Two ways to the same answer
Two correct methods reach the same answer by different routes.
What to look for
- Where do the two methods first part ways?
- What does each method save, and what does it cost?
- When would you choose each one?
Worked example with the teacher's key
Maths · Grade 8 · Easier to see
Task: Solve 3(x + 2) = 15.
A · Alex
3x + 6 = 15
3x = 9
x = 3
B · Sam
x + 2 = 5
x = 3
Teacher's key
Only A
Alex multiplies out the brackets first, then undoes the + 6 and the × 3. Three lines.
Both
The same answer, x = 3. Both do the same thing to both sides, so the equation stays balanced.
Only B
Sam divides both sides by 3 first, because 15 divides exactly by 3. Two lines.
- The rule
- Dividing first is quicker when the number outside the brackets divides the other side exactly. Otherwise, multiplying out first avoids working with fractions early on.
- Case C
- Solve 3(x + 4) = 20. Which method would you use, and why?
- Case C answer
- Multiply out first, because 20 does not divide exactly by 3: 3x + 12 = 20, 3x = 8, x = 8/3. Dividing first gives x + 4 = 20/3, and then you have to work out 20/3 − 4.
- Probe
- Change 3(x + 2) = 15 so that Sam's first step becomes the harder one. What did you change?
- Think back
- Before today, my first step was always ___.