Communicate a solution clearly

Detailed Explanation: Communicate a solution clearly

A clear mathematical solution helps the reader see:

1. What quantities are known and what they mean
2. Which operation or formula is being used
3. Why each step makes sense
4. The answer, with labels and units
5. A check to see whether the answer is reasonable

Example

A rectangular garden is $(12\text{ m})$ long and $(7\text{ m})$ wide. A $(2\text{ m})$ section is left open for a gate. How many meters of fencing are needed?

Step 1: Identify the quantities and assumption.

• Length: $(12\text{ m})$
• Width: $(7\text{ m})$
• Gate opening: $(2\text{ m})$

Assume the fence goes around the entire garden except for the gate.

Step 2: Find the full perimeter.

A rectangle has two lengths and two widths, so its perimeter is

First add the length and width:

Then double this amount:

So, fencing the entire garden would require $(38\text{ m})$.

Step 3: Remove the gate opening.

The gate does not need fencing, so subtract $(2\text{ m})$:

Conclusion:

The garden needs

of fencing.

Step 4: Check the answer.

Estimate the full perimeter using $(12\approx 10)$ and $(7\approx 10)$:

Removing a $(2\text{ m})$ gate gives an estimate of about $(38\text{ m})$. The exact answer, $(36\text{ m})$, is close to this estimate, so it is reasonable.