Students will be able to model functions and identify their important features.

Student created situations populate this modeling functions lesson plan.

10 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on **Math Practice 3** each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. As seen in the video narrative, this lesson’s Warm Up- Modeling Functions asks students to model a linear situation which is the introductory example in today's lesson.

Since this is the first day of a new unit, my students are placed with new partners. Since they will be having a lot of conversations with this person, I provide them with a conversation starter at the beginning of the first several lessons in this unit. Today's starter is: "*What was your favorite toy growing up?*"

37 minutes

The warm up is the introduction to today's lesson. I begin by talking about the expression from the warm up: *Alvin has a pool that has 80 cm of water. He is emptying it at a rate of 12 cm per minute. *This is a similar problem to the ones done in the first unit. I explain that we can rewrite this as a two variable situation: y = 80 – 12x where x represents minutes and y represents the depth of the pool.

I then introduce function notation as a different method for writing the same scenario and relate that f(x) is another method of writing y.

Now we review evaluating functions with function notation. I show them how to find f(1). Then the students try the second one, f(3), and the third one, f(10). I ask them to relate each answer back to the situation as this keeps their mind on the scenario which will deepen their understanding of how function notation works (**Math Practice 7**).

The students then make a table of the first five minutes of this situation and graph the ordered pairs. I make sure to have them label the intercepts with both the variable and the unit. Either a student that I choose or myself graph it on the white board to help with next portion of the activity.

Once they have a graph, we talk about some of the important terms associated to the graph of this function including x- intercept, y-intercept, domain, range, and independent/dependent variables. We define each of them and relate them back to both the graph and the situation (**Math Practice 2**).

I present them with a formal definition for a function and then we look at a non-linear model. *Write an equation that relates the side of a square to its area.* The students write an equation, make a table and graph it, and then identify the x-intercept, y-intercept, domain, range, and independent/dependent variables of both the graph and the situation. This helps them solidify some of these introductory concepts discussed in the first example.

3 minutes

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

This Exit Ticket asks students to describe the difference between the independent and the dependent variables of a function.

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