Students will be able to demonstrate their knowledge of functions by modeling a real life scenario.

Let's build a swimming pool!... ok, let's model its volume with a function.

5 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. This lesson’s Warm Up- Function Review, asks students to write and compare three separate functions from a given scenario (**Math Practice 4**).

45 minutes

The goal of this lesson is to review some of the important concepts surrounding functions using a real life scenario.

*Rachel’s family wants to build a rectangular swimming pool in their back yard. They decide to base it on the golden ratio which is approximately 1:1.6. The shallow end, which will extend half the length of the pool, will be three feet deep. The second half of the pool will slope continuously down to eight feet. *

I begin by asking the students to write a function to model the volume of the pool (**Math Practice 4**). Depending on the students, I will provide more or less whole-class scaffolding. A more reluctant class requires frequent check points. First, I encourage students to draw a diagram (**Math Practice 5**). This will help them visualize the volume. The final function is f(x) = 6.8x^{2}.

Next we identify the domain and range, make a table and graph the function, and find the inverse.

The final two tasks ask the students to use their model to answer several questions. I find it more meaningful for students to use their models after they create them rather that just create. This reminds them why do what we do in mathematics.

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