FOIL'ed again

Trying to teach FOIL, without just telling them.

I wanted my kids to discover it and to fight with the idea. Trying to make this topic apply to a "lab" or the real world was difficult for me. So, I stole the ol' adding areas of rectangles together.
1. Add two different colored slips of paper onto a normal sheet of paper

2. Find the total area

3. It was helpful to draw an example on the board as well (if my students had their own white boards, I could imagine this could be a great activity, or even better cutting their own paper).

4. Let them ask the questions, fill in the information, and teacher help guide questions

5. When the quest arrises about the 4th rectangle, I added a little red rectangle to our model.

6. We got to the total area by adding all of the rectangles, but now what is the total measurement of the L and W?

7. Write that as two binomials multiplied together.

8. Set that equal to our total area

9. Let the students discover FOIL

I was happy to see my students struggle. In the past I have seen the difficulty to just follow the steps. But here, I was able to see the struggle with the concept. I think the students feel like they came upon this pattern, more than being told to memorize steps.

We were able to have discussions about
a. what variables to assign to what
b. what to include in our dimensions
c. how to solve the problem of that extra space (the 4th/red rectangle)
d. discover how to multiply two binomials together

Did my students grasp the concept? I don't know yet. I wish I could have had about 10 more minutes of class time (we went off on a tangent about multiplying exponents in the beginning of class). The students that were engaged in our discussion have the tools to grasp the concept during their homework tonight. However, the students that turn off during our discussions will be lost tonight. They will ask me to "teach" them tomorrow, since I "didn't" today.