1) Solve the Ice Cream Cone Problem fully and explain your solution.
Write up a complete solution to the problem. This is an opportunity to extend your thinking on the problem – e.g., by exploring new cases of it. Your complete solution needs to include a diagram or other model, along with an explanation that helps us understand your reasoning.
Note: Significant engagement with at least one of those additional challenges is required for your work on the anchor task to ‘fully meet expectations.’ You don’t need to completely and correctly solve that additional challenge, but you must include at least some initial attempts to engage with that challenge.
(2) Write a reflection on your math learning from the problem.
You will write a 1-1.5 page (typed, 1.5-spaced) reflection on your mathematical learning both from your work on the problem and from our class discussion of it. You may insert photos of solutions and models into your reflection. To fully meet expectations your reflection must include the following:
- Clear thinking about the mathematics of this task. What mathematical ideas do you understand better or differently after having solved and discussed this problem? How did your understanding change as you solved and discussed the problem? (Note that this reflection isn’t a restatement of how you solved the problem, but a reflection on what you thought about over the course of the problem. That is, you’re not writing “What I did to solve this problem was….” Instead, you’re writing something like: “This problem was about … And after working on it, I am thinking a bit differently about…” And if you understood the problem solidly from the beginning, this might be an opportunity to reflect upon the mathematical ideas that you heard your peers considering as they solved the problem or to consider how you might adjust or extend the problem to start to consider other mathematical ideas.)
- Specific reference to the strategy of at least one of your peers and how it connects to your own thinking. (This might be a place to include photos or drawings of strategies or models.) Which solutions, models, or explanations shared in the discussion struck you as particularly useful or interesting? Why? You will explain the details of at least one of your peers’ thinking and speak to the specific ways it was similar to or different from your own thinking. (That is, instead of saying something like, “I thought that Maya’s strategy was really cool,” and leave it at that, you might say, “I thought that Maya’s strategy was really efficient because what she did was... That was different from how I thought about the problem because… But her strategy works because…”).
- Engagement with some of the following questions:
- What connections were you able to make between different solutions and models to this problem, between this and other problems we have solved, or between this and ideas from course readings or videos? What do those connections help you understand more deeply about mathematics?
- What questions do you still have about the problem or particular solutions to it? Which aspects of the problem or which particular solutions do you still find challenging? Why?
- What new mathematical questions are you asking now that you’ve solved this problem? How do those questions relate to this problem, and why are they interesting to you?