We explored quadratic scenarios a little more today. I loved it when one student said "That's it? That's easy.". My students can be very needy, but do great things with a little support and encouragement. We ended this portion by summarizing all 7 scenarios which allowed them to see the similarities and what they need to remember (things like symmetry) along the way.
Next up, factoring! Out came the algebra tiles and my doc cam. We started with common factoring, focusing on the fact that we are taking the area of a rectangle and finding out its length and width. If there is more than one way to make the rectangle, then we want the one closest to a square. Here is my written version of some of the algebra tiles work:
We talked about why a quadratic equation in factored form might be more useful than one in standard form, and went over how to find the zeros again (with a little help from Desmos). We put it all together with this example:
And that was it for today. I think we laid a good foundation for factoring monic trinomials. I'm not sure if I'll do that tomorrow as there are going to be a lot of students away due to Tournament of Champions and I want to make sure they all see how to factor.
As a side note, it was really great to have a student ask if she could explain SOH-CAH-TOA to a student who was away when we did that. The fact that she was able to explain it to her friend well means that she really did understand it. This makes me happy. The fact that she wanted to explain made me happier still.