## Problem Solving

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## Combination Locks - maths problem solving

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Last updated

22 February 2018

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Easy to use activity, especially for year5s

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## 20 Word Problems For Year 4: Develop Their Problem Solving Skills Across Single and Mixed KS2 Topics

Emma johnson.

Word problems for Year 4 play an important role in Year 4 maths. In Year 4, the main focus is to ensure that pupils are becoming more fluent with whole numbers and the four operations. Students work to develop efficient written methods and to be accurate with their calculations. Pupils in Year 4 are exposed to a wider range of problem-solving questions and progress from one to two-step problems.

It is important that all children are given regular opportunities to access reasoning and word problem style questions. Fluency, reasoning and problem solving should be intertwined through every lesson, with all children having the opportunity to tackle each of these question types.

## All Kinds of Word Problems Multiplication

Strengthen your students' problem solving and multiplication skills with this pack of multiplication word problems

## Place value

Addition and subtraction , multiplication and division, fractions, decimals and percentages, measurement, why are word problems important in year 4 maths, how to teach problem solving in year 4, addition word problems for year 4, subtraction word problems for year 4, multiplication word problems for year 4, division word problems for year 4, fraction and decimal word problems in year 4, time word problems in year 4, multi-step word problems in year 4., more primary word problems resources.

There can sometimes be a tendency for reasoning and problem solving questions to be treated as extension activities for only the higher attaining pupils to attempt, but children of all abilities need to be accessing them on a regular basis.

To help you with this, we have put together a collection of 20 word problems aimed at Year 4 pupils. For more Year 4 maths resources, take a look at our collection of Year 4 maths worksheets .

## Year 4 Maths Word Problems in the National Curriculum

In Year 4, pupils progress from solving one-step problems, to also being exposed to two-step problems across a range of topics, as set out in the National Curriculum.

Solve word problems involving counting in multiples of 6,7,9, 25 and 100; finding 1000 more or less than a given number; counting backwards through 0 to include negative numbers; ordering and comparing numbers beyond 1000 and rounding numbers to the nearest 10. 100 and 1000

Solve addition and subtraction word problems with up to 4 digits, including two-step word problems, deciding which operations and methods to use and why.

Solve problems involving multiplying and adding, including using the distributive law to multiply two-digit numbers by 1 digit, integer scaling problems and harder correspondence problems.

Solve problems involving increasingly harder fractions word problems to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number. Also Solve simple measure and money problems involving fractions and decimals to 2 decimal places.

Solve problems involving converting from hours to minutes, minutes to seconds, years to months, weeks to days.

Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.

Word problems are increasingly important as pupils move through Key Stage 2. As they become more confident with some of the core concepts pupils need to be applying this knowledge to a range of situations. By the end of Year 4, pupils should have memorised their multiplication tables up to and including the 12 times table and should be showing precision and fluency in their work.

Word problems in Year 4 should be fun and engaging for students. There are many ways to do this, including:

- acting out the problem;
- using manipulatives and visual images to help children understand the maths within the problem;
- use of talk partners to encourage children to discuss the question and share strategies for reaching a solution;
- using relatable problem solving situations.

Children need to be encouraged to read word problem questions carefully, to ensure they have identified the key information needed to be able to solve the problem. Pupils need to think about what they already know and how that information can help them to answer the question. They should also be encouraged to draw pictures and visual images, where appropriate, to help them to understand what the question is asking.

Here is an example:

A shop has an 8m roll of fabric.

The first customer buys 125cm of fabric and the second customer buys 3m from the same roll.

How much fabric is left on the roll, once the two customers have taken theirs?

How to solve:

What do you already know?

- The amount the first customer buys is given in cm, the amount the second customer buys is given in m. These needed to be converted to the same unit.
- Pupils in Year 4 need to be able to convert cm to m and vice versa. In this question, both the cm can be given as m or the m changed to cm to solve it.
- Once the units are the same, the two amounts need to be added together, to work out the total amount bought by the two customers.
- We can see this is a two-step question. To calculate how much fabric is left on the roll, the total amount bought by the two customers needs to be subtracted from the initial amount of fabric on the roll.

How can this be drawn/represented pictorially?

We can draw a bar model to represent this problem:

- To calculate the total amount of fabric bought, we need the units to be the same. We can either calculate in cm (300cm + 125cm = 425cm) or in m (3m + 1.25m = 4.25m)
- The amount of material bought needs to be subtracted from the original amount. This can again be solved in m or cm. Either in m: 8m – 4.25m = 3.75m or in cm: 800cm – 425cm = 375cm
- The total amount of material left is 3.75m or 375cm

In Year 4, addition word problems involve questions up to 4-digit numbers. They can include one and two-step addition and incorporate a range of concepts, such as measures and money word problems

## Addition question 1

It is 4164 miles to travel from London to Doha and 3266 miles to travel from Doha to Bangkok.

How far is it to travel from London to Bangkok, if the flight stops in Doha first?

Answer (1 mark): 7430 miles

## Addition question 2

Fill in the missing numbers in this calculation.

Answer (1 mark): 6840

## Addition question 3

On Saturday, 5486 fans attended a football game and 3748 fans attended a rugby game.

How many fans watched the two games in total?

Answer (1 mark): 9234

Subtraction word problems in Year 4, also involve numbers up to 4-digits, including both one and two-step problems, covering a range of concepts. By this stage, children should be confident in estimating and using the inverse, to check calculations.

## Subtraction question 1

3241 people visited the zoo on Saturday.

On Sunday 2876 people visited.

How many more people visited the lake on Saturday than on Sunday?

Answer (1 mark): 365

3241 – 2876 = 365

## Subtraction question 2

A teacher prints out 1242 worksheets in a term.

If 435 were maths worksheets, how many did she print out for the other subjects?

Answer (1 mark): 807

## Subtraction question 3

The temperature in Toronto dropped to minus 15 degrees celcius in December.

In July the temperature was 47 degrees celsius warmer than it was in December. What was the temperature in July?

Answer (1 mark): 32 degrees warmer

47 – 15 degrees = 32 degrees celsius

Counting on 47 degrees from minus 15 degrees = 32 degrees celsius

In Year 4, multiplication word problems can include recalling facts for times tables up to 12 x 12 and multiplying two and three-digit numbers by a 1-digit number, using formal written layout.

## Multiplication question 1

All the pupils in Year 4 complete a mental maths test.

27 pupils score 9 marks out of 10.

What is the total number of marks scored by the 27 pupils?

Answer (1 mark): 243

27 x 9 = 243

## Multiplication question 2

Year 3 and 4 children from a local primary school go on a school trip.

Six mini buses are used to transport the children.

There are 17 children on each minibus.

How many children go on the school trip?

Answer (1 mark): 102

17 x 6 = 102 children

## Multiplication question 3

Biscuits come in packs of 18.

Mrs Smith buys 8 packs for the parents at the Y4 maths workshop.

How many biscuits does she buy altogether?

Answer (1 mark): 144 biscuits

Division word problems in year 4 require pupils to be able to recall division facts for multiplication tables up to 12 x 12. Formal written method of division isn’t a requirement until Year 5 however, many schools choose to teach the formal method in Year 4. Pupils need to understand the concept of grouping and sharing and to understand the link between multiplication & division.

## Division question 1

Sam has 28 friends coming to his birthday party.

Each child will receive a cupcake, which come in packs of 4.

How many packs of cupcakes will Sam need to buy?

Answer (1 mark): 7 packs

28 ÷ 4 = 7

## Division question 2

4 children raised £96 between them on a sponsored walk.

If they split the money evenly between the four of them, how much did each pupil raise?

Answer (1 mark): £24 each

96 ÷ 4 = 24

## Division question 3

Ahmed is thinking of a number

He says, ‘when I divide my number by 12, the answer is 108.

What number was Ahmed thinking of?

Answer (1 mark): 9

108 ÷ 12 = 9

In Year 4, decimal and fraction problems involve increasingly harder fractions to calculate quantities and fractions to divide quantities, including non-unit fractions, where the answer is a whole number. Decimal word problems include measure and money problems involving fractions and decimals up to 2 decimal places.

## Fraction and decimal question 1

Jamie has 18 sweets.

He gives \frac{1}{6} of the sweets to his friend and keeps the rest himself.

How many sweets does Jamie have now?

Answer (1 mark): 15 sweets

\frac{1}{6} of 18 = 3

18 – 3 = 15

## Fraction and decimal question 2

Jaxon collected 36 conkers.

\frac{1}{4} of the conkers fell out of a hole in his bag, when he was walking home.

How many conkers did Jaxon have left, when he got home?

\frac{1}{4} of 36 = 9

36 – 9 = 37 or \frac{3}{4} of 36 = 29 (3 x 9)

## Fraction and decimal question 3

Sara ate \frac{3}{12} of a chocolate bar and gave \frac{2}{12} to her friend.

What fraction of the chocolate bar did she have left?

Answer (1 mark): \frac{7}{12}

In Year 4, time word problems include: converting from hours to minutes, minutes to seconds, years to months and weeks to days.

## Time question 1

A cake was put in the oven at 4:35pm and taken out at 4:57pm.

How long was the cake in the oven?

Answer (1 mark): 22 minutes

57-35 = 22 minutes

Using an number line:

## Time question 2

It took Evie 25 minutes to complete a page of number problems.

If she started at 2:45pm. What time did she finish?

Answer (1 mark): 3:10pm

In Year 4, children are introduced to multi-step word problems requiring up to two steps. These problems cover a range of concepts, including the four operations, fractions, decimals and measures.

Third Space Learning’s online one-to-one tutoring frequently incorporates multi-step questions to test students’ knowledge and problem solving skills. Our personalised tutoring programme works to identify gaps in students’ learning, fill those gaps, reinforce students’ knowledge and build confidence.

## Multi-step question 1

There are 6 handwriting pens in each pack.

A class has 30 children and each child needs 2 handwriting pens.

How many packs will the teacher need to buy?

Answer (2 marks): 10 packs of handwriting pens.

30 x 2 = 60

## Multi-step question 2

Sophie has £4.50.

She buy 3 books at a carboot sale, costing 50p, 65p and £1.20.

How much money does she have left?

Answer (2 marks): £2.15 left

## Multi-step question 3

Abullah is thinking of a number.

He doubles the number and adds 7.

He gets an answer of 25.

What was his original number?

Answer (2 marks): 9

Third Space Learning offers word problems for all primary year groups. Take a look at our word problems for year 3 , word problems for year 5 and word problems for year 6 . Our word problems span a range of 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.

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## 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.

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## Year 4 Maths Worksheets and Teaching Resources

Year 4 is going to bring about new mathematical challenges for children. And with the right support and resources, Year 4 maths lessons can be enjoyable as well as suitably challenging. Whether you’re a teacher of Year 4 children or a parent with a youngster in this year group, Master the Curriculum is here to help you engage your little ones in the Year 4 maths curriculum to encourage them to embrace new challenges with a smile.

Editable Worksheets

Downloadable Lesson Plans

White Rose Supporting

Reasoning Maths resources

## What Types Of Year 4 Teaching Resources Do We Offer?

## Year 4 White Rose Maths Resources: Help Children Master The Small Steps To Progression

As well as being fully aligned with the National Curriculum, our Year 4 resources are designed with White Rose Maths in mind. If you’re following the White Rose Schemes of Learning, the small steps to progression and teaching for mastery, our huge range of resources are the perfect fit, whether you’re teaching a large group or home-schooling your child.

Our worksheets, teaching slides, 10-minute activities and other resources all have clear learning objectives that match up with a White Rose small step, so you can quickly and easily find resources that are suited to your lesson plans and goals. And with our assessments and mini-assessments, you can track children’s progress through the small steps before moving on to more challenging lessons.

Our learning materials also challenge children’s reasoning, problem-solving and fluency skills so that they develop a lasting understanding of maths concepts. In doing these three types of activities, youngsters will tackle multi-step problems and apply their knowledge in different contexts, helping them to develop an even deeper understanding of the material. Check out our Supporting White Rose Maths Hub to find out more about how our resources can help you follow the White Rose Maths frameworks. The Hub has everything you need to know about how we use differentiation and harness the power of enjoyment to help youngsters master primary maths.

## Fun And Engaging Teacher-approved Resources

We’re a team of teachers who believe that fun is at the heart of education — we’ve seen first-hand just how important it is for children to enjoy learning. Enjoyment can improve children’s engagement, concentration, and learning retention. And often, the learning resources and activities used in lessons play a big role in children’s learning experiences.

But finding the right resources — ones that not only help children learn and grasp difficult concepts, but also have fun while doing so — isn’t always easy. It can be difficult and time-consuming. So we’ve created hundreds of Year 4 maths worksheets and resources that are not only educational but also fun, engaging and easily accessible. And with a Master the Curriculum membership, you’ll have instant access to all of the resources you need to complete your lesson plans or help children learn at home.

## Year 4 Maths Curriculum: What Will Children Learn?

As children go through Year 4 of primary school, they progress through more complex maths lessons and start working towards upper key stage 2. They’ll develop a deeper understanding of the four mathematical operations — addition, subtraction, multiplication and division. At the end of the academic year, they’ll sit the online multiplication tables check — a short online test.In addition to the four operations, the Year 4 maths curriculum will cover a variety of different mathematical concepts across seven key areas, helping children develop well-rounded mathematical understanding.

* Number and Place Value — Year 4 maths lessons on number and place value will help children develop their fluency with whole numbers. They will learn to count in steps of 6, 7, 9, 25 and 1000, round numbers to 10, 100 or 1000, count backwards into negative numbers, and recognise the place value of each digit in a four-digit number. * Addition and Subtraction — Working with numbers up to four digits, children will learn to add and subtract numbers both using written methods of calculation (column addition and subtraction). Children will also develop their maths reasoning skills by tackling two-step problems with different contexts — they will decide for themselves how best to approach maths problems. * Multiplication and Division — By the end of the academic year, children should have memorised their multiplication tables up to and including the 12 times table. They will also learn to multiply two-digit and three-digit numbers by single-digit numbers. At the end of the academic year, children will be tested on their understanding of multiplication tables. * Fractions — As children progress through Year 4, they’ll learn to solve problems with more difficult fractions. They will use fractions to divide quantities, create and interpret diagrams showing families of equivalent fractions, and practice adding and subtracting fractions with the same denominator. Fractions lessons will also help children count in hundredths, round decimals up and down, and divide by 10 and 100. * Geometry — Year 4 geometry has children delve deeper into the properties of shapes. They’ll learn to recognise obtuse and acute angles, lines of symmetry and different types of triangles and quadrilaterals. * Measurement — Children will build on their understanding of different measurements by learning to convert units of measurement, calculate the area and perimeters of shapes, and develop their understanding of time and amounts of money. * Statistics — During statistics lessons children will develop their understanding of data presentation by creating and interpreting charts, graphs and diagrams. Using these visual representations of data, children will solve comparison, sum and difference problems.

## How Our Year 4 Maths Worksheets And Resources Can Help

Our Year 4 maths worksheets and resources are fully aligned with the maths curriculum, so they can help children master all of the above maths topics. We help children grasp learning objectives, but our resources also help children develop a love of learning.

## Help Children Embrace and Enjoy Challenges

With engaging maths activities in the form of visual worksheets, fun interactive maths videos, flashcards and more, challenging maths problems are made approachable and even enjoyable. The right resources can take the frustration out of maths challenges, and help children get excited about tackling new topics.

## Prepare Children for the Year 4 Multiplication Test

Children in Year 4 will now sit the recently introduced multiplication tables check in June. This is an online test that will review children’s abilities to recall their times tables — a skill outlined by the UK’s Department of Education as “essential for future success in maths.”

The purpose of this test is to identify pupils who might need additional support so that all children can fully grasp their multiplication tables. By preparing children for this test, and encouraging them to do their best, you can help them consolidate their multiplication knowledge and minimise the stress of the assessment. This experience can also prepare them for future academic assessments.

With our Year 4 multiplication resources, children can build their understanding and memory of times tables. They can practice calculations with our worksheets or reasoning booklets, and even take mini-assessments at home or in the classroom.

## Plan Interesting and Engaging Lessons

Planning effective and exciting lessons is a constant challenge that teachers face. But our resources are designed to make lesson preparation simpler and easier. You can use our resources to give children hands-on learning experiences and bring your lesson plans to life. We also have weekly editable teaching slides and worksheets that can help with your lesson planning.

And with all of the resources you need in one place, finding the right resources for your class has never been easier.

## Gain Access To Hundreds Of Year 4 Maths Worksheets And Resources

If you’re ready to start downloading and printing valuable Year 4 maths worksheets and resources, all you need to do is sign up for a Master the Curriculum account. When signing up, you’ll have three options — a free membership, a year group membership or a full access membership.

With a free membership, you’ll have access to hundreds of free maths worksheets that you can download, print or view online as many times as you like. However, you’ll need to purchase premium resources individually or upgrade your membership to unlock them all.

An annual year group membership gives you access to all of the resources from a single year group of your choice. You could become a Year 4 member for just £33 for the year! Our best value membership, however, is our full access membership. This will grant you access to all of our resources across all primary year groups. This option is perfect for teachers or parents with children in different primary year groups. And this membership option costs only £49 per year.

## Browse Year 4 Resources By Topic

Quickly find the resources you need by browsing our Year 4 maths worksheets and resources by topic. Within each topic, you’ll find a wide variety of resources, from worksheets to videos, reasoning booklets, teaching slides and more, all created for specific learning objectives.

## Year 4 Resources

Maths assessments year 4.

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## Problem Solving

A selection of resources containing a wide range of open-ended tasks, practical tasks, investigations and real life problems, to support investigative work and problem solving in primary mathematics.

## Problem Solving in Primary Maths - the Session

Quality Assured Category: Mathematics Publisher: Teachers TV

In this programme shows a group of four upper Key Stage Two children working on a challenging problem; looking at the interior and exterior angles of polygons and how they relate to the number of sides. The problem requires the children to listen to each other and to work together co-operatively. The two boys and two girls are closely observed as they consider how to tackle the problem, make mistakes, get stuck and arrive at the "eureka" moment. They organise the data they collect and are then able to spot patterns and relate them to the original problem to find a formula to work out the exterior angle of any polygon. At the end of the session the children report back to Mark, explaining how they arrived at the solution, an important part of the problem solving process.

In a second video two maths experts discuss some of the challenges of teaching problem solving. This includes how and at what stage to introduce problem solving strategies and the appropriate moment to intervene when children find tasks difficult. They also discuss how problem solving in the curriculum also helps to develop life skills.

## Cards for Cubes: Problem Solving Activities for Young Children

Quality Assured Category: Mathematics Publisher: Claire Publications

This book provides a series of problem solving activities involving cubes. The tasks start simply and progress to more complicated activities so could be used for different ages within Key Stages One and Two depending on ability. The first task is a challenge to create a camel with 50 cubes that doesn't fall over. Different characters are introduced throughout the book and challenges set to create various animals, monsters and structures using different numbers of cubes. Problems are set to incorporate different areas of mathematical problem solving they are: using maths, number, algebra and measure.

## Problem solving with EYFS, Key Stage One and Key Stage Two children

Quality Assured Category: Computing Publisher: Department for Education

These three resources, from the National Strategies, focus on solving problems.

Logic problems and puzzles identifies the strategies children may use and the learning approaches teachers can plan to teach problem solving. There are two lessons for each age group.

Finding all possibilities focuses on one particular strategy, finding all possibilities. Other resources that would enhance the problem solving process are listed, these include practical apparatus, the use of ICT and in particular Interactive Teaching Programs .

Finding rules and describing patterns focuses on problems that fall into the category 'patterns and relationships'. There are seven activities across the year groups. Each activity includes objectives, learning outcomes, resources, vocabulary and prior knowledge required. Each lesson is structured with a main teaching activity, drawing together and a plenary, including probing questions.

## Primary mathematics classroom resources

Quality Assured Collection Category: Mathematics Publisher: Association of Teachers of Mathematics

This selection of 5 resources is a mixture of problem-solving tasks, open-ended tasks, games and puzzles designed to develop students' understanding and application of mathematics.

Thinking for Ourselves: These activities, from the Association of Teachers of Mathematics (ATM) publication 'Thinking for Ourselves’, provide a variety of contexts in which students are encouraged to think for themselves. Activity 1: In the bag – More or less requires students to record how many more or less cubes in total...

8 Days a Week: The resource consists of eight questions, one for each day of the week and one extra. The questions explore odd numbers, sequences, prime numbers, fractions, multiplication and division.

Number Picnic: The problems make ideal starter activities

Matchstick Problems: Contains two activities concentrating upon the process of counting and spotting patterns. Uses id eas about the properties of number and the use of knowledge and reasoning to work out the rules.

Colours: Use logic, thinking skills and organisational skills to decide which information is useful and which is irrelevant in order to find the solution.

## GAIM Activities: Practical Problems

Quality Assured Category: Mathematics Publisher: Nelson Thornes

Designed for secondary learners, but could also be used to enrich the learning of upper primary children, looking for a challenge. These are open-ended tasks encourage children to apply and develop mathematical knowledge, skills and understanding and to integrate these in order to make decisions and draw conclusions.

Examples include:

*Every Second Counts - Using transport timetables, maps and knowledge of speeds to plan a route leading as far away from school as possible in one hour.

*Beach Guest House - Booking guests into appropriate rooms in a hotel.

*Cemetery Maths - Collecting relevant data from a visit to a local graveyard or a cemetery for testing a hypothesis.

*Design a Table - Involving diagrams, measurements, scale.

## Go Further with Investigations

Quality Assured Category: Mathematics Publisher: Collins Educational

A collection of 40 investigations designed for use with the whole class or smaller groups. It is aimed at upper KS2 but some activities may be adapted for use with more able children in lower KS2. It covers different curriculum areas of mathematics.

## Starting Investigations

The forty student investigations in this book are non-sequential and focus mainly on the mathematical topics of addition, subtraction, number, shape and colour patterns, and money.

The apparatus required for each investigation is given on the student sheets and generally include items such as dice, counters, number cards and rods. The sheets are written using as few words as possible in order to enable students to begin working with the minimum of reading.

## NRICH Primary Activities

Explore the NRICH primary tasks which aim to enrich the mathematical experiences of all learners. Lots of whole class open ended investigations and problem solving tasks. These tasks really get children thinking!

## Mathematical reasoning: activities for developing thinking skills

Quality Assured Category: Mathematics Publisher: SMILE

## Problem Solving 2

Reasoning about numbers, with challenges and simplifications.

Quality Assured Category: Mathematics Publisher: Department for Education

## IMAGES

## VIDEO

## COMMENTS

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A selection of resources containing a wide range of open-ended tasks, practical tasks, investigations and real life problems, to support investigative work and