problem solving maths primary school

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!

Maths Problem Solving At KS2: Strategies and Resources For Primary School Teachers

John Dabell

Maths problem solving KS2 is crucial to succeeding in national assessments. If your Key Stage 2 pupils are still struggling with reasoning and problem solving in Maths, here are some problem solving strategies to try with your classes; all aligned to Ofsted’s suggested primary school teaching strategies.

Reasoning and problem solving are widely understood to be one of the most important activities in school mathematics. As far back as 1982, The Cockcroft Report , stated:

‘The ability to solve problems is at the heart of mathematics. Mathematics is only “useful” to the extent to which it can be applied to a particular situation and it is the ability to apply mathematics to a variety of situations to which we give the name “problem solving”. […] At each stage […] the teacher needs to help pupils to understand how to apply the concepts and skills which are being learned and how to make use of them to solve problems. These problems should relate both to the application of mathematics to everyday situations within the pupils’ experience, and also to situations which are unfamiliar.’

Thirty plus years later and problem solving is still the beating heart of the Maths curriculum and – along with fluency and reasoning – completes the triad of aims in the 2014 New National Curriculum.

Ofsted’s view on problem solving in the Maths curriculum

Despite its centrality, Ofsted report that ‘ problem solving is not emphasised enough in the Maths curriculum ’. Not surprisingly, problem solving isn’t taught that well either because teachers can lack confidence, or they tend to rely on a smaller range of tried and tested strategies they feel comfortable with but which may not always ‘hit home’. If you’re looking to provide further support to those learners who haven’t yet mastered problem solving, you probably need a range of different strategies, depending on both the problem being attempted and the aptitude of the pupil.

We’ve therefore created a free KS2 resource aimed at Maths Coordinators and KS2 teachers that teaches you when and how to use 9 key problem solving techniques: The Ultimate Guide to Problem Solving Techniques

The context around KS2 problem solving

According to Jane Jones, former HMI and National Lead for Mathematics, in her presentation at the Jurassic Maths Hub:

Problems do not have to be set in real-life contexts, beware pseudo contexts.
Providing a range of puzzles and other problems helps pupils to reason strategically to approach problems, sequence unfolding solutions, and use recording to help their mathematical thinking for next steps.
It is particularly important that teachers and TAs stress reasoning, rather than just checking whether the final answer is correct.
Pupils of all ability need to learn how to solve problems – not just the high attainers or fastest workers.

The Ultimate Guide to Problem Solving Techniques

9 ready-to-go problem solving techniques with accompanying tasks to get KS2 reasoning independently

How to approach KS2 maths problems

So what do we do? Well Ofsted advice is pretty clear on what to do when teaching problem solving. Jane Jones says we should:

Set problems as part of learning in all topics for all pupils.
Vary the ways in which you pose problems.
Try to resist prompting pupils too soon and focusing on getting ‘the answer’ – pupils need to build their confidence, skills and resilience in solving problems, so that they can apply them naturally in other situations.
Make sure you discuss alternative approaches with pupils to help develop their reasoning.
Ensure that problems for high attainers involve demanding reasoning and problem-solving skills, not just harder numbers.

Perhaps more than most topics in Maths, teaching pupils how to approach problem solving questions effectively requires a systematic approach. Pupils can face any number of multi-step word problems throughout their SATs and they will face them without our help. To truly give pupils the tools they need to approach problem solving in Maths we must ingrain techniques for approaching problems.

With this in mind, below are some methods and techniques for you to consider when teaching problem solving in your KS2 Maths lessons. For greater detail and details on how to teach this methods, download the Ultimate Guide to Problem Solving Techniques

Models for approaching KS2 problem solving

Becoming self-assured and capable as a problem solver is an intricate business that requires a range of skills and experience. Children need something to follow. They can’t just pluck a plan of attack out of thin air which is why models of problem solving are important especially when made memorable. They help establish a pattern within pupils so that, when they see a problem, they feel confident in taking the steps towards solving it.

Find out how we encourage children to approach problem solving independently in our blog: 20 Maths Strategies KS2 That Guarantee Progress for All Pupils.

The most commonly used model is that of George Polya (1973), who proposed 4 stages in problem solving, namely:

Understand the problem
Devise a strategy for solving it
Carry out the strategy
Check the result

Many models have followed the Polya model and use acronyms to make the stages stick. Which model you use can depend on the age of the children you are teaching and sometimes the types of word problems they are trying to solve. Below are several examples of Polya model acronyms:

C – Circle the question words U – Underline key words B – Box any key numbers E – Evaluate (what steps do I take?) S – Solve and check (does my answer make sense and how can I double check?)

R – Read the problem correctly. I – Identify the relevant information. D – Determine the operation and unit for expressing the answer. E – Enter the correct numbers and calculate

I – Identify the problem D – Define the problem E – Examine the options A – Act on a plan L – Look at the consequences

R – Read and record the problem I – Illustrate your thinking with pictures, models, number lines etc C – Compute, calculate and check E – Explain your thinking

R – Read the question and underline the important bits U – Understand: think about what to do and write the number sentences you will need C – Choose how you will work it out S – Solve the problem A – Answer C – Check

Q – Question – read it carefully U – Understand – underline or circle key elements A – Approximate – think about the size of your answer C – Calculate K – Know if the answer is sensible or not

T – Think about the problem and ponder E – Explore and get to the root of the problem A – Act by selecting a strategy R – Reassess and scrutinise and evaluate the efficiency of the method

The idea behind these problem solving models is the same: to give children a structure and to build an internal monitor so they have a business-like way of working through a problem. You can choose which is most appropriate for the age group and ability of the children you are teaching.

The model you choose is less important than knowing that pupils can draw upon a model to follow, ensuring they approach problems in a systematic and meaningful way. A far simpler model – that we use in the Ultimate Guide to KS2 Problem Solving Techniques – is UCR: Understand the problem, Communicate and Reflect.

You then need to give pupils lots of opportunities to practice this! You can find lots of FREE White Rose Maths aligned maths resources, problem solving activities and printable worksheets for KS1 and KS2 pupils in the Third Space Learning Maths Hub .

What’s included in the guide?

After reading the Ultimate Guide to KS2 Problem Solving Techniques , we guarantee you will have a new problem solving technique to test out in class tomorrow. It provides question prompts and activities to try out, and shows you step by step how to teach these 9 techniques

Open ended problem solving
Using logical reasoning

Working backwards

Drawing a diagram

Drawing a table

Creating an organised list

Looking for a pattern

Acting it out

Guessing and checking

Cognitive Activation: getting KS2 pupils in the lightbulb zone

If you need more persuasion, pupils who use strategies that inspire them to think more deeply about maths problems are linked with higher Maths achievement. In 2015 The National Education Research Foundation (NFER) published ‘ PISA in Practice: Cognitive Activation in Maths ’. This shrewd report has largely slipped under the Maths radar but it offers considerable food for thought regarding what we can do as teachers to help mathematical literacy and boost higher mathematical achievement.

Cognitive Activation isn’t anything mysterious; just teaching problem solving strategies that pupils can think about and call upon when confronted by a Maths problem they are trying to solve. Cognitive It encourages us as teachers to develop problems that can be solved in more than one way and ‘may require different solutions in different contexts’. For this to work, exposing children to challenging content and encouraging a culture of exploratory talk is key. As is:

Giving pupils maths problem solving questions that require them to think for an extended time.
Asking pupils to use their own procedures for solving complex problems.
Creating a learning community where pupils are able to make mistakes.
Asking pupils to explain how they solved a problem and why they choose that method.
Presenting pupils with problems in different contexts and ask them to apply what they have learned to new contexts.
Giving pupils problems with no immediately obvious method of solution or multiple solutions.
Encouraging pupils to reflect on problems.

Sparking cognitive activation is the same as sparking a fire – once it is lit it can burn on its own. It does, however, require time, structure, and the use of several techniques for approaching problem solving. Techniques, such as open-ended problem solving, are usually learned by example so we advise you create several models to go through with pupils, as well as challenge questions for independent work. Many examples exist and we encourage you to explore more (e.g. analysing and investigating, creating a tree diagram, and using simpler numbers).

Read these:

How to develop maths reasoning skills in KS2 pupils
FREE CPD PowerPoint: Reasoning Problem Solving & Planning for Depth
KS3 Maths Problem Solving

That time, effort, and planning will – however – be well spent. Equipping pupils with the tools to solve problems they have never seen before is more akin to teaching for life than teaching for Maths. The skills they gain from being taught problem solving successfully will be skills they use and hone for the rest of their life – not just for their SATs.

For a range of problem solving techniques, complete with explanations, contextual uses, example problems and challenge questions – don’t forget to download our free Ultimate Guide to KS2 problem solving and reasoning techniques resource here.

KS2 problem Solving FAQs

Here are some techniques to teach problem solving to primary school pupils: Open ended problem solving Using logical reasoning Working backwards Drawing a diagram Drawing a table Creating an organised list Looking for a pattern Acting it out Guessing and checking

Ofsted say that teachers can encourage problem-solving by: Setting problems as part of learning in all topics for all pupils. Varying the ways in which you pose problems. Trying to resist prompting pupils too soon and focusing on getting ‘the answer’ – pupils need to build their confidence, skills and resilience in solving problems, so that they can apply them naturally in other situations. Making sure you discuss alternative approaches with pupils to help develop their reasoning. Ensuring that problems for high attainers involve demanding reasoning and problem-solving skills, not just harder numbers.

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.

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

Skip to main content
Skip to primary sidebar
Skip to footer

Additional menu

Khan Academy Blog

Free Math Worksheets — Over 100k free practice problems on Khan Academy

Looking for free math worksheets.

You’ve found something even better!

That’s because Khan Academy has over 100,000 free practice questions. And they’re even better than traditional math worksheets – more instantaneous, more interactive, and more fun!

Just choose your grade level or topic to get access to 100% free practice questions:

Kindergarten, basic geometry, pre-algebra, algebra basics, high school geometry.

Trigonometry

Statistics and probability

High school statistics, ap®︎/college statistics, precalculus, differential calculus, integral calculus, ap®︎/college calculus ab, ap®︎/college calculus bc, multivariable calculus, differential equations, linear algebra.

Addition and subtraction
Place value (tens and hundreds)
Addition and subtraction within 20
Addition and subtraction within 100
Addition and subtraction within 1000
Measurement and data
Counting and place value
Measurement and geometry
Place value
Measurement, data, and geometry
Add and subtract within 20
Add and subtract within 100
Add and subtract within 1,000
Money and time
Measurement
Intro to multiplication
1-digit multiplication
Addition, subtraction, and estimation
Intro to division
Understand fractions
Equivalent fractions and comparing fractions
More with multiplication and division
Arithmetic patterns and problem solving
Quadrilaterals
Represent and interpret data
Multiply by 1-digit numbers
Multiply by 2-digit numbers
Factors, multiples and patterns
Add and subtract fractions
Multiply fractions
Understand decimals
Plane figures
Measuring angles
Area and perimeter
Units of measurement
Decimal place value
Add decimals
Subtract decimals
Multi-digit multiplication and division
Divide fractions
Multiply decimals
Divide decimals
Powers of ten
Coordinate plane
Algebraic thinking
Converting units of measure
Properties of shapes
Ratios, rates, & percentages
Arithmetic operations
Negative numbers
Properties of numbers
Variables & expressions
Equations & inequalities introduction
Data and statistics
Negative numbers: addition and subtraction
Negative numbers: multiplication and division
Fractions, decimals, & percentages
Rates & proportional relationships
Expressions, equations, & inequalities
Numbers and operations
Solving equations with one unknown
Linear equations and functions
Systems of equations
Geometric transformations
Data and modeling
Volume and surface area
Pythagorean theorem
Transformations, congruence, and similarity
Arithmetic properties
Factors and multiples
Reading and interpreting data
Negative numbers and coordinate plane
Ratios, rates, proportions
Equations, expressions, and inequalities
Exponents, radicals, and scientific notation
Foundations
Algebraic expressions
Linear equations and inequalities
Graphing lines and slope
Expressions with exponents
Quadratics and polynomials
Equations and geometry
Algebra foundations
Solving equations & inequalities
Working with units
Linear equations & graphs
Forms of linear equations
Inequalities (systems & graphs)
Absolute value & piecewise functions
Exponents & radicals
Exponential growth & decay
Quadratics: Multiplying & factoring
Quadratic functions & equations
Irrational numbers
Performing transformations
Transformation properties and proofs
Right triangles & trigonometry
Non-right triangles & trigonometry (Advanced)
Analytic geometry
Conic sections
Solid geometry
Polynomial arithmetic
Complex numbers
Polynomial factorization
Polynomial division
Polynomial graphs
Rational exponents and radicals
Exponential models
Transformations of functions
Rational functions
Trigonometric functions
Non-right triangles & trigonometry
Trigonometric equations and identities
Analyzing categorical data
Displaying and comparing quantitative data
Summarizing quantitative data
Modeling data distributions
Exploring bivariate numerical data
Study design
Probability
Counting, permutations, and combinations
Random variables
Sampling distributions
Confidence intervals
Significance tests (hypothesis testing)
Two-sample inference for the difference between groups
Inference for categorical data (chi-square tests)
Advanced regression (inference and transforming)
Analysis of variance (ANOVA)
Scatterplots
Data distributions
Two-way tables
Binomial probability
Normal distributions
Displaying and describing quantitative data
Inference comparing two groups or populations
Chi-square tests for categorical data
More on regression
Prepare for the 2020 AP®︎ Statistics Exam
AP®︎ Statistics Standards mappings
Polynomials
Composite functions
Probability and combinatorics
Limits and continuity
Derivatives: definition and basic rules
Derivatives: chain rule and other advanced topics
Applications of derivatives
Analyzing functions
Parametric equations, polar coordinates, and vector-valued functions
Applications of integrals
Differentiation: definition and basic derivative rules
Differentiation: composite, implicit, and inverse functions
Contextual applications of differentiation
Applying derivatives to analyze functions
Integration and accumulation of change
Applications of integration
AP Calculus AB solved free response questions from past exams
AP®︎ Calculus AB Standards mappings
Infinite sequences and series
AP Calculus BC solved exams
AP®︎ Calculus BC Standards mappings
Integrals review
Integration techniques
Thinking about multivariable functions
Derivatives of multivariable functions
Applications of multivariable derivatives
Integrating multivariable functions
Green’s, Stokes’, and the divergence theorems
First order differential equations
Second order linear equations
Laplace transform
Vectors and spaces
Matrix transformations
Alternate coordinate systems (bases)

Frequently Asked Questions about Khan Academy and Math Worksheets

Why is khan academy even better than traditional math worksheets.

Khan Academy’s 100,000+ free practice questions give instant feedback, don’t need to be graded, and don’t require a printer.

What do Khan Academy’s interactive math worksheets look like?

Here’s an example:

What are teachers saying about Khan Academy’s interactive math worksheets?

“My students love Khan Academy because they can immediately learn from their mistakes, unlike traditional worksheets.”

Is Khan Academy free?

Khan Academy’s practice questions are 100% free—with no ads or subscriptions.

What do Khan Academy’s interactive math worksheets cover?

Our 100,000+ practice questions cover every math topic from arithmetic to calculus, as well as ELA, Science, Social Studies, and more.

Is Khan Academy a company?

Khan Academy is a nonprofit with a mission to provide a free, world-class education to anyone, anywhere.

Want to get even more out of Khan Academy?

Then be sure to check out our teacher tools . They’ll help you assign the perfect practice for each student from our full math curriculum and track your students’ progress across the year. Plus, they’re also 100% free — with no subscriptions and no ads.