Place value to 100
By the end of this chapter you will be able to
- Count in twos, threes and fives, forwards and backwards
- Count in tens from any number
- Say how many tens and ones a number has, and what each digit is worth
- Write numbers to 100 in numerals and in words
- Compare two numbers with the signs <, > and =, and put numbers in order
- Place numbers on a number line, and solve simple problems using place value
You should already know
- Numbers to 100 (Year 1)
- Counting in tens (Year 1)
- Comparing numbers to 100 (Year 1)
Where this leads
- Adding and subtracting (Chapter 2)
- Multiplying and dividing in twos, fives and tens (Chapter 3)
National Curriculum for England, Key Stage 1 mathematics, Year 2. Content: Count in steps of 2, 3 and 5 from 0, forwards and backwards, Count in tens from any number, forwards and backwards, Recognise the place value of each digit in a two-digit number (tens and ones), Identify, represent and estimate numbers, including on a number line, Read and write numbers to 100 in numerals and in words, Compare and order numbers from 0 to 100, using the signs <, > and =, Use place value and number facts to solve problems.
Exercise P Do you remember?
Non-calculatorKey words. To count is to say one number for each thing, in order.
Method. Say one number for each one, and touch each one only once. The last number you say is how many there are.
- Count each one and say its number. Each one gets one number. Do not miss one and do not count one twice.1, 2, 3, 4, 5, 6, 7, 8, 9
- Look at the last number you said. The last number tells us how many there are altogether.The last number is 9.
- Write the answer. There are 9 stars.
Check. Count again from the other side. You get 9 again. ✓
Watch out. Move each one to one side as you count it, so you do not lose your place.
Key words. One more is the next number. One less is the number before.
Method. One more is the next number. One less is the number just before.
- Find 49. 49 is 4 tens and 9 ones.49 = 4 tens and 9 ones
- Count on one. Each number is one more or one less than its neighbour.49 + 1 = 50
- Write the answer. 50
Check. Count back one from 50. You reach 49. ✓
Watch out. Watch the tens. 49 + 1 is 50.
Key words. One more is the next number. One less is the number before.
Method. One more is the next number. One less is the number just before.
- Find 60. 60 is 6 tens and 0 ones.60 = 6 tens and 0 ones
- Count back one. Each number is one more or one less than its neighbour.60 − 1 = 59
- Write the answer. 59
Check. Count on one from 59. You reach 60. ✓
Watch out. Watch the tens. 60 − 1 is 59.
Key words. A ten is a bundle of ten ones. A one is a single thing.
Method. Count the groups of ten first. Then count the ones left over.
- Count the tens in 36. Each group of ten is one ten.30 is 3 tens
- Count the ones left over. The ones are what is left after the tens.36 − 30 = 6 ones
- Write the answer. 3 tens and 6 ones
Check. Put them back together: 30 + 6 = 36. ✓
Watch out. The tens come first when you say the number. 25 is 2 tens and 5 ones.
Method. Start at 17. Count on in ones.
- Start at 17. Put your finger on the number you start from.Start: 17
- Say each number, going on 1 each time. Each new number is 1 more than the one before.18, 19, 20
- Write the numbers in order. Write each number you said.18, 19, 20
Check. Count back from 20. You reach 17. ✓
Watch out. Do not say 17 again. Start with the next number.
Counting in twos, threes and fives
We can count in steps. A step is the same jump every time.
Counting in twos jumps 2 each time: 2, 4, 6, 8, 10.
Counting in threes jumps 3 each time: 3, 6, 9, 12.
Counting in fives jumps 5 each time: 5, 10, 15, 20.
We can count back too. Start high and take the step away each time.
Key ideas
- Counting in twos: 2, 4, 6, 8, 10.
- Counting in threes: 3, 6, 9, 12, 15.
- Counting in fives: 5, 10, 15, 20, 25.
- To count back, take the step away each time.
Method. Start at 0. Count on in twos.
- Start at 0. Put your finger on the number you start from.Start: 0
- Say each number, going on 2 each time. Each new number is 2 more than the one before.2, 4, 6, 8, 10
- Write the numbers in order. Write each number you said.2, 4, 6, 8, 10
Check. Count back from 10. You reach 0. ✓
Watch out. Do not say 0 again. Start with the next number.
Method. Start at 0. Count on in fives.
- Start at 0. Put your finger on the number you start from.Start: 0
- Say each number, going on 5 each time. Each new number is 5 more than the one before.5, 10, 15, 20, 25, 30
- Write the numbers in order. Write each number you said.5, 10, 15, 20, 25, 30
Check. Count back from 30. You reach 0. ✓
Watch out. Do not say 0 again. Start with the next number.
Method. Start at 18. Count back in threes.
- Start at 18. Put your finger on the number you start from.Start: 18
- Say each number, going back 3 each time. Each new number is 3 less than the one before.15, 12, 9, 6
- Write the numbers in order. Write each number you said.15, 12, 9, 6
Check. Count on from 6. You reach 18. ✓
Watch out. Do not say 18 again. Start with the next number.
Watch out
Watch out: the steps must stay the same. Count 2, 4, 6, not 2, 4, 7.
Exam tip
Grown-up tip. Clap on each number as your child says it. Ask: “What comes after 14 when we count in twos?”
Exercise 1A Counting in twos, threes and fives
Non-calculatorMethod. Start at 0. Count on in twos.
- Start at 0. Put your finger on the number you start from.Start: 0
- Say each number, going on 2 each time. Each new number is 2 more than the one before.2, 4, 6
- Write the numbers in order. Write each number you said.2, 4, 6
Check. Count back from 6. You reach 0. ✓
Watch out. Do not say 0 again. Start with the next number.
Method. The numbers go up by 2 each time.
- Look at the numbers around each gap. Each number is 2 more than the one before it.8, 10, ?, 14
- Work out each missing number. Add 2 to the number before the gap.10 + 2 = 12
- Write the missing numbers. 12
Check. Count on in 2s through the whole line. It works. ✓
Watch out. Check the numbers after the gap too. They should still go up by the same step.
Method. Start at 0. Count on in threes.
- Start at 0. Put your finger on the number you start from.Start: 0
- Say each number, going on 3 each time. Each new number is 3 more than the one before.3, 6, 9
- Write the numbers in order. Write each number you said.3, 6, 9
Check. Count back from 9. You reach 0. ✓
Watch out. Do not say 0 again. Start with the next number.
Method. The numbers go up by 3 each time.
- Look at the numbers around each gap. Each number is 3 more than the one before it.12, ?, 18, 21, ?
- Work out each missing number. Add 3 to the number before the gap.12 + 3 = 15
21 + 3 = 24 - Write the missing numbers. 15, 24
Check. Count on in 3s through the whole line. It works. ✓
Watch out. Check the numbers after the gap too. They should still go up by the same step.
Method. Start at 0. Count on in fives.
- Start at 0. Put your finger on the number you start from.Start: 0
- Say each number, going on 5 each time. Each new number is 5 more than the one before.5, 10, 15, 20
- Write the numbers in order. Write each number you said.5, 10, 15, 20
Check. Count back from 20. You reach 0. ✓
Watch out. Do not say 0 again. Start with the next number.
Method. The numbers go up by 5 each time.
- Look at the numbers around each gap. Each number is 5 more than the one before it.25, ?, 35, ?, 45
- Work out each missing number. Add 5 to the number before the gap.25 + 5 = 30
35 + 5 = 40 - Write the missing numbers. 30, 40
Check. Count on in 5s through the whole line. It works. ✓
Watch out. Check the numbers after the gap too. They should still go up by the same step.
Method. Start at 10. Count on in twos.
- Start at 10. Put your finger on the number you start from.Start: 10
- Say each number, going on 2 each time. Each new number is 2 more than the one before.12, 14, 16, 18
- Write the numbers in order. Write each number you said.12, 14, 16, 18
Check. Count back from 18. You reach 10. ✓
Watch out. Do not say 10 again. Start with the next number.
Method. Start at 20. Count back in twos.
- Start at 20. Put your finger on the number you start from.Start: 20
- Say each number, going back 2 each time. Each new number is 2 less than the one before.18, 16, 14, 12
- Write the numbers in order. Write each number you said.18, 16, 14, 12
Check. Count on from 12. You reach 20. ✓
Watch out. Do not say 20 again. Start with the next number.
Method. Start at 30. Count back in threes.
- Start at 30. Put your finger on the number you start from.Start: 30
- Say each number, going back 3 each time. Each new number is 3 less than the one before.27, 24, 21
- Write the numbers in order. Write each number you said.27, 24, 21
Check. Count on from 21. You reach 30. ✓
Watch out. Do not say 30 again. Start with the next number.
Method. Start at 50. Count back in fives.
- Start at 50. Put your finger on the number you start from.Start: 50
- Say each number, going back 5 each time. Each new number is 5 less than the one before.45, 40, 35
- Write the numbers in order. Write each number you said.45, 40, 35
Check. Count on from 35. You reach 50. ✓
Watch out. Do not say 50 again. Start with the next number.
Method. There are 4 groups of 2. Count in 2s to find the total.
- Count the groups: 4. Each group has 2 socks.4 groups of 2
- Count in 2s, one group at a time. Add 2 for every group.2, 4, 6, 8
- Write the total. 8
Check. Count in 2s to check. The last number you say is 8. ✓
Watch out. Count in 2s, not in ones. Each group is 2.
Method. There are 3 groups of 5. Count in 5s to find the total.
- Count the groups: 3. Each group has 5 marbles.3 groups of 5
- Count in 5s, one group at a time. Add 5 for every group.5, 10, 15
- Write the total. 15
Check. Count in 5s to check. The last number you say is 15. ✓
Watch out. Count in 5s, not in ones. Each group is 5.
Method. Count in threes from 0 and check whether 6 is said.
- Count in threes from 0. Say each number, one step at a time.3, 6, 9, 12
- Look for 6 in the list. Six is the second number we say.6 is in the list
- Write the answer. Two threes make six: 3 + 3 = 6.Yes
Check. Count on from 3: 3, then 3 more is 6. ✓
Watch out. Look at the steps, not just the start. 6 is two steps of 3.
Counting in tens from any number
A ten is a jump of 10. We can count in tens: 10, 20, 30, 40.
We can start at any number. Start at 34 and count on in tens: 44, 54, 64.
Only the tens digit changes. The ones digit stays the same.
Key ideas
- Counting in tens changes only the tens digit.
- 10 more: go down one row on the 100 square.
- 10 less: go up one row on the 100 square.
- The ones digit stays the same.
Method. Start at 34. Count on in tens.
- Start at 34. Put your finger on the number you start from.Start: 34
- Say each number, going on 10 each time. Each new number is 10 more than the one before.44, 54, 64
- Write the numbers in order. Write each number you said.44, 54, 64
Check. Count back from 64. You reach 34. ✓
Watch out. Do not say 34 again. Start with the next number.
Method. Start at 75. Count back in tens.
- Start at 75. Put your finger on the number you start from.Start: 75
- Say each number, going back 10 each time. Each new number is 10 less than the one before.65, 55, 45
- Write the numbers in order. Write each number you said.65, 55, 45
Check. Count on from 45. You reach 75. ✓
Watch out. Do not say 75 again. Start with the next number.
Method. 10 more changes only the tens digit.
- Find 58. 58 is 5 tens and 8 ones.58 = 5 tens and 8 ones
- Add one ten. The ones digit stays the same.5 tens + 1 ten = 6 tens and 8 ones
- Write the answer. 68
Check. 58 + 10 = 68. ✓
Watch out. Only the tens change. 58 becomes 68, not 59.
Watch out
Watch out: 10 more than 58 is 68, not 59. Only the tens change.
Exam tip
Grown-up tip. Point to a number on a 100 square. Ask: “What is 10 more?” Then move your finger down one row together.
Exercise 1B Counting in tens from any number
Non-calculatorMethod. Start at 23. Count on in tens.
- Start at 23. Put your finger on the number you start from.Start: 23
- Say each number, going on 10 each time. Each new number is 10 more than the one before.33, 43
- Write the numbers in order. Write each number you said.33, 43
Check. Count back from 43. You reach 23. ✓
Watch out. Do not say 23 again. Start with the next number.
Method. Start at 62. Count back in tens.
- Start at 62. Put your finger on the number you start from.Start: 62
- Say each number, going back 10 each time. Each new number is 10 less than the one before.52, 42
- Write the numbers in order. Write each number you said.52, 42
Check. Count on from 42. You reach 62. ✓
Watch out. Do not say 62 again. Start with the next number.
Method. 10 more changes only the tens digit.
- Find 47. 47 is 4 tens and 7 ones.47 = 4 tens and 7 ones
- Add one ten. The ones digit stays the same.4 tens + 1 ten = 5 tens and 7 ones
- Write the answer. 57
Check. 47 + 10 = 57. ✓
Watch out. Only the tens change. 47 becomes 57, not 48.
Method. 10 less changes only the tens digit.
- Find 81. 81 is 8 tens and 1 one.81 = 8 tens and 1 one
- Take away one ten. The ones digit stays the same.8 tens − 1 ten = 7 tens and 1 one
- Write the answer. 71
Check. 81 − 10 = 71. ✓
Watch out. Only the tens change. 81 becomes 71, not 80.
Method. 10 more changes only the tens digit.
- Find 35. 35 is 3 tens and 5 ones.35 = 3 tens and 5 ones
- Add one ten. The ones digit stays the same.3 tens + 1 ten = 4 tens and 5 ones
- Write the answer. 45
Check. 35 + 10 = 45. ✓
Watch out. Only the tens change. 35 becomes 45, not 36.
Method. The numbers go up by 10 each time.
- Look at the numbers around each gap. Each number is 10 more than the one before it.16, 26, ?, 46, ?
- Work out each missing number. Add 10 to the number before the gap.26 + 10 = 36
46 + 10 = 56 - Write the missing numbers. 36, 56
Check. Count on in 10s through the whole line. It works. ✓
Watch out. Check the numbers after the gap too. They should still go up by the same step.
Method. 10 more changes only the tens digit.
- Find 38. 38 is 3 tens and 8 ones.38 = 3 tens and 8 ones
- Add one ten. The ones digit stays the same.3 tens + 1 ten = 4 tens and 8 ones
- Write the answer. 48
Check. 38 + 10 = 48. ✓
Watch out. Only the tens change. 38 becomes 48, not 39.
Method. 10 more changes only the tens digit.
- Find 25. 25 is 2 tens and 5 ones.25 = 2 tens and 5 ones
- Add one ten. The ones digit stays the same.2 tens + 1 ten = 3 tens and 5 ones
- Write the answer. 35
Check. 25 + 10 = 35. ✓
Watch out. Only the tens change. 25 becomes 35, not 26.
Method. There are 6 groups of 10. Count in 10s to find the total.
- Count the groups: 6. Each group has 10 pencils.6 groups of 10
- Count in 10s, one group at a time. Add 10 for every group.10, 20, 30, 40, 50, 60
- Write the total. 60
Check. Count in 10s to check. The last number you say is 60. ✓
Watch out. Count in 10s, not in ones. Each group is 10.
Method. 10 more changes only the tens digit.
- Find 49. 49 is 4 tens and 9 ones.49 = 4 tens and 9 ones
- Add one ten. The ones digit stays the same.4 tens + 1 ten = 5 tens and 9 ones
- Write the answer. 59
Check. 49 + 10 = 59. ✓
Watch out. Only the tens change. 49 becomes 59, not 50.
Tens and ones
Every number to 100 has tens and ones. A ten is a bar of ten squares. A one is a single square.
The number 47 has 4 tens and 7 ones. The 4 is worth 40. The 7 is worth 7.
| Tens | Ones |
|---|---|
| 4 | 7 |
Key ideas
- A ten is a bar of ten ones.
- The tens digit is on the left.
- The ones digit is on the right.
- The place of a digit tells us what it is worth.
Key words. A ten is a bundle of ten ones. A one is a single thing.
Method. Count the groups of ten first. Then count the ones left over.
- Count the tens in 35. Each group of ten is one ten.30 is 3 tens
- Count the ones left over. The ones are what is left after the tens.35 − 30 = 5 ones
- Write the answer. 3 tens and 5 ones
Check. Put them back together: 30 + 5 = 35. ✓
Watch out. The tens come first when you say the number. 25 is 2 tens and 5 ones.
Key words. The value of a digit is how much it is worth.
Method. The place of a digit tells us what it is worth.
- Find the tens digit in 62. The tens digit is on the left.The tens digit is 6
- Work out what 6 tens is worth. 6 tens means 6 groups of ten.6 tens = 60
- Write the answer. 60
Check. 60 + 2 = 62, so the tens and ones make 62. ✓
Watch out. The digit is not always worth what it shows. In 62, the tens digit is worth 60.
Method. Start with the tens, then add the ones.
- Write 4 tens. The tens go on the left.4 tens = 40
- Add 9 ones. The ones go on the right, after the tens.40 + 9 = 49
- Write the number. 49
Check. Read it back: 49 has 4 tens and 9 ones. ✓
Watch out. The tens digit goes on the left. Write 4 tens and 9 ones as 49.
Watch out
Watch out: the 2 in 25 is worth 20, not 2. The place of the digit changes its value.
Exam tip
Grown-up tip. Put 10 buttons in a cup. The cup is one ten. Keep the loose ones on the table. Ask: “How many cups? How many loose ones?”
Exercise 1C Tens and ones
Non-calculatorKey words. A ten is a bundle of ten ones. A one is a single thing.
Method. Count the groups of ten first. Then count the ones left over.
- Count the tens in 23. Each group of ten is one ten.20 is 2 tens
- Count the ones left over. The ones are what is left after the tens.23 − 20 = 3 ones
- Write the answer. 2 tens and 3 ones
Check. Put them back together: 20 + 3 = 23. ✓
Watch out. The tens come first when you say the number. 25 is 2 tens and 5 ones.
Method. Count the tens in 70.
- Look at 70. 70 is 7 tens and 0 ones.70 = 7 tens and 0 ones
- Count the tens. Each ten is counted once.7 tens
- Write the answer. 7
Check. 7 tens and 0 ones make 70. ✓
Watch out. Read 70 as tens and ones first, then count the tens.
Method. Count the ones in 46.
- Look at 46. 46 is 4 tens and 6 ones.46 = 4 tens and 6 ones
- Count the ones. Each one is counted once.6 ones
- Write the answer. 6
Check. 4 tens and 6 ones make 46. ✓
Watch out. Read 46 as tens and ones first, then count the ones.
Method. Start with the tens, then add the ones.
- Write 5 tens. The tens go on the left.5 tens = 50
- Add 2 ones. The ones go on the right, after the tens.50 + 2 = 52
- Write the number. 52
Check. Read it back: 52 has 5 tens and 2 ones. ✓
Watch out. The tens digit goes on the left. Write 5 tens and 2 ones as 52.
Method. Start with the tens, then add the ones.
- Write 1 ten. The tens go on the left.1 ten = 10
- Add 8 ones. The ones go on the right, after the tens.10 + 8 = 18
- Write the number. 18
Check. Read it back: 18 has 1 ten and 8 ones. ✓
Watch out. The tens digit goes on the left. Write 1 ten and 8 ones as 18.
Key words. The value of a digit is how much it is worth.
Method. The place of a digit tells us what it is worth.
- Find the tens digit in 73. The tens digit is on the left.The tens digit is 7
- Work out what 7 tens is worth. 7 tens means 7 groups of ten.7 tens = 70
- Write the answer. 70
Check. 70 + 3 = 73, so the tens and ones make 73. ✓
Watch out. The digit is not always worth what it shows. In 73, the tens digit is worth 70.
Key words. The value of a digit is how much it is worth.
Method. The place of a digit tells us what it is worth.
- Find the ones digit in 41. The ones digit is on the right.The ones digit is 1
- Work out what 1 one is worth. A digit in the ones place is worth only itself.1 one = 1
- Write the answer. 1
Check. 40 + 1 = 41, so the tens and ones make 41. ✓
Watch out. The digit is not always worth what it shows. In 41, the ones digit is worth 1.
Key words. A ten is a bundle of ten ones. A one is a single thing.
Method. Count the groups of ten first. Then count the ones left over.
- Count the tens in 27. Each group of ten is one ten.20 is 2 tens
- Count the ones left over. The ones are what is left after the tens.27 − 20 = 7 ones
- Write the answer. 2 tens and 7 ones
Check. Put them back together: 20 + 7 = 27. ✓
Watch out. The tens come first when you say the number. 25 is 2 tens and 5 ones.
Method. Most of the numbers have 4 tens. Find the one that does not.
- Look at the tens of each number. Count the tens in each number.43: 4 tens 46: 4 tens 54: 5 tens 49: 4 tens
- Find the one that is different. 54 has 5 tens. The others have 4 tens.54 is different
- Write the answer. 54
Check. Check each of the others: they all have 4 tens. ✓
Watch out. Look at the tens digit, not at the ones.
Method. Start with the tens, then add the ones.
- Write 3 tens. The tens go on the left.3 tens = 30
- Add 4 ones. The ones go on the right, after the tens.30 + 4 = 34
- Write the number. 34
Check. Read it back: 34 has 3 tens and 4 ones. ✓
Watch out. The tens digit goes on the left. Write 3 tens and 4 ones as 34.
Method. Start with the tens, then add the ones.
- Write 9 tens. The tens go on the left.9 tens = 90
- Add 0 ones. The ones go on the right, after the tens.90 + 0 = 90
- Write the number. 90
Check. Read it back: 90 has 9 tens and 0 ones. ✓
Watch out. The tens digit goes on the left. Write 9 tens and 0 ones as 90.
Method. Work out each one, then compare the answers.
- Work out 40 + 6. 40 is 4 tens. Add 6 ones.40 + 6 = 46
- Work out 4 tens and 6 ones. Four tens is 40, and 6 ones is 6.4 tens and 6 ones = 46
- Compare the answers. They are both 46.Yes. Both make 46.
Check. Count in tens to 40, then count on 6 ones. You reach 46. ✓
Watch out. Four tens is the same as 40. The ones do not change.
Numbers in numerals and in words
We can write a number with digits, like 36. This is a numeral.
We can also write it in words, like thirty-six.
Numbers from 11 to 19 have special names. For example, fifteen.
Other numbers have a tens word and a ones word.
Key ideas
- A numeral uses digits, like 36.
- Words are the name of the number, like thirty-six.
- Numbers from 11 to 19 have special names.
- A hyphen joins the tens word and the ones word.
- One hundred is written as 100.
Key words. A numeral is a number written with digits, like 36. Words are written out, like thirty-six.
Method. Say the number out loud, then write the words for it.
- Split the number into tens and ones. The tens come first, then the ones.36 = 3 tens and 6 ones
- Write the tens word. 3 tens is written as thirty.thirty
- Add the ones word after a hyphen. A hyphen joins the tens word and the ones word.thirty-six
Check. Read it back: thirty-six is 36. ✓
Watch out. Put a hyphen between the tens word and the ones word, like thirty-six.
Method. Break the word into a tens word and a ones word.
- Find the tens word. forty means 4 tens.forty = 40
- Find the ones word. The ones word comes after the hyphen.two = 2
- Add the tens and the ones. Put the tens and the ones together.40 + 2 = 42
- Write the answer. 42
Check. Say the number: forty-two is 42. ✓
Watch out. The tens word comes first, like thirty in thirty-six.
Key words. A numeral is a number written with digits, like 36. Words are written out, like thirty-six.
Method. Say the number out loud, then write the words for it.
- Look at the number. Some numbers have their own names, from 0 to 19.15
- Write the name. Write the word for the whole number.fifteen
- Check the spelling. Spell each part carefully.fifteen
Check. Read it back: fifteen is 15. ✓
Watch out. Put a hyphen between the tens word and the ones word, like thirty-six.
Watch out
Watch out: thirteen and thirty sound alike. Thirteen is 13. Thirty is 30.
Exam tip
Grown-up tip. Say the number out loud and clap each part: thir-teen, thir-ty. Ask: “Which word ends in -teen?”
Exercise 1D Numbers in numerals and words
Non-calculatorKey words. A numeral is a number written with digits, like 36. Words are written out, like thirty-six.
Method. Say the number out loud, then write the words for it.
- Look at the number. Some numbers have their own names, from 0 to 19.13
- Write the name. Write the word for the whole number.thirteen
- Check the spelling. Spell each part carefully.thirteen
Check. Read it back: thirteen is 13. ✓
Watch out. Put a hyphen between the tens word and the ones word, like thirty-six.
Key words. A numeral is a number written with digits, like 36. Words are written out, like thirty-six.
Method. Say the number out loud, then write the words for it.
- Split the number into tens and ones. The tens come first, then the ones.20 = 2 tens and 0 ones
- Write the tens word. 2 tens is written as twenty.twenty
- Add the ones word after a hyphen. There are no ones, so there is no ones word.twenty
Check. Read it back: twenty is 20. ✓
Watch out. Put a hyphen between the tens word and the ones word, like thirty-six.
Method. Break the word into a tens word and a ones word.
- Find the tens word. thirty means 3 tens.thirty = 30
- Find the ones word. The ones word comes after the hyphen.four = 4
- Add the tens and the ones. Put the tens and the ones together.30 + 4 = 34
- Write the answer. 34
Check. Say the number: thirty-four is 34. ✓
Watch out. The tens word comes first, like thirty in thirty-six.
Key words. A numeral is a number written with digits, like 36. Words are written out, like thirty-six.
Method. Say the number out loud, then write the words for it.
- Split the number into tens and ones. The tens come first, then the ones.47 = 4 tens and 7 ones
- Write the tens word. 4 tens is written as forty.forty
- Add the ones word after a hyphen. A hyphen joins the tens word and the ones word.forty-seven
Check. Read it back: forty-seven is 47. ✓
Watch out. Put a hyphen between the tens word and the ones word, like thirty-six.
Key words. A numeral is a number written with digits, like 36. Words are written out, like thirty-six.
Method. Say the number out loud, then write the words for it.
- Split the number into tens and ones. The tens come first, then the ones.63 = 6 tens and 3 ones
- Write the tens word. 6 tens is written as sixty.sixty
- Add the ones word after a hyphen. A hyphen joins the tens word and the ones word.sixty-three
Check. Read it back: sixty-three is 63. ✓
Watch out. Put a hyphen between the tens word and the ones word, like thirty-six.
Key words. A numeral is a number written with digits, like 36. Words are written out, like thirty-six.
Method. Say the number out loud, then write the words for it.
- Split the number into tens and ones. The tens come first, then the ones.81 = 8 tens and 1 one
- Write the tens word. 8 tens is written as eighty.eighty
- Add the ones word after a hyphen. A hyphen joins the tens word and the ones word.eighty-one
Check. Read it back: eighty-one is 81. ✓
Watch out. Put a hyphen between the tens word and the ones word, like thirty-six.
Method. Break the word into a tens word and a ones word.
- Find the tens word. ninety means 9 tens.ninety = 90
- Find the ones word. The ones word comes after the hyphen.six = 6
- Add the tens and the ones. Put the tens and the ones together.90 + 6 = 96
- Write the answer. 96
Check. Say the number: ninety-six is 96. ✓
Watch out. The tens word comes first, like thirty in thirty-six.
Method. Break the word into a tens word and a ones word.
- Find the tens word. seventy means 7 tens.seventy = 70
- Find the ones word. The ones word comes after the hyphen.two = 2
- Add the tens and the ones. Put the tens and the ones together.70 + 2 = 72
- Write the answer. 72
Check. Say the number: seventy-two is 72. ✓
Watch out. The tens word comes first, like thirty in thirty-six.
Method. Break the word into a tens word and a ones word.
- Find the tens word. forty means 4 tens.forty = 40
- Find the ones word. The ones word comes after the hyphen.eight = 8
- Add the tens and the ones. Put the tens and the ones together.40 + 8 = 48
- Write the answer. 48
Check. Say the number: forty-eight is 48. ✓
Watch out. The tens word comes first, like thirty in thirty-six.
Method. Read each word carefully, then compare the numbers.
- Read the word Sam used. Forty-one is 41.forty-one = 41
- Look at the number 14. Fourteen is 14, one of the special teen names.fourteen = 14
- Compare them. They are different numbers.41 is not 14
- Write the answer. No. 14 is fourteen.
Check. Count on from 10: 11, 12, 13, 14. That is fourteen. ✓
Watch out. Look for the teen ending. Fourteen has the -teen sound.
Key words. A numeral is a number written with digits, like 36. Words are written out, like thirty-six.
Method. Say the number out loud, then write the words for it.
- Split the number into tens and ones. The tens come first, then the ones.35 = 3 tens and 5 ones
- Write the tens word. 3 tens is written as thirty.thirty
- Add the ones word after a hyphen. A hyphen joins the tens word and the ones word.thirty-five
Check. Read it back: thirty-five is 35. ✓
Watch out. Put a hyphen between the tens word and the ones word, like thirty-six.
Method. One hundred is written with three digits.
- Say the words. One hundred comes after ninety-nine.one hundred
- Write the digits. One hundred has 1 hundred, 0 tens and 0 ones.1 hundred, 0 tens, 0 ones
- Write the number. 100
Check. Count on from 99 to 100. ✓
Watch out. One hundred has three digits: 1, 0, 0.
Method. Count in tens from 0 up to 100.
- Count in tens. Each ten is one group of ten.10, 20, 30 ... 100
- Count how many tens. Each number in the list is one ten.10 tens make 100
- Write the answer. 10
Check. 10 tens = 100. ✓
Watch out. One hundred is ten tens.
Comparing and ordering numbers
We use signs to compare numbers. The sign < means less than.
The sign > means more than. The sign = means equal to.
Look at the tens first. More tens means a bigger number.
If the tens are the same, look at the ones.
Key ideas
- < means less than. The point faces the smaller number.
- > means more than. The open end faces the bigger number.
- = means equal to. Both numbers are the same.
- Look at the tens first, then the ones.
Key words. < means less than. > means more than. = means equal to.
Method. Compare the tens first. Only look at the ones if the tens are the same.
- Look at the tens of each number. The tens tell us the big part of each number.47: 4 tens 52: 5 tens
- Compare the tens. More tens means a bigger number.5 tens is more than 4 tens
- Write the sign. The point of the sign faces the smaller number.47 < 52
Check. Read it out loud: 47 is less than 52. ✓
Watch out. A number with more ones is not always bigger. Look at the tens first.
Key words. < means less than. > means more than. = means equal to.
Method. Compare the tens first. Only look at the ones if the tens are the same.
- Look at the tens of each number. The tens tell us the big part of each number.36: 3 tens 36: 3 tens
- The numbers are the same. Equal means the same amount.36 = 36
- Write the sign. Use the equals sign.36 = 36
Check. Read it out loud: 36 is equal to 36. ✓
Watch out. A number with more ones is not always bigger. Look at the tens first.
Key words. Smallest is the least. Biggest is the most.
Method. Compare the tens first, then the ones, and put the numbers in order.
- Look at the tens of each number. A number with fewer tens is smaller.63: 6 tens 36: 3 tens 90: 9 tens 58: 5 tens
- Put them in order, smallest first. Start with the smallest number, then the next one.36, 58, 63, 90
- Write the answer. 36, 58, 63, 90
Check. There are 4 numbers in the question and 4 in the answer. ✓
Watch out. Check you have not left a number out, and that each number is used once.
Watch out
Watch out: do not compare only the ones. 39 is less than 51, even though 9 is more than 1.
Exam tip
Grown-up tip. Write two numbers on cards. Ask your child to point to the bigger one. Then ask: “Which way does the sign point?”
Exercise 1E Comparing and ordering numbers
Non-calculatorKey words. Bigger means more. Smaller means less.
Method. Find the bigger number. Look at the tens first.
- Look at the tens of each number. The tens tell us the big part of each number.26: 2 tens 62: 6 tens
- Compare the tens. More tens means a bigger number.6 tens is more than 2 tens
- Write the answer. Bigger means more.62
Check. Put 26 and 62 in order to check. ✓
Watch out. Do not pick the number with the bigger ones digit. Look at the tens first.
Key words. < means less than. > means more than. = means equal to.
Method. Compare the tens first. Only look at the ones if the tens are the same.
- Look at the tens of each number. The tens tell us the big part of each number.70: 7 tens 67: 6 tens
- Compare the tens. More tens means a bigger number.7 tens is more than 6 tens
- Write the sign. The point of the sign faces the smaller number.70 > 67
Check. Read it out loud: 70 is more than 67. ✓
Watch out. A number with more ones is not always bigger. Look at the tens first.
Key words. < means less than. > means more than. = means equal to.
Method. Compare the tens first. Only look at the ones if the tens are the same.
- Look at the tens of each number. The tens tell us the big part of each number.25: 2 tens 52: 5 tens
- Compare the tens. More tens means a bigger number.5 tens is more than 2 tens
- Write the sign. The point of the sign faces the smaller number.25 < 52
Check. Read it out loud: 25 is less than 52. ✓
Watch out. A number with more ones is not always bigger. Look at the tens first.
Key words. < means less than. > means more than. = means equal to.
Method. Compare the tens first. Only look at the ones if the tens are the same.
- Look at the tens of each number. The tens tell us the big part of each number.40: 4 tens 40: 4 tens
- The numbers are the same. Equal means the same amount.40 = 40
- Write the sign. Use the equals sign.40 = 40
Check. Read it out loud: 40 is equal to 40. ✓
Watch out. A number with more ones is not always bigger. Look at the tens first.
Key words. Smallest is the least. Biggest is the most.
Method. Compare the tens first, then the ones, and put the numbers in order.
- Look at the tens of each number. A number with fewer tens is smaller.81: 8 tens 18: 1 ten 42: 4 tens
- Put them in order, smallest first. Start with the smallest number, then the next one.18, 42, 81
- Write the answer. 18, 42, 81
Check. There are 3 numbers in the question and 3 in the answer. ✓
Watch out. Check you have not left a number out, and that each number is used once.
Key words. Smallest is the least. Biggest is the most.
Method. Compare the tens first, then the ones, and put the numbers in order.
- Look at the tens of each number. A number with fewer tens is smaller.74: 7 tens 47: 4 tens 72: 7 tens 27: 2 tens
- Put them in order, biggest first. Start with the biggest number, then the next one.74, 72, 47, 27
- Write the answer. 74, 72, 47, 27
Check. There are 4 numbers in the question and 4 in the answer. ✓
Watch out. Check you have not left a number out, and that each number is used once.
Method. Look at the tens first. The biggest number has the most tens.
- Look at the tens of each number. Compare the tens first.58: 5 tens 85: 8 tens 52: 5 tens
- Find the biggest number. Look for the most tens, then the ones.85 is the biggest number
- Write the answer. 85
Check. Put the numbers in order to check. ✓
Watch out. Do not pick the number with the biggest ones digit. Look at the tens first.
Method. Look at the tens first. The smallest number has the fewest tens.
- Look at the tens of each number. Compare the tens first.31: 3 tens 29: 2 tens 60: 6 tens
- Find the smallest number. Look for the fewest tens, then the ones.29 is the smallest number
- Write the answer. 29
Check. Put the numbers in order to check. ✓
Watch out. Do not pick the number with the biggest ones digit. Look at the tens first.
Key words. < means less than. > means more than. = means equal to.
Method. Compare the tens first. Only look at the ones if the tens are the same.
- Look at the tens of each number. The tens tell us the big part of each number.19: 1 ten 91: 9 tens
- Compare the tens. More tens means a bigger number.9 tens is more than 1 ten
- Write the sign. The point of the sign faces the smaller number.19 < 91
Check. Read it out loud: 19 is less than 91. ✓
Watch out. A number with more ones is not always bigger. Look at the tens first.
Key words. < means less than. > means more than. = means equal to.
Method. Compare the tens first. Only look at the ones if the tens are the same.
- Look at the tens of each number. The tens tell us the big part of each number.55: 5 tens 50: 5 tens
- The tens are the same, so look at the ones. When the tens match, the ones decide.55: 5 ones 50: 0 ones
- Compare the ones. More ones means a bigger number.5 is more than 0
- Write the sign. The point of the sign faces the smaller number.55 > 50
Check. Read it out loud: 55 is more than 50. ✓
Watch out. A number with more ones is not always bigger. Look at the tens first.
Key words. < means less than. > means more than. = means equal to.
Method. Compare the tens first. Only look at the ones if the tens are the same.
- Look at the tens of each number. The tens tell us the big part of each number.28: 2 tens 82: 8 tens
- Compare the tens. More tens means a bigger number.8 tens is more than 2 tens
- Write the sign. The point of the sign faces the smaller number.28 < 82
Check. Read it out loud: 28 is less than 82. ✓
Watch out. A number with more ones is not always bigger. Look at the tens first.
Key words. Bigger means more. Smaller means less.
Method. Find the bigger number. Look at the tens first.
- Look at the tens of each number. The tens tell us the big part of each number.52: 5 tens 47: 4 tens
- Compare the tens. More tens means a bigger number.5 tens is more than 4 tens
- Write the answer. Bigger means more.Mei
Check. Put 52 and 47 in order to check. ✓
Watch out. Do not pick the number with the bigger ones digit. Look at the tens first.
Key words. Bigger means more. Smaller means less.
Method. Find the bigger number. Look at the tens first.
- Look at the tens of each number. The tens tell us the big part of each number.25: 2 tens 9: 0 tens
- Compare the tens. More tens means a bigger number.2 tens is more than 0 tens
- Write the answer. Bigger means more.25
Check. Put 25 and 9 in order to check. ✓
Watch out. Do not pick the number with the bigger ones digit. Look at the tens first.
Key words. Smallest is the least. Biggest is the most.
Method. Compare the tens first, then the ones, and put the numbers in order.
- Look at the tens of each number. A number with fewer tens is smaller.34: 3 tens 43: 4 tens 39: 3 tens 30: 3 tens
- Put them in order, smallest first. Start with the smallest number, then the next one.30, 34, 39, 43
- Write the answer. 30, 34, 39, 43
Check. There are 4 numbers in the question and 4 in the answer. ✓
Watch out. Check you have not left a number out, and that each number is used once.
Number lines and place value problems
A number line shows numbers in order. Bigger numbers are further to the right.
We can say which two tens a number is between. 47 is between 40 and 50.
An estimate is a sensible guess. We can check it on the line.
Key ideas
- Bigger numbers are further to the right on a number line.
- Find the two tens either side of a number.
- To estimate, think about which ten is closer.
- Use place value to solve problems: count the tens, then the ones.
Method. Find the ten just below the number and the ten just above it.
- Find the ten just below 47. 47 has 4 tens and 7 ones.40 is below 47
- Find the ten just above it. Add 10 to the ten below.40 + 10 = 50
- Write the answer. 40 and 50
Check. 47 is between 40 and 50. It is not a ten. ✓
Watch out. A number that ends in 0 is a ten. Other numbers sit between two tens.
Method. Start at the first number on the line and count along to the arrow.
- Look at the numbers at each end. The line goes from 30 to 40.30 to 40
- Count along from 30 to the arrow. Each mark on the line is one more than the one before.36 − 30 = 6 steps
- Write the number the arrow shows. 30 + 6 = 36.36
Check. Count on 6 from 30. You reach 36. ✓
Watch out. Start at 30, the first number on the line. Each mark is one more.
Method. Count on one more from 39.
- Make the number first. 3 tens and 9 ones is 39.30 + 9 = 39
- Add one more. One more than 39 is the next number.39 + 1 = 40
- Write the answer. 40
Check. Count back one from 40. You reach 39. ✓
Watch out. 39 + 1 is 40, not 30. The ones become 0 and the tens go up by one.
Watch out
Watch out: 39 + 1 is 40, not 30. The ones digit becomes 0 and the tens go up.
Exam tip
Grown-up tip. Draw a number line from 30 to 40 on paper. Ask: “Where would 36 go? Is it closer to 30 or to 40?”
Exercise 1F Number lines and place value problems
Non-calculatorMethod. Find the ten just below the number and the ten just above it.
- Find the ten just below 23. 23 has 2 tens and 3 ones.20 is below 23
- Find the ten just above it. Add 10 to the ten below.20 + 10 = 30
- Write the answer. 20 and 30
Check. 23 is between 20 and 30. It is not a ten. ✓
Watch out. A number that ends in 0 is a ten. Other numbers sit between two tens.
Method. Start at the first number on the line and count along to the arrow.
- Look at the numbers at each end. The line goes from 0 to 10.0 to 10
- Count along from 0 to the arrow. Each mark on the line is one more than the one before.7 − 0 = 7 steps
- Write the number the arrow shows. 0 + 7 = 7.7
Check. Count on 7 from 0. You reach 7. ✓
Watch out. Start at 0, the first number on the line. Each mark is one more.
Method. Start at the first number on the line and count along to the arrow.
- Look at the numbers at each end. The line goes from 60 to 70.60 to 70
- Count along from 60 to the arrow. Each mark on the line is one more than the one before.64 − 60 = 4 steps
- Write the number the arrow shows. 60 + 4 = 64.64
Check. Count on 4 from 60. You reach 64. ✓
Watch out. Start at 60, the first number on the line. Each mark is one more.
Method. Find which ten is closer by counting the steps to each ten.
- Find the two tens either side of 38. 38 is between 30 and 40.30 and 40
- Count the steps to each ten. Count how far it is to each ten.38 to 30: 8 steps 38 to 40: 2 steps
- Pick the closer ten. The ten with fewer steps is closer.40
Check. 40 is closer, with 2 steps. ✓
Watch out. Count the steps to both tens. Do not just guess.
Method. Find which ten is closer by counting the steps to each ten.
- Find the two tens either side of 52. 52 is between 50 and 60.50 and 60
- Count the steps to each ten. Count how far it is to each ten.52 to 50: 2 steps 52 to 60: 8 steps
- Pick the closer ten. The ten with fewer steps is closer.50
Check. 50 is closer, with 2 steps. ✓
Watch out. Count the steps to both tens. Do not just guess.
Method. Halfway means the same distance from each end.
- Find the gap from 40 to 50. Take the smaller number away from the bigger one.50 − 40 = 10
- Find half of the gap. Half of the gap is how far to go from the smaller number.10 shared into 2 equal parts = 5
- Add half to the smaller number. That gives the number in the middle.40 + 5 = 45
Check. 45 − 40 = 5, and 50 − 45 = 5. Both gaps are the same. ✓
Watch out. The middle number is not the same as the ones digit. Find half of the gap.
Method. Halfway means the same distance from each end.
- Find the gap from 0 to 100. Take the smaller number away from the bigger one.100 − 0 = 100
- Find half of the gap. Half of the gap is how far to go from the smaller number.100 shared into 2 equal parts = 50
- Add half to the smaller number. That gives the number in the middle.0 + 50 = 50
Check. 50 − 0 = 50, and 100 − 50 = 50. Both gaps are the same. ✓
Watch out. The middle number is not the same as the ones digit. Find half of the gap.
Method. The numbers go up by 10 each time.
- Look at the numbers around each gap. Each number is 10 more than the one before it.30, ?, 50
- Work out each missing number. Add 10 to the number before the gap.30 + 10 = 40
- Write the missing numbers. 40
Check. Count on in 10s through the whole line. It works. ✓
Watch out. Check the numbers after the gap too. They should still go up by the same step.
Key words. Bigger means more. Smaller means less.
Method. Find the bigger number. Look at the tens first.
- Look at the tens of each number. The tens tell us the big part of each number.35: 3 tens 29: 2 tens
- Compare the tens. More tens means a bigger number.3 tens is more than 2 tens
- Write the answer. Bigger means more.Ravi
Check. Put 35 and 29 in order to check. ✓
Watch out. Do not pick the number with the bigger ones digit. Look at the tens first.
Method. Start with the tens, then add the ones.
- Write 4 tens. The tens go on the left.4 tens = 40
- Add 6 ones. The ones go on the right, after the tens.40 + 6 = 46
- Write the number. 46
Check. Read it back: 46 has 4 tens and 6 ones. ✓
Watch out. The tens digit goes on the left. Write 4 tens and 6 ones as 46.
Method. There are 4 groups of 10. Count in 10s to find the total.
- Count the groups: 4. Each group has 10 stickers.4 groups of 10
- Count in 10s, one group at a time. Add 10 for every group.10, 20, 30, 40
- Write the total. 40
Check. Count in 10s to check. The last number you say is 40. ✓
Watch out. Count in 10s, not in ones. Each group is 10.
Method. Work out how far 46 is from each ten. Then pick the closer ten.
- Count the steps from 46 down to 40. Count how far it is to 40.46 to 40: 6 steps
- Count the steps from 46 up to 50. Count how far it is to 50.46 to 50: 4 steps
- Pick the closer ten. Four steps is fewer than six steps.No. 46 is closer to 50.
Check. Sam is wrong, because 4 is less than 6. ✓
Watch out. Count the steps to both tens before you decide.
Chapter summary
| Skill | Method |
|---|---|
| Counting in twos, threes and fives | Add the same step each time. To count back, take the step away. |
| Counting in tens | Only the tens digit changes. The ones digit stays the same. |
| Tens and ones | The tens digit is on the left. 4 tens is worth 40. |
| Numerals and words | Write the tens word, then a hyphen, then the ones word: thirty-six. |
| Comparing numbers | Look at the tens first. Use <, > or = to show which is bigger. |
| Number lines | Bigger numbers are further right. Find the two tens either side of a number. |
Can you…?
- I can count in twos, threes and fives, forwards and back
- I can count in tens from any number
- I can say how many tens and ones a number has
- I can say what a digit is worth
- I can write numbers to 100 in numerals and in words
- I can compare numbers with <, > and =, and put them in order
- I can place a number on a number line
Key terms
- number line
- a line with numbers in order, bigger numbers on the right
- tens digit
- the digit on the left, which tells how many tens
- ones digit
- the digit on the right, which tells how many ones
- place value
- how much a digit is worth, because of where it is
- numeral
- a number written with digits, like 36
- estimate
- a sensible guess at an amount or a place on a line
- step
- the same jump each time when we count
Exercise 1Z Check-up
Non-calculatorMethod. Start at 10. Count on in twos.
- Start at 10. Put your finger on the number you start from.Start: 10
- Say each number, going on 2 each time. Each new number is 2 more than the one before.12, 14, 16
- Write the numbers in order. Write each number you said.12, 14, 16
Check. Count back from 16. You reach 10. ✓
Watch out. Do not say 10 again. Start with the next number.
Method. The numbers go up by 5 each time.
- Look at the numbers around each gap. Each number is 5 more than the one before it.15, 20, ?, 30
- Work out each missing number. Add 5 to the number before the gap.20 + 5 = 25
- Write the missing numbers. 25
Check. Count on in 5s through the whole line. It works. ✓
Watch out. Check the numbers after the gap too. They should still go up by the same step.
Method. Start at 46. Count on in tens.
- Start at 46. Put your finger on the number you start from.Start: 46
- Say each number, going on 10 each time. Each new number is 10 more than the one before.56, 66
- Write the numbers in order. Write each number you said.56, 66
Check. Count back from 66. You reach 46. ✓
Watch out. Do not say 46 again. Start with the next number.
Method. 10 less changes only the tens digit.
- Find 73. 73 is 7 tens and 3 ones.73 = 7 tens and 3 ones
- Take away one ten. The ones digit stays the same.7 tens − 1 ten = 6 tens and 3 ones
- Write the answer. 63
Check. 73 − 10 = 63. ✓
Watch out. Only the tens change. 73 becomes 63, not 72.
Key words. A ten is a bundle of ten ones. A one is a single thing.
Method. Count the groups of ten first. Then count the ones left over.
- Count the tens in 68. Each group of ten is one ten.60 is 6 tens
- Count the ones left over. The ones are what is left after the tens.68 − 60 = 8 ones
- Write the answer. 6 tens and 8 ones
Check. Put them back together: 60 + 8 = 68. ✓
Watch out. The tens come first when you say the number. 25 is 2 tens and 5 ones.
Key words. The value of a digit is how much it is worth.
Method. The place of a digit tells us what it is worth.
- Find the tens digit in 53. The tens digit is on the left.The tens digit is 5
- Work out what 5 tens is worth. 5 tens means 5 groups of ten.5 tens = 50
- Write the answer. 50
Check. 50 + 3 = 53, so the tens and ones make 53. ✓
Watch out. The digit is not always worth what it shows. In 53, the tens digit is worth 50.
Method. Start with the tens, then add the ones.
- Write 7 tens. The tens go on the left.7 tens = 70
- Add 3 ones. The ones go on the right, after the tens.70 + 3 = 73
- Write the number. 73
Check. Read it back: 73 has 7 tens and 3 ones. ✓
Watch out. The tens digit goes on the left. Write 7 tens and 3 ones as 73.
Key words. A numeral is a number written with digits, like 36. Words are written out, like thirty-six.
Method. Say the number out loud, then write the words for it.
- Split the number into tens and ones. The tens come first, then the ones.84 = 8 tens and 4 ones
- Write the tens word. 8 tens is written as eighty.eighty
- Add the ones word after a hyphen. A hyphen joins the tens word and the ones word.eighty-four
Check. Read it back: eighty-four is 84. ✓
Watch out. Put a hyphen between the tens word and the ones word, like thirty-six.
Key words. < means less than. > means more than. = means equal to.
Method. Compare the tens first. Only look at the ones if the tens are the same.
- Look at the tens of each number. The tens tell us the big part of each number.39: 3 tens 93: 9 tens
- Compare the tens. More tens means a bigger number.9 tens is more than 3 tens
- Write the sign. The point of the sign faces the smaller number.39 < 93
Check. Read it out loud: 39 is less than 93. ✓
Watch out. A number with more ones is not always bigger. Look at the tens first.
Key words. Smallest is the least. Biggest is the most.
Method. Compare the tens first, then the ones, and put the numbers in order.
- Look at the tens of each number. A number with fewer tens is smaller.64: 6 tens 46: 4 tens 56: 5 tens
- Put them in order, smallest first. Start with the smallest number, then the next one.46, 56, 64
- Write the answer. 46, 56, 64
Check. There are 3 numbers in the question and 3 in the answer. ✓
Watch out. Check you have not left a number out, and that each number is used once.
Total 12 marks. Allow about 12 minutes.
Exercise 1X End-of-chapter quiz
Non-calculatorMethod. Start at 6. Count on in twos.
- Start at 6. Put your finger on the number you start from.Start: 6
- Say each number, going on 2 each time. Each new number is 2 more than the one before.8, 10, 12, 14
- Write the numbers in order. Write each number you said.8, 10, 12, 14
Check. Count back from 14. You reach 6. ✓
Watch out. Do not say 6 again. Start with the next number.
Method. There are 5 groups of 2. Count in 2s to find the total.
- Count the groups: 5. Each group has 2 socks.5 groups of 2
- Count in 2s, one group at a time. Add 2 for every group.2, 4, 6, 8, 10
- Write the total. 10
Check. Count in 2s to check. The last number you say is 10. ✓
Watch out. Count in 2s, not in ones. Each group is 2.
Method. Start at 21. Count back in threes.
- Start at 21. Put your finger on the number you start from.Start: 21
- Say each number, going back 3 each time. Each new number is 3 less than the one before.18, 15, 12
- Write the numbers in order. Write each number you said.18, 15, 12
Check. Count on from 12. You reach 21. ✓
Watch out. Do not say 21 again. Start with the next number.
Method. Start at 27. Count on in tens.
- Start at 27. Put your finger on the number you start from.Start: 27
- Say each number, going on 10 each time. Each new number is 10 more than the one before.37, 47
- Write the numbers in order. Write each number you said.37, 47
Check. Count back from 47. You reach 27. ✓
Watch out. Do not say 27 again. Start with the next number.
Method. 10 more changes only the tens digit.
- Find 84. 84 is 8 tens and 4 ones.84 = 8 tens and 4 ones
- Add one ten. The ones digit stays the same.8 tens + 1 ten = 9 tens and 4 ones
- Write the answer. 94
Check. 84 + 10 = 94. ✓
Watch out. Only the tens change. 84 becomes 94, not 85.
Method. Start with the tens, then add the ones.
- Write 9 tens. The tens go on the left.9 tens = 90
- Add 1 one. The ones go on the right, after the tens.90 + 1 = 91
- Write the number. 91
Check. Read it back: 91 has 9 tens and 1 one. ✓
Watch out. The tens digit goes on the left. Write 9 tens and 1 one as 91.
Key words. The value of a digit is how much it is worth.
Method. The place of a digit tells us what it is worth.
- Find the tens digit in 84. The tens digit is on the left.The tens digit is 8
- Work out what 8 tens is worth. 8 tens means 8 groups of ten.8 tens = 80
- Write the answer. 80
Check. 80 + 4 = 84, so the tens and ones make 84. ✓
Watch out. The digit is not always worth what it shows. In 84, the tens digit is worth 80.
Method. Break the word into a tens word and a ones word.
- Find the tens word. forty means 4 tens.forty = 40
- Find the ones word. The ones word comes after the hyphen.five = 5
- Add the tens and the ones. Put the tens and the ones together.40 + 5 = 45
- Write the answer. 45
Check. Say the number: forty-five is 45. ✓
Watch out. The tens word comes first, like thirty in thirty-six.
Key words. < means less than. > means more than. = means equal to.
Method. Compare the tens first. Only look at the ones if the tens are the same.
- Look at the tens of each number. The tens tell us the big part of each number.58: 5 tens 85: 8 tens
- Compare the tens. More tens means a bigger number.8 tens is more than 5 tens
- Write the sign. The point of the sign faces the smaller number.58 < 85
Check. Read it out loud: 58 is less than 85. ✓
Watch out. A number with more ones is not always bigger. Look at the tens first.
Method. Find which ten is closer by counting the steps to each ten.
- Find the two tens either side of 36. 36 is between 30 and 40.30 and 40
- Count the steps to each ten. Count how far it is to each ten.36 to 30: 6 steps 36 to 40: 4 steps
- Pick the closer ten. The ten with fewer steps is closer.40
Check. 40 is closer, with 4 steps. ✓
Watch out. Count the steps to both tens. Do not just guess.