Reasoning and Problem Solving (Year 4)
Reasoning and Problem Solving (Year 4) is the skill of applying the four operations, including multiplication and division facts up to 12 x 12, formal written methods for addition and subtraction, and measurement facts, to multi-step, real-life word problems.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the whole problem before starting, and note down the key numbers and exactly what is being asked for.
- Decide which operations are needed, looking for clue words such as 'altogether' (addition), 'difference' or 'left' (subtraction), 'each' or 'lots of' (multiplication), and 'shared equally' (division).
- For a two-step problem, work out the hidden first step before you can answer the actual question, writing this intermediate answer down clearly.
- Choose an efficient method for each step: known times tables facts up to 12 x 12 for multiplication and division, and the formal column method for larger addition or subtraction calculations.
- Write a full sentence answer that refers back to the original question, rather than leaving just a bare number.
- Check the answer using the inverse operation, or by estimating with rounded numbers, and make sure it is a sensible size for the situation described.
Worked example
A cinema has 9 rows of seats with 11 seats in each row. 84 tickets have already been sold. How many seats are still empty?
- Identify the hidden first step: work out the total number of seats using multiplication.
- Calculate 9 x 11 = 99 seats in total.
- Identify the second step: subtract the tickets already sold from the total number of seats.
- Calculate 99 - 84 = 15.
- There are 15 empty seats.
Practice questions
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Q1A baker makes 8 trays of muffins, with 12 muffins on each tray. How many muffins does she make altogether?Show answer
Answer: 96 muffins
Q2A box of 144 pencils is shared equally between 12 classes. How many pencils does each class get?Show answer
Answer: 12 pencils
Q3Priya has 3.50 pounds. She buys a drink for 1.20 pounds and a sandwich for 1.85 pounds. How much money does she have left?Show answer
Answer: 0.45 pounds (3.50 - 1.20 - 1.85)
Q4A school has 7 classes with 28 pupils in each class. 15 pupils are away on a school trip. How many pupils are in school today?Show answer
Answer: 181 pupils (7 x 28 = 196, then 196 - 15 = 181)
Q5A carton holds 6 eggs. How many eggs are there in 9 cartons?Show answer
Answer: 54 eggs
Q6A ribbon 84 cm long is cut into pieces that are each 7 cm long. How many pieces are there?Show answer
Answer: 12 pieces
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A theatre has 8 rows with 10 seats in each row. On Saturday, 63 seats are taken. How many seats are empty?
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A shop had 180 oranges. On Monday it sold 65. On Tuesday a delivery of 4 boxes arrived, each containing 15 oranges. How many oranges does the shop have at the end of Tuesday?
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A school orders 132 exercise books, to be shared equally between 11 classes. Each class then uses 6 of its books in the first week. How many exercise books does each class have left?
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Free printable worksheet
Want more practice on paper? Download the reasoning and problem solving (year 4) 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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