# Order Positive Integers

In this worksheet, students will practise ordering positive numbers using place value into ascending or descending order, plus locating which numbers are in specific positions within these sequences.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Number, Algebra

Curriculum subtopic:   Structure and Calculation, Algebraic Inequalities

Difficulty level:

### QUESTION 1 of 10

When you order numbers that each have a different amount of digits, the easiest method is to make them all have the same amount of digits.

You may be asked to put them in ascending order (smallest to biggest) or in descending order (biggest to smallest).

E.g. Put the following numbers in ascending order:

193, 34, 171, 204, 82

These numbers can all be changed to have three digits by putting a zero in front of the two digit numbers, like this:

193 , 034 , 259 , 171 , 204, 082

Starting with the first digit in each number, we need to deal with the numbers starting with zero first, then the numbers starting with 1, then the ones starting with 2 (and so on).

Numbers starting with 0

034 and 082

Putting these two in order gives us: 34, 82

Numbers starting with 1

193 and 171

Putting these two in order gives us: 171, 193

Numbers starting with 2

259 and 204

Putting these two in order gives us: 204, 259

The last step is just to write them out in the order you have just worked out, giving us:

34, 82 , 171, 193 , 204, 259

In this activity, you will practise ordering positive numbers into ascending and descending lists.

Let's get started!

If you put these numbers in ascending order, which would come last?

12, 15, 21, 8, 19

12

15

21

8

19

If these were put the numbers below into ascending order, which number would come fourth?

4, 18, 15, 27, 7

402, 4, 420, 4000, 42

When you have put them in order, match each to its position in the sequence, using 1 for the smallest and 5 for the largest.

## Column B

402
2
4
5
420
3
4000
4
42
1

If the numbers below were in descending order, which number would be second in the sequence?

25, 205, 200, 20, 250

25

205

200

20

250

Have a go at putting the numbers below in ascending order:

82, 802, 8, 80, 800

Once you have put them in order, match each to its position in the sequence, using 1 for the smallest and 5 for the largest.

## Column B

82
3
802
4
8
2
80
1
800
5

Now it's your turn, put the following numbers in ascending order:

12, 18, 6, 4, 21

## Column B

82
3
802
4
8
2
80
1
800
5

Hopefully you're starting to get really good at these!

Now put the numbers below in order:

904, 94, 940, 90, 9

Which number will be in the middle of the ordered sequence?

Take your time to put the numbers below in ascending order:

204, 24, 240, 2400, 2404

Using the same method, put the following numbers in ascending order:

81, 810, 80, 8101, 801

Which number is second in this sequence?

Finally, put the numbers below in descending order:

1700, 1705, 1750, 1755, 175

• Question 1

If you put these numbers in ascending order, which would come last?

12, 15, 21, 8, 19

21
EDDIE SAYS
To find the last number in an ascending sequence, we need to find the largest one. Remember, you can always put a zero in front of the numbers with only one digit, then the numbers beginning with a 1 follow, and so on.
• Question 2

If these were put the numbers below into ascending order, which number would come fourth?

4, 18, 15, 27, 7

18
EDDIE SAYS
The correct order would be: 4, 7, 15, 18, 27 Therefore, the number we are looking for is 18. Did you get this one right? No worries if not; we will keep trying.
• Question 3

402, 4, 420, 4000, 42

When you have put them in order, match each to its position in the sequence, using 1 for the smallest and 5 for the largest.

## Column B

402
3
4
1
420
4
4000
5
42
2
EDDIE SAYS
The correct order should be: 4, 42, 402, 420, 40002. In this example, the biggest number has the greatest number of digits, but it won't always be like this. Don't get caught out by always looking for this rule to help you out!
• Question 4

If the numbers below were in descending order, which number would be second in the sequence?

25, 205, 200, 20, 250

205
EDDIE SAYS
Did you notice that this question asked for descending order? In descending order our sequence would be: 250, 205, 200, 25, 20 The second number will therefore be 205.
• Question 5

Have a go at putting the numbers below in ascending order:

82, 802, 8, 80, 800

Once you have put them in order, match each to its position in the sequence, using 1 for the smallest and 5 for the largest.

## Column B

82
3
802
5
8
1
80
2
800
4
EDDIE SAYS
Did you notice that we switched back to an ascending pattern? You must always remember to read the question carefully in activities of these types or in your exam. The correct order would be: 8, 80, 82, 800, 802
• Question 6

Now it's your turn, put the following numbers in ascending order:

12, 18, 6, 4, 21

EDDIE SAYS
Remember to add extra zeros in for 4 and 6 to make them two-digit numbers: 04 and 06. Numbers starting with zero come first, then numbers starting with 1 and, finally, numbers starting with 2. Using this method should enable you to get these 5 numbers into their correct order.
• Question 7

Hopefully you're starting to get really good at these!

Now put the numbers below in order:

904, 94, 940, 90, 9

Which number will be in the middle of the ordered sequence?

94
EDDIE SAYS
Does it matter which order the numbers are placed in? If you used ascending order, you should have: 9, 90, 94, 904, 940 If you used descending order, you should have; 940, 904, 94, 90, 9 Either way, the correct answer is 94. Well done if you tried to double check the order that was requested in the question though - you don't want to waste time in an exam ordering both if you don't need to!
• Question 8

Take your time to put the numbers below in ascending order:

204, 24, 240, 2400, 2404

EDDIE SAYS
In this example, the largest number has four digits. We can make them all the numbers have four digits, so that they are easier to order, like this: 0204, 0024, 0240, 2400, 2404 Then, we need to put the number starting with double zero first, then the numbers starting with one, and then finally the numbers starting with two. If we do this, our correct order is: 0024, 0204, 0240, 2400, 2404 This one was tricky! Good job if you got it right.
• Question 9

Using the same method, put the following numbers in ascending order:

81, 810, 80, 8101, 801

Which number is second in this sequence?

81
EDDIE SAYS
If you wrote 801, you have forgotten to order them. Remember you must always read the question fully. The correct order should be; 80, 81, 801, 810, 8101 Therefore, 81 is the second number in this sequence.
• Question 10

Finally, put the numbers below in descending order:

1700, 1705, 1750, 1755, 175

EDDIE SAYS
Did you notice this question was another descending sequence? The correct order would be: 1755, 1750, 1705, 1700, 175 Well done, maths star! You have made it through this activity; now try another if you have time.
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