I have planned to share this lesson for several weeks but time has gotten away. My students were not where they needed to be with quadratics, so I pulled together some tried and true tasks-framing quadratics, Wylie Coyote, et al and a new one from Mathematics Assessment Project called Forming Quadratics. You can download lesson, domino cards and assessment in that link.
No big surprises on the pre-assessment, but I did use it to place students in pairs based on similar thinking/reponses. There are 4 equations students are asked to match to 4 graphs and explain their matches.
I like this lesson for a lot of reasons. Discussion of how different forms give us different information. Allows students to seek key features from graphs, connecting them to parts of different but equivalent forms of equations. Students work in their pair but also must visit other groups to confirm/dispute their responses. The lesson outlines its goals:
This lesson should be used after students are familiar working with different forms of quadratics. This is not an intro lesson, but one I see being successful about 2/3 way through unit or as a follow-up/review activity. They will encounter standard, factored and completed square/vertex forms.
I followed the lesson pretty true to outline, changing only minor things based on my classes. After the whole class intro, pairs worked at matching dominoe-style cards including sets of functions and graphs. I was adament about them taking turns explaining their matches. Some cards had all equation forms, some had only parts. They recorded their matches on a card for the next round.
Following the initial round, one person stayed and another person moved to a different group. In the new groups, they were asked to compare responses, then discuss any differences. This took only a few minutes. Upon returning to original partner, they now had to fill-in missing information on the equations. Again, upon completing their equations, one person stayed and the other traveled to a new partner to compare. Some a-ha’s came about during this part as they maneuvered between the different forms, such as the last term in vertex form does not necessarily correspond to the y-intercept as in standard form. So if and when would they be the same was a nice question for discussion.
As an exit slip this day, students were asked to fill-in front side of this foldable for their INBs.
The following class, I pased back their foldable and gave them a few minutes to respond to my feedback. They received smaller copies of the dominoe cards to cut apart and match inside their foldable. They were asked to write any missing equations, and Color With Purpose different parts of equations and graphs.
I used the same cards and was able to offer some feedback on simple mistakes, but in the future maybe I should have a fresh set and use it as a true formative assessment to see they are able to match new sets & write new equations.
A panel on the trifold was a place to record/review other important info concerning quadratics.
Classes were still somewhat split in the post assessment. 1/3 were right on track, 1/3 had trouble with writing the equations, 1/3 seemed almost clueless- I was like “what happened?” They couldn’t correctly identify key points from the graphs. Before passing back their work, I asked what made it difficult? Even if their matches were correct, they failed to give correct coordinates of key points. Their responses all very similar “there were no values on the graphs.” I passed them back and allowed them to talk over feedack with nearby students. After speaking with them individually, I was convinced all but a couple were now moving in the right direction.
Hmm. Maybe next go, I should scaffold the assessment. Part I, very similar to their practice, including labels on graphs. Part II, similar to current assessment with no labels on graphs. Part III writing equations for given information or identified points from graphs.
All in all, I was satisfied with the discussions students were having; How they had to explain their reasoning for matches made. I see these conversations prooving valuable as we continue in our next unit on other polynomial functions.
A post of the same lesson from Ms. Rudolph.