I love using maximizing area problems to talk about quadratics. The focus of today's lesson is for students to write a formula for area if they know the length of a rectangle with a fixed perimeter. I love this task, and others like it, because students can practice MP 8: Look for and express regularity in repeated reasoning. This activity pairs nicely with the previous lesson, A Fireworks Display, as it gives students the opportunity to work with a quadratic function in a completely different context.
I begin class by reading the problem, Rabbit Run, out loud with students and letting them ask clarifying questions. I also introduce some graphic organizers that might help them keep track of their work on the problem. I like to emphasize that the organizers are optional, and they may, in fact, find a way that works better for them to organize their numbers.
Note: The IMP Year 2 curriculum also has a similar task as this one on page 284 of their Year 2 textbook.
Next, students begin working on today’s task. I let them work in small groups or alone on this activity. As they work, I circulate, looking for students that have "ah ha" moments and providing support whenever necessary.
Issues to watch for:
What are some possible dimensions for a rectangle that has a perimeter of 72 feet? Let's start by choosing the length. If the length is (example), how can you find the width?
What if you changed the side that is 20 feet to another amount. Have the student choose an amount. Ask what would the width of the pen then have to be? What would be the resulting area?
Note: Instead of Question 5 on the Rabbit Run handout, I ask students to compare this problem to work they did on the Fireworks problem in the previous lesson.
DIFFERENTIATION: I like to provide a A Rabbit Run Organizer for struggling students to help them keep track of their dimensions.
Students who are more comfortable with this work can focus on comparing and contrasting the puppy pen problem to the rocket problem.
I like to finish class with a problem solving reflection. I have students respond to the following prompt on an index card: What was the most challenging part of the task, and why? I let them know we will be discussing their reflection along with their work on today's problem at the start of class tomorrow.
Rabbit Run is licensed by © 2012 Mathematics Vision Project | MVP In partnership with the Utah State Office of Education Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.