I’ve organized each of my SAT lessons around several general tools or problem-solving principles. When I present the material, I walk through several examples of how each tool is used, and then I give my students opportunity to try the tools out. As they work, I give them the disclaimer, “There is no absolute rule about which tool to use. It is your job to work that out.” Ultimately, the goal is that they will learn which tool works best where.
I’ve highlighted my approach on the SAT problem below.
The product of three consecutive odd integers will never be a multiple of which number?
- Who are the main characters? Three integers
- What do we know about them? Odd and consecutive
- What does the problem ask? About their product
Tool 1: Know the vocabulary.
product means to multiply
Tool 2: List relevant facts.
Two odd numbers multiply to another odd number.
Once we know that the product will be odd, we see that no odd number is a multiple of 2, so a. is the answer.
Tool 3: Disregard superfluous information.
It doesn’t matter that the integers are consecutive or that there are exactly three of them.
There are around ten tools which are applicable in a broad range of problem-solving situations and as students work, they grow familiar with how each one works.