We want students to be modelers of mathematics. This task provides them with an authentic opportunity to model with mathematics using data that they are generating. Students will come to understand that the mathematics behind these tasks is very messy and models are imperfect. So, students use their understanding about the parts of exponential functions to create a model from the data.
Provide students about 100-200 skittles in a small cup.
Debrief Question Ideas:
- The last activity eludes to the idea that the “half-life” for plutonium is 214,000 years…which means when students were dropping Skittles to represent a “year” that REALLY represented 214,000 years. Knowing this, what math needs to take place to scale this model to the correct number of years?
- How are different groups developing equations?
- What does the (1-r) part mean? Where does the 1 come from?
- What does the average common ratio mean in the context of radioactive plutonium?
- How could we improve the average common ratio?
- What needs to happen if we redo this experiment?
- How could we use the current information we’ve collected to better improve the results?
- Some Skittles don’t have an “S” on them…what could this model in the context of Plutonium?
- How good are our equation models? How do you know if they are really good, versus just okay?
This is a Level 3 task…with some modifications to the task instructions (removing the procedure, reducing the report structures) this task could easily represent a Level 4 task. In total, students must collect multiple sets of data, plot that data, make conclusions about that data (average common ratio), use the information collected and analyzed to generate an equation, graph that equation, and determine the goodness of their graph. With additional questions, students are asked to model and determine the quality of this model which requires a lot of mathematics. Teachers are encouraged to modify this task for their needs.