The first day back from a long weekend can be a struggle and it certainly was this morning. To be clear, I mean for my students, not for me. Although I was uptight too, as I felt the pressure of getting through today's work as the cycle 3 test is on Thursday. I normally take the time I need to work through concepts, but today, we had to get factoring monic trinomials done. It's amazing how putting pressure on myself affects how I teach - I had to force myself to stop worrying and just work with what they were giving me.
I started the class with multiplying two binomials again. I think they can do this in their sleep now. Then we talked about what information we can get from each form of the equation. We can read off the zeros if the equation is in factored form and can read off the y-intercept if the equation is in standard form. Then I asked where the vertex would be. We sketched what we knew and then they were stuck.
Desmos to the rescue! Here is the graph, conveniently not showing the vertex. They seemed to have no idea where the vertex might be. (You know, in between the talking and texting and generally not paying attention to what we were working on.)
I asked them if the vertex would be the to right of both zeros, to the left of both zeros, or between them. We agreed it had to be between them, so I asked where. They started throwing out random numbers so I added a potential line of symmetry to my graph. Is the vertex at x = -5? No. So, where is it?
We tried x = - 3 and x = -2 and finally someone said x = -2.5. And then we zoomed out and saw all the key points.
I'm pretty sure they understood that if they move in the same number of units from each zero, they will land on the axis of symmetry. Okay, time to move on.
Hopefully they saw the use of factored form as we launched into our second day of factoring using algebra tiles.
They seemed to do a good job of creating a rectangle with the algebra tiles and of stating the "length" and "width".
We used Gizmos to look at quadratics with negative terms. They practiced afterwards and, after some one-on-one or group help, were really grasping when they needed to add zero pairs to be able to factor. We did difference of square questions this way too; I'm hoping that they will notice a pattern next time we take a look at these.
We, that's Alex Overwijk (@AlexOverwijk), Sheri Walker (@SheriWalker72) and I, are having our final MFM2P meeting tomorrow, so I will be away from my school. I have made a lovely review package for my crew to work on in preparation for Thursday's test. I would like to publicly say a huge thank you to Alex for sharing his time, activities and experience with us this semester. I may have jumped into the deep end of the pool, but I did so knowing that he was there if I ever needed a rescue. I have loved the collaboration and hope it will continue beyond June.