Before you get ready for class, make sure you have graphing calculators out and accessible to students.
Begin class with a warm up problem for the whole class to work on individually that reviews what they have learned about the vertex form and x-intercepts. A good sample problem would be something like, “Find an equation for a parabola that has its vertex at (20, 10) and has an x-intercept at (40, 0).” Review with students what they already know about the vertex form and how to solve for a.
Tell students that today’s task will focus on applying these specific skills they have learned to a real-world problem.
Group students in homogenous groups of three to four students. Hand out Is It a Homeroom? and read through the problem together. Let them get started on the work.
Things to watch for while students work:
This is a great assignment to help students work on SMP1, Make Sense of Problems and Persevere in Solving Them. Push students to really think about what they have learned about the vertex form and x-intercepts and how they can combine and apply that knowledge to this context. You can also say that this is a challenging problem, but you know they are up to the task. You might cut up the problem solving guide and give out different pieces as hints if students need them to keep them moving forward and engaged in the problem.
If time permits, have groups that finish work put their work up on the board. You can have students share out the steps they went through to the solve the problem. Because the problem will have been challenging for most students, they will benefit from another look at how they went about solving it. You can ask them specific questions like, “how did you use the vertex to help you solve this problem?” “How did the x-intercepts come into play?”
At the end of class, be sure to allot students time to reflect on their problem solving. You can ask students a specific reflection question that references SMP1. You could guide this reflection by asking students a questions like:
This material is adapted from the IMP Teacher’s Guide, © 2010 Interactive Mathematics Program. Some rights reserved.