This problem was adapted by Patricia Helmuth, an adult education teacher from the Hudson Valley in NY.
The situation in the problem involves trying to figure out how many pennies in a 50-penny roll were minted before 1983 and how many were minted after, using only the weight of the roll to make your determination. The necessary background, provided in the problem, is that pennies before 1983 are heavier (3.11 grams) than pennies that were minted after 1983 (2.5 grams).
One of the things I like about the problem is that it can be solved using different problem -solving strategies: making tables, guess and check, or an algebraic approach.
The first page of the link above is the student handout. The second page is for teachers and 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.