maths problem solving questions ppt

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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Ideas and resources for teaching secondary school mathematics

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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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GCSE Maths: Problem Solving Higher Questions

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

27 February 2024

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GCSE Maths Problem Solving Higher Questions

This KS4 GCSE-Style Questions - Higher Set 1 Question Set contains GCSE-Style questions that typically appear on higher papers. There are a variety of topics and skills tested in order to prepare students for the GCSE exam. Registering for an LbQ account will give you access to the questions included in this resource and many 1,000s more. These 5 questions are a selection from a bigger Question Set of the same style, we also have a further 9 Higher GCSE-Style Question Sets; they can be used as a teaching starter, plenary or activity for pupils. It is designed to provide teachers a taste of what our content is all about. LbQ Maths Question Sets are based around the principles of mastery and have been developed by teachers and subject matter experts. Each Question Set targets a curriculum objective, though some objectives need more than one set, and has been guided by the White Rose Maths curriculum breakdown.

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Netflix's hit sci-fi series '3 Body Problem' is based on a real math problem that is so complex it's impossible to solve

• The three-body problem is a centuries-old physics question that puzzled Isaac Newton .
• It describes the orbits of three bodies, like planets or stars, trapped in each other's gravity.
• The problem is unsolvable and led to the development of chaos theory.

While Netflix's "3 Body Problem" is a science-fiction show, its name comes from a real math problem that's puzzled scientists since the late 1600s.

In physics, the three-body problem refers to the motion of three bodies trapped in each other's gravitational grip — like a three-star system.

It might sound simple enough, but once you dig into the mathematics, the orbital paths of each object get complicated very quickly.

Two-body vs. three- and multi-body systems

A simpler version is a two-body system like binary stars. Two-body systems have periodic orbits, meaning they are mathematically predictable because they follow the same trajectory over and over. So, if you have the stars' initial positions and velocities, you can calculate where they've been or will be in space far into the past and future.

However, "throwing in a third body that's close enough to interact leads to chaos," Shane Ross, an aerospace and ocean engineering professor at Virginia Tech, told Business Insider. In fact, it's nearly impossible to precisely predict the orbital paths of any system with three bodies or more.

While two orbiting planets might look like a ven diagram with ovular paths overlapping, the paths of three bodies interacting often resemble tangled spaghetti. Their trajectories usually aren't as stable as systems with only two bodies.

All that uncertainty makes what's known as the three-body problem largely unsolvable, Ross said. But there are certain exceptions.

The three-body problem is over 300 years old

The three-body problem dates back to Isaac Newton , who published his "Principia" in 1687.

In the book, the mathematician noted that the planets move in elliptical orbits around the sun. Yet the gravitational pull from Jupiter seemed to affect Saturn's orbital path.

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The three-body problem didn't just affect distant planets. Trying to understand the variations in the moon's movements caused Newton literal headaches, he complained.

But Newton never fully figured out the three-body problem. And it remained a mathematical mystery for nearly 200 years.

In 1889, a Swedish journal awarded mathematician Henri Poincaré a gold medal and 2,500 Swedish crowns, roughly half a year's salary for a professor at the time, for his essay about the three-body problem that outlined the basis for an entirely new mathematical theory called chaos theory .

According to chaos theory, when there is uncertainty about a system's initial conditions, like an object's mass or velocity, that uncertainty ripples out, making the future more and more unpredictable.

Think of it like taking a wrong turn on a trip. If you make a left instead of a right at the end of your journey, you're probably closer to your destination than if you made the mistake at the very beginning.

Can you solve the three-body problem?

Cracking the three-body problem would help scientists chart the movements of meteors and planets, including Earth, into the extremely far future. Even comparatively small movements of our planet could have large impacts on our climate, Ross said.

Though the three-body problem is considered mathematically unsolvable, there are solutions to specific scenarios. In fact, there are a few that mathematicians have found.

For example, three bodies could stably orbit in a figure eight or equally spaced around a ring. Both are possible depending on the initial positions and velocities of the bodies.

One way researchers look for solutions is with " restricted " three-body problems, where two main bodies (like the sun and Earth) interact and a third object with much smaller mass (like the moon) offers less gravitational interference. In this case, the three-body problem looks a lot like a two-body problem since the sun and Earth comprise the majority of mass in the system.

However, if you're looking at a three-star system, like the one in Netflix's show "3 Body Problem," that's a lot more complicated.

Computers can also run simulations far more efficiently than humans, though due to the inherent uncertainties, the results are typically approximate orbits instead of exact.

Finding solutions to three-body problems is also essential to space travel, Ross said. For his work, he inputs data about the Earth, moon, and spacecraft into a computer. "We can build up a whole library of possible trajectories," he said, "and that gives us an idea of the types of motion that are possible."

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