I start this lesson with a description of the key features of a function posted on the board and challenge my students to write a function to fit the features.
this function has roots at -2 and -3 with a minimum value between them, a y-intercept of (0,6) and both ends approach positive infinity. sample answer: f(x)=x^2 +5x+6
I give them a few minutes to work without any additional input or suggestions from me, then ask for volunteers to share the functions they've written. (MP1) I put each function into my graphing calculator and project the results, one at a time, on the front board asking my students to determine which one best fits the description. (MP3) I also ask them to share how they chose which kind of function to write. For example did they look first at the roots or maybe the end behavior? This discussion may seem simple but it's important for my students to actively consider why they're doing what they're doing so that they can apply that same thought process to other kinds of problems.
For this part of the lesson I tell my students that they will be working independently to find appropriate functions given key features and descriptions. I remind them of our discussion about how to choose which function to work with, distribute the Choosing Models handout, ask if there are any questions, and tell them they have about 25 minutes to finish this assignment. (MP1, MP2) While they're working I walk around offering encouragement and assistance as needed.
I pay attention to see if some students will struggle with modifying a parent function even if they understand how to choose the type of parent function. For these students I first suggest that they make a sketch to help them visualize the difference between the description and the parent function they've chosen.
When everyone is done or after about 25 minutes I tell my students they will be self-checking this assignment, a choice I explain further in my video that allows students to get more immediate feedback. As always, I encourage them to challenge any answers they don't agree with.
I close this lesson by asking my students to write answers to the following questions:
This gives them time to reflect on what they've been doing and to articulate their thoughts in a more concrete way than just discussing in class or with a partner.