Maths is a language
Doing maths in your head is one thing. Explaining it so others understand is a separate skill. Engineers, scientists, accountants and programmers all have to communicate their reasoning clearly.
The parts of clear communication
| Part | What it means |
|---|---|
| Correct notation | Use symbols properly. |
| Precise vocabulary | Use the right maths words. |
| Logical order | Steps follow from one another. |
| Words + symbols | Explain key steps in sentences. |
| Visuals | Diagrams, tables and graphs, labelled. |
| Conclusion | Answer the question in a sentence with units. |
Using notation correctly
| Correct | Incorrect | Why |
|---|---|---|
| 3 + 4 = 7, 7 × 2 = 14 | 3 + 4 = 7 × 2 = 14 | 3 + 4 doesn’t equal 7 × 2 |
| π ≈ 3.14 | π = 3.14 | It’s an approximation |
| x = 5 | 5 | Say what the 5 is |
| 20 cm² | 20 | Include units |
The equals sign must always join two things that are truly equal. Don’t use it to mean "next step".
Using precise vocabulary
| Vague | Precise |
|---|---|
| "the number in front of x" | the coefficient |
| "the line goes up" | the slope is positive |
| "the answer" | the product / the solution / the sum |
| "the box shape" | rectangular prism |
Know your audience
Your audience shapes how much detail you include:
- A teacher: show method and justify key steps.
- A classmate: explain why, with an example.
- A client or the public: plain language, clear conclusions and visuals.
A model solution
Problem: A rectangular garden has a perimeter of 36 m. Its length is twice its width. Find its area.
Solution:
Let w be the width in metres. Then the length is 2w.
Perimeter: 2(w + 2w) = 36
6w = 36, so w = 6.
Width = 6 m, length = 12 m.
Area = 6 × 12 = 72 m².
The garden’s area is 72 m².
Check: perimeter 2(6 + 12) = 36 ✓
Communicating with graphs and tables
- Give every graph a title.
- Label axes with quantities and units.
- Choose a sensible scale.
- Refer to visuals in your writing ("As the table shows…").
Oral communication
When explaining aloud: state the goal, walk through steps, point to visuals, and invite questions.
Worked examples
Example 1: Improve: "x is 4." → "The solution of the equation is x = 4."
Example 2: Fix: 5 + 3 = 8 ÷ 2 = 4. → "5 + 3 = 8, and 8 ÷ 2 = 4."
Example 3: Replace with precise vocabulary: "the bottom number of the fraction" → denominator.
Common mistakes
- Run-on equals signs.
- Missing units or labels.
- Answers with no concluding sentence.
- Skipping steps your audience needs.
Try it yourself
- What’s wrong with writing 4 × 5 = 20 + 3 = 23?
- Give the precise term for "the answer to a division".
- Write a concluding sentence: a car travels 180 km in 2.5 h; speed 72 km/h.
- Name two features every graph should have.
Answers: 1) 4 × 5 isn’t equal to 23. Write 4 × 5 = 20, then 20 + 3 = 23. 2) quotient 3) The car’s average speed is 72 km/h. 4) a title and labelled axes (with units)
Quick recap
- Communicate with correct notation and precise vocabulary.
- Organize steps logically and justify them.
- Aim for clarity for your audience.