate a number, learn the order of numbers, and to begin to find out one less and then a few less than a given number.
Children need to be able to understand the order of numbers remains the same and that when counting back the numbers get smaller by 1. They need lots of practice in counting backwards... Count back as you go down the stairs.... Do a countdown from 10 or 20 before you leave the house....Write the numbers to 10 on separate pieces of paper and get your child to order them in reverse, then try from 20.
Key Questions/Vocabulary
Count back, take away, subtract, less than, difference
between, distance between, leaves, equals
Find the number that is one less than ....? Five less
than....?
Count back 4 places from 8, where do you land?
How many is 5 less than 9?
How many between?
How far apart?
Order Numicon
1 – 10 set, note the difference between two shapes next to each other is 1.
Success criteria
I can use a number track to count back and find the answer to a given question starting from numbers up to 10, then up to 20.

5. Using a Blank Number Line for Subtraction.
Explanation
Blank number lines are used to enable children to count back with more than one jump. Children are taught to draw their own blank number lines, enabling them to do calculations within any range of numbers. There is no need to write -1 in each jump. Children learn to use ones jumps, subtracting single digit numbers and working within a range up to about 20, then 30. The start and end numbers are recorded below the line and there is no need to write -1 in the jumps. With subtraction they start at the right hand end of the line and jump back.
9 – 4 = – 6 = 8
Children can use Deines (one blocks) to make the start number and then place one in each jump to support the visual image of how many they need to count back.
Success criteria
I can use number lines to support the subtraction of two numbers starting from numbers up to 20, then 30.
I can use a number line to help me solve subtraction problems involving money , up to 30p, and measures, up to a similar amount.
Key Questions/Vocabulary
Count back, count back in ones, less than, take away,
Subtract, leaves, equals
Where are you going to start your number line?
Which number are you starting with?
How many jumps back do you need to do?
What number have you reached?

6. Understanding Subtraction as the Difference Between.
Explanation
When children have a secure understanding of subtraction as take away, they can learn how to solve subtraction calculations by counting on to find the difference between the numbers. Counting on is much easier than counting backwards and generally far fewer mistakes are made, however it is important that children know the link between addition and subtraction, that they undo each other, we call this INVERSE. It is also important for children to begin to get an idea of when counting on or counting back are the best methods to use we find the difference between when the numbers are close together and it is easier and quicker to count on than back. (eg for 87 – 12 counting back would be quicker and more efficient but for 76 – 59 finding the difference would be preferable)
37 – 32 (What is the difference between 32 and 37?)
Children start with the smaller number under the number line and jump on until they reach the larger number. They need to understand that when finding the difference between two numbers, the answer to the question is found by counting how many jumps they did.
So the difference between 32 and 37 is 5.
Success criteria
I can use a number line to find the difference between two numbers by counting on.
I can use a number line to help me solve subtraction problems involving money and measures, using the method of counting on.
Children can use Numicon to create both the numbers they are finding the difference between , laying them on top of each other to see the visual difference.
Key Questions/Vocabulary
Count on, difference between, distance between, how many
more than… , How many between? How far apart?
Equals, inverse
Where are you going to start your number line?
Which number are you starting with?
Which number are you going to stop at?
How many jumps on did you do?
What was the difference between the numbers?

7. Developing use of Number Lines, Subtracting Tens and Ones.
Children need to understand the place value of each digit in order to partition 2-digit numbers into tens and ones so they know how many tens and ones jumps to do.
-10
48g – 13g = 35g
(as subtraction by counting back)
35g g g
60p – 35p = 25p
(as the difference between so counting on)
35p p p p
Success criteria
I can use number lines more efficiently to subtract a 2-digit number by counting back or counting on the tens jumps and then the ones jumps.
Key Questions/Vocabulary
Subtract, take away, minus, less than,
ten less, count back in tens, one less,
count back in ones, leaves, equals,
inverse
Difference between (Eg for 53 – 47, it
is easier to count on from 47 to find the
difference between the two numbers
than count back 47 places.)
Explanation
Subtracting tens and ones is the same as for
addition. Jottings are set out as shown, with a
record of where you have reached kept under
the line and the jumps done recorded over the
line. There is no need to write -1 in the
small jumps, this would be inefficient. When
confident subtracting ‘teen’ numbers,
progress to subtracting numbers with more
than one ten.

8. Develop Efficient Use of Number Lines.
112cm – 94cm = 18cm
(as the difference between so counting on)
+6cm cm cm
94cm cm cm cm
152 – 68 = 84 (as subtraction by counting back) -6
-60 -2
Explanation
Once children are confident and accurate in the use of tens and ones jumps, they can progress to using
multiple of tens jumps. Encourage children to use their knowledge of number bonds to bridge through the nearest
multiple of 10 to make counting easier (as in the second eg). Make sure they keep a record inside their jumps of
what they are doing so that they can check they have subtracted the correct number.
Use mental recall of + and – facts to 20 and apply to problems.
Know all the + and –facts for multiples of 5 to 100 (eg , 80 – 55).
Derive rapidly all number pairs that total 100 (eg , )
Success Criteria
I can subtract chunks of tens and ones to make my calculations more efficient.
I can bridge through the nearest multiple of ten.
Key Questions/Vocabulary
Subtract, take away, minus, less than
Ten less, count in tens
One less, count in ones
Difference between, inverse
Equals, leaves, altogether

9. Partition for Subtraction.
To subtract 24 from 68, first subtract the tens and record where you have reached. Then you need to continue and subtract the units. It can be recorded initially as a number line so that the children can see the link between the two recording methods given here.
TU TU
= 48 (subtract the tens first)
= (subtract the units second)
SO 68 – 24 = 44
Children can make the start number from Deines or Numicon and physically remove the tens and then the units. This will act as a strong visual image to support the subtraction they are doing.
Explanation
Some children will find this a quick and easy method for subtraction, when
the digits being subtracted are smaller than the starting number, and
they will be able to do it mentally. Initially it is important to give
calculations where the ones and tens digits do not cross the tens boundary.
Success Criteria
I can partition the number being subtracted into tens and units to support subtraction.
I can subtract the units and then the tens for 2-digit subtraction calculations.
Key Questions/Vocabulary
Subtract, minus, take away, less
than, tens, units, partition, inverse
How many units are you
subtracting?
How many tens are you subtracting?
Confidently recall + and – facts to 10 then 20 (eg, 9 + 6, 13 – 7, )
Know all + and – facts for multiples of 10 to 100 (eg, , 90 – 20)

10. Expanded Column and Formal Written Subtraction.
87 – 52 = 35
Explanation
This method moves the children on from number lines and horizontal partitioning to vertical methods including the partitioning still.
They are able to see the number split up then recombine at the end.
** If you wish to insert an + sign between the partitioned numbers then this is an individual school decision.
e.g
Success Criteria
I can partition the number being subtracted into hundreds, tens and units to support subtraction.
I can subtract the units and then the tens for 2-digit subtraction calculations and continue for 3-digit calculations
Key Questions/Vocabulary
Subtract, minus, take away, less
than, hundreds, tens, units, partition, inverse
How many units are you
subtracting?
How many tens are you subtracting?
How many hundreds are you subtracting?

11. Formal Written Subtraction.
Explanation
This formal written method will only work once the children are secure in their understanding of place value and partitioning of numbers. Applying the process of units, tens, hundreds will ensure that they are subtracting in the correct manner.
Some calculations will be straightforward whilst others will require further thought as you ‘take’ a ten or hundred from the next column
Key Questions/Vocabulary
Subtract, minus, take away, less
than, tens, units, partition, inverse
Decompostition
Estimation
Operation
Success Criteria
I can subtract the units, then the tens, then the hundreds for 3-digit or more subtraction calculations.