Why is this skill important?
In any mental calculation which involves either adding or subtracting, it is essential that children do not have to work out the basic facts of number pairs up to and including ten each time. For example when adding 6 to 78 it is essential that children know that 2 more to 78 will take them to 80, and that this leaves us with 4 more to add, drawing upon the facts 8 + 2 = 10 and 6 = 4 + 2. Again, when subtracting 37 from 42, the child needs to know that 37 + 3 = 40 and then that 40 + 2 = 42 so that they can work out that the difference is 3 + 2 or 5.
These basic number facts are the pre-requisites for being able to do mental arithmetic quickly and with confidence.
What is the skill?
Given any number up to and including ten, children should be able to say the pairs of numbers you need to add together to make it,
e.g. 6 is 3 + 3, 4 + 2, 5 + 1 and 9 is 1 + 8, 2 + 7, 3 + 6, 4 + 5.
The most important of these facts are what teachers call the ‘bonds to ten’, 10 is 5 + 5, 6 + 4, 7 + 3, 8 + 2, 9 + 1. If children really know these pairs by heart, then they will be able to use their facts in doing other sums, e.g. 47 + 6 as 47 + 3 + 3 where they first add to the next multiple of ten and then add the rest. Teachers call this, ‘bridging ten’, and it is an incredibly important skill.
Look at these calculations:
75 + 8 is 75 + 5 (adding to the next multiple of 10) then add the extra 3.
52 – 47, is done by counting up to find the difference using number facts. So 47 + 3 (to the next multiple of ten) and then count on 2 more. We have counted on 5 in all.
So how is this skill taught?
This skill basically relies upon helping children to learn these basic facts by heart. They should know them so well that they do not have to even think about the answer.
This can only be taught by assisting children to memorise. Memory is a classic example of a ‘use it or lose it’ skill. Getting children to exercise their memories will have benefits far beyond the number facts!
Say different numbers to assess the following:
- Can the child give you a pair of numbers that make the number you said?
- Can they say what number goes with the number you said to make ten? Or twenty?
- Can they tell you the total if you give them two numbers under ten?
The children need to repeat the pairs of numbers that make ten as many times as possible. Games are the best way of making this fun but it will also be necessary to do a few sums! It is the combination of the two which help.
- Use the fact that we have ten fingers to help children remember their bonds to ten. Fold down some fingers. How many are standing? Say the sum, e.g. four and six make ten. If you say a number, e.g. seven, the child folds down that many fingers and responds with the number left standing. In this way, they learn the pairs to ten.
- Use 10 cubes. Hide some under a tea-towel. How many are hidden? (Repeat for other numbers, e.g. 9 cubes, or 8 cubes.)
- Write a number, the child has to write the matching number to make ten (or 9 or 8 or 7… as you decide in advance). Keep writing pairs as fast as you can. How many different pairs can you write with the same total?
- Say a two-digit number. The child must say what goes with that number to make the next multiple of ten, e.g. you say 34, they say 6, then you say the multiple of ten, e.g. 40. Then repeat this, but take opposite roles.
- Add two numbers under ten, e.g. 6 + 7. Agree the total using bonds to ten, if necessary, e.g. 7 + 3 + 3. Then write a matching addition with the same units pattern, e.g. 27 + 6 (33) then another 57 + 6 (63) etc.
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.