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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

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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 .

Do you have pupils who need extra support in maths? Every week Third Space Learning’s maths specialist tutors support thousands of pupils across hundreds of schools with weekly online 1-to-1 lessons and maths interventions designed to plug gaps and boost progress. Since 2013 we’ve helped over 150,000 primary and secondary school pupils become more confident, able mathematicians. Learn more or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

Subsidised one to one maths tutoring from the UK’s most affordable DfE-approved one to one tutoring provider.

Related Articles

## FREE Guide to Maths Mastery

All you need to know to successfully implement a mastery approach to mathematics in your primary school, at whatever stage of your journey.

Ideal for running staff meetings on mastery or sense checking your own approach to mastery.

## Privacy Overview

## Reasoning/Problem Solving Maths Worksheets for Year 5 (age 9-10)

Real life problem solving.

A collection of problem solving activities based on real life situations.

Some of the questions are quite long, but they can be answered with a single step operation.

Choosing sets of meals to save money with the meal deal.

Buying snacks and drinks from a vending machine.

Using bar models to help understand what to do to solve multi-step problems.

Much trickier questions as they all need more than one step to reach the right answer.

Multi-step problems with shopping.

Tricky multi-step problems on thew theme of hobbies.

Multi-step problems: using cards.

Multi-step problems: using place value charts.

Money, money, money! Lots of money questions which will need a lot of working out!

Straightforward addition of money which can be done mentally, maybe using jottings to help.

Work out the cost of the plants from the information given.

Addition of money to really stretch the brain!

Solving problems involving '3 for 2' voucher offer.

Solving money problems with 3 for 2 offers and percentages.

More percentage problems.

Tricky word problems needing more than one step to solve.

Questions all on the theme of measurement, including length, capacity and weight.

Hours, minutes seconds are all found in these questions on time.

Find the number from the clues given.

Solve multi-step problems and check by carrying out inverse operations.

Find the largest and smallest numbers and the difference between them.

Not so much the correct answer needed; more choosing the method and an explanation of how to solve the problem.

## Fractions, decimals and divisibility

Problem solving involving fractions, decimals and tests of divisibility.

Finding facts about decimal fractions, including bar modelling.

Finding facts about decimal fractions, including using bar modelling to help.

Order decimals.

Find half way between two decimals.

Word problems with decimals.

Ordering fractions.

Some tests of divisibility are easy, such as divisible by 2, 5 or 10. Others, such as divisible by 6 or 8 are much harder.

## Challenges and investigations

Further challenges, investigations and games requiring sound mathematical thinking and working in a systematic way.

Binary trees are often used in science, but here we use them to sort numbers.

More on odd and even numbers, plus a little bit on multiples.

Some great ideas for children to use as starting points to investigate further.

Find examples to back up general statements about numbers, shape etc.

Place the digits in the rows and columns to make the total shown in the middle.

A look at some of the maths concepts involved with investigations in year 5.

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## Year 5 tasks

To solve maths problems at year 5 it is very important for your child to be able to instantly recall addition and subtraction facts up to 20, and multiplication and division facts up to 10 x 10.

e-ako maths provides free online basic fact learning tools which will help your child learn their basic facts, as well as a collection of games to improve their speed and accuracy. If you think this would benefit your child, click to read how to access this resource (show instructions).

- To access e-ako maths, your child will need an account. You can make a new account for free, but check first whether they already have one that they use at school. If they do, they can use the same username and password to use e-ako maths at home.
- You can log in to e-ako maths or register a new account from the e-ako maths home page . If you are registering a new account to use at home you will need to click the "No join code? Click here." button and then "I am learning at home".

- The two large green boxes at the top are 'Learning tools' which will test the basic facts your child knows, and then help them learn the ones they don't already know.
- The blue buttons below are a collection of games designed to practise basic facts to improve speed and accuracy.
- In Year 3 your child should mostly be concentrating on learning and practising their addition and subtraction facts, the buttons on the left.

Click to read about the purpose of the tasks below (show purpose).

The tasks in this section are intended:

- for students in year 5
- to complement similar class tasks
- to be a selection only of enjoyable learning opportunities for your child (and for you)
- to generate useful explanations and discussions between you and your child.

The tasks in this section are NOT:

- intended to be comprehensive in their coverage of all maths at year 5
- drill and practice exercises to learn basic facts.

These Year 5 tasks recognise that students:

- are mostly working at early level 3 of the NZ Curriculum, growing in their understanding of number, algebra, geometry, measurement and statistics
- are all different, and some find parts of maths easier or harder than others
- are learning a range of approaches to solving problems that often involve several steps
- learn from and appreciate tasks presented in a variety of ways
- respond well to supportive questions from adults, such as, ‘What is the question asking you to do?’, or ‘What do you already know that might help you (solve the problem)?’
- enjoy exploring open tasks for which there can be a range of appropriate approaches and solutions (accordingly, set answers are not included for a number of these tasks).

We suggest that you ask your child what they are learning in maths at school, and select a task from this menu.

Click for versions with Māori content .

## Measurement

Financial literacy.

Reading & Math for K-5

- Kindergarten
- Learning numbers
- Comparing numbers
- Place Value
- Roman numerals
- Subtraction
- Multiplication
- Order of operations
- Drills & practice
- Measurement
- Factoring & prime factors
- Proportions
- Shape & geometry
- Data & graphing
- Word problems
- Children's stories
- Leveled Stories
- Context clues
- Cause & effect
- Compare & contrast
- Fact vs. fiction
- Fact vs. opinion
- Main idea & details
- Story elements
- Conclusions & inferences
- Sounds & phonics
- Words & vocabulary
- Reading comprehension
- Early writing
- Numbers & counting
- Simple math
- Social skills
- Other activities
- Dolch sight words
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- Prefixes & suffixes
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## 5th Grade Math Word Problems Worksheets

Math word problem worksheets for grade 5.

These worksheets present students with real world word problems that students can solve with grade 5 math concepts.

We encourage students to think about the problems carefully by:

- providing a number of mixed word problem worksheets
- including irrelevant data so students need to understand the context before applying a solution

## The four operations

Mixed 4 operations

Estimating and rounding word problems

## Grade 5 fractions and decimal word problems

Addition and subtraction of fractions

Addition and subtraction of mixed numbers

Division of numbers with fractional answers

Dividing by unit fractions

Multiplying fractions word problems

Mixed operations with fractions

More mixed fraction word problems

Decimals word problems

## Measurement word problems

Mass and weight word problems

Volume and capacity word problems

Length word problems

## Word problems worksheets with variables

Variables and expressions

Variables and equations

## Other grade 5 word problems worksheets

Volume of rectangular prisms

GCF / LCM word problems

Mixed grade 5 word problems

Sample Grade 5 Word Problem Worksheet

## More word problem worksheets

Explore all of our math word problem worksheets , from kindergarten through grade 5.

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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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Problem-solving maths investigations for year 5.

Hamilton provide an extensive suite of problem-solving maths investigations for Year 5 to facilitate mathematical confidence, investigative inquiry and the development of maths meta skills in 'low floor – high ceiling' activities for all.

Explore all our in-depth problem solving investigations for Year 5 .

Use problem-solving investigations within every unit to encourage children to develop and exercise their ability to reason mathematically and think creatively.

Investigations provide challenges that offer opportunities for the development of the key mathematical skills while deepening conceptual understanding. They are designed to be accessible in different ways to all children. An added bonus is the substantial amount of extra calculation practice they often incorporate! The problems are designed to help children identify patterns, to explore lines of thinking and to reason and communicate about properties of numbers, shapes and measures.

Hamilton provide a mix of our own specially commissioned investigations, that include guidance for teachers together with a child-friendly sheet to guide your pupils through the investigation, as well as links to investigations on other highly regarded websites.

I am very grateful for Hamilton Trust resources, particularly the maths investigations. Julia, teacher in Wiltshire

## You can find Hamilton's investigations for Year 5:

- Individually, they are incorporated into every unit in our Year 5 flexible maths blocks .
- Collectively, they appear on our resources page where you can explore all our in-depth problem solving investigations for Year 5 .

Do read our extensive range of advice for more information about the investigations and for tips on how to use them effectively.

Hamilton’s problem-solving investigations are 'low floor, high ceiling' activities that give all children opportunities to develop mastery and mathematical meta-skills. Explore a set for a whole year group.

Hamilton’s Problem-solving Investigations provide school-wide solutions to the challenges of building investigative skills from Early Years to Year 6.

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Math word problem worksheets for grade 5. These worksheets present students with real world word problems that students can solve with grade 5 math concepts.

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.

Hamilton provide an extensive suite of problem-solving maths investigations for Year 5 to facilitate mathematical confidence, investigative inquiry and the

Open-Ended Maths Problem Solving PowerPoint - Upper Primary. A PowerPoint with 20 open-ended problem solving questions covering a range of mathematical concepts