math problem solving questions year 5

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Maths Problems with Answers for Grade 5

Grade 5 maths problems with answers are presented. Also Solutions and explanations are included.

• Three toy cars and 4 toy trains cost $18. Two toy cars and 3 toy trains cost $13. What is the price of one toy car and the price of one toy train if both prices are whole numbers of Dollars? (Hint: Use a table) Solution
• 450 chocolate bars
• 4 hours and 30 minutes
• 11,800 TV sets
• Tom: 22 , Bob: 27
• same time , 12 minutes
• Jim: 5 years , Carla: 10 years , Tomy: 16 years
• 10,080 minutes
• 700 meters squared
• 114 centimeters squared
• one toy car costs $2 and 1 toy train costs $3.

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Fifth Grade Math Worksheets

Free & printable grade 5 math worksheets.

Our grade 5 math worksheets cover the 4 operations, fractions and decimals at a greater level of difficulty than previous grades. We also introduce variables and expressions into our word problem worksheets .  

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18 Word Problems For Year 5: Develop Their Problem Solving Skills Across Single and Mixed KS2 Topics

Emma Johnson

Word problems for Year 5 are a great way to assess pupils’ number fluency. By the time primary school children reach Upper Key Stage 2, they will be building on their knowledge and understanding of the number system and place value, working with larger integers. An increased understanding of the connections between the different maths concepts is crucial, as children will be expected to tackle more complex, multi-step problems.

It is important children are regularly provided with the opportunity to solve a range of word problems and Year 5 maths worksheets with reasoning and problem solving incorporated alongside fluency, into all lessons.

To help you with this, we have put together a collection of 18 word problems aimed at Year 5 maths pupils.

Place value 

Addition and subtraction , multiplication and division , fractions, decimals and percentages, measurement , why are word problems important in year 5 maths, how to teach problem solving in year 5, addition word problems for year 5, subtraction word problems for year 5,  multiplication word problems for year 5, division word problems for year 5, fraction and decimal word problems in year 5, mixed four operation word problems, word problem resources.

All Kinds of Word Problems

Download this free pack of multiplication word problems to help your Year 5 class grow their problem solving skills

Year 5 maths word problems in the national curriculum

The National Curriculum states that by Year 5, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. Children also begin to use the language of algebra for solving a range of problems.

By Year 5, pupils should be starting to gain confidence in solving more complex two-step and multi-step word problems, covering topics across the Year 5 curriculum.

Solve number and practical problems involving ordering and comparing numbers to at least 1,00,000; counting forwards or backwards in steps of powers of 10; interpreting negative numbers in context and rounding to the nearest 10,100, 1000, 10,000 and 100,000.

Solve addition and subtraction word problems and a combination of these, including understanding the meaning of the equals sign.

Solve problems involving multiplication and division, including using knowledge of factors, multiples, squares and cubes and scaling by simple fractions.

Solve problems involving numbers up to 3 decimal places and problems which require knowing percentage and decimal equivalents.

Solve time word problems and those involving converting between units of time and problems involving measure (for example, length, mass, volume and money word problems ) using decimal notation and scaling.

Solve comparison, sum and difference problems, using information presented in a line graph.

Word problems are an important element of the Year 5 curriculum. By this stage, children need to be building confidence in approaching a range of one, two and multi-step word problems . They require children to be creative and apply the skills they have learnt to a range of real-life situations. 

Children need to be taught the skills for successfully approaching and tackling word problems. Reading the question carefully and identifying the key information needed to tackle the problem, is the first step, followed by identifying which calculations are required for solving it and deciding whether it will be helpful to draw a picture/ visual representation to understand and answer the question. 

Using mental maths skills to round and estimate an answer is also very helpful for children to establish whether their final answer is realistic. Children need to also be able to calculate the inverse, to be able to check their answer, once the problem has been completed.

See also: Mental maths year 5

Here is an example:

A transport museum has 1243 visitors on Monday morning and another 1387 visitors in the afternoon. On Tuesday 736 fewer visitors go to the museum than who visited on Monday.

How many visitors were there altogether on Tuesday?

How to solve:

What do you already know?

• The number of visitors on Monday morning and Monday afternoon are given separately. They need to be added together to give the total number of visitors for Monday.
• ‘Fewer’ means I will need to subtract the number of fewer visitors on Tuesday from the total number of visitors on Monday.
• Column addition and subtraction will be needed to solve this question.

How can this be drawn/represented pictorially?

We can draw a bar model to represent this problem:

• To calculate the total number of visitors on Monday, we need to add 1243 and 1387 together. 1243 + 1387 = 2630
• The number of fewer visitors on Tuesday needs to be subtracted from Monday’s total: 2630 – 736 = 1894.
• The total number of visitors on Tuesday was 1894.

In Year 5, addition word problems can involve whole numbers with over 4 digits and decimal numbers. Children should be able to round number to check the accuracy and begin to solve two step number problems 

Addition question 1

Gemma picks two cards from the cards below and adds them together.  She is able to make three different totals. What will they be?

2365     6281      9782

Answer (2 marks) : 12,147   16,063  8646

Addition question 2

Ahmed adds two of these numbers mentally.

357         280          294          232

In his calculation, he exchanges twice to create one ten and one hundred. Write Ahmed’s calculation and work out the total.

Answer (1 mark) : 357 + 294 = 651

Addition question 3

Change one digit in the calculation below, so that the answer is a multiple of 10.

Answer (1 mark) : 723 + 347 = 1070

Subtraction word problems in Year 5 require pupils to be confident subtracting numbers over 4 digits and problems involving decimal numbers. Pupils need to be able to round numbers to check accuracy and to use subtraction when solving mixed word problems. 

Subtraction question 1

A coach is travelling 4924 km across the USA It has 2476 km to go. How many kilometres has the coach already travelled?

Answer (1 mark) : 2448 km

Subtraction question 2

A primary school printed 7283 maths worksheets in the Summer term. 2156 were for Key Stage 1 pupils. How many were printed for Key Stage 2?

Answer (1 mark): 5127 worksheets

Subtraction question 3

 A clothing company made £57,605 profit in 2021 and £73,403 in 2022.  How much more profit did the company make in 2022 than in 2021?

Answer (1 mark): £15,798

In year 5, multiplication word problems include problems involving times tables and multiplying whole numbers up to 4-digits by 1 or 2-digit numbers. Pupils also need to be able to combine multiplication with other operations, in order to solve two-step word problems. 

Multiplication question 1

In this diagram, the numbers in the circles are multiplied together to make the answer in the square between them.

Complete the missing numbers.

Answer (1 mark)

Multiplication question 2

Mrs Jones was printing the end of year maths test. Each test had 18 pages and 89 pupils were sitting the test. Mrs Jones also needed to print out 12 copies for the teachers and Teaching Assistants who were helping to run the test. 

How many pieces of paper did Mrs Jones need to put in the photocopier, to make sure she had enough for all the tests?

Multiplication question 3

A school is booking a trip to Alton Towers. Tickets cost £22 per pupil. There are 120 children in each year group and all the children from 3 year groups will be going.

What will be the total price for all the tickets?

Answer (2 marks): £7920

Third Space Learning often ties word problems into our online one-to-one tutoring. Each lesson is personalised to the needs of the individual student, growing maths knowledge and problem solving skills.

In Year 5, division word problems can involve whole numbers up to 4 digits being divided by 1-digit numbers. Pupils need to understand how to answer word problems, when the answer involves a remainder.

Division question 1

Tom has 96 cubes and makes 12 equal towers. Masie has 63 cubes and makes 9 equal towers. Whose towers are tallest and by how many cubes?

Answer (2 marks): Tom

Tom’s tower has more cubes. His towers have 1 more cube than Maise’s towers.

96 ÷ 12 = 8

Division question 2

A cake factory has made cakes to deliver to a large event. 265 cakes have been baked. How many boxes of 8 cakes can be delivered to the event?

Answer (2 marks) : 33 boxes

Division question 3

Lily collected 1256 stickers. She shared them between her 8 friends. How many stickers did each friend get

Answer (1 mark): 157 stickers

In Year 5, fractions word problems and decimals can include questions involving ordering, addition and subtraction of fractions. They can also involve converting between fractions and decimals. 

Fraction and decimal question 1

Isobel collected 24 conkers. She gave \frac{1}{8} of the conkers to her brother. How many conkers did she have left?

Answer (1 mark): 21 conkers left

\frac{1}{8} of 24 = 3

24 – 4 = 21

Fraction and decimal question 2

Ahmed counted out 32 sweets. He gave \frac{1}{4} of the sweets to his brother and \frac{3}{8} of the sweets to his friend. How many sweets did he have left?

Answer (2 marks): 12 sweets

\frac{1}{4} of 32 = 8

\frac{3}{8} of 32 = 12

He gave away 20 sweets, so had 12 left for himself.

Fraction and decimal question 3

Two friends shared some pizzas, 1 ate 1 \frac{1}{2} pizzas, whilst the other ate \frac{5}{8} of a pizza. How much did they eat altogether?

Answer (1 mark): 2 \frac{1}{8} of pizza

1 \frac{1}{2} = \frac{12}{8}

\frac {12}{8} + \frac{5}{8} = \frac{17}{8} = 2 \frac{1}{8} pizzas

Problems with mixed operations, or ‘multi-step’ word problems, require two or more operations to solve them. A range of concepts can be covered within mixed problems, including the four operations, fractions, decimals and measures. These are worth more marks than some of the more straightforward, one-step problems.

Mixed operation question 1

At the cake sale, Sam buys 6 cookies and a cupcake . He pays £2.85 altogether. Naya buys 2 cookies and pays 90p altogether.

How much does the cupcake cost?

Answer (2 marks): 60p for one cupcake

Mixed operation question 2

Large biscuit tin – 48 biscuits (picture of boxes here) Small biscuit tin – 30 biscuits Ben bought 2 large tins of biscuits and 3 small tins.

How many biscuits did he buy altogether?

Answer (2 marks): 186 biscuits

2 x 48 = 96

3 x 30 = 90

96 + 90 = 186 biscuits

Mixed operation question 3

The owner of a bookshop bought a box of 15 books for £150.

He sold the books individually for £12 each. 

How much profit did he make?

Answer (2 marks)

Third Space Learning offers a wide array of maths and word problems resources for other year groups such as word problems for year 6 , word problems for year 3 and word problems for year 4 . Our word problem collection covers all four operations and other specific maths topics such as ratio word problems and percentage word problems .

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Mental Maths Practise Year 5

Welcome to the Math Salamanders Year 5 Mental Maths Practise sheets. Here you will find a wide range of Mental Maths Worksheets aimed at Year 5 children which will help your child to learn number facts and practise their number skills.

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Mental Maths Worksheets

Our selection of mental maths worksheets is a great way of practising your number and maths skills.

The sheets can be used in a variety of ways, as a test or revision practise, or as part of a weekly quiz to help reinforce skills.

They can also be used as an oral and mental starter to a lesson to get brains working!

One of the best ways to use these sheets is to get children to work in pairs, discussing the questions as they work through them.

The questions have been designed to practise a range of maths skills from number to geometry and measurement facts, including using time and money.

The quizzes are in order of difficulty with the questions getting slightly harder in each quiz.

Our Year 5 Mental Math Worksheets contain a wide range of different questions and math skills.

Each sheet contains 16 questions, and is provided with an answer sheet.

The level of difficulty gets harder as you progress through the sheets.

The topics covered include:

• mental arithmetic - addition, subtraction, multiplication and division;
• missing fact questions;
• place value questions up to 10000 including decimals;
• geometry questions based around 2d and 3d shape properties;
• money questions;
• fraction and decimal problems;
• measures problems;
• word problems;
• time questions, including date and calendar questions.

Year 5 Mental Math Worksheets

• Year 5 Mental Maths Sheet 1
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Looking for some easier Mental Math Worksheets?

The worksheets in this section have been designed for children at a Year 4 level.

The sheets follow the same format as the ones on this page, but are at a simpler level.

• Year 4 Mental Maths Tests

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The worksheets in this section have been designed for children at a Year 6 level.

The sheets follow the same format as the ones on this page, but are at a more advanced level.

• Year 6 Mental Maths Tests

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Fifth Grade Printable Math Games

Here you will find a range of free printable 5th Grade Math games.

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Year 5 maths questions

This comprehensive review of maths questions for year 5 is just the boost your child needs to succeed in maths this year.

Author Amber Watkins

Published February 2024

Key takeaways

• In year 5 maths, it is important to master multi-digit multiplication, fractions, and decimals.
• A variety of maths questions for year 5 students  can be solved using a number line.
• To supplement your child’s year 5 maths skills, consider using our maths app .

Table of contents

Multiplication

26 maths word problems for year 5​.

Year 5 maths has a strong focus on multiplication , division , and fractions . As we cover a variety of year 5 maths questions together, pay attention to the methods we use, including breaking down fractions and using number lines to solve real-world word problems. 

Answer: Sam bought 144 bottles of water. There are 12 bottles in a dozen. 12 x 12 = 144.

Answer: Mr. Rodger bought 1,600 juice boxes. 100 x 16 = 1,600.

Answer: They bought 80 total binders. 6 x 5 = 30. 10 x 5 =50. 50 + 30 = 80.

Answer: Crystal has saved a total of 350 pence. 35 x 10 =350.

Answer: Jason will have 720 new Pokemon cards after two years. There are 12 months in every year, so in two years there are 24 months (12 x 2 = 24). 24 x 30 =720.

Answer: Jack should plant 14 seeds in each row. 98 / 7 = 14.

Answer: Kim should fill Polly’s dog bowl 8 times a day.  480 / 60 = 8

Answer: The sunflower has been growing for 10 weeks. There are 100 centimetres in a metre, so there are 200 centimetres in two metres (100 x 2 =200). 200 centimetres divided by 20 is equal to 10.

Answer: Cait will have to walk her dog 50 times to save £500. 500 / 10 = 50

Answer: Jason will have 720 new baseball cards after two years. There are 12 months in every year, so in two years there are 24 months (12 x 2 = 24). 24 x 30 =720.

Answer: Yes, they ran the same distance.

Answer: Yes they completed the same portion of their homework.

Answer: 900

Answer: 6,000

Answer: 360

Answer: 500

Answer: 2,000

Answer: Jake’s grass will grow .7 millimetres in one week. .1 x 7 = .7

Answer: Jason has a total of 60 pence (.60). 0 .05 x 12 is .60.

Answer: Reese spent a total of £19.50 at the movie theater. 

£4.50 x 3 = £13.50. £3.00 x 2 = £6.00. £13.50 + £6.00 = £19.50 

Answer: Steve has £6.50 left over in his budget. £11.00 + £12.50 + £20.00 = £43.50. £50.00 – £43.50 = £6.50

Answer: Yes, he will have enough money for a £200 deposit. £52.12, £69.40, £42.80, and £35.75 added together equal £200.07.

Our maths help app provides maths help for year 5 students in a way that keeps children engaged, rewards their effort, and scaffolds their learning. Plus, the app gives parents access to a dashboard that shows their child’s progress on maths topics they struggle with. Take learning into your own hands, and check out our maths app today!

Lesson credits

Amber Watkins

Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring students in maths. "Knowing that my work in maths education makes such an impact leaves me with an indescribable feeling of pride and joy!"

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Geometry in Year 5 (age 9–10)

In Year 5, children will be expected to be able to solve problems about shapes by reasoning using their knowledge of geometric properties. This includes:

• drawing and measuring angles in degrees
• finding missing angles at a point, on a line and in rectangles
• describing translations and reflections of shapes on a four-quadrant coordinate grid.

Measurement in Year 5 (age 9–10)

In Year 5, children will be expected to be able to convert between metric units of measurement and solve problems involving decimal measurements, money and time. This includes:

• calculating the perimeter and area of shapes (including those made up of squares and rectangles)
• estimating volumes of 3D shapes and capacities of containers
• learning some imperial units, such as inches, pounds and pints.

Statistics in Year 5 (age 9–10)

In Year 5, children will interpret and present data in a range of ways. This includes:

• solving problems by comparing, adding, and subtracting using data presented in line graphs
• representing data in time graphs by using the scales on the axes to plot points
• completing, reading, and interpreting information in tables, including timetables.
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Year 5 mixed operation word problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

12 May 2020

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A range of mixed operation Maths word problems that are in line with NC targets for Year 5 but suitable across all of Key Stage Two

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