Equations & Problem Solving
What is problem solving?
- Problem solving in mathematics involves using several stages, across a variety of topics, to answer a question
- In this set of notes all the problems will involve equations
- These could be linear equations, quadratic equations or simultaneous equations and other, relatively straightforward equations
- You may notice there are not many subheadings in these notes
- That is deliberate so the examples are not labelled or dealt with in an order
- This is the nature of problem solving questions!
- You never know exactly what’s coming ... !
- In an ordinary mathematics question you would be given an equation to solve
- In a problem solving question you would have to generate the equation ...
- ... using information from the question
- ... using your knowledge of standard mathematical results
- A key feature of problem solving questions is to interpret the answer in context
- An answer on a calculator may be 2
- If the question was about money then your final answer should be £1.20
- A quadratic equation can have two solutions
- Only one may be valid if only positive values are relevant (eg distance)
- In problem solving questions you are typically given less information about the type of maths involved
- It is impossible to list every type of problem solving question you could see
- There are endless contexts questions can be set in
- There is no one-fits-all step-by-step method to solving problems
- Practice, experience and familiarity are the keys to solving problems successfully
- Do not necessarily expect whole number (integer) or “nice” solutions
- Especially where a calculator is allowed
- Rounding appropriately may be one of the skills being tested
- eg Rounding a value in cm only needs to be to one decimal place;
so it indicates mm
- eg Rounding a value in cm only needs to be to one decimal place;
Examiner Tip
- Do not start by focusing on what the question has asked you to find, but on what maths you can do
- If your attempt turns out to be unhelpful, that’s fine, you may still pick up some marks
- If your attempt is relevant it could nudge you towards the full solution – and full marks!
- Add information to a diagram as you work through a problem
- If there is no diagram, try sketching one