Problem Solving Skills Pack
The Problem Solving Skills Pack teaches the general strategies pupils need for KS2 SATs reasoning questions rather than a single area of content, including drawing a bar model to represent a word problem, breaking a multi-step problem into single-step calculations, and working backwards from a known result.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the whole question first and note down the numbers given and exactly what is being asked.
- Decide whether the problem needs just one calculation (single-step) or several calculations done in order (multi-step).
- Draw a simple bar model to show how the given quantities relate to each other, such as a whole bar split into parts, or two bars being compared.
- Choose the correct operation for each step based on the bar model or the words used, for example 'altogether' usually means add, and 'how many more' usually means subtract.
- Work through the steps in order, using the answer from one step as an input to the next step.
- If a problem gives you the final result and asks for a starting value, work backwards from the result, reversing each operation and applying them in the opposite order to how they happened.
- Check your final answer makes sense in the context of the question, for example a number of people should always be a whole number.
Worked example
Amelia has some stickers. She gives 15 to her brother and then buys 24 more. She now has 47 stickers. How many stickers did Amelia start with?
- This is a 'working backwards' problem, so start from the final amount, 47, and reverse each step in the opposite order to how it happened.
- The last thing that happened was buying 24 more, so reverse it by subtracting: 47 - 24 = 23.
- Before that, she gave away 15, so reverse it by adding: 23 + 15 = 38.
- Check by working forwards from 38: 38 - 15 = 23, then 23 + 24 = 47, which matches the given total.
- So Amelia started with 38 stickers.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A shop has 84 apples. It sells 37 in the morning and 19 in the afternoon. How many apples are left?Show answer
Answer: 28 apples (84 - 37 - 19)
Q2Tickets cost 6 pounds for adults and 4 pounds for children. A family of 2 adults and 3 children buys tickets. What is the total cost?Show answer
Answer: 24 pounds (2 x 6 + 3 x 4)
Q3A number is trebled and then 8 is subtracted. The result is 25. What was the original number?Show answer
Answer: 11 ((25 + 8) divided by 3)
Q4A bus has 52 seats. At the first stop, 18 people get on. At the second stop, 9 people get off and 14 get on. How many people are on the bus now?Show answer
Answer: 23 people (18 - 9 + 14)
Q5A recipe needs 250g of flour for every 4 people. How much flour is needed for 10 people?Show answer
Answer: 625g
Q6A charity raises 145 pounds on day 1, and 3 times as much on day 2. How much did it raise altogether over the two days?Show answer
Answer: 580 pounds (145 + 3 x 145 = 145 + 435)
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A cinema sells 3 types of ticket: adult (8 pounds), child (5 pounds) and senior (6 pounds). One evening it sells 45 adult tickets, 30 child tickets and 20 senior tickets. Work out the total amount of money taken.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
Ben thinks of a number. He doubles it, then adds 9. The result is 41. What number did Ben start with? Show your method.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
Free printable worksheet
Want more practice on paper? Download the problem solving skills pack worksheet pack - 11 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.
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