Quadratic Modeling (DAY 3)

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Objective

SWBAT apply their understanding of quadratic equations and the Pythagorean Theorem to solve a spatial problem.

Big Idea

How do large vehicles determine how wide to take the turns so they don't run over sidewalks and bike lanes? The math behind these calculations involves quadratic equations!

Warm-up

10 minutes

I provide students with a warm up almost every day in order to make the best use of class time.  When I don't structure the first 10 minutes or so with a warm-up, students will spend the time chatting and waiting for announcements.  The simple act of providing a warm-up helps me reclaim that time and also gets students in the right frame of mind to do some productive work.  

For this warm-up, students practice solving quadratic equations by factoring, completing the square and using the Quadratic Formula.  Warm-up Solve Quadratics has 6 equations to solve that encourage the use of all three methods.

Collaborative Solution

30 minutes

In the previous class, students had the opportunity to attempt an individual solution to the MAP Assessment Task, Cutting Corners. Today, I will assign students to groups of three based on facility with problem solving.  Each group will be assigned at least one student who is confident with word problems.  

I hand back student work from the previous day and give students a chance to read my comments.  I then ask them to get into their groups and share their work with their peers.  The goal is for the group to come up with something better than any of the individuals came with. Everyone in the group has to agree on the method that is submitted in the end [MP1, MP4].

Working with an enlarged copy of the diagram and a large piece of paper, students will work out their group solution that will be hung on the bulletin board. 

Evaluation of Sample Responses

30 minutes

After students come up with their group solution, they are provided with four possible selections of sample work to review and critique.  If a group has been successful in solving the task before looking at sample responses, I ask the group to find a sample in which the task was solved in another way.  

Groups take 20 minutes to look over the samples and answer questions provided in Cutting Corners. Students are asked to describe the method used, correct errors, and conjecture about why the student took the steps they did [MP3].

When students have had a chance to critique the work samples, we have a whole-group discussion about each sample.  I project each sample response on the board and ask one of the groups to lead the discussion about the sample.    

Self-Evaluation

10 minutes

The final step in this assessment task is a for each group to evaluate how well they worked together.  Students will complete the form group work evaluation, which is provided in the Cutting Corners activity in order to give each other and me feedback on how well they worked as a group [MP3].  I ask students to reflecting on how the group functioned because I care that they leave my class with a better understanding of how to collaborate to get a job done.  Although not explicitly stated in the CCSS, teaching students to work together productively is considered one of the primary goals of K-12 education in my school district.