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8.3 Take the Cake!
15 minutes
This context was chosen because it is possible to represent the sequence with both a recursive and closed-form function. The purpose of this activity is to recognize that although the domain is still a subset of the integers (since it’s a sequence), the outputs are not all integers. Further, the context puts some limitations on the domain. Students engage in aspects of mathematical modeling (MP4) by articulating why.
Instructional Routines
• Aspects of mathematical modeling
What: In activities tagged with this routine, students engage in scaled-back modeling scenarios, for which students only need to engage in a part of a full modeling cycle. For example, they may be selecting quantities of interest in a situation or choosing a model from a list.
Why: Mathematical modeling is often new territory for both students and teachers. Opportunities to develop discrete skills in the supported environment of a classroom lesson make success more likely when students engage in more open-ended modeling.
Launch
Display the task for all to see and ask students to read the description of the situation. Then ask, “Is there still cake left after three people each take some cake?” Ask students who reply “yes” to explain how they know. If any of them create a diagram to help explain, ask them to demonstrate for the class. Ensure students understand that each new person takes of what is left (not of the
original amount).
Student Task Statement
A large cake is in a room. The rst person who comes in takes of the cake. Then a second person takes of what is left. Then a third person takes of what is left. And so on.
Unit 1 Lesson 8: What’s the Equation?
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