This problem was adapted by Patricia Helmuth, an adult education teacher from the Hudson Valley in NY.
The situation in the problem involves someone who needs to hire a mechanic to fix their furnace. There are three different companies to choose from, each with their own function for calculating labor costs. Students have to choose the best company and to defend their choice.
One of the things I like about the problem is that it can be solved using tables, graphs, or an algebraic approach. I also like that it requires students to use math to make an mathematical argument about which company is the best choice.
In addition to the student handout, the link above also includes support questions (to help struggling students) and push questions (to engage finished student in further exploration). The push and support questions Patricia has written are a great way to keep all the students in a mixed-level math class productively engaged with the same problem.<<Read here for more information on how to use push and support questions.>>
This problem can be used to explore the the following TASC standard:
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
This problem is also a good way to reinforce the concepts of rate of change and starting amount which are raised in Unit 3 of the CUNY HSE Curriculum Framework.
Here’s the original problem that Patricia adapted for use in the adult numeracy and HSE classroom. It comes from the Illustrative Mathematics website.