Reflection: Checks for Understanding The Tortoise and the Hare Project Day 4  Section 1: Warm Up
My students came in this year with a particularly large range of abilities and mathematical confidence. With the new junior year Common Core tests coming up in exchange for our old sophomore test, we realized that our students needed to have Algebra 2. This pushed many students into Algebra 2 that historically haven't taken it at our school. When you combine that with the curriculum changes resulting from the Common Core, I need to be mindful that my students are very diverse in prior knowledge and ability.
This was evident in the responses obtained from this warm up. I did have many students who understood linearity as seen in Student Work 1 and Student Work 3. Student Work 2 represents a common misconception that all graphs are linear since this is the function many students have had the most experience with. My objective is that after today's lesson, most students will be able to accurately describe a linear function.
NOTE: If there is time, having students revisit their warm up could be an alternate or additional exit ticket.
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.
Resources (4)
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).
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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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