In this warm up, I focus on the importance of defining the variables in mathematical modeling (Math Practice 4). The context for this warm up is Warm Up: Ordering Softballs. Students will define a system that can be used to identify how many of each size of softballs were in the original order.
I plan for this task to take about five minutes for the students to complete. I will use another five minutes to review the warm up with the students to introduce the goals of the lesson.
After defining the variables, I again review with students how to write the equations from the constraints given in the problem. I model writing the equations, and solving using elimination in the video below.
In these guided problems I first work with students to define the variables. Then, we work together to set up the equations. I walk around the room to monitor students. I provide one-on-one help to students who need it. Then, I ask students to begin working on solving the equations using elimination. The worksheet includes a graphic organizer for each problem to organize each step of the process.
Students need to be able:
In order to emphasize Math Practice 6, I require that students label their answer to the final questions with correct units.
To end the lesson, I use a Self Reflection as a formative assessment. I want to provide each student with an opportunity to assess his/her ability to solve linear combination problems. I decided to use self-reflection instead of peer grading because there are so many different parts and details to determine the mistakes or misconceptions. I think it is helpful for students to see their own mistakes working through the worksheet, to provide immediate feedback.
At the end of the unit, on a summative assessment, students are able to solve a system of equations using any method, as long as the solution is supported with mathematical and verbal reasoning. For this assignment, I provided specific procedures for to setting up the problem, defining the variables, writing the equations, and describing the solution.