Year 2: Number lines and place value problems
Part of the Year 2 place value to 100 chapter. Chapter overview · whole chapter on one page
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.