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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New Math Word Problem Worksheets
Math word problems challenge students to think critically and apply their knowledge of addition and subtraction stories. However, relying on a single strategy can limit their problem-solving skills. That’s why you must teach students multiple strategies when solving word problems.
Check out this resource and grab the freebie at the bottom of this post.
Different Types of Word Problems
This resource covers five different types of word problems, so students encounter a variety of scenarios such as “add to” and “take from” problems to “put together” situations, “both addends unknown,” and exploring “ways to make 10.”
Get more math problem strategies, tips, and activities here.
With math task cards , students can practice problem-solving independently or in groups. The math center activity encourages acting out word problems using objects.
Digital Word Problems provide a self-checking, Google Slides-ready option for interactive solving.
In addition to the interactive activities, this resource includes valuable tools to support students’ problem-solving. Math mats enable students to apply multiple strategies and visualize their thinking. Picture Vocabulary Cards serve as a visual menu of math strategies, empowering students to choose the approach that resonates with them. These additional resources allow students to gain independence and solve problems with minimal teacher support. The included math strategy cards further empower students to select a strategy that suits their learning style.
When can I use this?
You can use this resource for morning work, warm-ups, exit tickets, homework, math center work, and post-lesson follow-up activities. Teachers can also use printables to model specific problem-solving strategies, providing valuable guidance to students. This resource integrates into existing math instruction and provides ample practice to reinforce skills, promote critical thinking, and deepen students’ understanding of word problems.
Grab a freebie page from this resource here.
You can get the packet here.
How do you teach math word problems in your classroom? Let me know in the comments section.
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Problem Solving Strategies
The following are some examples of problem solving strategies.
Explore it//Act it/Try it (EAT) method (Basic)
Explore it//Act it/Try it (EAT) method (Intermediate )
Explore it//Act it/Try it (EAT) method (Advanced)
Finding a Pattern (Basic)
Finding a Pattern (Intermediate)
Finding a Pattern (Advanced)
Explore It/Act It/Try It (EAT) Method (Basic)
In this lesson, we will look at some basic examples of the Explore it//Act it/Try it (EAT) method of problem solving strategy.
A plumber has to connect a pipe from a storage tank at the corner, S , of the roof to a tap at the diagonally opposite corner, T , in the figure below. Find the number of paths for the pipe if the pipe can only run along the edges of walls A , B , or roof C .
Three stamps are to be torn from a sheet of nine stamps as shown below. The three stamps must be intact so that each stamp is joined to another stamp along at least one edge. Find the possible patterns for these three stamps.
Rachel has to spend exactly $100 on the following gifts. What are the combinations of gifts that she can buy?
B, E, F or B, D
The figure below shows 9 matchsticks arranged as an equilateral triangle. Rearrange exactly 5 of the matchsticks to form 5 equilateral triangles, without leaving any stray matchsticks.
The figure below shows the roads linking cities R and S . What are the different routes to travel from R to S ?
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Problem Solving Worksheets & Workbooks
Are you looking for fresh, new ideas to help your pupils with maths problem-solving? Problem-solving is a key skill that children need to learn to be successful in maths. Maths education should prioritise problem-solving, as it provides children with the foundational skills they need to tackle any challenge that comes their way.
Do you have all you need to teach problem-solving in maths?
Prim-Ed Publishing has many great resources available that can help teachers successfully implement problem-solving into their maths curriculum. From boxed resources and worksheets to teachers notes and photocopiable books, covering a wide range of exciting and high-interest problem-solving activities, we have the tools to support teachers to confidently deliver problem-solving in class.
What is problem-solving?
In its simplest form, problem-solving is the process of finding solutions to problems and challenges that we encounter in our lives. It is a fundamental skill that we use daily, often without even realising it. The ability to solve problems often depends on our capacity to think flexibly and see things from different perspectives.
With problem-solving embedded at the heart of all maths lessons, pupils can master the core concepts and strategies needed to succeed in any situation.
Why is mathematics problem-solving important?
At every stage of life and in every development context, problem-solving skills are invaluable.
Whether we are negotiating with a client, tackling a challenging task at work or simply navigating our way through crowded streets and busy social situations, problem-solving skills help us to cope more effectively with the obstacles and challenges we encounter. Fortunately, these skills can be learned and developed through education.
Developing problem-solving skills in young learners
Problem-solving should be at the heart of maths education because it is a fundamental life skill. By teaching pupils how to break down a problem into smaller steps, you can help pupils overcome their natural aversion to difficulties and give them the confidence to tackle anything that comes their way.
Learning to solve problems encourages mathematical thinking
One of the benefits of problem-solving is that it encourages pupils to think mathematically.
Mathematical thinking enables us to make sense of the world around us using numbers, shapes and patterns. It helps us understand relationships, detect trends and make predictions. Mathematical thinking is not just about being able to do sums; it’s a way of looking at and understanding the world.
In mathematics, pupils learn to analyse the information given in maths problems and then use their maths knowledge and skills to find answers.
Problem-solving skills in primary mathematics
Problem-solving skills are best developed through opportunity and practice. Teachers must provide opportunities for young learners to engage in problem-solving activities regularly.
By developing the ability to problem-solve, pupils gain a better understanding of the concepts and skills underlying mathematical objectives, concepts and processes. In addition, problem-solving allows children to practise critical higher-order thinking skills such as reasoning, interpretation, synthesis and evaluation.
A problem-solving approach to teaching
Problem-solving should be taught explicitly, with rich mathematical tasks and practice opportunities included in every lesson. This also involves developing pupils’ understanding of mathematical concepts such as:
- Shape and space
There are many ways to incorporate problem-solving into your classroom lessons.
- Problem-solving activities and worksheets can be used to assess pupils’ understanding.
- Provide opportunities for pupils to engage in collaborative problem-solving tasks, with partners or groups.
- Challenge young learners with problems presented visually, such as tasks interpreting the data in tables, graphs and charts.
- The three-book series, Maths through Language , is a great way to integrate language into your maths lessons.
- Hands-on games and puzzles come in all shapes and sizes and can be adapted to suit any age group or ability level.
- Puzzles will help pupils develop patience, persistence, and attention to detail – all essential qualities for good problem-solvers.
Problem-solving resources from Prim-Ed Publishing
With Prim-Ed Publishing , teachers have access to a wide variety of problem-solving resources – including worksheets, boxed materials, photocopiable books, ebooks and digital resources – that provide engaging activities designed to help pupils thrive in this area.
Our problem-solving resources are designed to engage pupils and focus on key problem-solving strategies, such as visualising, reasoning, working systematically and making models and diagrams.
Our resources include extensive background information, curriculum links, extension activities and teachers notes to teach young people the specific skills needed for problem-solving.
A few of the most popular products available from Prim-Ed Publishing include:
- Measurement and Geometry
- Number and Algebra
- Statistics and Chance
- Primary Problem-Solving In Mathematics
Prim-Ed Publishing's problem-solving resources will support teachers and help to develop pupils' problem-solving skills, encouraging mathematical thinking along the way.
Why not browse our full range of mathematics resources today?
Frequently asked questions
What is problem-solving in primary maths.
One of the most important skills pupils learn in maths is how to solve problems. A maths problem can be defined as a question or task that requires pupils to use their skills and knowledge to find the answer.
What are some of the best problem-solving techniques?
There are a number of problem-solving techniques that can be useful for pupils.
- One strategy is to use logical reasoning, connecting the facts and evidence to reach a conclusion.
- Another strategy is to visualise the problem, picturing it in your mind and exploring different solutions.
- You can also break the problem into smaller pieces, analysing each part and looking for patterns.
- Finally, it can be helpful to get feedback from others and ask for their suggestions.
How can problem-solving skills be taught effectively in the mathematics curriculum?
There is no definitive way to teach effective problem-solving skills, as the approach will vary depending on the problem and the child's age. However, there are some different approaches that can be useful.
- Strategic thinking: teaching pupils to solve problems through strategic thinking can be helpful.
- Presentation styles: problems can be presented visually to help pupils see the relationships between different aspects of the problem.
- Spatial visualisation exercises: help pupils understand relationships between objects in space, which can be helpful for solving mathematical problems.
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Maths Problem Solving Booklets
Age range: 11-14
Resource type: Worksheet/Activity
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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Great resource to use at KS3
Just what I have been looking for. Thanks so much!
Good resources. Thanks you!
Thanks for sharing. Really useful booklets.
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Free worksheet – addition and subtraction word problems strategy.
Free word problem comprehension strategy teaches students to apply reading comprehension strategies using CUBES or CUBED method – FREE!
This easy-to-use CUBES word problem strategy provides your students with the tools to solve addition and subtraction word problems. This strategy works because students are given a solid, concrete method to organize information.
Math word problems are always a bug-a-boo to teach – but they don’t have to be when students break the problem down into smaller pieces.
Concrete Strategy for Addition and Subtraction Word Problems
I’ve tried several different math word problem strategies for teaching students to truly understand story problems. However, CUBES or CUBED is the one method that I keep returning to year after year.
Plus, with these worksheets, students learn to apply the strategies they learn in reading class to their math problems – this brings REAL results!
Keep reading for a FREE SAMPLE!
Solving multi-step problems is difficult for students, and using either the CUBES or CUBED strategy helps break down the steps. A straightforward, easy-to-understand method also promotes confidence and provides a consistent strategy to follow.
Each page lists either the CUBES or CUBED procedure in a checkbox format. Most teachers are already familiar with CUBES, and with CUBED, the “D” stands for “Draw a picture.” Students are encouraged to draw a picture to help promote comprehension and problem-solving.
I love the twist on CUBES – drawing pictures helps visual learners make the story problem concrete enough to visualize and solve .
Want to learn more about CUBES and CUBED?
To learn more about CUBES and CUBED math word problem-solving strategies, you’ll like the article Struggling with Math Story Problems? CUBES to the Rescue!
To learn more about steps to solve math word problems in general, you’ll like the article How to Teach Math Word Problems – CUBES Math Strategy .
Now for the FREE Addition and Subtraction Worksheet
Try a FREE sample worksheet for yourself! Click on the image to visit my Teachers Pay Teachers store.
You’ll find the FREE worksheet in the PREVIEW! Enjoy!
FREE – did someone say “ Free ?? ” Visit my Teachers Pay Teachers Store for a FREE SAMPLE – try it out and see what you think!
You’ll find the free worksheet in the PREVIEW on Teachers Pay Teachers.
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