The following mathematical modeling task is from a source I can’t recall. As soon as I do, I will edit this page. I used it in my work with teachers and students when I was a math teacher on special assignment several years ago.
Main Bank in __________ County was robbed this morning. A lone robber carried the loot away in a big leather bag. The manager of the bank said that most of the stolen bills were 1s, 5s, and 10s. Early reports said the robber took approximately $1,000,000 in small bills. The Channel 2 News team thinks this sounds like more money than one person could carry. What do you think?
Channel 2 News needs help determining how hard it would be for one person to
carry $1,000,000 in small bills. Investigate this question to determine if it is possible.
Prepare a report for Channel 2 News describing and explaining your findings. Your report should help investigative reporters at Channel 2 understand the situation and plan better for tonight’s broadcast.
The goal here, is not for students to get the same answer. As a matter of fact, I would be surprised if even two groups in the same class got the same answer. The goal is for students to determine what variables are most important, then use those variables to create a model and find a solution that makes sense based on those variables and the context.
Students will need to make assumptions and may need to look up some information, like: dimensions of U.S. bills, weight of U.S. bills, dimensions of big leather bags, etc.
Depending on your students, you may provide information if they ask for it, like:
All bills weigh the same, regardless of their denomination.
1 bill weighs 0.03456 ounces
1,000 of any bill weigh about 2.2 pounds
Some students may focus on what will fit in the bag they choose. Others may focus on different combinations of bills to get to a million and the weight of those bills. The models they create show the mathematical reasoning they used as well as the assumptions they made. As they listen to other groups’ models, they may make notes about their assumptions and models and how they might improve them.
The problem itself is about finding a numerical answer – it’s just about finding out if it’s possible to carry $1,000,000, made up mostly of small bills, in a large leather bag. So, the multiple models, as long as they agree whether it’s possible or not, should still be able to answer the question.
This is a great task and there is so much content embedded here:
- Place value
- Multiplication
- Decimals
- Weight
- Volume
- Comparing
- Equivalence
- and more!
Introduce this as a long-term problem. Allow groups time to research – find information they need, based on their assumptions. It’s not just about computation. It’s about reasoning and mathematical modeling.
When sharing, students will be interested to see what information other groups found important. Encourage students to ask clarifying questions like, “What made you think to focus on the volume of the bag first?” and “How did you decide to include some 20s and 50s in the bag?” and “How did you decide how many?” These kinds of questions often refocus students back to the problem and open some eyes to different interpretations.
Don’t be surprised if students ask to revise their models after sharing OR if they have more questions they’d like answers to, like: “Is it possible that the bank manager was in on it?” One group I worked with got the rest of the class excited with this question. 😀
Give mathematical modeling a try and let me know how it goes. I’d love to hear from you!