Working through multi-step number and word problems — one clear step at a time.
6 lessons · 35 questions (A–G) · 20 calculation + 15 word problems · no time pressure
A calculation problem is a worded maths question where you have to decide which operations to use, and in what order, before you work out the answer. Pupils most often go wrong by choosing the wrong operation, doing the steps out of order, or forgetting what units the answer should be in.
At Improve Tuition, a qualified teacher works through a pupil’s reasoning to find where the method slips, then rebuilds it, in small worked steps — with read-aloud, comfort spacing and a reading tint for pupils who take in maths more easily that way.
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Lesson 1
Adding and subtracting
Aim: Add and subtract whole numbers carefully, lining up the columns.
When you add or subtract, line the digits up by place value — units under units, tens under tens. Work one column at a time, starting from the right, and carry or borrow when a column needs it. A quick estimate first tells you roughly what to expect.
Add each column from the right, carrying a ten across when a column goes past 9.
Worked example
Work out 247 + 189.
Line the numbers up by place value, units under units.
Add the units first: 7 + 9 = 16. Write the 6 and carry the 1 ten.
Add the tens: 4 + 8 = 12, plus the carried 1 makes 13. Write the 3 and carry the 1 hundred.
Add the hundreds: 2 + 1 = 3, plus the carried 1 makes 4.
So 247 + 189 = 436. Check: 436 − 189 = 247. ✓
Watch out
Keep the columns straight and remember to carry. Estimating (250 + 190 ≈ 440) shows the answer is sensible.
Aim: Multiply whole numbers, including by 10 and 100.
Multiplying by 10 shifts every digit one place to the left (put a 0 on the end); by 100, two places. For bigger numbers, split one number into tens and units, multiply each part, then add the parts back together.
Split 23 into 20 and 3, multiply each part by 4, then add: 80 + 12 = 92.
Worked example
Work out 23 × 4.
Split 23 into 20 and 3 so each part is easy.
Multiply each part by 4: 20 × 4 = 80, and 3 × 4 = 12.
Add the parts back together: 80 + 12 = 92.
So 23 × 4 = 92. Check: 92 ÷ 4 = 23. ✓
Watch out
Multiply every part, then add. 23 × 4 is not 2×4 and 3×4 written side by side.
Try one
Work out 34 × 6.
Show answer
Split 34 into 30 and 4.
30 × 6 = 180, and 4 × 6 = 24.
Add: 180 + 24 = 204.
Check: a bit more than 30 × 6 = 180, so 204 is sensible. ✓
Aim: Divide whole numbers by sharing equally or grouping.
Dividing asks “how many equal groups?” or “how much in each group?”. Use short division (the ‘bus stop’ method): work from the left, carrying any leftover to the next digit.
Dividing shares the total into equal groups: 96 into 4 groups is 24 in each.
Worked example
Work out 96 ÷ 4.
How many 4s in the first digit, 9? Two 4s make 8, with 1 left over.
Write 2, and carry the leftover 1 across to the next digit, making 16.
How many 4s in 16? Exactly 4.
So 96 ÷ 4 = 24. Check: 24 × 4 = 96. ✓
Watch out
Carry any leftover to the next digit. Always check by multiplying your answer back.
Try one
Work out 84 ÷ 7.
Show answer
How many 7s in 8? One, with 1 left over. Write 1, carry 1 to make 14.
Aim: Do calculations in the right order: brackets, then × and ÷, then + and −.
When a calculation mixes operations, the order matters. Do anything in brackets first, then multiply and divide, and only then add and subtract. Working blindly left to right often gives the wrong answer.
Do × before +: work out 4 × 5 = 20 first, then add the 6 — so the answer is 26.
Worked example
Work out 6 + 4 × 5.
There is a + and a ×. Multiply and divide come before add and subtract.
So do the multiply first: 4 × 5 = 20.
Now the addition: 6 + 20 = 26.
So 6 + 4 × 5 = 26. (Not 10 × 5 = 50 — that would add too early.) ✓
Watch out
× and ÷ happen before + and −. Brackets come before everything.
Aim: Solve money problems with pounds and pence, keeping the decimal points lined up.
Money is written with two decimal places: £3.50 means 3 pounds and 50 pence. When adding or subtracting amounts, line up the decimal points. To find change, subtract the cost from the amount paid.
Line up the decimal points: add the pence, then the pounds — £4.50 + £1.20 = £5.70.
Worked example
A book costs £4.50 and a pen costs £1.20. What is the total?
Line up the decimal points and add, just like whole numbers.
Add the pence: 50p + 20p = 70p.
Add the pounds: £4 + £1 = £5.
So the total is £5.70. Check: £5.70 − £1.20 = £4.50. ✓
Watch out
Keep the decimal points lined up. £4.5 means £4.50, not 45p.
Try one
Pay for a £6.35 item with a £10 note. How much change?
Show answer
Change = paid − cost = £10.00 − £6.35.
Count up from £6.35: 65p makes £7, then £3 more makes £10.
Aim: Plan and solve problems that need more than one step, then check.
Many real problems need two or three steps. Read carefully, decide what to work out first, do one step at a time, and write down each result. At the end, check your answer makes sense against the question.
One step at a time: first find the total (5 × 12 = 60), then subtract what was sold.
Worked example
A shop has 5 boxes of 12 apples. It sells 48 apples. How many are left?
Step 1 — find the total: 5 boxes of 12 is 5 × 12 = 60 apples.
Step 2 — take away what was sold: 60 − 48 = 12.
So 12 apples are left.
Check: 48 sold + 12 left = 60, the total we started with. ✓
Watch out
Do the multiplying before the subtracting, and label each step so you don’t lose track.
Try one
Sam saves £8 a week for 6 weeks, then spends £15. How much is left?
31.A class of 28 children each pay £3 for a trip. How much is collected in total? Give your answer in pounds.
Answer:
Show working
Total = amount each × number of children = £3 × 28.
3 × 28 = 84.
Total = £84. Check: 28 × £3 = £84. ✓
32.A shop has 5 boxes of 12 apples and sells 48 apples. How many apples are left?
Answer:
Show working
Step 1 — total apples: 5 × 12 = 60.
Step 2 — subtract sold: 60 − 48 = 12.
12 apples left. Check: 48 + 12 = 60. ✓
33.Sam saves £8 a week for 6 weeks, then spends £15. How much money is left? Give your answer in pounds.
Answer:
Show working
Step 1 — saved: 8 × 6 = £48.
Step 2 — subtract spending: £48 − £15 = £33.
£33 left. Check: £33 + £15 = £48. ✓
34.Three coaches, each holding 52 people, are booked for a group of 140 people. How many seats are empty?
Answer:
Show working
Step 1 — total seats: 3 × 52 = 156.
Step 2 — subtract people: 156 − 140 = 16.
16 seats empty. Check: 140 + 16 = 156. ✓
35.Tickets cost £9 for adults and £5 for children. A family of 2 adults and 3 children buy tickets. What is the total cost? Give your answer in pounds.
A calculation problem (often a ‘word problem’) gives you a real situation — money, measures, time, quantities — and asks you to choose the right operations and carry them out in the right order. The numbers are usually easy; the skill is deciding what to do with them.
A reliable method is to read the question twice, underline what you are asked to find, list the steps in order, then check the answer makes sense and carries the right units (pounds, metres, minutes).
Common mistakes. Picking the wrong operation, working the steps in the wrong order, rounding too early, or giving a bare number with no units.
Common questionsWhat is a word problem in maths?
A word problem describes a real situation and asks a maths question about it. You decide which operations to use, carry them out in order, and answer with the correct units.
How do you know which operation to use?
Look at what the question asks: combining amounts suggests adding; taking away or finding a difference suggests subtracting; equal groups suggest multiplying or dividing. Underlining the key words helps.
What order do you do the steps in?
Within a single calculation, follow BIDMAS — brackets, indices, division and multiplication, then addition and subtraction. Across a problem, do the steps in the order the situation needs.
Why does my answer need units?
A number on its own can be unclear. Writing £6 or 6 cm shows what the answer measures and is usually needed for full marks.
How can I check my answer?
Estimate roughly before you start and compare; ask whether the answer is a sensible size; and re-read the question to be sure you answered what was asked.
Stuck on this topic?
A teacher can find the exact gap
Practising these calculation problems on your own is a strong start. If the same marks keep slipping, a qualified teacher can pinpoint the precise gap and fix it. Improve Tuition offers one-to-one maths tuition with our maths tutors in Batley and online — the first assessment is free.