problem solving task ks2

• STEM Ambassadors
• School trusts
• ITE and governors
• Invest in schools
• Student programmes
• Benefits and impact
• Our supporters
• Advertising and sponsorship
• Become a STEM Ambassador
• Request a STEM Ambassador
• Employer information
• Training and support
• STEM Ambassadors Partners
• Working with community groups
• Search icon
• Join the STEM Community

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

• Topmarks Search
• Whiteboard Resources
• Learning Games
• Topmarks Apps
• Topmarks Blog

• 11-16 Years

Play these fun Maths Games for 7-11 year olds

Choose a category:, problem solving games.

Bead Numbers - Place Value

Bead Numbers is a place value investigation involving a tens and ones abacus. The game provides a good context for encouraging learners to think systematically.

Thinking of a Number

Guess the number by revealing the clues on the clouds one by one. Children will need knowledge of rounding, odd and even and tens and ones.

Tables Teaser

Can you work out which number goes in each row and column heading to make the interactive tables grid work? It is quite a challenge!

Mystic Numbers

Solve the number puzzles and collect the treasures.

Or search by topic

Number and algebra.

• Place value and the number system
• Fractions, decimals, percentages, ratio and proportion
• Calculations and numerical methods
• Algebraic expressions, equations and formulae
• Coordinates, functions and graphs
• Patterns, sequences and structure
• Properties of numbers

Geometry and measure

• 3D geometry, shape and space
• Transformations and constructions
• Vectors and matrices
• Measuring and calculating with units
• Pythagoras and trigonometry
• Angles, polygons, and geometrical proof

Probability and statistics

• Handling, processing and representing data
• Probability (spec_group)

Working mathematically

• Thinking mathematically
• Mathematical mindsets

Advanced mathematics

• Decision mathematics and combinatorics
• Advanced probability and statistics

For younger learners

• Early years foundation stage

Multiplication and Division KS2

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

One Wasn't Square

All the Digits

Cycling squares.

Multiplication Square Jigsaw

Shape Times Shape

What Do you Need?

How do you do it?

Table patterns go wild!

Journeys in Numberland

Ordering cards

Let us divide!

• Teach Early Years
• Teach Primary
• Teach Secondary

• New for Schools

Home > Learning Resources

KS1 and KS2 Maths – Problem solving

• Author: Mike Askew
• Main Subject: CPD
• Subject: Maths
• Date Posted: 20 June 2012

Share this:

If children use well worn techniques to solve problems without understanding or modelling the context, their maths skills won't fully evolve

Children, from birth, are proficient problem solvers. By the age of two or three they have solved what are probably life’s two biggest problems - how to walk and how to talk. As they get older they solve practical problems, such as sharing a bag of sweets fairly with others, long before they’ve heard of division. In this article, I look at how we can build on this natural propensity to solve problems in teaching mathematics.

Routine and non-routine problems

Routine problems are problems children know how to solve based on their previous experiences. The sort of thinking required by routine problems can be described as reproductive: the child only needs to recall or reproduce a procedure or method they have previously learnt. A problem like ‘Apples’, for example (see below), is likely to be a routine problem for most children at the upper end of primary school; they know to multiply the two numbers together without having to think deeply about what operation to use.

• Apples on a supermarket shelf are in bags of eight. • If Jane buys six bags, how many apples is that?

In contrast, non-routine problems are where the learner does not immediately have a solution tucked under his belt. The problem solver has to put some effort into understanding the problem and creating, rather than recalling, a solution strategy. Non-routine problems engage learners in productive thinking.

We often think of non-routine problems as needing to be unusual or not having, to us as adults, an immediately obvious method of solution. ‘Stamps’ is typical of this type of non-routine problem.

• Clearing out a desk draw I found a collection of 5p and 6p stamps. • I have a parcel to post that needs 58p worth of stamps on it. • Can I create this exactly using the stamps I found? • If so, is there more than one way of doing this?

In choosing problems to work with, we need to decide whether or not we think a problem will be routine or non-routine for the particular children working on it. In the rest of this article, the problems chosen are being treated as though they are non-routine problems for the children working on them. That’s not to say that I don’t think routine problems have a place in the curriculum - they do. Here, however, I want to deal with some of the issues around teaching and learning non-routine problems.

The importance of context

• Four hungry girls share three pizzas equally. • Eight hungry boys share six pizzas equally. • Does each girl get more pizza than each boy, less or the same?

As a routine problem, the ‘story’ of pizzas and hungry children doesn’t serve any real purpose: children quickly learn to disregard the context, to strip out the mathematics and to work some procedure. The problem could just as easily have been put in the context of builders sharing bricks and many learners would happily say each builder would get 3/4 of a brick, without stopping to question the near impossibility of sharing out bricks.

We can, however, treat ‘Pizzas’ as a non-routine problem and use it to introduce children to thinking about fractions and equivalences. The context of hungry children and pizzas then becomes important. It is not chosen simply to be window-dressing for a fraction calculation. Nor are pizzas chosen because children are intrinsically motivated by food, making the unpalatable topic of fractions digestible. No, the context s chosen because children know about fair shares and slicing up pizzas - they can solve this problem without any formal knowledge of fractions. As the researcher Terezhina Nunes once pointed out, young children would not be able to solve the ‘bald’ calculation 3 divided by 4 but, “show me four young children who, given three bars of chocolate to share out fairly, hand the bars back saying ‘it can’t be done.”

Children have ‘action schemas’ for solving problem like ‘Pizzas’ - they can find ways to solve this with objects, pictures, diagrams and, eventually, symbols. Teaching can then build on the children’s informal solutions to draw out the formal mathematics of fractions. From being one of 20 ‘problems’ on a worksheet to complete in a lesson, ‘Pizzas’ can become a ‘rich task’ taking up the best part of a lesson, if children work on it in pairs and carefully selected solutions are then shared with the class.

Creating mathematical models

Part of the productive thinking in working on rich, non-routine problems requires children to create mathematical models, and we can teach to support this.

• At the supermarket Myprice, milk costs £1.08 per litre. • This is 7 pence less per litre than milk costs at Locost. • How much does 5 litres of milk cost at Locost?

What is missing from this approach is attention to setting up an appropriate model of the problem. Ultimately this could be a mental model of the problem context, but it helps initially to encourage children to put something on paper that can be shared and discussed. In problems involving quantities, like ‘Milk’, simple bar diagrams can help children create the appropriate model. These help children examine the relationships between the quantities (as opposed to simply fixing on specific numbers and keywords).

Setting up a diagrammatic model begins with creating a representation of what is known in the situation. In this example, we know milk at Myprice costs £1.08, so a diagram for this would look like:

MYPRICE £1.08

This provides the basis for talking about what the picture for the price of milk at Locost is going to be. Will the bar be longer or shorter? Where is the bar for the 7 pence to be drawn?

Two different models can be set up and children asked to describe the relationship between the prices at the two supermarkets, to see which diagram fits with the information in the problem. If the diagram for the price at Locost is shorter by 7, then two statements can be made:

MYPRICE £1.08p LOCOST     7p

• Myprice milk costs 7 pence more than milk at Locost.

• Locost milk costs 7 pence less than milk at Myprice.

In comparison, making the bar for milk at Locost longer by 7 gives different comparative statements:

MYPRICE £1.08p 7p LOCOST    

• Myprice milk costs 7 pence less than milk at Locost.

• Locost milk costs 7 pence more than milk at Myprice.

Children can then talk about which of these situations fits with the wording in the problem.

Having established that Locost milk must be £1.15 a litre, children can go on to produce the bar diagram model for this.

Supporting non-routine problem solving

Where the problems were played out as non-routine, three factors identified are worth noting. First, in choosing the tasks, the teachers made sure they would build on learners’ prior knowledge - as I suggest a problem like ‘Pizzas’ can. Second, in contrast to focusing on getting the answer, the researchers observed what they called ‘sustained pressure for explanation and meaning’. In other words, the teachers pressed for children to explain what and why they were doing what they were doing rather than simply focusing on whether or not they had got the correct answer. Third, the amount of time children were allowed to work on the problem was neither too long or too short: children need enough time to ‘get into’ a problem, but too much time can lead to a loss of engagement.

Share good practice

Gather together a collection of problems covering all the years of education in your school (or ask teachers to each contribute two or three problems).

Working together in small groups, teachers sort the problems into three groups:

1. Problems they think would be routine for the children they teach 2. Problems they think would be non-routine for their children 3. Problems they think would be much too difficult for their age group

Everyone agrees to try out a problem from group 2 with their class. Discuss how too much focus on getting the answer can reduce the challenge and stress the importance of pressing children to explain their working. At a subsequent meeting, people report back, focusing in particular on strategies they used to keep the problem solving non-routine.

About the author

Mike Askew is Professor of Primary Education at Monash University, Melbourne. Until recently, he was Professor of Mathematics Education at King’s College, University and Director of BEAM.

You may also be interested in...

• Download your free digital copy of the brand new January issue of Teach Primary now
• Teach Primary Awards 2019 Finalists Announced
• Oxford University Press celebrate double victory
• Free resources for teaching film in primary schools
• National Curriculum Key Stage 2 assessments reveal increased attainment in primaries

Subscribe to Our Newsletter

I agree to the Terms & Conditions and Privacy & Cookies Policy.

Tried & Tested

Power Maths – A Child-Centred, ‘Can-Do’ Mastery Teaching Programme for KS1 and KS2

Category: Maths

Fit To Dance Schools From Disney On Ice

Category: Other

‘S!ng Sensational’ And ‘A King Is Born’ – Two Fun New Musical Masterpieces That Children Will Love

Category: Music

Product review: Schofield & Sims Fractions, Decimals & Percentages

See all Tried & Tested products

Recommended for you...

Use coaching to turn failures into learning success

Ace-Classroom-Support

How to be a singing school

Why Boarding School Fiction Feels Comfortably Familiar

Powerful Questions Can Help Children Remember Key Maths Concepts

Follow us on Twitter @teachprimary :

Share teach primary:.

Home | Tried & Tested | Interactive | Book Reviews | Resources | News | Hot Products | Advertising Contact Us | Primary Resources | Primary Teaching Resources | Privacy Policy

Copyright 2024 Artichoke Media Ltd

Registered in England and Wales No 14769147 | Registered Office Address: Jubilee House, 92 Lincoln Road, Peterborough, PE1 2SN

Cookie Consent

We use cookies to help provide a better website experience for you, and help us to understand how people use our website. Our partners will also collect data and use cookies for ad personalisation and measurement.

Clicking "Accept" will allow us and our partners to use cookies, learn more in our cookie policy or to change your cookie preferences, click "Manage".

To find out more about cookies and the types of cookies we are setting please visit our cookie policy .

If you'd prefer that certain types of cookie are not saved on your browser when visiting our website, use the toggles below to adjust those preferences and click "Save choices".

Strictly Necessary

These cookies are necessary for the website to function and without them you would not be able to reliably use the website. For example, logging into your account or completing forms.

Analytics Cookies

A series of cookies that collect anonymised data on how users interact with our website. This anonymous data helps us improve the website with a focus on its users, for example, ensuring the most popular content is easier to access.

View associated providers +

Marketing Cookies

These cookies track your online activity to help advertisers deliver more relevant and personalised advertising or to limit how many times you see an ad. These cookies can share that information with other organisations or advertisers.

Mastery-Aligned Maths Tutoring

“The best thing has been the increase in confidence and tutors being there to deal with any misunderstandings straight away."

FREE daily maths challenges

A new KS2 maths challenge every day. Perfect as lesson starters - no prep required!

25 Fun Maths Problems For KS2 And KS3 (From Easy To Very Hard!)

Fun maths problems are one of the things mathematicians love about the subject; they provide an opportunity to apply mathematical knowledge, logic and problem solving skills all at once.  In this article, we’ve compiled 25 fun maths problems, each covering various topics and question types. They’re aimed at students in KS2 & KS3. We’ve categorised them as:

Maths word problems

Maths puzzles, fraction problems, multiplication and division problems, geometry problems, problem solving questions, maths puzzles are everywhere, how should teachers use these maths problems.

Teachers could make use of these maths problem solving questions in a number of ways, such as:

• embed into a relevant maths topic’s teaching.
• settling tasks at the beginning of lessons.
• break up or extend a maths worksheet.
• keep students thinking mathematically after the main lesson has finished.

Some are based on real life or historical maths problems, and some include ‘bonus’ maths questions to help to extend the problem solving fun! As you read through these problems, think about how you could adjust them to be relevant to your students or to practise different skills. 

These maths problems can also be used as introductory puzzles for maths games such as those introduced at the following links:

• KS2 maths games
• KS3 maths games

Need more support teaching reasoning, problem solving and planning for depth ? Read here for free CPD for you and your team of teachers.

1. Home on time – easy

Type: Time, Number, Addition

A cinema screening starts at 14:35. The movie lasts for 2 hours, 32 minutes after 23 minutes of adverts. It took 20 minutes to get to the cinema. What time should you tell your family that you’ll be home?

Answer: 17:50

2. A nugget of truth – mixed

Type: Times Tables, Multiplication, Multiples, Factors, Problem Solving 

Chicken nuggets come in boxes of 6, 9 or 20, so you can’t order 7 chicken nuggets. How many other impossible quantities can you find (not including fractions or decimals)?

Answer: 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 22, 23, 25, 28, 31, 34, 37, or 43

There is actually a theorem which can be used to prove that every integer quantity greater than 43 can be ordered.

3. A pet problem – mixed

Type: Number, Problem Solving, Forming and Solving Equations, Simultaneous Equations, Algebra

Eight of my pets aren’t dogs, five aren’t rabbits, and seven aren’t cats. How many pets do I have?

Answer: 10 pets (5 rabbits, 3 cats, 2 dogs)

4. The price of things – mixed

Type: lateral thinking problem

A mouse costs £10, a bee costs £15, and a spider costs £20. How much does a duck cost? Answer: £5 (£2.50 per leg)

Looking for more word problems, solutions and explanations? Read our article on word problems for primary school.

25 Fun Maths Problems - Printable

Download a printable version of these fun maths problems together with answers and mark scheme.

5. A dicey maths challenge – easy

Type: Place value, number, addition, problem solving

Roll three dice to generate three place value digits. What’s the biggest number you can make out of these digits? What’s the smallest number you can make?

Add these two numbers together. What do you get?

Answer: In most cases, 1,089.

Bonus: Who got a different result? Why?

6. PIN problem solving – mixed

Type: Logic, problem solving, reasoning

I’ve forgotten my PIN. Six incorrect attempts locks my account: I’ve used five! Two digits are displayed after each unsuccessful attempt: “2, 0” means 2 digits from that guess are in the PIN, but 0 are in the right place.

What should my sixth attempt be?

Answer: 6347

7. So many birds – mixed

Type: Triangular Numbers, Sequences, Number, Problem Solving

On the first day of Christmas my true love gave me one gift. On the second day they gave me another pair of gifts plus a copy of what they gave me on day one. On day 3, they gave me three new gifts, plus another copy of everything they’d already given me. If they keep this up, how many gifts will I have after twelve days?

Answer: 364

Bonus: This could be calculated as 1 + (1 + 2) + (1 + 2 + 3) + … but is there an easier way? What percentage of my gifts do I receive on each day?

8. I 8 sum maths questions – mixed

Type: Number, Place Value, Addition, Problem Solving, Reasoning

Using only addition and the digit 8, can you make 1,000? You can put 8s together to make 88, for example.

Answer: 888 + 88 + 8 + 8 + 8 = 1,000 Bonus: Which other digits allow you to get 1,000 in this way?

9. Quizzical – easy

Type: Fractions, Adding Fractions, Equivalent Fractions, Fractions to Percentages

4 friends entered a maths quiz. One answered \frac{1}{5} of the maths questions, one answered \frac{1}{10} , one answered \frac{1}{4} , and the other answered \frac{4}{25} . What percentage of the questions did they answer altogether?

Answer: 71%

10. Ancient problem solving – mixed

Type: Fractions, Reasoning, Problem Solving

Ancient Egyptians only used unit fractions (like \frac{1}{2} , \frac{1}{3} or \frac{1}{4} ). For \frac{2}{3} , they’d write \frac{1}{3} + \frac{1}{3} . How might they write \frac{5}{8} ?

Answer: \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8} is correct. So is \frac{1}{2} + \frac{1}{8} .

Bonus: Which solution is better? Why? Can you find any more? What if subtractions are allowed?

Learn more about unit fractions here

11. everybody wants a pizza the action – hard.

An infinite number of mathematicians buy pizza. The first wants \frac{1}{2} pizza. The second wants \frac{1}{4} pizza. The third & fourth want \frac{1}{8} and \frac{1}{16} each, and so on. How many pizzas should they order?

Answer: 1 Each successive mathematician wants a slice that is exactly half of what is left:

12. Shade it black – hard

Type: Fractions, Reasoning, Problem Solving What fraction of this image is shaded black?

Answer: \frac{1}{3}

Look at the L-shaped part made up of two white and one black squares: \frac{1}{3} of this part is shaded. Zoom in on the top-right quarter of the image, which looks exactly the same as the whole image, and use the same reasoning to find what fraction of its L-shaped portion is shaded. Imagine zooming in to do the same thing again and again…

13. Giving is receiving – easy

Type: Number, Reasoning, Problem Solving

5 people give each other a present. How many presents are given altogether?

14. Sharing is caring – mixed

I have 20 sweets. If I share them equally with my friends, there are 2 left over. If one more person joins us, there are 6 sweets left. How many friends am I with?

Answer: 6 people altogether (so 5 friends!)

15. Times tables secrets – mixed

Type: Area, 2D Shape, Rectangles

Here are 77 letters:

BYHRCGNGNEOEAAHGHGCURPUTSTSASHHSBOBOREOPEEMEMEELATPEPEFADPHLTLTUT IEEOHOHLENRYTITIIAGBMTNTNFCGEIIGIG

How many different rectangular grids could you arrange all 77 letters into?

Answer: Four: 1⨉77, 77⨉1, 11⨉7 & 7⨉11. If the letters are arranged into one of these, a message appears, reading down each column starting from the top left.

Bonus: Can you find any more integers with the same number of factors as 77? What do you notice about these factors (think about prime numbers)? Can you use this system to hide your own messages?

16. Laugh it up – hard

Type: Multiples, Lowest Common Multiple, Times Tables, Division, Time

One friend jumps every \frac{1}{3} of a minute. Another jumps every 31 seconds. When will they jump together? Answer: After 620 seconds

17. Pictures of matchstick triangles – easy

Type: 2D Shapes, Equilateral Triangles, Problem Solving, Reasoning

Look at the matchsticks arranged below. How many equilateral triangles are there?

Answer: 13 (9 small, 3 medium, 1 large)

Bonus: What if the biggest triangle only had two matchsticks on each side? What if it had four?

18. Dissecting squares – mixed

Type: Reasoning, Problem Solving

What’s the smallest number of straight lines you could draw on this grid such that each square has a line going through it?

19. Make it right – mixed

Type: Pythagoras’ theorem

This triangle does not agree with Pythagoras’ theorem. 

Adding, subtracting, multiplying or dividing each of the side lengths by the same integer can fix it. What is the integer?

Answer: 3 

8 – 3 = 5

The new side lengths are 3, 4 and 5 and  32 + 42 = 52.

20. A most regular maths question – hard

Type: Polygons, 2D Shapes, tessellation, reasoning, problem-solving, patterns

What is the regular polygon with the largest number of sides that will self-tessellate?

Answer: Hexagon.

Regular polygons tessellate if one interior angle is a factor of 360°. The interior angle of a hexagon is 120°. This is the largest factor less than 180°.

21. Pleased to meet you – easy

Type: Number Problem, Reasoning, Problem-Solving

5 people meet; each shakes everyone else’s hand once. How many handshakes take place?

Person A shakes 4 people’s hands. Person B has already shaken Person A’s hand, so only needs to shake 3 more, and so on.

Bonus: How many handshakes would there be if you did this with your class?

22. All relative – easy

Type: Number, Reasoning, Problem-Solving

When I was twelve my brother was half my age. I’m 40 now, so how old is he?

23. It’s about time – mixed

Type: Time, Reasoning, Problem-Solving

When is “8 + 10 = 6” true?

Answer: When you’re telling the time (8am + 10 hours = 6pm)

24. More than a match – mixed

Type: Reasoning, Problem-Solving, Roman Numerals, Numerical Notation

Here are three matches:

How can you add two more matches, but get eight? Answer: Put the extra two matches in a V shape to make 8 in Roman Numerals:

25. Leonhard’s graph – hard

Type: Reasoning, Problem-Solving, Logic

Leonhard’s town has seven bridges as shown below. Can you find a route around the town that crosses every bridge exactly once?

Answer: No!

This is a classic real life historical maths problem solved by mathematician Leonhard Euler (rhymes with “boiler”). The city was Konigsberg in Prussia (now Kaliningrad, Russia). Not being able to find a solution is different to proving that there aren’t any! Euler managed to do this in 1736, practically inventing graph theory in the process.

Many of these 25 maths problems are rooted in real life, from everyday occurrences to historical events. Others are just questions that might arise if you say “what if…?”. The point is that although there are many lists of such problem solving maths questions that you can make use of, with a little bit of experience and inspiration you could create your own on almost any topic – and so could your students. 

For a kick-starter on creating your own maths problems, read our article on KS3 maths problem solving .

Looking for additional support and resources at KS3? You are welcome to download any of the secondary maths resources from Third Space Learning’s resource library for free. There is a section devoted to GCSE maths revision with plenty of maths worksheets and GCSE maths questions . There are also maths tests for KS3, including a Year 7 maths test , a Year 8 maths test and a Year 9 maths test For children who need more support, our maths intervention programmes for KS3 achieve outstanding results through a personalised one to one tuition approach.

DO YOU HAVE STUDENTS WHO NEED MORE SUPPORT IN MATHS?

Every week Third Space Learning’s specialist online maths tutors support thousands of students across hundreds of schools with weekly online 1 to 1 maths lessons designed to plug gaps and boost progress.

Since 2013 these personalised one to 1 lessons have helped over 169,000 primary and secondary students become more confident, able mathematicians.

Learn how the programmes are aligned to maths mastery teaching or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

Related articles

Maths Problem Solving: Engaging Your Students And Strengthening Their Mathematical Skills

Free Year 7 Maths Test With Answers And Mark Scheme: Mixed Topic Questions

What Is A Number Square? Explained For Primary School Teachers, Parents & Pupils

What Is Numicon? Explained For Primary School Teachers, Parents And Pupils

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

Play of the Wild

Education is an admirable thing, but it is well to remember from time to time that nothing that is worth knowing can be taught. -Oscar Wilde

Outdoor Problem Solving Activities KS2- Learning Maths

Outdoor Problem Solving Activities KS2 – Learning Maths Outdoors

These are some ideas for outdoor problem solving activities for KS2 to help children with learning maths outdoors. One of the most critical aspects of teaching and learning maths is to be able to solve problems. While teaching maths in school, I found that it can become easy to get overly focused on teaching the rules and procedures for doing maths. These are essential tools that everyone needs, but the actual point is to be able to apply those skills in real life. Therefore, children must be given opportunities to practice problem-solving and make it purposeful.

I hope you find these outdoor problem solving activities for KS2 useful, and perhaps they will also inspire you to try other ideas. If you would like some other ways to take learning maths outdoors, you may also want to see my post, Outdoor Maths Activities KS2 .

Nim is a mathematical strategy game where two players take turns removing objects from a pile. Each player must take at least one object per turn. The goal is to either take or avoid taking the last item from the stack. Children can play nim with a pile of sticks or rocks.

Ordering natural objects by different features

Children can place in order objects such as rocks or pinecones based on the characteristic(s) they decide upon. It might be longest to shortest, least to the greatest circumference or smallest to greatest volume.

Observing the sun & moon

Children can explore and investigate the sun and moon, including changes that take place over time. They can try to figure out some of the following questions, and ask some of their own questions as well.

• What time does the sun set and rise? Does this ever change? How do you know?
• Where on the horizon do you first/last see the sun or the moon? Does this change? How do you know?
• Can you observe the phases of the moon- how does it change? Are there any patterns that you notice?

Measuring circles

Children can measure circles (such as flower pots, tree stumps or other circular objects found outside). They can measure the circumference, radius and diameter and then investigate the relationship between radius/diameter and circumference. What do children notice? Is there a pattern? They may even be able to ‘discover’ pi.

How tall is a tree?

Measure / calculate the height of a tree with the shadow & calculation method, triangle method and/or clinometer method.  If children try more than one method, do they get the same results?  Which method might be more accurate?

(ex. Estimating by height, clinometer method, looking through legs method, pencil method, meter stick method)

Different ways children can help with planning in a garden

Children can figure out how much space is available in the garden and how many different types of plants can be planted. Can they figure out how many of one kind of plant will fit into one planter box? Can they figure out how many different sized plants fit into the same planter box? Children would need to use their measuring skills to calculate the surface area of the garden. Then they would need to find out how much space each plant requires (e.g. from seed packets) and then determine how many and which of the plants can be used.

If a new planter box is purchased, children can help work out how many bags of compost would be needed to fill it. (They would need to measure, calculate the size, etc.) Will there be any leftover soil from one of the bags? How do you know?

If children grow crops such as pumpkins, they can do things like ordering them from heaviest to lightest. This way they might see which is the ‘prize-winning pumpkin’ in a harvest festival.

They might also consider how much each pumpkin could be sold for.  This would involve calculating each pumpkin’s cost, based on a price of £1.00 per kilo, £2.00 per kilo (or whatever reasonable price is determined). They might also try to figure out if larger pumpkins (or other crops like corn) always weigh more than smaller ones? *The children will have to define what is the larger, longer, or wider circumference.

Children could get involved with selling the crops they grow.  This will give them plenty of opportunities to use mathematical skills and handle money in real-life contexts. They will also need to plan the pricing of different vegetables based on weight, the number of vegetables, or selling them in combinations. Children could even try to figure out the appropriate amount to charge for each crop based on the cost of the seeds, the growing time, grocery store costs or any other factors.

If they do sell some of what they grow after school or possibly at a market, then the children can apply their maths skills to figure out how much each customer will need to pay when buying any particular fruit or vegetable.  

Monitoring Plant Growth

See if children can figure out how quickly different plants grow. Can they determine the rate of growth (e.g. mm per week)? Which seedlings / plants grow fastest? Is it a steady rate of growth, or does it change?

*To take this further, children might also conduct an experiment to compare different groups. They might compare the growth or the growth rate of plants whose seeds have been frozen vs those that have not, or something else.  

Making Shapes

How many shapes can you make (including shapes within shapes) using a set number of sticks (ex. 6 large sticks and 6 small sticks)? Is there a way to make more or fewer shapes using the same number of sticks?

Planning and holding a bake sale

(Some parts of this activity take place inside and some outside. This activity can be linked further to learning maths outdoors if children use some ingredients grown from a school garden).

Baking for a bake sale is a great way to give children hands-on practice solving problems in real contexts. For a baking project they will need to follow recipes and accurately use measuring cups and weighing scales. They might also want to make larger quantities and scale up recipes by doubling, tripling, or quadrupling them. The children will need to plan ahead and calculate how much of each ingredient they need to buy to make a set number of cookies, cupcakes, etc. They must also determine how many batches would be needed to make 200 cupcakes if the recipe makes 2 dozen.

Then when they hold an actual sale they will be using their maths skills to calculate how much to charge people.  They must also learn how to give people the proper change (just like selling vegetables above). They can setup a stall outside of school and sell them after school one day. 

Organizing and running a track & field event

Children can get involved in organizing a sports day or track and field event. They can first decide which events to include and then figure out how much space is needed for each activity (e.g. measuring the appropriate length and width required). The children can then help measure and set up the activities.

Once races are held, that data can be used to make calculations. For example – for a jumping event, children can measure how far people jump, and after several tries, figure out if there is improvement and how much (finding the difference). Children can time how far it takes them to run certain distances, e.g. 500 meters versus ½ a mile. They can figure out how fast they are running. They might then calculate how fast they ran different races (e.g. miles per hour) and then figure out when they ran faster or slower.  

Finding ways to approximate measurements

See if children can find different ways to measure the approximate distance between two far points with a meter stick and string. This might be the length of the playground or the distance between two trees, etc. Children might compare different ways of measuring the approximate distance such as measuring the length it takes them to take one step and then counting the number of steps between two points. They might also use the string to go between the two points and measure the string’s length. See if they can find any other ways to find the approximate distances.

I hope that you find these outdoor problem solving activities for KS2 helpful and it helps you take teaching and learning maths outdoors!

Arithmetic , Gardening , Geometry , Maths , Measurement , Number & Place Value , School Age , Sticks

hands-on learning , Learning Outdoors , learning outside , outdoor learning , Sticks

One thought on “ Outdoor Problem Solving Activities KS2- Learning Maths ” Leave a comment ›

• Pingback: Outdoor Maths Activities KS2 – Teaching Maths Outside – Play of the Wild

Leave a Reply Cancel Reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Notify me of follow-up comments by email.

Notify me of new posts by email.

Solving practical coordinate problems (Part 2)

Switch to our new maths teaching resources.

Slide decks, worksheets, quizzes and lesson planning guidance designed for your classroom.

Play new resources video

Lesson details

Key learning points.

• In this lesson, we will use rules around x and y coordinates for horizontal and vertical lines to solve more complex problems involving coordinates.

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

Starter quiz

5 questions.

• International
• Education Jobs
• Schools directory
• Resources Education Jobs Schools directory News Search

Team Building & Problem Solving

Subject: Physical education

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

8 July 2013

• Share through email
• Share through twitter
• Share through linkedin
• Share through facebook
• Share through pinterest

Creative Commons "Sharealike"

Your rating is required to reflect your happiness.

It's good to leave some feedback.

Something went wrong, please try again later.

Inspirational! Thanks!

Empty reply does not make any sense for the end user

Great ideas! - Very clear and easy to understand.

Great ideas - simple to understand and setup!

Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch.

Not quite what you were looking for? Search by keyword to find the right resource: