maths problem solving questions gcse

The resources on this page will hopefully help you teach AO2 and AO3 of the new GCSE specification - problem solving and reasoning.

This brief lesson is designed to lead students into thinking about how to solve mathematical problems. It features ideas of strategies to use, clear steps to follow and plenty of opportunities for discussion.

The PixiMaths problem solving booklets are aimed at "crossover" marks (questions that will be on both higher and foundation) so will be accessed by most students. The booklets are collated Edexcel exam questions; you may well recognise them from elsewhere. Each booklet has 70 marks worth of questions and will probably last two lessons, including time to go through answers with your students. There is one for each area of the new GCSE specification and they are designed to complement the PixiMaths year 11 SOL.

These problem solving starter packs are great to support students with problem solving skills. I've used them this year for two out of four lessons each week, then used Numeracy Ninjas as starters for the other two lessons.  When I first introduced the booklets, I encouraged my students to use scaffolds like those mentioned here , then gradually weaned them off the scaffolds. I give students some time to work independently, then time to discuss with their peers, then we go through it as a class. The levels correspond very roughly to the new GCSE grades.

Some of my favourite websites have plenty of other excellent resources to support you and your students in these assessment objectives.

@TessMaths has written some great stuff for BBC Bitesize.

There are some intersting though-provoking problems at Open Middle.

I'm sure you've seen it before, but if not, check it out now! Nrich is where it's at if your want to provide enrichment and problem solving in your lessons.

MathsBot  by @StudyMaths has everything, and if you scroll to the bottom of the homepage you'll find puzzles and problem solving too.

I may be a little biased because I love Edexcel, but these question packs are really useful.

The UKMT has a mentoring scheme that provides fantastic problem solving resources , all complete with answers.

I have only recently been shown Maths Problem Solving and it is awesome - there are links to problem solving resources for all areas of maths, as well as plenty of general problem solving too. Definitely worth exploring!

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Solving 'number' problems

Number problems often involve a combination of fractions, decimals, percentages and ratio. They can be set in a real-life context. A framework can be used to tackle these problems.

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Number problems

Number problems are often set in a context, typically involving money or an amount of an item. To be confident at solving number problems, it is essential to understand the basics of fractions, decimals, percentages and ratio .

Always ensure that your working out is clear and that you show all of it. If a calculator is allowed, ensure that any calculations are also recorded.

A problem solving framework can be used to tackle number problems.

The six step framework is used to solve a number problem

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Beyond GCSE Revision

Gcse-grade revision from beyond, powered by twinkl, gcse maths problem solving questions with algebra.

Problem solving is a major part of the new GCSE format. The most important point is that, if you see a question that is unlike anything you have seen before, don’t panic or assume that you don’t know how to answer it! You may well know all of the maths content needed to solve the problem but the challenge is working out what you have to use. Join Beyond’s Maths Team as we explore GCSE Maths problem solving questions using Algebra…

First thing’s first: don’t panic!

• Think about what the question has presented to you and if this links in with any of the topics you’ve covered. You may wish to underline the important information in the question, so that you can focus on that and not the irrelevant things.
• Sometimes, a question will give you lots of information in a very roundabout way. Can you think of a better way to present the information, to make it easier to process? Perhaps you could use a two-way table or a Venn diagram.

Sample GCSE Maths problem solving questions

At a party, guests are offered chicken, lasagne or quiche to eat. 7 of the adults choose quiche. There are 100 guests altogether. 16 of the 48 people who choose chicken are children. 28 people eat lasagne and a quarter of these are children. How many children are at the party?

A two-way table really helps with this:

• Using algebra is often a good way to solve problems. If the information in the question suggests a sum, where you have the answer, but not the numbers that go into the sum, using algebra would be a sensible approach.

For example, ‘Aeron is 3 years older than Lily. Heather is 3 times as old as Aeron. The sum of their ages is 67. How old is Lily?’

The calculation that this suggests is: Aeron’s age + Lily’s age + Heather’s age = 67 We don’t know any of the ages but we do know the result of adding them together. Let’s say that Aeron is a years old. In that case, Lily is a – 3 years old and Heather is 3 a years old.

Therefore, the sum of their ages is a + ( a – 3) + 3 a = 67.

Now we can find a by solving the equation and find the ages of the people.

• Coming up with an algebraic expression can be tricky. Say you buy c cartons of juice at x pence each and a hat for £ y ; how much change would you get from £ m ? If you can’t see the answer, make the letters be numbers for a moment and then come up with the sum. Let’s make c be 5, x be 30, y be 2 and m be 20. The cost of the juices would be 5 x 30 pence; with the hat that would be a total cost of (200 + 5 x 30) pence. The change, in pence, from £20 would be 2000 – (200 + 5 x 30). Putting letters back in gives 100 m – (100 y + cx ).
• When a question asks you to ‘show’ something, don’t focus on the final answer; focus on the information that has been given to you, up to that point. Try to build an equation from that information, then try to simplify to give the result.

The perimeter of the shape is 24cm, y = 3 x and z = 2 x , show that x = 2

Perimeter = horizontal sides + vertical sides

( x + y + x + y )+ ( z + z ) = 24

Substituting in y and z in terms of x gives:

x + 3 x + x + 3 x +   2 x + 2 x = 24

• Be comfortable about using methods in reverse. For example, you can use a Venn diagram and prime factors to find the HCF and LCM of two numbers. If you know the HCF and LCM, starting with the Venn Diagram, you can work backwards to find the numbers.

Beyond resources for Maths problem solving questions

GCSE Probability and Statistics Problem Solving Worksheets

GCSE Algebra Problem Solving Worksheets

Long Multiplication Word Problems Differentiated Worksheets

Edexcel Foundation Specimen Papers

You can find our other Maths blogs here – you might find our Maths Mastery Blogs particularly useful! While we’ve got you, don’t forget to  subscribe to Beyond  for access to thousands of secondary teaching resources. You can  sign up for a free account here  and take a look around  at our free resources  before you subscribe too. Happy revising from the Beyond Maths Team.

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Resourceaholic

Ideas and resources for teaching secondary school mathematics

• Blog Archive

Problem Solving

• Problem Solving Booklet - Complete Mathematics
• GCSE Mathematics - 90 Problem Solving Questions - AQA (and PowerPoint collated by @EJMaths)
• Additional Mathematics Problem Solving Questions (& Teacher Guide ) - AQA
• GCSE Problem Solving  - MEI
• 55 Problems - MathsBox
• Maths problems, puzzles and ideas - Cubed Maths
• UKMT Problems PowerPoint - collated by Dan Walker
• San Gaku Problems - Dan Walker
• Support for Problem Solving  - OCR
• Badger Maths Problem Solving Samples (Years 1 - 6) - via National Stem Centre
• Daily Maths Puzzles (Key Stage 2) - Sarah Farrell
• Mathematical challenges for able pupils in Key Stages 1 and 2 - DfE
• Problem solving with EYFS, Key Stage 1 and Key Stage 2 children - DfE
• Solve My Maths
• Catriona Agg
• Maths Problem Solving
• MathsChallenge.net
• Brilliant.org
• Underground Mathematics
• Openmiddle.com
• United Kingdom Mathematics Trust
• 1001 Math Problems

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Problems of the day

March Problems of the Day 2020 – KS2/KS3 Full Set

Here's the full set of KS2/KS3 problems from this year, along with answers.

March Problems of the Day 2020 – KS1 Full Set

Here's the full set of KS1 problems from this year, along with answers.

March Problems of the Day 2019 – GCSE Full Set

A set of GCSE problems covering content for foundation, foundation/higher crossover and higher. We hope they are useful in the run up to the exams. Good luck! #MathsEveryoneCan

March Problems of the Day 2019 – KS2 Full Set

Here is the full set of questions for KS2 Problems of the Day from March 2019.

March Problems of the Day 2019 – KS1 Full Set

Here is the full set of KS1 Problems of the Day that were released throughout March 2019.

March Problems of the Day 2018 – KS2 Full Set

For the month of March, each day we publish some reasoning and problem solving questions for use with your classes in the run-up to SATs. Practice is crucial to maths success, and our questions are designed to support your daily routines. These problems can be used across Y5 and Y6 throughout the year.

March Problems of the Day 2018 – KS1 Full Set

For the month of March, each day we publish some reasoning and problem solving questions for use with your classes in the run up to SATs. Practice is crucial to maths success, and our questions are designed to support your daily routines. These problems can be used across Y1 and Y2 throughout the year.