Function Review

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

Big Idea

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

Warm Up

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).  

Building a Pool

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) = 6.8x2.  

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.