## Why is this skill important?

This skill shows that children can use their understanding of how our number system works when they come to perform harder calculations. This matters because it makes it possible for children to do two essential things:  First to find quick and efficient ways to do sums in their heads; and second, to understand and therefore remember the procedures for written computation.

## What is the skill?

Adding 1, 10, 100 or 1000 is not like ‘normal’ addition. Most calculations require the person doing them to work something out, for example the addition 17 + 8 requires that a child either starts at 17 and counts on 8, or else that they realise that 17 and 3 more is 20, so 17 and eight is simply 20 and five more.

This second way is better in two ways. Firstly, it is more flexible, in that the child can use it if they are doing a calculation with larger numbers, e.g. 67 + 8 is 67 + 3 + 5 and secondly it paves the way for quicker mental calculations.

However, adding 10, 100 or 1000 requires not that we work something out but that we understand ‘place value’ (see Number: Place Value and Counting in 10s and 100s).  Children should be able to count on from any number in ones, in tens, in hundreds or in thousands. Thus, if I say, ‘six hundred and ninety-four’, I expect a child to be able to count on in ones (695) or in tens (704) or in hundreds (794) or even in thousands (1694).  If they can do this, they demonstrate a good understanding of place value, that is, of the way thousands, hundreds, tens and ones work in our number system.

It follows that some calculations should – if we understand the mathematics of numbers – require no working out at all!  127 + 1 and 127 + 10 and 127 + 100 are all calculations to which children should ‘know’ the answers without having to do any calculation or expending any effort.  They are what we like to call ‘no-calorie sums’!  It should not require a single calorie to say the answer!

## So how is this skill taught?

Being able to say the number one more or less depends on being able to count in ones. Similarly, being able to say the number ten more or ten less depends on being able to count in tens. The same is true for saying the number one hundred more or less or one thousand more or less.  So the best teaching relies upon helping children to count in ones, tens, hundreds and thousands.

The difficult bits in counting are always when we cross a multiple of 100 or 1000.  Thus, most children will have no trouble in counting, 361, 371, 381, 391, but may well have difficulty in saying the next number in the count: 401. This is because they are crossing a multiple of one hundred. So the first important thing to do is to check which of the counts, 1s, 10s, 100s or 1000s, the child finds hard. Ask children to count with you to assess the following:

• Can they count in ones across a multiple of 100 but not in tens? (Saying 397, 398, 399, 400, 401, 402, etc. correctly but not saying 397, 407, 417… correctly.)
• Can they cross a multiple of 1000 if they are counting in hundreds but not if they are counting in tens?  (Saying 783, 883, 983, 1083, 1183 correctly, but not saying 983, 993, 1003, 1013, 1023 correctly.)
• Can they count backwards as well as forwards, e.g. going back from 902 (901, 900, 899…etc). Can they count back in 10s and 100s and 1000s?

To help them with their difficulties in counting in tens, hundreds or thousands, we try the following techniques:

• Practise chanting the numbers aloud. Focus on those which cross a multiple of 100 or 1000. Do this by passing a toy or a beanbag back and forth between you as you each say a number in turn. I say ‘five hundred and seventy-six’, and pass the beanbag to the child. They say ‘five hundred and eighty-six’, and pass the beanbag back to me.  I say ‘five hundred and ninety-six’, and pass the beanbag back. What does the child now say?
• Show children the sequence of written numbers and ask them to read it to you.  576, 586, 596, 606…etc. Point out which digit changes each time.
• Use place value cards or coins to help them understand the value of each digit (see Number: Place Value).

Chanting the numbers and reading them are both key to children’s memory and understanding in this area. If a child is having real problems, return to teaching place value (see Number: Place Value).

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: 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.

7-9: Lower Juniors

9-11: Upper Juniors