Why is this skill important?
Although most calculations involving subtraction are best done by counting up (see Addition and Subtraction: Mental addition and subtraction and Know doubles and halves to 20) there are some types of subtraction, which, whilst they can be solved by this method, do cry out for counting back. These include what we call ‘place value’ subtractions, such as 1426 – 26 or 274 – 70 as well as those where we are taking away a small number from a much larger number such as 345 – 26.
Counting back or taking away is also useful for children since it develops some of the mathematical skills they will require in the upper juniors (Y5 and Y6) when they come to develop more formal written subtraction methods such as decomposition or equal addition.
Finally, some contexts will only allow a subtraction to be done by counting back. If a pudding has to be ready for 12:15 and it takes 50 minutes to cook, the only way to discover what time to put it in the oven is to count back!
What are the skills?
The main skills involved in this mental strategy are very similar to those required in the other mental strategies for addition and subtraction. Children need a good understanding of place value and a robust recall of their number facts, especially the bonds to ten.
The place value aspects are most crucial in counting back since it is frequently the case that, either the subtraction involves crossing a multiple of 10 or 100 counting backwards, or it is actually dependent on an understanding of how numbers work in order to be able to do it at all.
Examples of the first type include calculations like:
- 83 – 15
- 103 – 8
In all of these the ‘taking away’ involves crossing a multiple of 10
Examples of the second type include:
- 537 – 20
- 346 – 40
- 803 – 500, etc.
In all of these, the child has to understand how the hundreds, tens or ones can be changed irrespective of the other digits.
So how is this skill taught?
There are two main images on which we draw when teaching counting back. The first and most important is the number line.
Children can be encouraged to hop back along the number line, first going to the multiple of 10 or 100, then going over it.
So that 83 – 15 is done by taking away 10 to leave 73, then counting back 3 then 2 more.
- 83 – 10, then 73 – 3, then 70 – 2 = 68.
For the place value subtractions, the easiest way to encourage children to see which digit they are dealing with is to get them to articulate or say the number to be taken away really clearly and then to identify the corresponding digit in the larger number, e.g.
537 – 20 is best taught by focussing on the tens digit in the larger number and counting back in tens.
- 537, count back two tens (20) to leave 517.
Stress that none of the other digits change.
- Coins can be used to help children see this, as long as we refer to one pound as one hundred pence.
537 is £5 (500p) and three 10ps and seven 1ps.
We are simply taking away two of the 10ps. None of the other coins are touched.
Practise Together: These activities are intended to be shared. Read the Explanation of the skill being practised and then play the game or share the task. Watch out for the points highlighted in the Explanation and if necessary, help your child, following the advice in ‘How this skill is taught’ section. Shared activities are not only more fun – they enable you to actively support your child’s learning.
Explanation & Worksheets:
Test: Take a test, questions from this area
Say numbers 10 100 1000
Pairs up to 10
Skill with single digit numbers
Mental addition & subtraction
Know doubles & halves to 20
Add 2 or 3 digits with writing
Counting back to subtract
Subtract by counting up
Say numbers 10 100 1000: Say immediately the numbers 10, 100, 1000 more or less than any number up to 10,000
Pairs up to 10: Know by heart the pairs of numbers to make all the numbers up to and including ten
Skill with single digit numbers: Add several single-digit numbers spotting pairs to 10 and doubles
Mental addition & subtraction: Add or subtract two 2-digit numbers in their heads without writing anything down (and without groaning!)
Know doubles & halves to 20: Know by heart the doubles of all numbers up to 20 and the corresponding halves
Add 2 or 3 digits with writing: Add several 2-digit or 3-digit numbers using a written method
Counting back to subtract: Subtract a small number from a large number by counting back, e.g. 345 – 26 (take off 20, then 6)
Subtract by counting up: Subtract two numbers by counting up to find the difference, e.g. 345 – 287 by counting from 287 to 300 then to 345
Number Concepts: Count in different ways, understand how numbers work, become fluent in the ways of numbers
Adding and Subtracting: Mentally add or subtract numbers with confidence and develop written ways of adding and subtracting larger numbers or more of them!
Multiplying and Dividing: Know the times tables and use these to perform mental multiplication and divisions; develop written methods for multiplication and division.