Year 4: Two-step problems with money and measures
Part of the Year 4 column addition and subtraction chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Two-step problems with money and measures
A two-step problem needs two calculations. The answer to the first calculation helps you do the second. These problems are often about money and measures (length, mass and capacity).
Use these five steps every time:
- Read the problem twice. What do you know? What do you need to find?
- Draw a bar model.
- Plan your two steps. What do you find first?
- Calculate with a written or mental method.
- Check that your answer makes sense and answers the question.
Money. Use the same units all the way through. £1 is 100p, so £10 is 1,000p. If a problem mixes pounds and pence, change them to the same unit first. Change is the money left over when you pay with more than the cost. Measures. Do the same with length (cm, m, km), mass (g, kg) and capacity (ml, l): all the amounts must be in the same unit before you add or subtract. Write the unit in your answer.
Many two-step problems follow one of these patterns:
- Add, then subtract: add up the amounts used, then take them from the start (stock, money left, distance still to go).
- Subtract, then add: follow a story where some leave and some join.
- Compare, then total: use “more than” or “fewer than” to find the second amount, then add both.
- Total, then compare: add two amounts, then find the difference from a third.
Key words. Change is the money you get back. Pence (p) are the small units of money. A unit is a measurement word such as cm, kg or ml.
Key ideas
- Two steps means two calculations. Do them in a sensible order.
- Draw a bar model first.
- Make sure all amounts are in the same unit (£ with £, p with p, cm with cm).
- Change = money paid − total cost.
- Check your answer with the inverse, and ask: does it make sense?
Method. This is a two-step problem. First add up everything that was used. Then take that total away from the amount at the start.
- Draw a bar model. The whole bar is 6,000. It is split into the two amounts used and the part that is left.
- Step 1: add the two amounts used. Put the two parts together.1,850 + 2,375 = 4,225
Th H T O 1 8 5 0 + 2 3 7 5 4 2 2 5 1 1 - Step 2: take the total away from the start. What is left is the whole minus the parts that were used.6,000 − 4,225 = 1,775
Th H T O 5 69 09 010 0− 4 2 2 5 1 7 7 5 - Write the answer. 1,775 stickers
Check. Add everything back: 1,850 + 2,375 + 1,775 = 6,000, which is the start amount. ✓
Watch out. Do not take away just one of the amounts. Both amounts were used, so take away the total of both.
Key words. Change is the money you get back when you pay with more than the cost. Pence (p) are the small units: 100p = £1.
Method. This is a two-step problem. First add up how much everything costs. Then take the cost away from the money we have. What is left is the answer.
- Make the units the same. £1 is the same as 100p, so we change the £10 note to pence.£10 = 10 × 100p = 1,000p
- Draw a bar model. The whole bar is the money we start with (or pay). It is split into the cost of each thing and what is left.
- Step 1: find the total cost. Add the prices.695p + 249p = 944p
H T O 6 9 5 + 2 4 9 9 4 4 1 1 - Step 2: find the change. Take the total cost away from the money we started with.1,000p − 944p = 56p
Th H T O 0 19 09 010 0− 9 4 4 5 6 - Write the answer. 56p change
Check. Add the cost and what is left: 944p + 56p = 1,000p, which is the money we started with. ✓
Watch out. Do not take away just one price. Both things were bought, so take away the total cost. The units must match: pounds with pounds, or pence with pence.
Method. This is a two-step problem. First use the comparison to find the second amount. Then add the two amounts to find the total.
- Draw a comparison bar model. The two bars show both amounts. The dashed part is the difference, 640.
- Step 1: find how many Cara has. Cara has 640 more, so we add.2,350 + 640 = 2,990
Th H T O 2 3 5 0 + 6 4 0 2 9 9 0 - Step 2: find the total. Add the two amounts: Ben and Cara.2,350 + 2,990 = 5,340
Th H T O 2 3 5 0 + 2 9 9 0 5 3 4 0 1 1 - Write the answer. 5,340 points
Check. The difference between the two amounts should be 640: 2,990 − 2,350 = 640. ✓
Watch out. A common mistake is to stop after step 1. The question asks for the total of BOTH amounts.
Method. This is a two-step problem. First find the total. Then compare it with the other amount by finding the difference.
- Step 1: find the total. Put the two amounts together.£1,245 + £1,380 = £2,625
Th H T O 1 2 4 5 + 1 3 8 0 2 6 2 5 1 - Draw a comparison bar model. The dashed part is the difference we want.
- Step 2: find the difference. Take the smaller amount from the bigger one.£3,000 − £2,625 = £375
Th H T O 2 39 09 010 0− 2 6 2 5 3 7 5 - Write the answer. £375
Check. Add the difference to the smaller amount: £2,625 + £375 = £3,000. ✓
Watch out. Take the SMALLER amount from the BIGGER amount to find the difference.
| Day | People |
|---|---|
| Friday | 2,845 |
| Saturday | 4,160 |
| Sunday | 3,925 |
How many more people came on Saturday and Sunday together than on Friday?
Method. This is a two-step problem. First add the people on Saturday and Sunday. Then compare with Friday by finding the difference.
- Step 1: find the total for Saturday and Sunday. Put the two days together.4,160 + 3,925 = 8,085
Th H T O 4 1 6 0 + 3 9 2 5 8 0 8 5 1 - Draw a comparison bar model. One bar is Saturday and Sunday together. The other is Friday. The dashed part is what we want.
- Step 2: find the difference. Take the smaller amount from the bigger amount.8,085 − 2,845 = 5,240
Th H T O 7 810 08 5 − 2 8 4 5 5 2 4 0 - Write the answer. 5,240 more people
Check. Add the difference to Friday: 2,845 + 5,240 = 8,085. ✓
Watch out. Read the question carefully. It asks about Saturday and Sunday together, so add those two days first.
Watch out
Check the units before you calculate. £5 and 250p cannot be added until they are both in pounds or both in pence. And remember that two-step problems have two answers on the way: the answer to step 1 is not the final answer.Exercise 2F Two-step problems
Non-calculatorMethod. This is a two-step problem. First add up everything that was used. Then take that total away from the amount at the start.
- Draw a bar model. The whole bar is 5,000. It is split into the two amounts used and the part that is left.
- Step 1: add the two amounts used. Put the two parts together.1,265 + 1,840 = 3,105
Th H T O 1 2 6 5 + 1 8 4 0 3 1 0 5 1 1 - Step 2: take the total away from the start. What is left is the whole minus the parts that were used.5,000 − 3,105 = 1,895
Th H T O 4 59 09 010 0− 3 1 0 5 1 8 9 5 - Write the answer. 1,895 eggs
Check. Add everything back: 1,265 + 1,840 + 1,895 = 5,000, which is the start amount. ✓
Watch out. Do not take away just one of the amounts. Both amounts were used, so take away the total of both.
Method. This is a two-step problem. First add up everything that was used. Then take that total away from the amount at the start.
- Draw a bar model. The whole bar is £9,000. It is split into the two amounts used and the part that is left.
- Step 1: add the two amounts used. Put the two parts together.£2,485 + £1,350 = £3,835
Th H T O 2 4 8 5 + 1 3 5 0 3 8 3 5 1 - Step 2: take the total away from the start. What is left is the whole minus the parts that were used.£9,000 − £3,835 = £5,165
Th H T O 8 99 09 010 0− 3 8 3 5 5 1 6 5 - Write the answer. £5,165
Check. Add everything back: £2,485 + £1,350 + £5,165 = £9,000, which is the start amount. ✓
Watch out. Do not take away just one of the amounts. Both amounts were used, so take away the total of both.
Key words. Change is the money you get back when you pay with more than the cost. Pence (p) are the small units: 100p = £1.
Method. This is a two-step problem. First add up how much everything costs. Then take the cost away from the money we have. What is left is the answer.
- Draw a bar model. The whole bar is the money we start with (or pay). It is split into the cost of each thing and what is left.
- Step 1: find the total cost. Add the prices.£385 + £27 = £412
H T O 3 8 5 + 2 7 4 1 2 1 1 - Step 2: find the change. Take the total cost away from the money we started with.£500 − £412 = £88
H T O 4 59 010 0− 4 1 2 8 8 - Write the answer. £88 change
Check. Add the cost and what is left: £412 + £88 = £500, which is the money we started with. ✓
Watch out. Do not take away just one price. Both things were bought, so take away the total cost.
Method. This is a two-step problem. First use the comparison to find the second amount. Then add the two amounts to find the total.
- Draw a comparison bar model. The two bars show both amounts. The dashed part is the difference, 475.
- Step 1: find how many Mei has. Mei has 475 more, so we add.1,850 + 475 = 2,325
Th H T O 1 8 5 0 + 4 7 5 2 3 2 5 1 1 - Step 2: find the total. Add the two amounts: Leo and Mei.1,850 + 2,325 = 4,175
Th H T O 1 8 5 0 + 2 3 2 5 4 1 7 5 1 - Write the answer. 4,175 stickers
Check. The difference between the two amounts should be 475: 2,325 − 1,850 = 475. ✓
Watch out. A common mistake is to stop after step 1. The question asks for the total of BOTH amounts.
Method. This is a two-step problem. First use the comparison to find the second amount. Then add the two amounts to find the total.
- Draw a comparison bar model. The two bars show both amounts. The dashed part is the difference, 1,275 kg.
- Step 1: find how many Van has. Van has 1,275 kg fewer, so we subtract.3,640 kg − 1,275 kg = 2,365 kg
Th H T O 3 5 613 410 0− 1 2 7 5 2 3 6 5 - Step 2: find the total. Add the two amounts: Lorry and Van.3,640 kg + 2,365 kg = 6,005 kg
Th H T O 3 6 4 0 + 2 3 6 5 6 0 0 5 1 1 - Write the answer. 6,005 kg
Check. The difference between the two amounts should be 1,275 kg: 3,640 kg − 2,365 kg = 1,275 kg. ✓
Watch out. A common mistake is to stop after step 1. The question asks for the total of BOTH amounts.
Method. This is a two-step problem. First add up everything that was used. Then take that total away from the amount at the start.
- Draw a bar model. The whole bar is 3,000 m. It is split into the two amounts used and the part that is left.
- Step 1: add the two amounts used. Put the two parts together.1,250 m + 875 m = 2,125 m
Th H T O 1 2 5 0 + 8 7 5 2 1 2 5 1 1 - Step 2: take the total away from the start. What is left is the whole minus the parts that were used.3,000 m − 2,125 m = 875 m
Th H T O 2 39 09 010 0− 2 1 2 5 8 7 5 - Write the answer. 875 m
Check. Add everything back: 1,250 m + 875 m + 875 m = 3,000 m, which is the start amount. ✓
Watch out. Do not take away just one of the amounts. Both amounts were used, so take away the total of both.
Method. This is a two-step problem. First find the total. Then compare it with the other amount by finding the difference.
- Step 1: find the total. Put the two amounts together.1,865 km + 2,740 km = 4,605 km
Th H T O 1 8 6 5 + 2 7 4 0 4 6 0 5 1 1 - Draw a comparison bar model. The dashed part is the difference we want.
- Step 2: find the difference. Take the smaller amount from the bigger one.4,605 km − 3,980 km = 625 km
Th H T O 3 415 610 05 − 3 9 8 0 6 2 5 - Write the answer. 625 km
Check. Add the difference to the smaller amount: 3,980 km + 625 km = 4,605 km. ✓
Watch out. Take the SMALLER amount from the BIGGER amount to find the difference.
Method. This is a two-step problem. Follow the story in order. First take away the amount that goes out. Then add the amount that comes in.
- Draw what happens. A number line shows the story in order: first it goes down, then it goes up.
- Step 1: take away. 365 get off, so we subtract.840 − 365 = 475
H T O 7 813 410 0− 3 6 5 4 7 5 - Step 2: add. Now 278 get on, so we add to the new total.475 + 278 = 753
H T O 4 7 5 + 2 7 8 7 5 3 1 1 - Write the answer. 753 passengers
Check. Work backwards: 753 − 278 = 475 and 475 + 365 = 840. ✓
Watch out. Follow the story in order. The first thing that happens is the first calculation.
| Day | Milk used (ml) |
|---|---|
| Monday | 1,750 |
| Tuesday | 2,395 |
| Wednesday | 1,860 |
How much more milk is used on Monday and Wednesday together than on Tuesday?
Method. First add the milk used on Monday and Wednesday. Then find the difference from Tuesday.
- Step 1: add Monday and Wednesday. The question asks about these two days together.1,750 ml + 1,860 ml = 3,610 ml
Th H T O 1 7 5 0 + 1 8 6 0 3 6 1 0 1 1 - Draw a comparison bar model. The dashed part is the difference.
- Step 2: find the difference. Take the smaller amount from the bigger one.3,610 ml − 2,395 ml = 1,215 ml
Th H T O 3 5 610 110 0− 2 3 9 5 1 2 1 5 - Write the answer. 1,215 ml more
Check. 2,395 ml + 1,215 ml = 3,610 ml. ✓
Watch out. Write the unit (ml) with your answer.
Key words. Change is the money you get back when you pay with more than the cost. Pence (p) are the small units: 100p = £1.
Method. This is a two-step problem. First add up how much everything costs. Then take the cost away from the money we have. What is left is the answer.
- Make the units the same. Dev has £12, but the prices are in pence. Change £12 to pence.£12 = 12 × 100p = 1,200p
- Draw a bar model. The whole bar is the money we start with (or pay). It is split into the cost of each thing and what is left.
- Step 1: find the total cost. Add the prices.475p + 360p = 835p
H T O 4 7 5 + 3 6 0 8 3 5 1 - Step 2: find the money left. Take the total cost away from the money we started with.1,200p − 835p = 365p
Th H T O 0 111 29 010 0− 8 3 5 3 6 5 - Write the answer. 365p left
Check. Add the cost and what is left: 835p + 365p = 1,200p, which is the money we started with. ✓
Watch out. Do not take away just one price. Both things were bought, so take away the total cost. The units must match: pounds with pounds, or pence with pence.
A 2,450 + 1,380 + 645
B 2,450 − 1,380 − 645
C 2,450 − 1,380 + 645
D 2,450 − (1,380 + 645)
Method. Think about the story. Rolls are sold twice, so both amounts must be taken away. Then work out each choice to see which two give the same answer.
- Think about the story. The baker starts with 2,450. She sells 1,380 and then 645. Both are taken away.2,450 − 1,380 − 645
- Work out each choice. Do the brackets first.A: 2,450 + 1,380 + 645 = 4,475
B: 2,450 − 1,380 − 645 = 425
C: 2,450 − 1,380 + 645 = 1,715
D: 2,450 − (1,380 + 645) = 425 - Choose the two that match the story. B takes the two amounts away one after the other. D adds the two sold amounts first and then takes the total away. Both give 425.B and D
Check. Add everything back: 1,380 + 645 + 425 = 2,450. ✓
Watch out. Choice C adds the 645 on by mistake. Choice A adds both amounts to the start. Neither makes sense for rolls that are sold.
Method. Work out the problem step by step and see what 4,725 is.
- Do step 1. Ben scores 1,275 more than Aisha, so add.3,450 + 1,275 = 4,725
Th H T O 3 4 5 0 + 1 2 7 5 4 7 2 5 1 - Compare with Ravi’s answer. 4,725 is Ben’s score, not the total.Ravi stopped after step 1.
- Do step 2. The question asks for both scores together.3,450 + 4,725 = 8,175
Th H T O 3 4 5 0 + 4 7 2 5 8 1 7 5 1 - Write the correct answer. 8,175 points
Check. Aisha scores 3,450 and Ben scores 4,725. 4,725 − 3,450 = 1,275. ✓
Watch out. Read the last sentence of the question again before you write your answer. It tells you what to find.
Method. Tom started with all the parts put together: what he spent plus what he has left.
- Draw a bar model. The whole is what Tom had at the start. The parts are the bike, the helmet and the money left.
- Step 1: add the two things Tom bought. Put the money spent together.£1,250 + £385 = £1,635
Th H T O 1 2 5 0 + 3 8 5 1 6 3 5 1 - Step 2: add the money left. Whole = spent + left.£1,635 + £2,365 = £4,000
Th H T O 1 6 3 5 + 2 3 6 5 4 0 0 0 1 1 1 - Write the answer. £4,000
Check. Take away what he spent: £4,000 − £1,250 − £385 = £2,365. ✓
Watch out. This is a “working backwards” problem. The whole is bigger than every part, so you add, not subtract.