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Step-by-step practice: Maths · Level 2Chapter 3 · Comparing and ordering to 100
Level 2 · Chapter 3

Comparing and ordering to 100

By the end of this chapter you will be able to

  • Compare numbers with < > and =
  • Order up to five numbers
  • Find the greatest and least
  • Find 10 more and 10 less
  • Find numbers between two others on a number line

You should already know

  • Tens and ones (Level 2, Chapter 2)
  • Counting to 100 (Level 2, Chapter 1)
  • Numbers to 20 (Level 1)

Where this leads

  • Number bonds to 20 (Chapter 4)
  • Adding and subtracting within 100 (Chapter 7)

Step-by-step practice: maths (Level 2). Small steps, repeated until fluent. Content: Compare two numbers up to 100 using the signs <, > and =, Put a set of up to five numbers in order, smallest to largest and largest to smallest, Find the greatest and the least number in a set, Find 1 more, 1 less, 10 more and 10 less than any number up to 100, Use a number line to find a number between two others.

Exercise P  Do you remember?

Non-calculator
1
FWrite <, > or = to make it true: 29 □ 41
2
FPut these numbers in order from smallest to largest: 16, 8, 12
3
FWhat is 1 more than 24?
4
FWhich number is the greatest: 13, 19, 11?
5
FWrite <, > or = to make it true: 50 □ 50
3.1

Greater than, less than and equal to

Level 2
Compare two numbers up to 100 with the signs <, > and =
Video lesson: Greater than, less than and equal toComing soon

The sign < means less than. The sign > means greater than.

The sign = means the two numbers are the same. The open end of the sign faces the bigger number.

Key ideas

  • < means less than, > means greater than, = means equal to.
  • Compare the tens first.
  • If the tens are the same, compare the ones.
Worked example 3.1.1
Write <, > or = to make it true: 38 □ 52

Method. Compare the tens first. If the tens are the same, compare the ones.

  1. Compare the tens digits. The tens digit is worth the most.
    3 and 5
  2. Tens are different, so the tens decide. 3 tens is fewer than 5 tens.
    3 tens and 5 tens
  3. Write the sign. 38 is less than 52.
    <

Check. 38 < 52 is true.

Watch out. Compare tens first. 61 is greater than 58, because 6 tens is more than 5 tens.

Worked example 3.1.2
Write <, > or = to make it true: 74 □ 67

Method. Compare the tens first. If the tens are the same, compare the ones.

  1. Compare the tens digits. The tens digit is worth the most.
    7 and 6
  2. Tens are different, so the tens decide. 7 tens is more than 6 tens.
    7 tens and 6 tens
  3. Write the sign. 74 is greater than 67.
    >

Check. 74 > 67 is true.

Watch out. Compare tens first. 61 is greater than 58, because 6 tens is more than 5 tens.

Worked example 3.1.3
Write <, > or = to make it true: 45 □ 45

Method. Compare the tens first. If the tens are the same, compare the ones.

  1. Compare the tens digits. The tens digit is worth the most.
    4 and 4
  2. Tens are the same, so compare the ones. Both numbers have the same ones too.
    5 and 5
  3. Write the sign. 45 is equal to 45.
    =

Check. 45 = 45 is true.

Watch out. Compare tens first. 61 is greater than 58, because 6 tens is more than 5 tens.

Watch out

Watch out. Point the open end at the bigger number, like a mouth that wants the bigger one.

Exam tip

Grown-up tip. Write two numbers on cards. Hold them up and ask: “Which is bigger?” before you write the sign.

Exercise 3A  Practice: comparing numbers

Non-calculator
1
FWrite <, > or = to make it true: 63 □ 63
2
FWrite <, > or = to make it true: 74 □ 44
3
FWrite <, > or = to make it true: 56 □ 37
4
FWrite <, > or = to make it true: 85 □ 56
5
FWrite <, > or = to make it true: 14 □ 67
6
FWrite <, > or = to make it true: 74 □ 12
7
FWrite <, > or = to make it true: 81 □ 72
8
FWrite <, > or = to make it true: 56 □ 18
9
FWrite <, > or = to make it true: 64 □ 82
10
FWrite <, > or = to make it true: 83 □ 79
11
FWrite <, > or = to make it true: 72 □ 40
12
FWrite <, > or = to make it true: 10 □ 69
13
FWrite <, > or = to make it true: 30 □ 74
14
FWrite <, > or = to make it true: 97 □ 74
15
FWrite <, > or = to make it true: 10 □ 38
16
FWrite <, > or = to make it true: 55 □ 29
3.2

Putting numbers in order

Level 2
Put up to five numbers in order from smallest to largest, Put up to five numbers in order from largest to smallest
Video lesson: Putting numbers in orderComing soon

To put numbers in order, look at the tens first. The number with the fewest tens is the smallest.

Then look at the ones when two numbers have the same tens.

Key ideas

  • Smallest to largest: the numbers get bigger.
  • Largest to smallest: the numbers get smaller.
  • Check your list by reading it again.
Worked example 3.2.1
Put these numbers in order from smallest to largest: 45, 27, 63, 38

Method. Put the numbers in order, smallest to largest. Find the first one and then the next.

  1. Look at the tens of each number. The numbers with fewer tens are smaller.
    45: 4 tens, 27: 2 tens, 63: 6 tens, 38: 3 tens
  2. Find the first number in the order. It is the smallest, or the largest if we go the other way.
    27
  3. Write the numbers in order. Check that each one fits between the ones next to it.
    27, 38, 45, 63

Check. Read the list again. Each number is bigger than the one before.

Watch out. Compare tens first. 52 comes before 61 because 5 tens is less than 6 tens.

Worked example 3.2.2
Put these numbers in order from largest to smallest: 81, 19, 50, 64, 33

Method. Put the numbers in order, largest to smallest. Find the first one and then the next.

  1. Look at the tens of each number. The numbers with fewer tens are smaller.
    81: 8 tens, 19: 1 tens, 50: 5 tens, 64: 6 tens, 33: 3 tens
  2. Find the first number in the order. It is the smallest, or the largest if we go the other way.
    81
  3. Write the numbers in order. Check that each one fits between the ones next to it.
    81, 64, 50, 33, 19

Check. Read the list again. Each number is smaller than the one before.

Watch out. Compare tens first. 52 comes before 61 because 5 tens is less than 6 tens.

Worked example 3.2.3
Put these in order from smallest to largest: 67, 61, 76, 16.

Method. Put the numbers in order, smallest to largest. Find the first one and then the next.

  1. Look at the tens of each number. The numbers with fewer tens are smaller.
    67: 6 tens, 61: 6 tens, 76: 7 tens, 16: 1 tens
  2. Find the first number in the order. It is the smallest, or the largest if we go the other way.
    16
  3. Write the numbers in order. Check that each one fits between the ones next to it.
    16, 61, 67, 76

Check. Read the list again. Each number is bigger than the one before.

Watch out. Compare tens first. 52 comes before 61 because 5 tens is less than 6 tens.

Watch out

Watch out. 19 is smaller than 91, even though the ones digit 9 is the same. Look at the tens first.

Exam tip

Grown-up tip. Write each number on a card and lay them in a line. Move the cards until the line goes up.

Exercise 3B  Practice: putting numbers in order

Non-calculator
1
FPut these numbers in order from smallest to largest: 36, 47, 78, 68, 97
2
FPut these numbers in order from largest to smallest: 20, 97, 74, 59, 96
3
FPut these numbers in order from largest to smallest: 37, 51, 96, 46
4
FPut these numbers in order from largest to smallest: 44, 35, 48, 55, 22
5
FPut these numbers in order from largest to smallest: 97, 16, 84, 11, 73
6
FPut these numbers in order from smallest to largest: 68, 91, 34, 41
7
FPut these numbers in order from largest to smallest: 45, 92, 16, 34
8
FPut these numbers in order from largest to smallest: 20, 16, 32, 34
9
FPut these numbers in order from smallest to largest: 67, 75, 37, 58
10
FPut these numbers in order from largest to smallest: 27, 66, 30, 90
11
FPut these numbers in order from largest to smallest: 24, 88, 55, 41
12
FPut these numbers in order from largest to smallest: 66, 78, 28, 24, 29
13
FPut these numbers in order from smallest to largest: 53, 60, 94, 77
14
FPut these numbers in order from smallest to largest: 33, 31, 30, 87
15
FPut these numbers in order from smallest to largest: 90, 86, 30, 51
16
FPut these numbers in order from smallest to largest: 15, 64, 63, 79, 78
3.3

Finding the greatest and the least

Level 2
Find the greatest number in a set, Find the least number in a set
Video lesson: Finding the greatest and the leastComing soon

The greatest number is the biggest. The least number is the smallest.

You can find them by comparing the tens, then the ones. You do not need to put every number in order.

Key ideas

  • Greatest means biggest.
  • Least means smallest.
  • Look at the tens first.
Worked example 3.3.1
Which number is the greatest: 56, 61, 49, 58?

Method. Find the greatest number by comparing the tens first.

  1. Look at the tens. The numbers with the most tens are the greatest.
    5, 6, 4, 5
  2. Check the ones if two numbers have the same tens. The ones decide between them.
    56, 61, 49, 58
  3. Choose the greatest. It is the biggest of the numbers in the list.
    61

Check. Put the others in order to check: 61 is the greatest of them all.

Watch out. The number with the largest ones digit is not always the greatest.

Worked example 3.3.2
Which number is the least: 72, 27, 70, 79?

Method. Find the least number by comparing the tens first.

  1. Look at the tens. The numbers with the most tens are the greatest.
    7, 2, 7, 7
  2. Check the ones if two numbers have the same tens. The ones decide between them.
    72, 27, 70, 79
  3. Choose the least. It is the smallest of the numbers in the list.
    27

Check. Put the others in order to check: 27 is the least of them all.

Watch out. The number with the largest ones digit is not always the greatest.

Worked example 3.3.3
Which number is the greatest: 38, 83, 33, 28?

Method. Find the greatest number by comparing the tens first.

  1. Look at the tens. The numbers with the most tens are the greatest.
    3, 8, 3, 2
  2. Check the ones if two numbers have the same tens. The ones decide between them.
    38, 83, 33, 28
  3. Choose the greatest. It is the biggest of the numbers in the list.
    83

Check. Put the others in order to check: 83 is the greatest of them all.

Watch out. The number with the largest ones digit is not always the greatest.

Watch out

Watch out. The greatest number does not always have the biggest ones digit. Compare the tens first.

Exam tip

Grown-up tip. Ask: “Which is the biggest?” and “Which is the smallest?” with the same set of numbers.

Exercise 3C  Practice: greatest and least

Non-calculator
1
FWhich number is the least: 10, 80, 66?
2
FWhich number is the least: 82, 88, 91, 87, 64?
3
FWhich number is the greatest: 85, 63, 99, 34, 76?
4
FWhich number is the greatest: 45, 26, 51?
5
FWhich number is the greatest: 97, 38, 46, 84?
6
FWhich number is the greatest: 50, 93, 94?
7
FWhich number is the greatest: 29, 39, 86, 14?
8
FWhich number is the greatest: 41, 63, 13, 15, 88?
9
FWhich number is the greatest: 86, 48, 68, 78, 16?
10
FWhich number is the least: 75, 88, 76?
11
FWhich number is the least: 65, 90, 24, 44?
12
FWhich number is the least: 19, 43, 23?
13
FWhich number is the greatest: 76, 33, 46, 78, 56?
14
FWhich number is the greatest: 19, 65, 16?
15
FWhich number is the least: 32, 55, 82, 28?
16
FWhich number is the least: 32, 44, 86, 28?
3.4

One more, one less, ten more and ten less

Level 2
Find 1 more and 1 less than any number up to 100, Find 10 more and 10 less than any number up to 100
Video lesson: One more, one less, ten more and ten lessComing soon

To find 1 more, count on one. To find 1 less, count back one.

To find 10 more, the tens digit goes up by one. To find 10 less, the tens digit goes down by one.

Key ideas

  • 10 more is one more ten.
  • 10 less is one less ten.
  • The ones digit stays the same when you add or take away ten.
Worked example 3.4.1
What is 10 more than 47?

Method. Change the number by the amount in the question.

  1. Start with the number. It is the number we change.
    47
  2. Change it. Add ten. The tens digit goes up by one.
    47 + 10 = 57
  3. Write the answer.
    57

Check. Reverse the change: 57 - 10 gives 47.

Watch out. Ten more changes only the tens digit. One more can change the tens too: 1 more than 59 is 60.

Worked example 3.4.2
What is 10 less than 83?

Method. Change the number by the amount in the question.

  1. Start with the number. It is the number we change.
    83
  2. Change it. Take away ten. The tens digit goes down by one.
    83 - 10 = 73
  3. Write the answer.
    73

Check. Reverse the change: 73 + 10 gives 83.

Watch out. Ten more changes only the tens digit. One more can change the tens too: 1 more than 59 is 60.

Worked example 3.4.3
What is 1 more than 59?

Method. Change the number by the amount in the question.

  1. Start with the number. It is the number we change.
    59
  2. Change it. Add one. Count on to the next number.
    59 + 1 = 60
  3. Write the answer.
    60

Check. Reverse the change: 60 - 1 gives 59.

Watch out. Ten more changes only the tens digit. One more can change the tens too: 1 more than 59 is 60.

Watch out

Watch out. 10 more than 47 is 57, not 48. Ten more changes the tens.

Exam tip

Grown-up tip. Use a hundred square. Ask the child to move down one row for 10 more and up one row for 10 less.

Exercise 3D  Practice: one more, ten more and less

Non-calculator
1
FWhat is 1 less than 70?
2
FWhat is 10 more than 3?
3
FWhat is 10 less than 76?
4
FWhat is 10 less than 87?
5
FWhat is 10 more than 73?
6
FWhat is 10 more than 43?
7
FWhat is 10 more than 79?
8
FWhat is 10 less than 71?
9
FWhat is 1 less than 20?
10
FWhat is 10 more than 47?
11
FWhat is 1 less than 99?
12
FWhat is 1 more than 17?
13
FWhat is 1 less than 39?
14
FWhat is 1 more than 40?
15
FWhat is 10 more than 75?
16
FWhat is 1 less than 50?
3.5

Numbers between two others

Level 2
Use a number line to find a number between two others, Find the number exactly halfway between two numbers
Video lesson: Numbers between two othersComing soon

A number between two numbers comes after the smaller one and before the bigger one.

On a number line, count along from the smaller number to see which numbers are between.

3334353637383940
The numbers between 34 and 39 are 35, 36, 37 and 38.

Key ideas

  • Between means after the smaller number and before the bigger one.
  • The two end numbers are not between.
  • Halfway means the same distance from both ends.
Worked example 3.5.1
Write a number between 34 and 39.

Method. Count on from the smaller number. Stop just before the bigger one.

  1. Start at 34. The smaller number is where we start.
    34
  2. Count on until just before 39. Numbers between come after the smaller one and before the bigger one.
    35, 36, 37, 38
  3. Write one of the numbers. Any of these is correct.
    Accept any of 35, 36, 37, 38

Check. Check: any number from the list is bigger than 34 and smaller than 39.

Watch out. Do not write 34 or 39. They are the ends, not the numbers between.

Worked example 3.5.2
What number is exactly halfway between 40 and 50?

Method. Halfway is the number in the middle when we count along the line.

  1. Start at 40. It is one end of the line.
    40
  2. Count on in ones to the middle. Five steps from 40 reaches the middle.
    41, 42, 43, 44, 45
  3. Write the answer. It is the same distance from both ends.
    45

Check. 45 is 5 more than 40, and 5 less than 50.

Watch out. Halfway means the same number of steps from both ends.

Worked example 3.5.3
What number is exactly halfway between 70 and 80?

Method. Halfway is the number in the middle when we count along the line.

  1. Start at 70. It is one end of the line.
    70
  2. Count on in ones to the middle. Five steps from 70 reaches the middle.
    71, 72, 73, 74, 75
  3. Write the answer. It is the same distance from both ends.
    75

Check. 75 is 5 more than 70, and 5 less than 80.

Watch out. Halfway means the same number of steps from both ends.

Watch out

Watch out. When you write a number between 34 and 39, do not write 34 or 39. Those are the ends.

Exam tip

Grown-up tip. Draw a long number line on paper with the two numbers at the ends. Ask: “Which numbers fit in the middle?”

Exercise 3E  Practice: numbers between

Non-calculator
1
PSWhat number is exactly halfway between 30 and 40?
28293031323334?36373839404142
2
PSWrite a number between 28 and 32.
3
PSWrite a number between 45 and 50.
4
PSWhat number is exactly halfway between 40 and 50?
38394041424344?46474849505152
5
PSWhat number is exactly halfway between 50 and 60?
48495051525354?56575859606162
6
PSWrite a number between 81 and 84.
7
PSWrite a number between 92 and 97.
8
PSWhat number is exactly halfway between 60 and 70?
58596061626364?66676869707172
9
PSWrite a number between 22 and 26.
10
PSWrite a number between 74 and 78.
11
PSWhat number is exactly halfway between 20 and 30?
18192021222324?26272829303132
12
PSWrite a number between 48 and 52.
13
PSWrite a number between 30 and 35.
14
PSWhat number is exactly halfway between 90 and 100?
88899091929394?96979899100101102
15
PSWrite a number between 27 and 30.
16
PSWhat number is exactly halfway between 10 and 20?
891011121314?16171819202122

Chapter summary

SkillMethod
CompareCompare tens first, then ones. Use <, > or =
OrderLook at the tens, then the ones. Read the list again
Greatest and leastThe biggest and the smallest, found by comparing tens
10 more and 10 lessChange the tens digit by one. The ones stay the same
BetweenAfter the smaller number, before the bigger one

Can you…?

  • I can use <, > and = to compare two numbers
  • I can put up to five numbers in order
  • I can find the greatest and the least number in a set
  • I can find 1 more, 1 less, 10 more and 10 less
  • I can find a number between two others

Key terms

less than
smaller; the sign is <
greater than
bigger; the sign is >
order
the way numbers go, smallest to largest or largest to smallest
between
after the smaller number and before the bigger number

Exercise 3Z  Check-up

Non-calculator
1
Put these numbers in order from smallest to largest: 88, 43, 60, 79
2
Write <, > or = to make it true: 95 □ 34
3
What is 1 less than 92?
4
Put these numbers in order from smallest to largest: 82, 93, 26, 96
5
What is 10 less than 13?
6
What is 10 less than 73?
7
Which number is the greatest: 38, 70, 61?
8
What is 1 less than 58?
9
Write <, > or = to make it true: 10 □ 85
10
Put these numbers in order from smallest to largest: 93, 67, 60, 11, 96

Total 19 marks. Allow about 19 minutes.

Exercise 3X  Practice test questions

Non-calculator
1
FWhat is 10 less than 35?[1 mark]
2
PSWhat number is exactly halfway between 70 and 80?[1 mark]
68697071727374?76777879808182
3
PSWhat number is exactly halfway between 30 and 40?[1 mark]
28293031323334?36373839404142
4
FWhich number is the least: 71, 87, 97?[1 mark]
5
PSWrite a number between 75 and 79.[2 marks]
6
FPut these numbers in order from smallest to largest: 99, 56, 14, 75[2 marks]
7
FWhich number is the least: 34, 87, 65?[2 marks]
8
FWrite <, > or = to make it true: 92 □ 62[3 marks]
9
FPut these numbers in order from smallest to largest: 29, 69, 85, 80[3 marks]
10
FWrite <, > or = to make it true: 99 □ 71[3 marks]
← Chapter 2: Tens and onesChapter 4: Number bonds to 20 →

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