Skip over navigation
Guide and features
Guide and features
Science, Technology, Engineering and Mathematics
Featured Early Years Foundation Stage; US Kindergarten
Featured UK Key Stage 1&2; US Grades 1-4
Featured UK Key Stage 3-5; US Grades 5-12
Featured UK Key Stage 1, US Grade 1 & 2
Featured UK Key Stage 2; US Grade 3 & 4
Featured UK Key Stages 3 & 4; US Grade 5-10
Featured UK Key Stage 4 & 5; US Grade 11 & 12
A Guide to Problem Solving
When confronted with a problem, in which the solution is not clear, you need to be a skilled problem-solver to know how to proceed. When you look at STEP problems for the first time, it may seem like this problem-solving skill is out of your reach, but like any skill, you can improve your problem-solving with practice.
How do I become a better problem-solver?
First and foremost, the best way to become better at problem-solving is to try solving lots of problems! If you are preparing for STEP, it makes sense that some of these problems should be STEP questions, but to start off with it's worth spending time looking at problems from other sources. This
collection of NRICH problems
is designed for younger students, but it's very worthwhile having a go at a few to practise the problem-solving technique in a context where the mathematics should be straightforward to you. Then as you become a more confident problem-solver you can try more past STEP questions.
One student who worked with NRICH said:
"From personal experience, I was disastrous at STEP to start with. Yet as I persisted with it for a long time it eventually started to click - ‘it’ referring to being able to solve problems much more easily. This happens because your brain starts to recognise that problems fall into various categories and you subconsciously remember successes and pitfalls of previous ‘similar’ problems."
A Problem-solving Heuristic for STEP
Below you will find some questions you can ask yourself while you are solving a problem. The questions are divided into four phases, based loosely on those found in George Pólya's 1945 book "How to Solve It".
Understanding the problem
What area of mathematics is this?
What exactly am I being asked to do?
What do I know?
What do I need to find out?
What am I uncertain about?
Can I put the problem into my own words?
Devising a plan
Work out the first few steps before leaping in!
Have I seen something like it before?
Is there a diagram I could draw to help?
Is there another way of representing?
Would it be useful to try some suitable numbers first?
Is there some notation that will help?
Carrying out the plan
Try special cases or a simpler problem
Guess and check
Work towards subgoals
Imagine your way through the problem
Has the plan failed? Know when it’s time to abandon the plan and move on.
Have I answered the question?
Sanity check for sense and consistency
Check the problem has been fully solved
Read through the solution and check the flow of the logic.
Throughout the problem solving process it's important to keep an eye on how you're feeling and making sure you're in control:
Am I getting stressed?
Is my plan working?
Am I spending too long on this?
Could I move on to something else and come back to this later?
Am I focussing on the problem?
Is my work becoming chaotic, do I need to slow down, go back and tidy up?
Do I need to STOP, PEN DOWN, THINK?
Finally, don't forget that STEP questions are designed to take at least 30-45 minutes to solve, and to start with they will take you longer than that. As a last resort, read the solution, but not until you have spent a long time just thinking about the problem, making notes, trying things out and looking at resources that can help you. If you do end up reading the solution, then come back to the same problem a few days or weeks later to have another go at it.
Meet the team
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
Register for our mailing list
Copyright © 1997 - 2012. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the
Millennium Mathematics Project