Goal: Think Like a Mathematician! Read the problem multiple times.
Patrice Bergeron is tutoring NNHS students in order to make money since he is injured and can’t play hockey for the Bruins. He currently has 20 students and charges $50/hr. He has discovered that for every $5/hr he increases his charge, he loses one student. Find out how much he should charge to maximize his income.
Source: Shared by Stephanie Paintedosi, Newton North High School Math Teacher. Written by Shawn Wallace, Newton North High School Math Teacher.
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Stephanie and Shawn, thank you for sharing high school maximizing income task. How did your students rephrase the question?
This problem is a common word problem in the Quadratics Unit. In the past, students have often gotten lost in the problem and provide answers such as “$20,” which does not answer the question. We thought it would be a good problem to have students read and understand without answering so that they would interpret the scenario before focusing on the process of how to get the answer. My coworker and I decided to give this problem on the quiz to reinforce the idea of the “3 reads.”
Attached is the question. The students did much better than I expected. I honestly think it was because they were not worried about solving the problem and could just focus on the context. Almost all of the students rephrased the question as “How can we make the most money [without losing too many students]?”
The document will not upload, so here it is:
Problem 3: Read the situation below and answer the “3-read” questions.
YOU ARE NOT SOLVING THE PROBLEM.
Patrice Bergeron is tutoring NNHS students in order to make money since he is injured and can’t play hockey for the Bruins. He currently has 20 students and charges $50/hr. He has discovered that for every $5/hr he increases his charge, he loses one student. Find out how much he should charge to maximize his income.
1) What is the problem about?
2) What is the problem that you are being asked to solve in your own words?
3) What quantities are important? (What do we know and what do we need to know?)