Developing your talent for maths problem solving is definitely one of the most important steps to take when you want to succeed in maths - and that's because, really, all maths problems are just puzzles and problem solving questions - that includes geometry questions, algebra questions, even the infamous calculus problems!
To approach a maths problem, whether you're a primary school student, or studying for a masters degree in Mathematics, adopting a problem-solving frame of mind will go a long way in helping you get a handle on the problem.
Lots of people get pretty apprehensive when it comes to tackling maths problems, and as a result they don't think as clearly as they normally would - which just compounds the issue! Follow our maths guides though, and you'll be able to boost your confidence in your mathematics, and make quick work of tackling tricky maths problems.
Defining Maths Problems
Before we get stuck in with solving problems with maths help, we should first be clear on what they actually are. Throughout your academic career, the only thing that changes about maths problems is their difficulty: the principle of each problem is the same, even when the content itself changes (the same thought process can be used for word problems, or calculus problems).
Here's what my handy dictionary has to say about maths problems:
A maths problem is a question to solve through scientific means
We can change this definition a little, though: making it more specific depending on where in your academic career you are:
You should consider the problem like a puzzle to solve, using the information given in the question. In this stage of your learning, it's important to familiarise yourself with numbers, figures and counting. You first focus on the basics of arithmetic, multiplying, place values, the like. Later on, you'll look at word problems like the one below.
Here's an example of a question you might see in school:
It's 2PM. John and Tim are going to go for a walk in the forest. What time will they get back if their walk lasts 1 hour and 45 minutes?
Secondary School Maths Problems
During the first stages of your secondary education, you'll learn about expressions and fractions. Things are getting trickier now, but it's still pretty manageable. Here's a problem for which you'd need to find a solution in secondary school:
John has 10 sweets. He hands two to Sally, and twice as many to Jane as he gave to Sally. Finally, he gives Fred a third of the number of sweets that Sally and Jane have together. How many sweets is John left with?
GCSE Maths Revision / A Level Problems
Heading into your GCSEs and A levels is where things really start to get tricky, and where having a well-honed problem solving skill set can really come in handy. Every problem you come across at this level will require some thought and problem solving knowhow. They will also mix together topics you have previously studied: algebra and fractions may come up in the same question, for example.
Here's an example of such a problem:
Nick has 75 metres of fence. He wants to mark out an area in a field with his fence, and this area must be rectangular. It must also be as large as possible, in order to fit as many sheep in as possible. What's the largest area that Nick can fence off, and how can he calculate this?
The level of difficulty in each of the stages of academia differs, but the principle remains the same. We're given a scenario, some clues, and a question to answer.
If you don't like thinking about maths, picture yourself as a private detective, given several clues to crack a case wide open!
Making the Most of Maths Lessons
Your maths teacher won't ever give you a piece of homework, or an exercise, that doesn't match up with something you've done before in class.
Lessons normally work as follows: you will have a lesson on a particular subject, and then you have to practise by yourself (usually by attempting problems), and work out how much of the content you understand. Then, normally your teacher will set a test at some point on the content.
As much as you might find the lessons a little dry at the time, they're the first step in improving your understanding of mathematical concepts, and it's essential you put the effort in and get it right.
Before trying to tackle a math problem, make sure you've understood the concepts you were taught during the lesson, because they'll undoubtedly be linked in some way.
So, summing up - to make the most of your maths lessons...
- Listen carefully to your teacher (for the whole lesson!)
- Test yourself with questions on topics you're uncertain of, so you can get some practise in!
- Learn off by heart important and simple concepts (for example: Pythagoras' theorem).
- Start making your own revision folder, detailing all of the concepts covered in class.
If you want to go further in your studies, or maybe you're struggling a little in class, you could consider an online math tutor, who can go through the content with you at home, at your own pace.
Reading the Question: Take your Time
Faced with math problems, at home, in an exam, or in class, your first instinct should be to read the question. And then read it again. Maybe even a third time for good measure.
Basically, missing one small detail could be the difference between getting the correct answer, and only being able to present witty doodles to the examiner!
Fear not, though! Just follow these simple steps, and you'll have the maths cracked in no time:
- Keep your workspace as tidy and distraction free as possible: make sure everything is organised, and only have the essentials cluttering the desk.
- Make sure you read the question several times.
- If you can, draw a diagram or model of the problem.
- Highlight anything in the question you think will be key to solving it.
- Try and put into your own words what the question is asking.
Follow these steps, and practise with them too, and you'll find yourself doing them out of habit when it comes to exam time.
Examining the Clues
The text of a maths question you've been given is stuffed full of clues, you just need to assemble them correctly to work out how to solve the problem!
Some people find this tricky, and that's where some maths home tuition might suit you. Having concepts explained to you at your own pace, within the comfort of your own home, works better for some people than sitting in a classroom with 25 other students!
To get a feel for this, here's an example question about equations...
When Gina was born, her mum was 30 years old, and her brother 4 years old. Today, the ages of Gina, her brother, and her mother, add up to 100 years.
- If we call Gina's age 'x', express the ages of her brother and mum as a function of 'x'.
- How old is Gina today?
Have a read through of the question a few times, and try and pick out the key information. Once you've done this, here's a breakdown:
- We know that Gina's mum was 30 years old at Gina's birth.
- We know that Gina's brother is 4 years older than she is.
- We know that all of their ages added together is equal to 100 years.
So, from these facts, we can fairly easily determine an equation:
- We call Gina's age 'x'.
- The age of Gina's brother is 'x + 4'
- The age of Gina's mother is 'x + 30'
Really, we're looking at some fairly basic math problems, just dressed up as a fancy word problem.
What About Harder Maths Problems?
This example was pretty simple, but it shows you how you can extract information from a worded question and turn it into figures used to solve a problem using concepts you learnt in your math lessons.
For a harder problem, you might have to take the clues you've identified and then test a few different theories and see what works.
This is when all the practise you put in earlier really counts, and listening to your math teacher pays off. Have a repertoire of mathematical concepts and theories you can call upon to work out how to solve the problem really makes finding the solution easier.
If you're still stuck, try thinking back to questions you've done before. Particularly in exams, the questions often follow some sort of format or pattern, and being able to recall a previous question of a similar style might help you solve the one currently in front of you.
Checking Your Answers!
Of course, all of the hard work you just put into answering the question is in vain if you didn't get the correct answer - this is why it's so important to check the answer you got! This is especially easy in questions involving equations, which is helpful, as it's quite easy to slip up while factoring.
Check through your calculations again, making sure you didn't slip up anywhere and make a small mistake - especially early on, where any mistakes made will cascade into later parts of the question.
It's also worth reading the question again, to check you haven't made any assumptions about the question accidentally, or didn't miss any key facts.
Finally, remember that not all maths questions simply require you to throw any old number in as the answer. Some (particularly in exams) require you to justify your answer, or add some detail to it in some other way. And yes, this may (gasp) involve writing a small paragraph. This is especially true with math word problems, where the question was given as a paragraph.
If this is the case, make sure you do fully answer the question, and make sure you write legibly, and that your answer makes sense, and is free of spelling or grammatical errors.
So, to sum up, solving maths problems is all about having a sound and simple method for approaching problems, and rigorously practising applying this method. From kindergarten through to college, the same processes can be used to work out the answer to a maths problem. Simply follow logical reasoning and you'll get the solution in the end!
If anything above sounded a bit tricky to you, or maybe you just want to gain an extra edge, consider taking up some private maths tuition. Private tutors can work at your pace, and target their teaching approach towards what works for you personally - they can really make a difference when it comes to boosting your grades! Search for 'maths tutors near me' at Superprof. :)