Hi,
Consider this past-year question on the topic of inequalities:
Solve exactly, |2x - 3| < |x +1|.
If one makes a small change, the problem solving approach to the new problem will vary and other concepts/skills are likely to be applied as well.
Let's see the kinds of variation that are possible:
1. |2x - 3| < x + 1.
2. |2x - 3| < |x| + 1.
3. 2|x| - 3 < |x + 1|.
4. 2|x| - 3 < |x| + 1.
5. |ax - 3| < |x + 1| where a > 0.
6. |ax - 3| < |x + 1| where a < 0.
7. |2x - a| < |x + 1| where a > 0.
8. |2x - a| < |x + 1| where a < 0.
9. |2x - 3| < |x + a| where a > 0.
10. |2x - 3| < |x + a| where a < 0.
11. 2x - 3 < |x + 1|, etc...
With these modifications, one is able to learn deeply and he/she then begins to "think about thinking". Most practical of all, the student will never run out of questions to practise :)
Thanks!
Cheers,
Wen Shih
Hi,
As the learner goes through the variations, he/she has to consider whether:
1. the algebraic approach should be used,
2. the graphical approach should be used,
3. the arbitrary variable affects any of the above two approaches.
Thanks!
Cheers,
Wen Shih