Download Counting on using an empty number line

N1/E3.2
N1/E3.3
Counting on using an empty number line
Counting on using an empty number line is a good method for subtracting numbers mentally.
Use this method to find the difference between 37 and 50. This is the same as the sum
50 - 37.
When you’ve pictured that line, count on from 37 to 40, which makes 3. Keep that 3 in your
head. Then, count from 40 to 50, which is 10.
Have a look below to see how this works.
Now all you need to do is add the 3 to the 10. This makes 13. So:
The difference between 37 and 50 is 13.
Or:
50 - 37 = 13
© BBC 2011
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Mental subtraction key words
Here are some of the words that will crop up when doing subtraction calculations:
Look below to see how these words can be used in simple subtraction:
8 - 5 = 3.
Subtract
8 subtract 5 is 3.
Minus
8 minus 5 is 3.
Decrease
If you decrease 8 by 5 you get 3.
Difference
The difference between 8 and 5 is 3.
Less than
3 is 5 less than 8.
Take away
8 take away 5 is 3.
Fewer than
3 is 5 fewer than 8.
Reduce
If you reduce 8 by 5 you get 3.
© BBC 2011
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Help with subtraction: reminders
N1
Here are two reminders to help you with mental subtraction:
Place value
Have a look at the number 623.
6 is the hundreds digit.
2 is the tens digit.
3 is the units digit.
Addition and subtraction are opposites
Check the answer to a subtraction calculation by adding your answer to the number you
subtracted. Have a look below:
Here you've done the calculation 25 - 10 and got the answer 15.
To check the answer, add it to the number you subtracted: 15 + 10 = 25
This is the number you started with so the answer is correct.
© BBC 2011
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Subtracting by splitting up numbers
Splitting up numbers is a good method to use for both addition and subtraction. It’s sometimes
called partitioning.
Subtraction
Take a look at this subtraction calculation:
150 - 34
To make it easier, split the -34 into -30 -4. This makes the calculation:
150 - 30 - 4
First, subtract the 30 from 150:
150 - 30 = 120
Then, subtract the 4 from the 120 to get the answer:
120 - 4 = 116
© BBC 2011
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Subtraction methods
N1
There are many ways numbers can be subtracted. The best method will depend on the problem.
Bridging: this works well when subtracting a small number from another number.
Subtract to the nearest 10 and then subtract the remaining part. For example, subtracting from
43, take away 3 to get to 40 and then the remainder.
43 - 6 = 43 - 3 - 3 = 40 - 3 = 37
43 -15 = 43 - 3 - 12 = 40 - 12 = 30 - 2 = 28
143 - 17 = 143 - 3 - 14 = 140 - 14 = 130 - 4 = 126
Counting back: this is good if you think visually.
Use a number line to count back. For 43 - 22:
starting at 43, moving back 20 lands on 23 and then a
further 2 leaves 21.
Compensation: this is effective when the number you’re taking away is close to a ‘round’
number, usually a 10.
Subtract an approximate value and then adjust.
For 125 - 38, use 125 - 40 and then add back 2 to give 85 + 2 = 87
For 545 - 129, use 545 - 130 and add 1 giving the answer 415 + 1 = 416
Partitioning: this works for all problems (but it can get very long).
Break the numbers into units, tens, hundreds and so on.
445 - 212 = (400 - 200) + (40 -10) + (5 - 2) = 200 + 30 + 3 = 233
Formal methods: this works for all (although it’s easy to make errors).
Line up the units, tens etc in columns and subtract from right to left, remembering to
use tens from the next column when needed (sometimes called ‘borrowing’). See the
‘Written methods’ factsheet for more details.
Informal methods
As with addition (see the factsheet), there are a number of informal methods that can be used in
combination with the methods above, including the use of physical objects (eg your fingers).
© BBC 2011
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Rounding subtraction 2
These tables contain more information to help you with subtraction by rounding.
The first table shows methods and examples for subtracting a number between 11 and 14 from
another number.
This table shows methods and examples for subtracting a number between 15 and 19 from
another number:
© BBC 2011
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Rounding subtraction 1
Rounding is a method for mental subtraction that’s useful in many different situations.
Imagine you’re shopping and need to work out an amount quickly.
£3.70 - £1.00 = £2.70. Adding 10p gives £2.80.
Have a look at how this subtraction calculation can be solved with rounding:
64 - 17
First, round the 17 up to 20 and work out the answer:
64 - 20 = 44
As 20 is 3 more than 17, you have taken 3 too many from the total. So you need to add 3:
44 + 3 = 47
So you can see that:
64 - 17 = 47
© BBC 2011
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Subtraction glossary
Here are some words that will crop up when doing subtraction calculations:
Look below to see how these words can be used in the simple calculation 8 - 5 = 3.
Decrease
If you decrease 8 by 5 you get 3.
Decomposition
A method of subtraction whereby numbers are broken down into smaller place values: eg one ten
is broken down into ten units.
Difference
The difference between 8 and 5 is 3.
Exchange
You can exchange one ten for ten lots of units.
Fewer than
3 is 5 fewer than 8.
Less than
3 is 5 less than 8.
Minus
8 minus 5 is 3.
Reduce
If you reduce 8 by 5 you get 3.
Subtract
If you subtract 5 from 8 you are left with 3.
You’ll find more maths words explained in the
Skillswise glossary.
www.bbc.co.uk/skillswise/glossary/
Take away
8 take away 5 is 3.
© BBC 2011