Chapters

Would you rather:

a) sit through a horror movie marathon,

b) go shark cage diving, or

c) tackle a Maths problem?

If you answered *a* or *b* then this article is definitely for you - so keep reading! We get it, Math problems can seem big and scary. The good news is, with some Math magic tricks, solving them doesn’t have to be.

Our hope with this article is to give you **the help you need **to confidently sit down and solve any Maths problem, whether it is made up of decimal numbers, linear equations, inequalities, square roots, absolute value or exponents.

## Maths Problem Solving: Explained

Before getting to the problem-solving tricks, let’s look at what the National Council of Teachers of Mathematics (NCTM) considers to be the definition of Maths problem solving:

"Problem solving means engaging in a task for which the solution method is not known in advance. In order to find a solution, students must draw on their knowledge, and through this process, they will often develop new mathematical understandings. Solving problems is not only a goal of learning Mathematics, but also a major means of doing so."⁓ Make Sense of Problems and Persevere in Solving, NCTM, 2000 (p. 52)

Another way of putting it, according to the mathematician George Pólya, is that every Maths problem comes down to “finding the connection between the data and the unknown”.

What we’re concerned with in this article is how to navigate the space between point A (the data) and point B (the unknown), a.k.a. finding the connection. Well we’re in luck! Pólya, in his 1945 book *How to Solve It* did a lot of the groundwork for us. We’ll get into his tricks for Math problem solving in a bit, but first, we want to acknowledge that not all Math problems are created equal.

It makes sense that equations will, of course, look very different depending on where you are in your academic career. That’s OK. The great thing about having a full-proof plan is that although their difficulty may change, the principles behind solving them remain the same.

Let’s take a look at how they differ, from primary school through to Matric.

**Primary School (1**^{st} Grade – 5^{th} Grade) Maths Problems

^{st}Grade – 5

^{th}Grade) Maths Problems

In Primary School, students can look forward to learning the basics of addition, subtraction, multiplication and division, i.e. the four operations. In the earlier grades (1 - 3), children may use apparatus or physical aids. From Grade 3 onward, children will be encouraged to adopt written methods.

A Grade 1 problem will look something like this:

*Mark has 2 apples. Kathy has double this number of apples. How many apples does Kathy have? *

* *In Grades 4 and 5, word problems will have more than one step:

*Kathy has 20 apples. She shares them equally between 3 friends. How many apples does each friend get? How many apples does she have left? *

**High School (8**^{th} Grade – 11^{th} Grade) Maths Problems

^{th}Grade – 11

^{th}Grade) Maths Problems

A lot of what is covered in high school is cumulative, i.e. built onto what was learned in primary school. So, it’s imperative for high school students to have mastered what was taught in the earlier grades before they can move on to more advanced Maths concepts and equations. During these four years, students will be introduced to Algebra, Geometry, Trigonometry and Calculus.

What follows is an example of a 10^{th} Grade Algebra problem:

*The cost of 2 apples, 4 oranges and 3 pears is R35. The cost of 5 apples, 5 oranges and 2 pears is R35. What is the total cost of 1 apple, 1 orange and 1 pear?*

The solution here would be to start by assigning variables to the unknown quantities, i.e. let *x* be the price of 1 apple, *y* be the price of 1 orange and *z* be the price of 1 pear etc.

**Matric (12**^{th} Grade) Maths Problems

^{th}Grade) Maths Problems

By now, students will be solving multi-step problems, involving not only more than one operation, but also fractions, percentages and decimals - potentially all part of the same equation!

Here’s an example of a Matric-level question:

*Kathy deposited a R100 starting amount in her brand-new savings account. She will earn 10% interest, compounded annually. Using a formula, what will her balance be after 2 years?*

As you can see, although the problems continue to get trickier and trickier, at their very core, they can all be reduced to three things: the unknown, the data and the connection or condition.

## Why Are Maths Tricks So Important?

Maths encourages students to develop their problem-solving skills.

These skills are so important because the more we use them, the easier it is for us to take initiative, learn from our mistakes and get creative. Basically, practising Maths is one way we can train our mind to **be curious rather than afraid**. These are all critical 21^{st} century skills in an ever-changing world. The good news is, our tips on how to solve Math problems can be used in the real world too, not simply in the classroom. Are you ready to put your detective hat on?

Before we explain the techniques, we need to share with you a secret step, which is one of the most important – yet often overlooked – of the Maths magic tricks: Your Maths lessons.

**Make Friends with Your Maths Lessons**

Every Maths lesson is **an opportunity to discover a new concept**. If that doesn’t get you excited, then maybe this will: The more effort you put into your Maths classes, the greater your takeaways will be and the less time you’ll need to give to homework and studying!

How to get the most out of Maths class:

The night before, have a glance at the chapters you’re going to cover in class – this will give you a head start!

Take notes, but remember, you don’t have to write down everything! After all, you have a textbook for a reason. It’s more important and beneficial to

listen carefullyto what your Maths teacher is saying.

Ask thoughtful questions. As long as they’re not for the sake of it, your peers and teacher will thank you for it! Promise.

That said, Maths lessons - in a classroom with sometimes thirty other students - aren’t for everyone. Some learners benefit more from one-on-one attention. If this is you, then you may want to give Math help online a try.

## Maths Magic Tricks

Now that we’ve built a solid Mathematics foundation, are you ready to bring Pólya’s problem solving tricks into play? Math help is on the way!

**Trick ****№ ****1: Read Carefully**

**№**

The next time you’re in need of some Maths help, remember this: The first trick to solving any problem is to **make sure that you understand it fully**. You can do this by reading it again and again then asking yourself these questions:

Can I put the problem into my own words?

What is the unknown?

What is the data?

Is there enough information for me to find a connection between the unknown and the data?

The more you practise this Maths trick, the more you’ll find yourself doing it out of habit. Which is a good thing! Especially when it comes to being exam-ready.

**Trick ****№ ****2: Everything Is a Clue**

**№**

Rule number 1 of being a Maths detective is **knowing which clues to look for**. This is why a solid foundation is so important. Throughout your academic career, one of the skills you develop is how to recognise a clue word and how to know which of the four operations it’s a clue for, i.e. addition, subtraction, multiplication or division.

Let’s go back to our primary school (4^{th} Grade and 5^{th} Grade) example:

*Kathy has 20 apples. She shares them equally between 3 friends. How many apples does each friend get? How many apples does she have left? *

The clues here are the words “shares” and “left”. These tell us that we’ll be performing two operations, i.e. division and subtraction respectively.

Once you’ve identified all the clue words, you can **start coming up with a plan or strategy**. As we mentioned before, some equations are harder or more layered than others. For these, you may need to ask additional questions, such as:

- Have you seen a problem like this before?
- If yes, what do you remember doing to solve it?

By now, your plan should be taking shape, which means it’s time for you to advance to the next step.

**Trick ****№**^{ }**3: Play**

**№**

You’ve done all the groundwork of coming up with a plan. Now it’s time for you to **be curious and see what happens**. If your strategy doesn’t work, don’t get disheartened. Simply go back to the beginning and keep trying. Remember, every mistake has a silver lining.

**Trick ****№ ****4: Review**

**№**

Here is where all your hard work could go to waste. To prevent careless mistakes, we recommend even the most advanced students **go back and check** their calculations.

## The Moral of the Story

In summary, success at solving scary Maths problems (or any problems, really) starts with cultivating a curious mind-set.

Why?

Because the opposite of fear is curiosity. So, it makes sense that if you think of a problem as a harmless puzzle, then the easier it will be for you to solve it. There’s nothing scary about puzzles, is there? It doesn’t hurt to have Maths help in the form of a fool proof, four-step method either.

If you’re still feeling a bit shaky factoring polynomials, calculating compound interest or solving systems of equations, you may want to consider seeking Math help from a private tutor. Your tutor will be able to take you through the Math concepts you’re unsure of, in a safe space and at your own pace, and share with you some cool Math strategies to help you succeed.