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In this worksheet, students will practise partitioning into tens and units, adding tens and counting forwards or back for quick mental computations in exams.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Number, Number Operations and Integers

Curriculum subtopic:   Structure and Calculation, Calculations with Integers

Difficulty level:

### QUESTION 1 of 10

There are a number of methods for addition and subtraction, but sometimes they take a lot longer and make your steps more complicated.

When the number you are adding or subtracting is small, it's easier to use a mental method.

The method we will discuss today is called partitioning.

What is partitioning?

Partitioning is where you take a number and split it up into numbers that are easier to work with.

Examples:

Subtracting 15 is the same as subtracting 10 then subtracting 5

Subtracting 28 is the same as subtracting 30 then adding 2

In this activity, we will explore how to simplify additions and subtractions so that we can reach an answer more quickly.

This skill will be helpful in all areas of your maths and particularly in exams.

To add 17 to a number you could...

To subtract 8 from a number you could...

Subtracting 30 and adding 4 is the same as subtracting...

Which of the following operations is the same as subtracting 17?

- 20 + 3

- 3 + 20

- 10 - 7

+ 20 - 3

Which of the following operations is the same as subtracting 11?

- 5 - 6

- 6 + 5

- 10 - 1

- 1 + 10

Match these partitioned additions with their correct overall result.

## Column B

+ 18
+ 28
+ 11
+ 8

Match these partitioned subtractions with their correct overall result.

## Column B

Subtract 10 then subtract 4
- 14
Subtract 20 then subtract 3
- 16
- 23
- 8

Which of these partitioned additions are correct?

Which of these partitioned subtractions are correct?

• Question 1

To add 17 to a number you could...

EDDIE SAYS
Here we need to partition (another word we can use here is split) 17 into two terms. It's best to have one of the numbers as a multiple of 10, as these are really easy to add. Then we can use counting on for what is left to add. Do you find it easier to add 10 then 7, or 17 in one go?
• Question 2

To subtract 8 from a number you could...

EDDIE SAYS
Here we need to partition (or split) 8 into two terms. Again, it's best to have one of the numbers as a multiple of 10 and then we can add back on the extra we subtracted.
• Question 3

21
EDDIE SAYS
Nice and easy, just put them together here to reach the answer. 20 + 1 = 21
• Question 4

Subtracting 30 and adding 4 is the same as subtracting...

26
EDDIE SAYS
This is a bit more complicated. The common mistake here is to say that this is the same as subtracting 34. Remember to think about the direction of the number. If we take away 30 but then add 4, we am going in the opposite direction, so we have subtracted less than 30 overall. - 30 + 4 = - 26
• Question 5

Which of the following operations is the same as subtracting 17?

- 20 + 3
- 10 - 7
EDDIE SAYS
Did you spot that more than one options worked here? You need to think carefully here about the answers to ensure they involve subtraction. For example, the sum + 20 - 3 would give us 17, but would be an addition sum instead of a subtraction. Both - 20 + 3 and -10 - 7 will result in a subtraction of 17 overall. Then you just have to choose which option you prefer to use!
• Question 6

Which of the following operations is the same as subtracting 11?

- 5 - 6
- 10 - 1
EDDIE SAYS
Another tricky one! A good example to consider here is that the sum -1 + 10 would give a result of + 9 overall. Both - 5 - 6 and -10 - 1 will result in a subtraction of 11 overall.
• Question 7

Match these partitioned additions with their correct overall result.

## Column B

+ 11
+ 18
+ 8
+ 28
EDDIE SAYS
Take your time, you've got this! This challenge is about number lines. For example, if you added 8 and then added 3, you would have moved 11 to the right so the overall amount added would be 11.
• Question 8

Match these partitioned subtractions with their correct overall result.

## Column B

Subtract 10 then subtract 4
- 14
Subtract 20 then subtract 3
- 23
- 8
- 16
EDDIE SAYS
Again, we're all about number lines in this question. If you subtracted 20 and then added 4, you would have moved 20 to the left and then 4 to the right. So overall, we have moved 16 to the left which is -16.
• Question 9

Which of these partitioned additions are correct?

EDDIE SAYS
Remember to think about the number line. If you added 10 (10 to the right) then subtracted 2 (2 left), overall would you be 12 to the right? Or 8 to the right? You would be 8 to the right. Take your time and calculate each separately.
• Question 10

Which of these partitioned subtractions are correct?

EDDIE SAYS
Good work if you used your mental number line here! If you subtracted 20 (20 left) then added 6 (6 right), overall would you be 26 to the left? Or 14 to the left? You would be at 14 to the left. Great focus, that's another activity under your belt!
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