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## Strategies For ‘Attacking’ Maths Problems, A Guide For Students And Teachers

In the first article, “How to Answer Questions in a Formal Exam-A Student’s Guide”, I discussed how to answer questions to get the best possible results in an exam. This article continues with that theme but this time in relation to answering questions on a formal Mathematics exam. The strategies discussed in the previous article should be used in the Mathematics exam as well as those discussed below.

It is important to define what I mean by a Mathematical problem before you start studying strategies for solving it.

These problems are almost entirely ‘word’ problems. More often than not, the student needs to use different Mathematical skills or ideas to come up with a solution. Often, especially in the senior years of high school, there are unfamiliar contexts in which to apply your knowledge of Mathematics. On the other hand, there may be a series of sometimes complex steps required to achieve the result. In the end, the answer is not an obvious one.

Below is a list of strategies that, when used together, will help you achieve greater success in solving real Math problems, not just the ones you’ve practiced. However, remember, if you don’t know your Math basics then no set of strategies will help you solve the problems.

So strategy Number 1 is and will always be:

“Know all your learning work and methods as you can.”

The remaining strategies are as follows:

2. Remember, everything you need to solve the problem is in the question itself. (So list what data the problem gives you as your starting point).

3. Analysis is a mandatory part of every problem you solve. Here is the check method to use:

• It is best to check as you go through each step of the problem as this saves time and often prevents unnecessary extra work.

• Make sure you only do what you are told to do. Check, in fact, that you have answered the question completely.

• Check that you have copied all the data for the query correctly.

• Check that your answer (its size, etc.) fits, in a practical sense, the scenario/context of the question.

4. Make sure you are neat, orderly, organized, logical, clear, and concise. This will help you in your assessment and allow the examiner/teacher to follow your logic easily.

5. This strategy was discussed in the first article. It is part and parcel of answering any exam problem, especially in Mathematics. It is: List the steps you need to take, in order, to get a solution.

Below is an example of what I mean by this Mathematical strategy.

The Swimming Pool Problem

“How long does it take to fill a swimming pool with a bucket?”

Here’s how I teach this strategy:

Step 1: I will write the above problem on the board.

When I do this, I ask the students for their reaction:

It will be: “We can’t do it”

You ask: “Why?”

Their answer: “No dimensions”

Your response: “You don’t need it. If I gave it to you what would you do?”

Step 2: Now I have the students write down the steps they will use.

Step 3: Then I discuss the steps chosen by the class and list the steps on the board.

eg Find the volume of the pool.

Find the volume of the bucket.

How long does it take to fill the bucket and pour into the pool?

How many buckets of water do I need to fill the pool?

Find the total time to fill the pool.

Step 4: Now, I make the point that the above steps do not mention the dimensions of the pool. It doesn’t matter what scale it is you still follow the same process.

Step 5: Finally, I emphasize that the correct answer depends on the correct steps, ie solution method.

As a student, you cannot learn these strategies overnight and expect them to ‘come to you’ easily in a formal exam setting. You have to practice using it. Make a list of strategies and take them with you as you try each new problem. Evaluate how well you are using them and work to improve the ones you find the most difficult to use or easy to forget. Look to your teacher for help with this process. Remember, in an exam, be disciplined, write down the list of strategies you will use before you start and use them to solve problems.

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