Reasoning and Problem Solving (Year 3)
Reasoning and problem solving at Year 3 level is not a new set of facts but the skill of applying place value, addition and subtraction, and multiplication and division to multi-step, real-life word problems.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the problem through fully before starting, and note the key numbers and what is being asked for.
- Decide which operation or operations are needed: look for words like 'altogether' or 'total' (addition), 'left' or 'fewer' (subtraction), 'each' or 'groups of' (multiplication), and 'shared' or 'grouped into' (division).
- For a two-step problem, work out what the hidden first step is before you can answer the actual question, and write down the answer to that step separately.
- Choose an efficient method for each step: mental methods for easy facts, a formal written method (column addition or subtraction, known times tables) for harder ones.
- Write a full sentence answer that refers back to the question, not just a bare number, so it is clear what has been found.
- Check the answer by estimating first (rounding the numbers) or by using the inverse operation, and check it is a sensible size for the problem.
Worked example
A school buys 6 boxes of pencils. Each box has 12 pencils in it. The school already had 34 pencils. How many pencils does the school have now?
- Identify the hidden first step: work out how many pencils are in the 6 new boxes, using multiplication.
- Calculate 6 x 12 = 72 pencils in the new boxes.
- Identify the second step: add the new pencils to the pencils the school already had, using addition.
- Calculate 72 + 34 = 106.
- The school now has 106 pencils in total.
Practice questions
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Q1A baker makes 45 buns. She sells 28 of them. How many buns are left?Show answer
Answer: 17 buns
Q2There are 7 tables in a classroom, each with 4 chairs. How many chairs are there altogether?Show answer
Answer: 28 chairs
Q3A jar has 60 sweets. They are shared equally between 5 children. How many sweets does each child get?Show answer
Answer: 12 sweets
Q4Ali has 145 stickers. He gives 38 to his sister and buys 60 more. How many stickers does he have now?Show answer
Answer: 167 stickers (145 - 38 = 107, then 107 + 60 = 167)
Q5A box holds 8 eggs. How many eggs are there in 9 boxes?Show answer
Answer: 72 eggs
Q6A farmer has 120 sheep. He sells 45 and buys 30 more. How many sheep does he have now?Show answer
Answer: 105 sheep (120 - 45 = 75, then 75 + 30 = 105)
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A cinema has 9 rows of seats with 8 seats in each row. On Saturday, 59 seats are taken. How many seats are empty?
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A shop had 250 apples. On Monday it sold 86 apples. On Tuesday a delivery of 5 boxes arrived, each containing 20 apples. How many apples does the shop have at the end of Tuesday?
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A theatre has 120 seats. On Friday, 3/4 of the seats are filled. How many seats are empty?
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Free printable worksheet
Want more practice on paper? Download the reasoning and problem solving (year 3) worksheet pack - 6 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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