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The Guidelines of Accurate Mathematical Working

In maths we are presented with problems, and with these problems, examiners are expecting you to showcase your mathematical prowess and ability to solve them, but what good does that do if they can’t interpret your work through your examination booklet? It will most likely result in losing marks you shouldn’t have!

There is a lot to learn before we tackle some more practical examples such as how to set out your algebraic, geometric, or graphical working out discussed in later articles. Here right now, I’m going to discuss with you the guidelines of accurate mathematical working out, the sort of working out that will ensure you receive the highest mark you deserve!

1. Read The Question Carefully

The first principle is obvious, yet, it is probably the most important. Read the question carefully! Then read it again! Then again! If I can recall all the times I myself have made this mistake of not reading the question carefully and received a dollar for it I’d probably be $13,573 richer.  As a tutor however, time and time again I’ve seen students who had just began with me present their answer to me in their homework where it is obvious they hadn’t read the question carefully, a habit that was quickly corrected. Don’t just assume you know what the question is asking because you’re usually wrong, take your time and read. I came to this conclusion because I have marked homework that has working out which has omitted crucial values or relationships the question had stated. What good does all your practice and hard work do if you haven’t answered the question correctly in the first place? Almost nothing.

The common problem student’s face who don’t read the question carefully is that they rush through their work. I tell them time and time again “you must be slow before you are fast” a common phrase that is repeated to all eager students who forget the importance of taking their time… but it is true and will always be true.
When you approach your homework, or your examination questions take your time, approach each question before you attempt it with a calm, collected, and mindful attitude. Think:


What does the question say?


what type of question is it?


what are the important values or links in the question?

Ask yourself each of these questions before you even begin attempting the answer and I can ensure you with a 100% guarantee that you will notice a stark difference in the quality of your working out, from reading the question carefully alone! You will notice at first your silly mistakes occurring less frequently and then finally being able to identify the type of math problem it is and the important values of the question more quickly than before. At first you must take it slowly, read the question, think about what type of math problem it is, what are the values, what are the links?, what does it say again? This is the first and most important guideline to accurate mathematical working out.

2. Make Your Work Presentable

The most logical step after reading the question carefully is to consider how it is you plan on presenting your working out. Ask yourself, does this question involve diagrams or graphs? Do I have to come back and label aspects of the answer? Is the question in multiple parts?  You should provide adequate space for every aspect of your working out as you may find that you will return to certain parts to redo or edit certain areas. Work down the page and don’t try and ever save space for the next question, use what you need for the question at hand.

The process of finding a solution especially for more difficult mathematical problems is a constant process of reiteration and attempting the question from different angles to reach the final answer, which can be a messy process. Save yourself the hassle of running out of room or sacrificing the legibility of your working out by ensuring your working out is neat, and formatted correctly in the first place.

Making your work presentable allows you to come back to your own solutions and review them quickly and with accuracy. You shouldn’t have to squint your eyes or second guess what you have written down. If you find this happening, then it is a key indication to make your work neater, and to take your time writing out your maths working out in the next question.

Remember to leave adequate room for diagrams and graphs, and to make them large enough, a general rule is to let them take up at least a quarter of the space on your paper so it is clearly visible and can be interpreted accurately. Your algebraic working out should follow in steps line after line and follow logically one after the other. Your numbers, pronumerals, and symbols should be legible and readable to you and to others.

A bonus to making your work presentable is that it also leaves a good impression on the teacher or examiner, and will also make you more confident in coming to them to discuss any problems from your maths working out in the future. Which ultimately leads to better marks.

3. Show All Your Working Out

Finally the last guideline. Show all your working out! Just show it! As long as you have read the question carefully, and made sure your work is presentable, it never hurts to show all your working out. Tutors will always emphasise the importance of showing all your working out, why? It allows us to adequately verify your solutions, and to find mistakes when they occur, especially in more difficult maths problems.

A key to setting out correct working out is to follow the way solutions are structured in math examples shown by the tutor/teacher or past exam papers and some textbooks. By setting out complete and full working out including both the easiest bits to the hardest, you ensure yourself maximum marks in examinations as examiners will look to all aspects of your solution in determining the mark you should receive for that question.

The benefit of showing all your working out is that it significantly eliminates the chances of making a silly mistake. Confidence is important, but not when it comes at a cost to your progress as a student and your exam marks. Make sure to be thorough in your working out and to show each step you took to solve a problem. You may find that you have to refer to previous sections of your mathematical working to solve the next stage of the question, so it is important that is well documented enough on your booklet or worksheet so that you can utilise it to the fullest. To add to this, revision of your past homework or booklets becomes an easier and quicker task.

By keeping a constant habit of showing all your working out, and I mean every single aspect of your working out, is that it leads to mastery. At times you may feel that one aspect of your working is too simple to be included, but it takes discipline and patience to write it down and present it as part of your solution. Discipline and patience is what it takes to succeed in mathematics and it all begins here, so make sure to ask yourself this question, have I included everything? If the answer is yes, then you’ve followed this guideline and can expect better marks.

Remember accurate mathematical working out is of the utmost of importance in ensuring you receive the highest possible marks you deserve, and to develop a greater ability and understanding of mathematics as a whole. By following these guidelines in every aspect of your work, you will become a stronger student.

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