Select an appropriate video for the introduction of this lesson well in advance of the class so you can slant your lesson toward that video if you choose. Please see the resource entitled “data sources” for possible videos or choose one with an explicit or implied trig function that is particularly relevant to your students. I begin this lesson with a short video clip about farm produce that demonstrates the value of being able to model data with an equation. This gives my students an immediate connection to why modeling data accurately is important since we are a farming community. My students have already explored weather data, so they’re comfortable working with real data and recognize that it’s not usually possible to make a model that is a perfect fit. After the clip I ask my students to pair-share with their right-shoulder partner what information they need to plot data that will allow them to answer questions and make predictions about at least three different farm commodities of their choosing. These might include corn, wheat, rye, barley, soybeans, canola, or garbanzo beans to name a few. (I have them choose three so that if they don’t find enough information about their first choice easily, they already have alternatives selected.)
Because the primary goal of this lesson is to help students develop a confidence about selecting and using different models, I spend a great deal of class time on discussion about making choices. After the partners have shared their ideas about which items to study and what they need to know, I ask random students share with the whole class, but I don’t ask them to share what they chose, I ask them to share how they decided which information they needed. (MP1) This is really tough for some of my students who may respond with a shrug or “I don’t know”, in which case I ask directed questions like “You said you wanted to work on corn prices. What made you choose corn?” That’s an easier question for most students to field and can lead to additional questions like “Why do you want to study the prices of corn?” and then “What else do you need to know besides the price to look for a pattern?” I have found that walking a few students through the process gives the whole class a better sense of what they’re thinking. I make a point of selecting students for this first step that are comfortable being the focus of class scrutiny. After several students have shared their reasoning, I ask if there are any students who need further clarification of the process of choosing data. I answer those questions then tell my students they will be working with their partner for most of today’s lesson.
There is a video narrative that supplements this section of the lesson in my resources. In order to cement this lesson for my students, I give each one a notecard and ask them to write a brief summary (three to five sentences) of why they selected the function they finally chose. (MP3) I also assign as homework the challenge to come up with two different conclusions/predictions that can be made about their commodity and supported by both their data and the function they chose to model it.