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Deciding when there is too little cake left to reasonably subdivide is up to the modeler. After 8 people take their cake, less than 5% is left and after 12 people, less than 1% is left. Depending on the size of the original cake, these might be reasonable limits on the domain.
It is not crucial at this time that students represent the domain using inequality notation. For example, for the last question, they might say “whole numbers between 0 and 10.”
Lesson Synthesis
Ask students to respond to one of these prompts, either in writing or by discussing with a partner. (Either let them choose one, or select one prompt for all students.)
• The most challenging part of the past few lessons was . . . because . . . • The most important thing I learned over the past few lessons was . . . • Some new terms I’ve learned are . . . and this is what they mean . . .
• I used to think . . . but now I think . . .
8.4 Ow, My Jaw
Cool Down: 5 minutes
Student Task Statement
Here are two de nitions of the same sequence. Recursive: and when
Closed form:
1. List the rst 4 terms of this sequence.
2. Write an expression to represent
3. A person is trying to quit chewing gum. They decide they will have 64 pieces in week 1, but each week have half as many as the week before. The function represents the pieces of gum they will have in week . What is a reasonable domain for this function?
Student Response
1. 64, 32, 16, 8
2. or equivalent
3. Possible response: or “integers from 1 to 7.” In the 7th week they will have 1 piece of gum, and it is reasonable to conclude that the following week, they have quit chewing gum and the function no longer represents the situation.
Unit 1
Lesson 8: What’s the Equation? 87