I began the day by going over the homework - I explained that although it was just arithmetic, it would help with our algebra later today.
I then put a quadratic on the board in factored form and we discussed what it told us, went to general form and talked about what it told us, and then we went from factored form to vertex form and talked about why we knew it was right using the roots of the factored form to get the coordinates of the vertex. I had the function graphed on Sketchpad on the screen for us to refer to.
I began the new lesson with a “triangle diagram” showing the three forms of quadratics with arrows going from one to the other for the changes from one form to another that we could do. I then drew in an arrow going from standard form to factored form in another color to show that was what we were going to do today.
I wrote a quadratic in standard form on the board and using the area rectangle we figured out what the factored form would be. I then showed them the same problem using the CPM circle diagram from the previous night’s homework. Finally, I wrote underneath the equation what we needed our constants to add and multiply to (assuming a = 1) like this:
And we did lots of them - one at a time - as I walked around the room checking their work. The biggest hangup wasn’t the procedure, but their arithmetic skills. It is very difficult for them especially when there are negative values involved.
In one class, I had enough time at the end to go back and ask what the x-intercepts of each equation was after they were written in factored form and then asked what the x-coordinate of the vertex would be. I didn’t have time to give any homework.
