## Why is this skill important?

This skill relates to understanding how numbers work. If children don’t understand this, their ability to get very far in maths, and even to become fluent at basic mental or written arithmetic, is severely reduced. All complex calculations rely upon a thorough understanding of place value (see Number: Place value) and this understanding is reinforced and developed by counting in tens and hundreds.

## So why does counting in tens and hundreds matter?

It is only possible to count if you understand how the numbers work. If I am counting from 1497 onwards, I can count in ones - 1498, 1499, ... - and then I have to think what comes next. It is only if I understand that I will now need to change the hundreds digit, in this case the 4 becoming a 5 in 1500, that I can continue. Counting in tens or hundreds depends upon being able to manipulate the numbers because we understand how they work. The sum 256 + 10 should never be done by counting on in ones because children should understand that:

• Only one digit will need to change and that is the tens digit
• We can add 10 in the same way as adding one – by changing one digit to the number one more. In this case, 256 changes to 266.
• We do not need to do any work to add 10!

It is for this reason that adding 10, adding 100 and even adding 1000 are seen as ‘special cases’ of addition, and by the same token, subtracting 10, 100 or 1000 are ‘special cases’ of subtraction. They do not depend upon being able to count up or back or to calculate. Instead they require an understanding of how the numbers work.

It is worth noting that children often write 1001 for ‘one hundred and one’, indicating that they have not understood place value (see Number: Place value).
If we ask a child to count in tens, we will help to reinforce their understanding of this important concept: 61, 71, 81, 91, 101, 111, 121, etc.  Being able to ‘count on’ from 1074 in tens (i.e. 1074, 1084, 1094, ????) really tests whether children understand how the numbers work. Many children will write 2004 for the next number, instead of the correct 1104.

## So how is this skill taught?

Primarily, it is important that children count out loud in tens, starting by counting forward from random two-digit and three-digit numbers, e.g. Ask the child to count in tens: six, sixteen, twenty-six, thirty-six, forty-six … and so on up to ninety-six. It is at this point that the going gets a little tricky!  Ninety-six, one hundred and six. Then what? A lot of children will then say ‘two-hundred and six’ instead of ‘one hundred and sixteen’, thus slipping into counting in hundreds and not tens. It is often best to start with a number that is a few numbers away from a multiple of a hundred.

• Children count in tens starting at any two-digit number, e.g. 34, 44, 54, 64, etc.
• Extend this over one hundred, e.g. 94, 104, 114, etc.
• Help children to see that the last two digits behave the same as when we were counting in tens from a two-digit number, e.g. 114, 124, 134, 144, is exactly the same pattern as 14, 24, 34, 44, etc.
• Children then cross multiples of 100, e.g. 194, 204, 214, 224, 234, etc.

Quite often it is good to play ‘ping-pong’ where you say a number, then the child says a number, and you keep going like this, keeping up a fast pace. You say, ‘five hundred and six,’ they say, ‘five hundred and sixteen,’ you say ‘five hundred and twenty-six’, they say ‘five hundred and thirty-six’, etc. At this stage the count is basically exactly the same as if you were counting two-digit numbers. But when we get to ‘five hundred and ninety-six’, we have to really think about what to say next. Try and arrange it so the child has to do this one by starting the child on, say, 804 and you saying 814 … that way, it is the child who has to cross the multiple of one hundred.

Similarly, we can count in hundreds: 642, 742, 842, said as six hundred and forty-two, seven hundred and forty-two, etc. Once again, start quite a way from the multiple of one thousand. Then give help as you cross this. It is often useful to write these numbers down so children can see the pattern: 942, 1042, 1142, 1242, 1342… You can point out which digit changes, namely the hundreds digit. It is only when the hundreds digit gets to ‘9’ that we will need to change the thousands digit as well, as in 1942 then 2042.

Summarising, counting in tens and hundreds, and, subsequently in thousands, is a very good way of both testing and reinforcing children’s understanding of place value – that is the value of each digit in the number. They can only count in tens or ones across a multiple of ten or one hundred or one thousand if they are focussing on the correct digits and making sure that the change is the right one each time.

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: Having practised a skill together using the shared activities, children can then rehearse the skill using the ‘Child alone’ sheets. These are presented in order of difficulty 1-5 and should only be given to the child AFTER the Practise Together activities. In this way you can be sure that the child has acquired this skill first. We cannot rehearse what something have not yet learned!

Test: Take a test, questions from this area

Counting in sequence: Count any sequence of numbers from 1 to 10,000 forward or back with confidence

Place value: Understand that 4392 is made up of 4000 + 300 + 90 + 2 and that 4092 has no hundreds

Money: Begin to understand that £6.54 is six pounds and 54 pence and that £6.04 is six pounds and 4p while £6.40 is six pounds and 40p

Counting in tens & hundreds: Count in tens or hundreds forward and back from any number, e.g. 284, 294, 304, 314, etc. understanding how to cross a multiple of 10, 100 or 1000

Count multiples: Count in (add or subtract) multiples of 10, 100 or 1000 (800+300)

Writing fractions: Understand how fractions are written, e.g. ½ and ¾ and begin to realise that ½ is the same as 2/4 or 3/6 etc.

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