Proper Communication

[2025-09-03 Wed]

1. Communication is a critical skill in maths.

You need to communicate properly so the audience can understand what you are telling them. When your ideas are communicated properly, the following results occur:

Your classmates can follow your solution and learn from it without having to ask questions
Your teacher can be sure that you know what you are doing
You get the correct result more often

2. How can I improve my communication?

2.1. Use a ruler.

Draw diagrams with a ruler to ensure lines are straight

2.2. Write let statements to define variables

Any variables that were not defined previously must be defined with a let statements

2.3. Write proper conclusions in English

If a question is asked in English, answer it in English
Never refer to variables you defined in your solution
Your conclusion should always use hte same units that are used in the questions

2.4. Use proper precision

If a precision is specified use it If no precision is specified, use the numbers given in the question as your guide?
Answer questions given as a fraction with a fraction
Do not use an equals sign when you approximate

2.5. Only use equals signs when they make sense.

Only use them when they make sense
As an example, consider this common misuse

\begin{equation} \begin{aligned} & 3x + 5 = 20 \\ & = 3x = 15 \\ & = x =5 \end{aligned} \end{equation}

Although the answer is correct, the form is terrible. The leading equal signs on lines 2 and 3 are not necessary and make absolutely no sense

2.6. Draw your diagrams large enough to be useful

Always draw diagrams that are as close to realist as you can and make sure they are large enough to reader

2.7. Label your diagrams/graphs

It is difficult for your reader to know which diagram describes what unless you title your diagrams
Label important features and color code them
All graphs should have the axes labeled
All graphs should have the graph itself labeled
Scale should be clearly indicated
All graphs should have the graph itself labeled

2.8. Remember your audience!

Assume you writing for a classmate who does not know how to do the question and will want to learn from your work without asking you any questions
Solutions should be well structured and easy to follow. They should move from top-to-bottom and left-to-right