Why is this skill important?
Counting may seem initially like a really easy skill, and sometimes people wonder why teachers spend quite a bit of time on this skill once children reach junior school. The answer lies in the fact that counting may seem easy but that this is a misleading impression!
If we ask someone – even an adult – to count back five numbers from 10,003 and ask them to say the number they get to, many people will be reluctant to speak loudly in a group since they are not sure that they have done this right! It is not that easy; 10,003, 10,002, 10,001, 10,000 – so far so good. Then the next one is hard; 10,000, 9,999, 9,998, and after that it is plain sailing again.
Counting, whether forward or back, is always tricky when we cross a tens, hundreds or thousands barrier. That is to say, if children are counting from 397 to 405, they have to negotiate the 400 where all the digits change: 398, 399, 400, 401, etc. This gets quite complicated as we get into thousands and ten thousands; 19,998, 19,999, …
What comes next? (20,000).
Because counting demonstrates that a child understands how numbers work, and therefore has a good grasp of place value (see Number: Place value), it often forms part of mathematical tests and assessments. Asking children to demonstrate that they can write the next three or four numbers in a counting sequence is a good way of checking that they understand the number system.
What is the skill?
Counting is perhaps the easiest mathematical skill to understand as it does what it says on the tin – it is the ability to say the numbers in order, either forward or back. However, this does incorporate a wide variety of different sequences. Children first need to learn to count up to 100 and back again. This is generally secure by the time children reach the age of 6 or 7. After that, we extend their counting to 3-digit numbers, and subsequently to 4-digit and 5-digit numbers. This then will involve the children knowing how to cross multiples of 10, multiples of 100 and multiples of 1000 or 10,000. As we have already mentioned, this can be tricky – especially when counting backwards!
The easiest way to find out if a child does understand how the numbers work and therefore is fluent in counting both forwards and backwards, is to give them a sequence of numbers with some missing and ask them to read it to you, inputting the missing numbers. You give the simple instruction: ‘Read this sequence, saying the number that should be in the box’ and then provide a sequence suitable to the age and ability of the child:
- Not very confident 7 year old: 67 68 69 _ 71 72 _ 74
- Age 7 or 8 years old: 497 498 _ _ _ 502 503
- Age 7 or 8 years old: 803 802 801 _ _ 798 _ 796
- Age 8 or 9 years old: 2298 2299 _ _ 2302 2303
- Age 8 or 9 years old: 7097 7098 7099 _ 7101 7102 7103
- Age 8 or 9 years old: 9997 9998 _ _ _ 10,002 10,003
- Age 8 or 9 years old: 21,103 21,102 21,101 _ _ 21,098
Seeing whether a child can fill in the missing numbers when speaking (NOT writing – this is a different skill) will tell you a great deal about how good their counting really is. Crossing these multiples of 100 or 1000 often alerts us to the fact that a child’s counting is not actually as good as we thought it was!
So how is this skill taught?
We can really only teach counting in conjunction with teaching children how the number system works. So this section should be read in conjunction with Number: Read and write numbers and Place value.
Counting is essentially a ‘chant’, so there really is no substitute for saying the numbers out loud. It is very useful to develop the back and forth chant here, where you say one number, the child says the next number, you say the next, and so on, e.g. You say ‘one thousand and eighty-seven’, they say ‘one thousand and eighty-eight’, and so on up to you saying ‘one thousand and ninety-seven’, they say ‘one thousand and ninety-eight’, you say ‘one thousand and ninety-nine’, and they have to think what to say next. It is easiest to have a ‘run’ up to these difficult crossing points where we cross a multiple of 100 or 1000.
If children are stuck here it very often helps to write the numbers to show them what comes next.
Now which digit is going to change? We are crossing a hundred NOT a thousand - it is a common error for children to say 2000 instead of 1100.
1101 … etc.
If we match the written number to the spoken number each time, it helps children to focus on which digit needs changing.
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
Read & write numbers
Counting in tens & hundreds
Counting in sequence: Count any sequence of numbers from 1 to 10,000 forward or back with confidence
Read & write numbers: Read and write the numbers 0-10,000
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.