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Patterns, Functions, and Algebra
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Notes for Session 3, Part D

Note 5

Groups: Work on Problems D1-D7 and discuss what everyone finds.

The problem with the algorithm in Problem D3 is the step "add your original number." It's not clear how to model that with machines. Even if we are able to adapt the machine metaphor to work, we can't "undo" that step of the process.

Consider going through a symbolic representation of the algorithm to see that it does not share this weakness with the machine, because you can combine terms, essentially creating an equivalent algorithm that you can undo:

[(n + 3) x 2 + n - 4] x 3 = (3n + 6 - 4) x 3

(This is just one of many equivalent algorithms.)

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