fun problem solving activities ks3

Mr Barton Maths Podcast

Long-form conversations about teaching and learning with craig barton, tes top 10 resources: problem solving and rich tasks.

The following collection of resources have been assembled by the TES Maths Panel . They can be downloaded for free by registering on the TES website.

Here, I have compiled my top 10 problem solving and rich tasks. Enjoy there are some crackers in here.

Carpet your bedroom – functional maths

Age Range:  11-16  Format:  PPT

An activity for students to design a tessellation of carpet tiles for their bedroom. From the design, they need to work out costs from screenshots of carpet tile prices, calculate the cost of the glue. There are three levels to this task, from a basic bronze version to the gold version which includes an algebra extension related to cost of getting a carpet fitted. Very real world focus and some good discussion if you let the students use their own bedroom.

Rich maths tasks to engage KS3

Age Range:  11-16  Format :  Webpage

This website includes many helpful resources relating to the pedagogy associated with Rich Tasks as well as many sources for further tasks. Each Rich Task has been trialled in the classroom and most are accompanied by a detailed task plan which contains an overview and lesson plan.

Maths investigations

Age Range:  11-16  Format:  PDF

Based on science tasks produced in East Sussex, these investigation starter sheets give an introduction to a topic for investigation and progression guide to allow self- and peer-assessment. Targeted at year 7, these may be suitable for several year groups in KS2/3. Please note that the levelling guide is a first draft and may change.

Maths mystery activity: Thinking skills

This is an ideal thinking skills activity for higher KS3 and KS4 students. This is a mystery activity, where learners are presented with a set of cards containing clues to answer a central focus question, in this case: ‘Does Amelie make it to the catwalk?’. Learners will need to work together (in pairs or threes) and use various strands of mathematics to be able to make sense of the clues and come to a conclusion.

My bedroom: Lesson plans and activities 

This is a complete pack of activities, interactive whiteboards and lesson plans for KS3. This activity can be done in pairs or individually. It has lots of differentiation opportunities from the various materials I have created to provide help in groups, individuals or to the whole class, depending on ability. In addition to this, there are also two good extension activities.

Functional maths skills and enterprise task

Age Range:  11-16  Format:  Excel

This is a business game where players compete to make as much money as possible from an initial investment of £200. All pupils need to do is decide how much to spend on making their product, what the sale price should be and the amount to spend on advertising. When every group has entered their decisions into the spreadsheet the figures are compared and sales are decided. Pupils can then predict their available capital for the next round to earn a cash bonus. It was used across the department with all ages and abilities.

Mathematical Rich Tasks

I created this website with a BECTA grant. There are resources (written, interactive, audio and video) to support teachers and students accessing six rich mathematical tasks, that are ripe for creative exploration!

Holiday planning maths investigation

Age Range:  11-16  Format:  Doc & PDF

A structured problem-solving activity based on booking a holiday for a family of four. Includes a resource booklet containing flight, accommodation, car hire and passport prices, and a task sheet setting students task. Suitable for able KS2 pupils. Also includes differentiation by increasing level of difficulty in the tasks set.

Nrich  differentiated mathematical problem solving

Age Range:  11-18  Format:  WEB

Focussed mathematical problem solving on all the required topics of any mathematical syllabus. A good resource to include in the gifted and talented policy and something that allows the children to access mathematics with real-life problem solving, taking them away from the more difficult abstract questions.

Functional mathematics lessons – projects

Age Range:  11-16  Format:  WEB

Maths functional skills classroom projects to use in lessons. Projects designed for one at the end of each half term for years 7, 8 and 9.

Damian Watson,  Maths Secondary Panel

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Creating Maths Problems At KS3 Doesn’t Have To Be Hard: How To Make Yours Fun, Engaging, And Curriculum-Focused

Andy brighouse.

Here we look at how to plan for successful maths problem solving lessons with a range of tried and tested KS3 maths problem solving questions that are fun, engaging and curriculum-focused.

The notion of creating original problem solving maths questions can strike fear deep into the heart of the uninitiated teacher. For some, simply delivering a lesson featuring untried problems is anxiety invoking.

Lessons based solely around maths problem solving activities need planning, and when doing this for the first time it may seem like you are devising a strategic military operation, with your lesson plan resembling the tactical objectives of a dawn raid. However, it doesn’t have to be like this; maths is FUN (that’s why we teach it).

The art of teaching problem solving at key stage 3, and the associated planning, is to focus it on harnessing a particular mathematical strand. Ultimately, your problem solving lessons need to be targeting the skills that are necessary to make learners successful in the future and bridge the gap from primary school to secondary school. You can refresh your memory of KS2 problem solving here . As the teacher your knowledge of GCSE maths  and the problems to be encountered there will feed back into the planning so that the learning attributes gathered during problem solving can feed forward into exam success for the students.

How to teach problem solving

Understanding how to get students solving problems (especially those unfamiliar, thought provoking and often slightly perplexing word problems) can be usefully reduced to getting students to consider just two questions…

• “ What do I know? ”  
•  “ What do I need? ”

These two questions are useful for us as educators too (think data driven planning), but here we are going to explore how to use them to drive forward our students’ ability and desire to find some solutions.

How to link problem solving to the national curriculum

Your first task is to think carefully about which strand of maths you want the problem to originate from. All strands of maths are intrinsically linked, but if you’ve recently worked through an algebra unit, focus your maths problem there.

Students can call upon skills from other strands but their immediate thinking should be related to recent learnings or you will swiftly trigger their cognitive overload . Always consider cognitive load theory in the classroom when designing activities.

Don’t force a topic or real life context to fit a strand of maths; consider the skills you want students to draw upon, and think about which sorts of numeracy questions would use those skills.

How to structure a problem solving session

Any problem solving session should commence with a hook; this could be a starter related to the problem at hand or a contextual discussion about why the problem is interesting. Once you have devised a problem, attempt it yourself; this will show you what resources you need, and also the general thought processes and pitfalls your students are going to face.

It’s often a good idea to base your activities around topics that you know very well, and ones that you are confident your students have the relevant skills to be successful. Feel free to delay a particular lesson you have an idea for until you are comfortable with the subject matter. Do some research and practise; this should be enjoyable because maths is FUN. You’ll learn lots of new things, and become an even better teacher in the process.

Curriculum maths problems

To get you started there follows some suggestions of the types of maths problems and approaches you can take in each of the main maths curriculum areas. You will clearly need to adjust your approach, and perhaps provide more or less differentiation and support at each stage depending on the age group you are teaching. But with the right support you’ll be amazed how far students will get in trying to answer these maths questions if they feel sufficiently motivated.

Number and place value maths problems

Number theory is exciting. We know that, but our students don’t always, and it’s never too soon to introduce them to it. The plethora of conjectures, although fiendishly difficult to prove, are mostly based on concepts met at Key Stage 3.

Number problem example: Collatz conjecture

One of my “go to” examples of this would be the Collatz Conjecture. If you’re not familiar with this problem, I suggest looking it up; there are numerous great resources available suitable for all levels. The premise is quite simple…

• If the number is even, half it
• If the number is odd, triple it and then add one
• Take your answer, then repeat step 1 (ie either half it or triple it and add one).
• Continue until you think you have seen a pattern

The scope for the directions you can take in a lesson by using this problem and trying it out with smaller and larger numbers is enormous. A well structured discussion with quality targeted questioning will conjure the ideas of mathematical algorithms, sequences and patterns, through to the trickier concept of evidence versus proof.

Students can understand the problem easily, it’s straightforward to differentiate for ability and resource development is relatively minimal.

Watch the look on your students’ faces when you tell them that after so many years since its formulation, the Collatz Conjecture still has unclaimed prize money for a proof. This instills the idea that even professional mathematicians struggle at times, and that problem solving is about investigating and building a toolkit of mathematical problem solving strategies.

Geometry maths problems

Problem solving lessons focussed on geometry and mensuration lend themselves to practical activities; grab the coloured paper, scissors, glue and then construct solutions. This is where maths can meet other disciplines, whether it’s engineering, art, architecture or even sport science. The reasons I do this are multiple:

• It demonstrates how applicable maths is to EVERYTHING.
• It teaches students that maths goes beyond the exercise book. Maths is a way of critical thinking and is not “just about doing sums”.
• It allows students to be creative in maths, which accesses more parts of the brain, and can give many students those magical lightbulb moments.

Geometry problem example: Packing boxes

A great idea for a very practical problem solving lesson would be looking at how objects pack into boxes. This could be done using concrete resources  such as tennis balls in various sized boxes, but with planning could involve also converting the problem to two dimensions, using circles with different shape mats to investigate layout configurations.

Students can then be encouraged to compare how the 2D and 3D are dealt with. For teachers wishing to brush up on the theory behind this type of work, we would need to look at the differences between geometry  and topology .

Data handling and probability maths problems

Data handling and probability are far more contemporary than the other strands we teach in school, so I would let the problem solving reflect this; choose very modern problems to focus on. In terms of the real world aspect, data and probability have huge implications regarding human actions.

This indicates that a good hook for the students is to have them use their knowledge of data and probability to solve a human problem.

Think about issues that are big in the news or that are prevalent in other subjects. There are great activities that can be created from issues involving the climate and environment. A well written brief could not only boost the students’ mathematical problem solving skills, but could also lead to the solution of wider problems with the school or local area.

Data handling problem example: Recycling around the school

Why not get your students to solve the school’s recycling problems using maths? Ask your students to analyse the locations and numbers of waste bins and recycling bins around the school site. Automatically, this allows for rehearsal of the concepts from the data handling cycle, but also provides raw data for other problem solving activities linked to the overarching theme.

Students could be asked to consider the probability that upon leaving a canteen with food, they will pass a bin of the necessary type before arriving at their next lesson (whilst following a direct route). The scope here is huge, as the problem solving process includes use of estimation, modelling and mensuration (of distance and time).

Algebra maths problems

Designing problem solving lessons based around algebra  may seem scary, but we are not setting out to prove Fermat’s Last Theorem. Start with the basics; building and using expressions. You could use shapes made from paper, denoting side lengths with variables; as new shapes are created, students use the variables to determine linear expressions for perimeter and quadratic expressions for area (if they have met those concepts). What we are looking for is any activity that allows students to use algebra to generalise.

We now come back to those important questions I mentioned:

“ What do I know? ”  And   “ What do I need to know? ”

Algebra problem example: Definitions and representations using algebra

When it comes to problem solving with algebra, students should build a “tool kit”. I usually begin by asking how we define an even number, an odd number; how do we represent this using algebra?

Then, move on to a square number, one more than a cube number, etc. Students can record their results and create a dictionary of algebraic phrases. Later on, we can use these to look at whether the square of an odd number is always odd, or why the square of an even number is a multiple of four.

Students can use these terms to create and manipulate a variety of polynomial expressions through addition and subtraction. They can go onto form and solve equations through inverse operations and even explore decimal and fractional terms. 

These investigations can use simple or more complex numbers and be tailored to the abilities of your class.

Factorising worksheet

30 Problem Solving Maths Questions, Solutions & Strategies

How to lead a problem solving lesson step by step

For any maths problem, but particularly in your lessons specifically focused on problem solving, students need to be coaxed into realising how much they know about the problem already; combining this with what they need as an outcome should create a journey that contains the steps of a solution.

I’ll use an example to illustrate this.

Problem solving example: Waring’s prime number conjecture

Waring’s prime number conjecture states that every odd number (excluding 1) is a prime or the sum of three primes.

Your students need to know certain things in order to look at this:

• The definition of an odd number
• What a prime number is

Ideally, your starter activity will include some assessment for learning (for more on these see this article on teaching strategies ) and a discussion to bring these ideas to the forefront of your students’ minds.

Save mentioning that this is a named conjecture until the end of the lesson.

A possible line of enquiry could be

 “Which odd numbers less than 50 can be written as the sum of three primes?”

Depending on your class, you may need a more open question, or you may need to scaffold the problem into steps.

Ultimately, as long as students are encouraged to consider what they know about the problem already, and what their objective is, they will be able to actively engage in the problem solving process.

If you’ve taken my advice, you will have already attempted this problem; you know which numbers are tricky and which numbers have several solutions.

 By the way, have you worked out why some numbers have a unique three prime sum and why some don’t? Maybe you should investigate this problem; remember maths is FUN.

If, during an activity, you are asked if/why/how something works and you don’t know; be honest. Students tend to welcome honesty from their teachers. Sit down with the students and try and work it out; this is great for building relationships and encourages a collaborative approach.

It also instills in students that, as mathematicians, we try to solve problems because we don’t yet have all the answers.

Read more: Collaborative Lesson Planning

Reviewing the problem solving process

I now return to my military operation analogy: the mission debrief. Make sure you have plenty of time at the end of problem solving activities for a rich and lively discussion, with all your students involved.

Plan your questions well in advance; I think of my questions when I am having my own attempts at solving the problem. Your questioning strategy should draw out if a solution was found, and how. If a solution eluded everyone, discuss why.

Is a solution possible? Was something else needed? Is an approximate solution the best we could hope for.

It‘s well worth explaining to your students that not all problems have exact solutions; sometimes we have to optimise or estimate as best we can, and that is our solution.

Growing resilience through problem solving

The key thing is to keep reminding your students of the maths skills and strategies they are using. Resilience should build over time as students encounter a wider range of problems and have to deploy their skills in different ways. It is this resilience, and lack of fear, when faced with the unfamiliar that gives students the confidence to pause and think…

• “What do I know?”        
• “What do I need?”

By asking students to consider these two questions, and using your love of maths to inject some fun into the solution process, you can create an environment where students engage with unfamiliar and challenging problems. Your students will become the problem solvers you want them to be.

Students will make mistakes, they will struggle and occasionally they will complain. It is through talking to your students about these difficulties and how to overcome them that they become stronger; this is the idea of a growth mindset .

Discuss what worked, what didn’t, mind-map strategies in groups, incorporate tasks based on collaboration and then next time use competition. As well as improving engagement, your students will adapt to new scenarios with greater ease.

Resources to support problem solving at KS3

If you find that your KS3 students need revision or support in applying any of the topics that your maths problems are investigating, there are free step by step teaching and learning guides available within Third Space Learning’s GCSE maths revision resources as well as other maths resources, such as practice maths questions and downloadable worksheets on topics from factorising to fractions.

Your KS3 students come to you as new recruits; they have a fear of the unknown and may lack confidence. Armed with the ideas in this article, as well as the teaching resources and worksheets available, you will soon find your ability to build them up into problem solving soldiers that can tackle any problem on the mathematical battlefield.

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Being Curious - Secondary Students

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Here are some problems that require you to be resilient. We hope you'll stick with them and feel a sense of achievement at the end!

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Here are some problems that require careful consideration. Immerse yourself in them - we think they are worth the effort!

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Here are some problems that are ideal for working on with others. Find a friend, share ideas, and see if two heads really are better than one!

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Problem solving

Problem solving lesson plan

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Problem Solving: Lesson plan

Problem solving: Presentation slides

Demonstrating your skills quick fire activity

Problem solving in practice: Interactive worksheet

Our problem solving content focuses on one of these skills and develops understanding of the six stages of problem solving, as well as identifying different types of situations in which young people might already be using these skills. Furthermore, it encourages them to use an adaptive approach, explaining that different types of problems can be approached in different ways.

The activities on this page support your teaching of these skills through an independent activity, quick activities or a full length, curriculum-linked lesson plan. 

Teaching resources:

• Problem solving: Lesson plan and presentation slides – full lesson plan including icebreaker for use with a group of students in the classroom
• Demonstrating your skills: Quick-fire activity  – 10 minute activity for a group of students in the classroom, can be used as an icebreaker for the lesson plan
• Problem solving in practice: Interactive worksheet – activity for independent learning whether remote or in class

Lesson plan

(60 -75 minutes)

This lesson is designed to equip young people with an adaptable approach to solving problems, large or small. It includes a short film and scenarios that encourage development of practical problem solving skills which can be useful for learning, day to day life, and when in employment.

By the end of the lesson, students will be able to:

• Identify problems of different scales and what is needed to solve them
• Illustrate the use of an adaptable approach to solving problems
• Understand that problem solving is a core transferable skill and identify its usefulness in a work setting
• Work on a problem solving activity in a team

The lesson aims to reinforce students’ understanding of the potential future applications of this skill as they move into the world of work, particularly in an activity differentiated for an older or more able group on creating new opportunities.

Quick-fire activity

(5 - 10 minutes)

The demonstrating your skills quick-fire activity focuses on helping young people understand the key skills that are needed in the workplace, including the importance of problem solving.

Students will be asked to name the skills being demonstrated in a variety of scenarios, and identify ways they’re already using those skills in this short activity.

You might find it useful as a starter or icebreaker activity to begin a lesson, or at the end to allow students to put what they have just learnt in the Problem solving lesson into practice.

Interactive worksheet

(20 - 25 minutes)

Please note that students below the age of 14 cannot sign up for their own LifeSkills account. Any independent tasks must be printed or downloaded and provided digitally for them to complete as they are currently hosted on educator pages.

The Problem solving in practice interactive worksheet introduces some of the themes from the full lesson plan and gives students some practical strategies for problem solving, including introducing the six stages of problem solving. The worksheet can be printed or completed digitally, so can be used flexibly to give students practise putting their problem solving skills into action. You might choose to assign it:

• As homework following the Problem solving lesson
• For independent study
• For remote learning

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Other lessons that may prove useful for students to build on these activities include the  Adaptability  and  Innovation and idea generation  lessons. Alternatively, consider encouraging them to apply their skills through  Steps to starting a business  or the  Social action toolkit .

Why not build problem solving in as a focus in your students’ wider curriculum? Refer to our  Content guide to find out how this resources can be used as part of your teaching.

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• Free Teaching Resources For The Entire Ks3 Maths Curriculum

Free maths worksheets and resources for every part of the KS3 curriculum

An entire breakdown of the National curriculum in England: mathematics programmes of study for Year 7-9 with worksheets, activities, ideas, PowerPoints and more for every element…

Maths homework worksheets

Help students practise their maths skills with these free maths homework question packs for Year 7 , Year 8 , Year 9 and GCSE maths .

You can also download 100+ problem-solving questions in our KS3 maths worksheets pack from White Rose Maths.

Pupils should be taught to:

Understand and use place value for decimals, measures and integers of any size

• Place value problem cards for decimals

Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥

• Negative numbers worksheet – KS3 maths resource with answers
• Problem solving with negative numbers worksheets

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

• Adding fractions with the same denominator
• Adding and subtracting fractions
• Multiplying and dividing fractions codebreakers
• Multiplying and dividing fractions PowerPoint

Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

• BODMAS questions for KS3 maths – Order of operations worksheet with answers
• BIDMAS first steps worksheets
• Order of operations (BIDMAS)

Recognise and use relationships between operations including inverse operations

Use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations

• Finding powers and roots lesson

Interpret and compare numbers in standard form A x 10n 1≤A<10, where n is a positive or negative integer or zero

• Standard form activities
• Codebreaker – Standard form

Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8)

• Ordering fractions and decimals

Define percentage as ‘number of parts per hundred’, interpret percentages and one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%

• Percentage questions – KS3 maths worksheet with answers
• Non-calculator method percentages lesson and worksheets

Interpret fractions and percentages as operators

• Fractions, decimals and percents worksheets – KS3 maths resource with answers
• Fractions, decimals and percentages

Use standard units of mass, length, time, money and other measures, including with decimal quantities

• Advert maths – Units of measurement worksheet

Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]

• Rounding and approximation

Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<x≤b

• Rounding, estimation, standard form grades F to A

Use a calculator and other technologies to calculate results accurately and then interpret them appropriately

• Calculator skills revision lesson
• Virtual Casio calculator button explanations for IWB

Use and interpret algebraic notation, including: ab in place of a × b; 3y in place of y + y + y and 3 × y; a2 in place of a × a; a3 in place of a × a × a; a2b in place of a × a × b; a/b in place of a ÷ b; coefficients written as fractions rather than as decimals; brackets

• Writing formulae

Substitute numerical values into formulae and expressions, including scientific formulae

• Simplifying expressions and formulae PowerPoint

Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors

• Algebraic expressions

Simplify and manipulate algebraic expressions to maintain equivalence by: collecting like terms; multiplying a single term over a bracket; taking out common factors; expanding products of two or more binomials

• Simplifying expressions codebreaker
• Algebraic expressions spiders

Understand and use standard mathematical formulae; rearrange formulae to change the subject

• Algebraic fractions and simplifying
• Simplify algebraic fractions worksheet and answers

Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs

• Simultaneous equations and graphs lesson

Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

• Solving equations matching activities
• Solving linear equations worksheets from Level 4-7

Work with coordinates in all four quadrants

• Plotting and identifying coordinates in all four quadrants worksheet

Recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane

• Sketching quadratic graphs worksheet

Interpret mathematical relationships both algebraically and graphically

• Solving simultaneous equations graphically worksheet

Reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically

• Introduction lesson to straight line graphs, linear functions and y=mx+c

Use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations

• Simultaneous equations graphically PowerPoint and worksheet

Find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs

• ‘Defuse the Bomb’ linear and non-linear graphs worksheets

Generate terms of a sequence from either a term-to-term or a position-to-term rule

• Graph sequences – grades F to C
• Introduction to sequences

Recognise arithmetic sequences and find the nth term

• Nth term questions – KS3/4 linear sequences worksheet with answers
• Graph sequences – Grades F to C
• Arithmetic sequences worksheets

Recognise geometric sequences and appreciate other sequences that arise

• Advanced sequences – Linear, geometric, quadratic and sequence proofs

Ratio, proportion and rates of change

Change freely between related standard units [for example time, length, area, volume/capacity, mass]

• Ratio and proportion

Use scale factors, scale diagrams and maps

• Enlargement with negative scale factors
• Similar shapes volume worksheet using scale factors

Express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1

• Fractions of amounts worksheet

Use ratio notation, including reduction to simplest form

• Simplifying ratios worksheet

Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio

• Ratio worksheet
• Simplifying ratios treasure hunt

Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction

• Three multiplicative relationships lessons on ratio problems

Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions

• Fraction, ratio and percentage reasoning tasks

Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics

• Percentage changes in football wages worksheet
• Homes Under the Hammer percentage change worksheet
• Storage Hunters percentage change (profit/loss) worksheet

Solve problems involving direct and inverse proportion, including graphical and algebraic representations

Use compound units such as speed, unit pricing and density to solve problems

• Compound measures

Geometry and measures

Derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)

• Area and perimeter codebreakers Worksheets
• Area and perimeter

Calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes

• Area of a circle worksheets and PowerPoint with detailed solutions

Draw and measure line segments and angles in geometric figures, including interpreting scale drawings

• Simple construction worksheet for drawing and measuring line segments

Derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line

• The Walking Dead Season 5 shape construction activity

Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric

• Reflective and rotational symmetry activity with company logos

Use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles

• Properties of triangles and quadrilaterals worksheet

Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies

• Properties of quadrilaterals PowerPoint

Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures

• Transformations

Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids

Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles

• Angles on a straight line worksheet

Understand and use the relationship between parallel lines and alternate and corresponding angles

• Angles in parallel lines worksheet – KS3 maths resource with answers
• Angles in parallel lines – comparing methods
• Angles of Parallel Lines PowerPoint

Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons

• Angles in triangles treasure hunt activity

Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs

• Pythagoras’ theorem PRET homework worksheet
• Pythagoras’ theorem and coordinates lesson
• Pythagoras’ theorem questions

Use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles

• Introductory trigonometry lesson PowerPoint
• Trigonometry levelled activity
• Trigonometry in right-angled triangles matching activities

Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D

• Advanced trigonometry for KS3 and GCSE maths – 3D trigonometry, Pythagoras and sine/cosine rules

Interpret mathematical relationships both algebraically and geometrically.

• Problem solving question of the day compilation worksheets

Probability

Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale

• Introduction to probability and probability scale lesson
• Probability full lesson PowerPoint and worksheets

Understand that the probabilities of all possible outcomes sum to 1

• Probability lesson

Enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams

• S1 Chapter 5 probability lesson

Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.

• Sample spaces and calculating probabilities worksheet

Describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

• Find the median and mean averages and range worksheet
• Average and range codebreaker activities

Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data

• Interpreting statistical graphs
• Calculating, displaying and interpreting statistics tutorials

Describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.

• Scatter diagrams
• Plotting scatter graphs PowerPoint and worksheet
• Correlation street draw and use scatter graphs activity

Browse more KS3 maths games and lesson ideas.

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Problem Solving Games, Activities & Exercises for Adults

Here is our list of the best problem solving games, activities and exercises for adults.

Problem solving games are activities that require players to use critical thinking skills to solve puzzles. Example activities include escape rooms, Sudoku, and murder mysteries. The purpose of these exercises is to sharpen reasoning and decision-making skills in group settings and to do team building with employees.

These activities are a subset of remote team games , found in problem solving books , and are similar to team puzzles , team building brain teasers and team riddles .

This article contains:

• team building problem solving activities for employees
• free problem solving games for adults
• virtual problem solving activities for students
• group problem solving activities
• problem solving team builders

Here we go!

List of problem solving games & activities

From word and number puzzles to role-playing games, here is a list of inexpensive and free problem solving team builders that help groups practice the art of critical thinking and compromise.

1. Espionage! (Team Favorite)

For an exciting game of social deduction, check out Espionage! This thrilling experience will put your team’s wits and instincts to the test.

Espionage! offers the following:

• a 90-minute session led by an experienced host
• undercover teams of agents and spies
• challenging puzzles, tasks, and maneuvers
• team conversations to help uncover secret identities

The best part is we will bring all the necessary game materials to your preferred location. If you are interested in boosting communication and critical-thinking skills within your team, then consider Espionage!

Learn more about Espionage!

2. Art Heist: The Vanishing of Van Gogh (Hosted)

You can turn your team into skilled detectives with Art Heist: The Vanishing of Van Gogh! In this captivating mystery, participants will locate the stolen artwork, The Bedroom .

Key features of this experience include:

• a 90-minute adventure led by a world-class host
• detailed puzzles, clues, and mysteries to unravel
• trails of evidence and hidden secrets
• group discussions to find the art

Additionally, you can include a cocktail kit to spice up your event. Through Art Heist, you will enhance your team’s ingenuity and problem-solving skills!

Learn more about Art Heist: The Vanishing of Van Gogh .

Get our free team building toolbox

• icebreaker games
• bingo cards

3. War of the Wizards (Popular)

With War of the Wizards, teams roleplay as minions of powerful wizards to vanquish forces of evil. Participants will play thrilling games and go on a quest to restore harmony to the realm!

War of the Wizards offers the following:

• a 90-minute journey guided by a distinguished host
• immersive storytelling that transports players into a magical realm
• engaging activities like world-building, role-playing games, and storytelling
• opportunities for forming alliances, facing challenges, and going on quests

Through the power of imagination and teamwork, your team can overcome tasks and participate in an epic fantasy battle. To improve communication and bonds, include War of the Wizards in your agenda!

Learn more about War of the Wizards .

Sudoku is one of the most popular free problem solving games for adults. The objective of this game is to fill each box of a 9×9 grid so that every row, column, and letter contains each number from one to nine. The puzzle makes a great team challenge. To play Sudoku on Zoom, screen share the game board. Then, turn on the annotation features. Using the add text functions, participants can fill in the numbers on the grid.

We made a starter puzzle you can use in your next meeting or virtual team bonding session:

Here are more online Sudoku puzzles .

5. Crossword puzzles

Crossword puzzles are word games that ask players to fill in words based on clues. Words interconnect, and players must think critically about the surrounding words to select the right phrase for the space.

You can use an online crossword puzzle maker to create a custom puzzle. Here are a few themes you may want to consider:

• teammates’ tastes and interests
• company knowledge and history
• industry terms and trends

Or, create a miscellaneous puzzle just for fun.

We made a sample puzzle you can use for your game:

To complete puzzles during online meetings, you can use the share screen function and add text through annotations.

Or, subscribers can play the New York Times’ daily crossword puzzle virtually . Dictionary.com also offers a free daily online crossword puzzle .

Check out more vocabulary games .

6. Online Escape Rooms

Escape rooms are timed games that get groups working together to solve puzzles. Traditionally, players enter a locked room and must complete all puzzles in an hour or two to unlock the door. However, groups can also play escape rooms online.

Digital escape rooms typically come in one of two forms: in a Zoom room and led by a host, or in a choose-your-own adventure format via Google Forms or websites. To play escape rooms virtually, enter a video meeting and follow the prompts, or screen share the Google Form and work out the puzzles together.

Check out our full list of online escape rooms .

7. Murder Mysteries

Murder Mysteries are story-based games that ask players to take on the roles of suspects or detectives while trying to identify a killer. These games often involve reading lines from a script, searching for clues, and occasionally solving puzzles to get hints.

These games make participants pay attention to conversations, analyze other characters’ behavior, and search for hidden meaning in the script. Players must use their powers of observation and logic to unravel the mystery.

Check out our list of Zoom murder mystery games .

8. Treasure Hunts

Treasure hunts are scavenger hunts with intention. While virtual scavenger hunts often ask players to collect random items, treasure hunts require participants to locate clues that lead to other prompts and hints. The game typically ends with players finding a treasure or solving a mystery, sometimes both.

The treasure hunt can have a specific theme such as secret agent missions or a hunt for pirate treasure, or you can run a more general hunt. Teammates can either compete simultaneously via Zoom call, or can play the hunt on an app individually and compete to beat each other’s scores.

Check out our list of treasure hunt apps .

9. Poem or story challenge

Most team building problem solving activities for employees revolve around science, math, and logic. Poem/story challenges rely on writing skills and are sure to appeal to the language lovers on your team.

Each player receives a limited word bank to use to create a story or poem. Then, players have a few minutes to craft their pieces. Afterward, everyone reads out or screen shares their creations.

Here are a few word challenge activities you can do remotely:

• Found poems or stories : Participants make poems or stories out of words they find by visiting websites, searching emails, glancing out the window, or taking a walk or drive around the neighborhood.
• Random word generators : Teammates use a random word generator to populate a word bank, and must use each word in the poem or story.
• Poetry magnets : Group members make poems using poetry magnets. You can send poetry magnet sets to employees and assemble the verses on a cookie pan during a Zoom call. Or, teammates can play with poetry magnets online .
• Page poems: Participants receive one page of a book or magazine, and must make a poem or story by blocking out other words so only the chosen text remains visible. This activity is part storytelling, part art, since story crafters can illustrate the pages as part of the design.
• Ransom note stories or poems : Players cut out letters from magazines and must form new words to make poems and stories. Or, players can receive a mix of random letters, form words, and run the text through a ransom note generator .

These activities are suitable for teams and individual players.

10. Moral challenge

Some problems are ethical rather than factual. Moral judgment plays just as important a role in the decision-making process as technical prowess. Players can flex their moral problem-solving skills by tackling ethical dilemmas or social puzzles.

Here are some social problem solving games online:

• Moral machine
• Scruples – the game of moral dilemmas
• Morality play

To play these games, either download the apps, or pull up the website and then screen share the prompts. These games are best played when discussed as a group, because the more belief systems and opinions, the harder an issue is to resolve. These exercises provide practice for real-life conflict resolution.

You can find similar challenges on our list of online personality tests .

11. Frostbite

Frostbite is a group game that hones team leaders’ communication skills while sharpening teammates’ listening and cooperation skills. The premise behind the game is that a group of explorers gets caught in a snowstorm and must build a shelter. Frostbite has paralyzed the leaders’ hands and snow-blinded the rest of the team. The leader must give the team instructions to build a tent that can resist arctic winds.

To play Frostbite, each teammate wears a blindfold. Then, the leader gives directions. Once the structures are complete, players turn on a fan to test whether tents can withstand the wind.

Frostbite is usually an in-person game, however you can also play virtually. In the remote version of the game, teammates construct tents out of cards and tape, while the leader surveys the scene on screen.

This exercise demonstrates the challenges of leading remotely, as teams need to operate with minimal oversight or supervisor observation. Therefore, instructions need to be clear and direct to be effective.

Check out more team building games .

12. Virtual Hackathons

Hackathons are events where participants have a set amount of time to design and pitch a new product or solution. This type of event originated in the programming world and is often used to create new apps, however you can apply the game to any industry or school subject.

Virtual hackathons are online versions of the event. Teams enter the competition, then work with each other via virtual meeting software or remote work communication platforms to design the solution. At the end of the competition, teams pitch ideas to a panel of judges and a winner is decided.

To run a virtual hackathon, first announce the theme of the event and collect sign-ups. So that no teams work ahead, hint at the general idea of the issue, and only explain the precise problem when the event begins. Then, give teams anywhere from a few hours to a few days to complete the project.

Discover more virtual hackathon ideas .

13. Improv games

Improv games are excellent problem solving activities. These exercises force participants to think and respond quickly to keep scenes moving in a logical and entertaining way.

Here are some good problem solving improv games:

Banned words : Performers cannot say certain words. Scene partners will conceive of situations that encourage the actors to use those words, and the actors must find alternatives, such as using synonyms or taking the scene in a new direction.

Scenes from a chat : Audience gives a suggestion for a scene, and players act the scene out. Though it’s a fictional and often ridiculous scenario, actors must react to the situation and solve the problem in order for the scene to end.

Miracle cure : Miracle cure is a quick-moving exercise that follows a simple format. One player declares, “I have a problem.” Another player responds, “I have a….[random object.]” The first player then replies, “great! I can use the [random object] to….” and describes how they will solve the problem.

Check out more problem-solving improv games .

14. Spaghetti Tower

The spaghetti tower is a classic team building game. Participants gather uncooked spaghetti and marshmallows, and must construct the tallest freestanding tower.

During the in-person version, players must construct one tall freestanding tower. However, for the virtual version of the game, players construct individual towers. You can send groups to breakout rooms for the build, then reconvene in the main room for judging. Teams are judged on three main factors: number of towers, height, and uniformity.

This version of the game not only tests the structural integrity of the tower, but also consistency and quality control. This exercise teaches teams to align and collaborate remotely, and produce a consistent product even when far apart.

15. What Would You Do?

What Would You Do? is a simple situational game that challenges participants to react to different circumstances. To play this game, read prompts one by one, and then ask participants to respond with gameplans. You can use the polling or raise hand feature to vote for the best option.

Here are some problem solving scenarios for adults or kids to use in the game:

• Zombies attack and you have to find a place to hide.
• You are at the zoo and the animals escape. Which one do you try to corral back into the pen first?
• After waiting in line for hours, someone cuts in front of you last minute. The person appears to be visually and hearing impaired, and doesn’t notice your protests. An official announces that due to diminishing supply, this individual will be the last in line to be served.
• You are eating a meal with important clients and/or your partner’s parents, and you want to impress. The individuals make you a dish that does not fit within your dietary restrictions, but you do not speak the same language and cannot explain why you do not want to eat.
• An imposter has infiltrated the organization, who looks, speaks, and behaves exactly like you. How do you convince your peers that you are the original?

For similar dilemmas, check out this list of Would You Rather? questions.

16. Desert Island Survival

Desert Island Survival is a game that challenges players to prioritize. The premise is that players have been stranded on an island, and must decide what order to perform survival steps.

Here are the possible actions:

• Set up shelter
• Explore the island
• Try to signal for help
• Make weapons for self-defense
• Build a raft to escape the island
• Start a fire
• Choose a group leader
• Search for other survivors

All group members must agree on the order of the steps. Players should explain the reasoning for the order of each step while ranking the actions.

Another version of the game involves players receiving a list of 15 to 20 items, and selecting five or so to bring to the island. You can also vary the location of the game, substituting remote islands for destinations like outer space or the distant past.

17. Choose Your Own Adventure

Choose Your Own Adventure stories enable readers to determine the outcome of the story by making decisions. Each action has a consequence that takes the tale in a different direction. Participants can try to guess how the story may unfold by talking through the different choices. When completing the activity in a group setting, the majority of the team must agree on an action before moving forward in the story.

There are a few ways to facilitate these activities online:

• Play an online role playing video game
• Watch an interactive movie like Black Mirror: Bandersnatch
• Read from a Choose Your Own Adventure book on Zoom
• Click through a Choose Your Own Adventure platform
• Create your own story using a Google Form

Whichever way you choose to do the exercise, you can use the screen share feature in your virtual meeting software so that listeners can more easily follow along.

18. MacGyver

MacGyver is a show where the hero escapes sticky situations by improvising tools out of unlikely materials. For example, in one episode the hero makes a telescope out of a newspaper, magnifying lens, and a watch crystal.

To play MacGyver, you can either list three to five objects participants can use, or challenge players to use items that are within arms reach.

Simply state a desired end result, such as “a way to open a locked door,” or “a getaway vehicle,” and then ask teams to explain what they will build and how they will build it. To make the activity more collaborative, you can give teams five or ten minutes in breakout rooms to strategize and design a prototype.

19. Dungeons & Dragons

Dungeons & Dragons is a roleplaying game where players pretend to be magical figures and creatures. One player serves as the dungeon master, who guides the game, while the other players pick characters and make decisions to move the story forward. Upon choosing a course of action, players roll a twenty-sided die to determine whether or not the plan succeeds. The game is story-based, the possibilities are nearly limitless, and truly creative problem solving options arise. Also, since gameplay is mostly verbal, Dungeons & Dragons is an easy activity to do over Zoom.

Here are the basic rules for Dungeons & Dragons .

20. Pandemic

Pandemic is a game that pits players against the forces of nature in a race to contain and control disease outbreaks. At the beginning of the game, each player receives a role such as containment specialist or operations expert. Participants must carry out the duties of their roles by choosing appropriate actions. Pandemic is a great game for groups because each team member has a clear part to play, and players must collaborate and work together instead of competing against each other.

To play the game online, you can use a Pandemic game app , or talk through the exercise while one attendee moves and displays pieces on the board.

Note: The subject of this game might hit too close to home for some players, considering recent history. You can find games with similar mechanics that deal with different subject matter, such as Forbidden Island.

Check out more team building board games .

21. Model UN

Model UN is one of the best virtual problem solving activities for students. This exercise casts participants in the role of international diplomats who must negotiate to solve realistic problems. Each player assumes the role of a country ambassador and must form alliances and propose solutions to solve crises.

Here are some sample Model UN scenarios:

• Human rights violation by powerful country
• Food shortage
• Disease epidemic
• Technology privacy violations
• Civil war branching into surrounding countries
• Natural disasters

Depending on the size of the group, participants either take on the part of an entire government of a country, or play a certain role within the government. To carry out the activity on Zoom, players can take turns giving speeches, message other countries privately via the chat, meet in breakout rooms to form alliances or have more intimate discussions, and use the polling feature to vote on propositions.

If politics does not resonate with your group, then you can alter the exercise by applying the same activity structure to a different theme, such as the Justice League, movie characters, business board members, or reality TV stars.

The main purpose of the exercise is to research, talk through problems, and compromise. As long as these elements are present, then the specifics of the setup do not matter.

There are many types of problem solving activities for adults. You can do online problem solving games, which require a different skill set than in-person problem solving. For instance, communication must be much clearer and more abundant when group members are far apart and unable to demonstrate or pick up physical cues.

Though many problem solving games include props and in-person elements, there are many games you can play together online. These exercises work well as educational tools as well as team bonding accelerators. Upon completion, participants are likely to feel a sense of accomplishment and increased confidence. These games are also great practice for real life conflict resolution, creative thinking and team building.

Next check out this list of connection games , this collection of crime-solving games , and this post with conflict resolution games .

We also have a list of the best decision making books and a list of team building problems for work .

Book wildly fun team building events with expert hosts

FAQ: Problem solving activities

Here are common answers to questions about group problem solving activities.

What are problem solving games?

Problem solving games are challenges that ask players to think critically and use logic to overcome issues or answer riddles. Examples include sudoku, murder mysteries, and spaghetti towers. These games are also known as “problem solving exercises”, “problem and solution games” and “group problem solving activities.”

What are the best problem solving games for groups?

The best problem solving games for groups include online escape rooms, moral challenges, and improv games.

What are some good problem solving team building activities for students?

Some good problem solving activities for students include crossword puzzles, choose your own adventure stories, and model UN.

How do you play problem solving games online?

The best way to play problem solving games online is to join a video call meeting to talk through the issue. Using the screen sharing and digital whiteboard features helps participants visualize the problem more clearly. Breakout rooms give teams the chance to discuss the issue more intimately.

Author: Angela Robinson

Marketing Coordinator at teambuilding.com. Team building content expert. Angela has a Master of Fine Arts in Creative Writing and worked as a community manager with Yelp to plan events for businesses.

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Maths Problem Solving Booklets

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

23 August 2022

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Maths problem solving booklets covering a wide range of mathematical problems designed to improve problem solving strategies as well as numeracy and mathematical ability.

Designed to be printed as A5 booklets.

Disclaimer: These are free because the problems are from a wide variety of sources, most of which I have forgotten. I am a maths problem magpie and collect maths problems wherever I find them. All I have done is bundled these ones up to make it convienent.

If you find a problem that is yours and you don’t want it used please comment and I’ll remove it - cheers.

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Catch The Ball

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