Once all of the models have been put on the board, we discuss them as a class, noting trends. This portion will all depend on the models that students wrote. They should be fairly similar but there will probably be some differences. This is an opportunity for students to defend their position as well as critique the reasoning of others (Math Practice 3). I am always enthusiastic about differences, even when they are incorrect, and try to encourage students to look at their mistakes as learning experiences. When dealing with a glaring error, it is good to talk about it but depending on the students, it may be wise to discuss it without calling them out. A possible way to deal with an error would be to ask students to consider why this mistake was made (again enthusiasm goes a long way here to dispel embarrassment).
Another important conversation to have would be about which model is the “best”. While some issues will be obvious (like period), others will not be quite as clear. The vertical transformation may be slightly different. The same for amplitude. It is important for students to realize that there isn’t always a single right answer (Math Practice 5). Particularly with modeling, there may be many good solutions.
One other thing to discuss would be why the shape didn’t match exactly. The actual answer lies in the fact that the earth’s orbit is elliptical therefore our seasons don’t lie on a cosine since cosine models circular behavior.
Стратмору нужен был козел отпущения. Кроме всего прочего, Хейл был настоящим ходячим несчастьем, готовым свалиться на голову в любую минуту. Из задумчивости Стратмора вывел звонок мобильного телефона, едва слышный в завывании сирен и свисте пара.