Worded Problems Set E
Worded Problems Set E is a mixed practice set that hides several arithmetic and reasoning skills (the four operations, fractions, money, and time) inside real-life worded scenarios. It is the format GL Assessment and CEM-style papers use to test whether a student can translate a story into the correct calculation, not simply whether they can calculate.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the whole question once for the story, then read it again underlining the actual numbers and what is being asked for.
- Decide what operation the words are asking for: total or altogether usually means add, difference or left means subtract, each or share often means divide, and times or lots of means multiply.
- Write the calculation as a number sentence before working it out, so a slip in the arithmetic does not also cost the method mark.
- For a multi-step problem, work out and label each intermediate answer before combining them into a final answer.
- Check the final answer makes sense in the context of the story, for example a number of people should be a whole number.
- Check units carefully, such as converting between pounds and pence, or hours and minutes, before the final step.
- If you are short of time, attempt the calculation stage even without full working, since a correct final answer can still earn marks.
Worked example
A school orders 18 boxes of pencils. Each box contains 24 pencils. The pencils are then shared equally between 8 classes. How many pencils does each class receive?
- Find the total number of pencils: 18 x 24.
- Calculate: 18 x 24 = 18 x 20 + 18 x 4 = 360 + 72 = 432.
- Share the total equally between 8 classes: 432 / 8.
- Calculate: 432 / 8 = 54.
- State the answer: each class receives 54 pencils.
Practice questions
Try each question, then tap to reveal the answer.
Q1A shop sells apples at 35p each. How much do 6 apples cost, in pounds?Show answer
Answer: 35 x 6 = 210p = £2.10.
Q2A train journey takes 2 hours 45 minutes. It departs at 09:20. What time does it arrive?Show answer
Answer: 09:20 + 2:00 = 11:20, then + 45 minutes = 12:05.
Q3A recipe needs 250g of flour to make 10 cakes. How much flour is needed for 25 cakes?Show answer
Answer: 250 / 10 = 25g per cake, so 25 x 25 = 625g.
Q4Tom has £15. He spends 2/5 of it on a book. How much money does he have left?Show answer
Answer: 2/5 of 15 = 6, so 15 - 6 = £9 left.
Q5A car park has 4 rows with 15 spaces each. If 38 spaces are full, how many are empty?Show answer
Answer: 4 x 15 = 60 total spaces, so 60 - 38 = 22 empty.
Q6Three friends share a bill of £42 equally. How much does each pay?Show answer
Answer: 42 / 3 = £14.
Q7A factory makes 150 toys a day. How many toys does it make in a 5-day working week?Show answer
Answer: 150 x 5 = 750 toys.
Q8A jug holds 1.5 litres. How many millilitres is this?Show answer
Answer: 1.5 x 1000 = 1500ml.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A cinema sells tickets for £8 for adults and £5 for children. A group buys 3 adult tickets and 4 child tickets, and pays with a £50 note. How much change do they receive?
Show mark scheme
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A charity walk covers 3/4 of a 20km route on Saturday. The rest of the route is completed on Sunday, split equally between two walkers. How many kilometres does each walker cover on Sunday?
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Tick each line you got. Your score builds from the marks on the scheme.
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Free printable worksheet
Want more practice on paper? Download the worded problems set e worksheet pack - 9 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 17 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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