Reflection: Perseverance The Tortoise and the Hare Project Day 4  Section 2: NonLinear Models
This lesson challenged my students in ways I wasn't expecting. They were more afraid to explore the functions than I expected and kind of froze when I presented the task. I ended up modeling the first group of equations. I graphed the very first equation for the tortoise on my graphing emulator and then talked through its shape in relationship to the tortoise’s race. We then did the other tortoise equations as a guided practice. I was pleased that once they saw and worked on the tortoise, they were able to complete the hare and rat. I have included the work from several students (1, 2, and 3). Notice that the tortoise solutions are similar while the hare and rat have more varied explanations. I am truly pleased at the good thinking at occurred by the end of class. I think this is an excellent example of where off the cuff scaffolding can really make a lesson.
The Tortoise and the Hare Project Day 4
Lesson 15 of 24
Objective: Students will be able to determine and justify appropriate nonlinear models to fit a scenario.
Big Idea: Will the tortoise win again? Students will not only find out but write a mathematical story about it.
Warm Up
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. Today's Warm Up Tortoise and Hare Project Day 4 which has students explain how they know if a scenario is linear or nonlinear.
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NonLinear Models
Today is an extension that extends this project fully into the Common Core Algebra 2 standards. We begin with a thinkpairshare discussing whether it was realistic for the animals to run at a constant speed for the entire race. I then share that each animal did adjust their speed during the race although their end times where correct.
The rest of the period is spent with students working in pairs to:

determine which of three functions (quadratic and exponential) best model each animal’s distance during the race (Math Practice 5)

Using the chosen models student then determine (different from prior lesson) at what point each animal met the other two and how this affects their story (Math Practice 2).
I walk around and provide scaffolding as needed. Some may need reminding that their calculator will be tremendously helpful in this activity. There is one function for each animal that is a best choice but not necessarily the only possibility. The key is that students provide their reasoning (Math Practice 3).
Resources (2)
Exit Ticket
I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.
Today's Exit Ticket asks students to explain how they determined the best model for each animal.
Resources (1)
Resources (1)
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