Download `Shared`: five ways to add (and subtract) in your head

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‘Shared’: five ways to add (and subtract) in your head
Mental methods are about trying to get to the correct answer in the quickest and easiest way.
There are lots of ways to add (and subtract) numbers in your head.
By the time you have looked through the factsheets in this module you will have used 5 different
methods for mental addition (and subtraction).
Try to remember them by using the word ‘SHARED’.
When you’ve read about them, practise the methods you like and can remember most
easily.
Ask other people about the methods they use - and share your methods too.
Keep practising, and have fun!
© BBC 2011
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Addition
There are many ways that numbers can be added together. Which is best can depend upon the
problem.
Bridging works best for adding a single digit number to another number.
Add up to the nearest 10 (using number bonds)
and then add the remaining part. For example,
adding on to 36, we use 36 + 4 = 40 so that
36 + 6 = 36 + (4 + 2) = 40 + 2 = 42
136 + 17 = 136 + (4 + 13) = 140 + 13 = 153
Compensation works when a number is close to a nice ‘round’ number.
Add an approximate value and then adjust
For 125 + 38, use 125 + 40 and subtract 2 which gives
165 - 2 = 163
For 525 + 129, use 525 + 130 and subtract 1 giving the
answer 655 - 1 = 654
For 669 + 218, use 670 + 220 and subtract 3 giving the answer 890 - 3 = 887
Partitioning works for all (although it can get very long).
Break the numbers into units, tens, hundreds and so on…
445 + 212 = (400 + 200) + (40 + 10) + (5 + 2) = 600 + 50 + 7 = 657
Formal methods works for all (although it is easy to make errors).
Line up the units, tens etc in columns and add up from right to left, remembering to
‘carry tens’ to the next column. See the Written methods factsheet for more details.
Informal methods
It is helpful to use a range of informal methods when calculating. For example, using
fingers to keep count, or making notes on paper.
When you have a string of numbers to add, it might help to change order. This might bring
together numbers that add up to 10 (number bonds) or other numbers easier to add together.
For example,
128 + 35 + 72 + 151 = 128 + 72 + 35 + 151 = (128 + 72) + (35 + 151) = 200 + 186 = 386
© BBC 2011
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Hundreds, tens and ones
To make addition easier, you can separate the hundreds, tens and units and add them up
separately.
Have a look at how
separating works for this
calculation:
31 + 22
Using this method you can
work out that
31 + 22 = 53.
Now look at this
calculation with hundreds
as well as tens and units:
125 + 100 + 235 + 132
Using this method you can
work out that
125 + 100 + 235 + 132
= 592.
© BBC 2011
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Key words for mental addition
Here are some of the words that are used for doing addition calculations.
Have a look below to see how they can be used in the simple addition
3+4=7
Add
3 add 4 is 7
Sum
The sum of 3 and 4 is 7.
Altogether
Altogether, 3 and 4 make 7.
Increase
If you increase 3 by 4 you get 7.
Total
The total of 3 and 4 is 7.
More
7 is 3 more than 4.
Plus
3 plus 4 is 7.
© BBC 2011
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Reminders to help you add
Here are two reminders to help you with mental addition.
A reminder about place value
Have a look at the number 623.
6 is the hundreds digit.
2 is the tens digit.
3 is the units digit.
A reminder about adding
Have a look at these calculations.
Here you can see that the same numbers added together in a different order will give the same
answer so the order doesn’t matter when you are adding.
© BBC 2011
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Splitting up numbers
Splitting up numbers is a good method to use for addition.
It is sometimes called partitioning.
Addition
Take a look at this addition calculation: 80 + 49
To make it easier, split the 49 into 40 + 9. This makes the calculation:
80 + 40 + 9 = 129
First, add the first two numbers:
80 + 40 = 120
Then add the result of that calculation to the third number to get the answer:
120 + 9 = 129
© BBC 2011
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Rounding addition methods and examples
These tables have some more information to help you with addition by rounding.
The first shows methods and examples for adding a number between 11 and 14 to another
number.
This table shows methods and examples for adding a number between 15 and 19 to another
number.
© BBC 2011
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Rounding addition
Rounding is a method for mental addition that is useful in many different situations.
Imagine you are in a shop and you have to quickly work out an amount.
£3.70 + £1.00 = £4.70. Taking away 10p gives £4.60
Have a look at how this addition calculation can be solved with rounding:
75 + 19
First, round the 19 up to 20 and work out the sum:
75 + 20 = 95
As 20 is 1 more than 19, you then need to subtract 1 from the total:
95 - 1 = 94
Then you can see that:
75 + 19 = 94
© BBC 2011