Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Learning Math Home
Patterns, Functions, and Algebra
Session 3 Part A Part B Part C Part D Part E Homework
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Session 3 Materials:



Solutions for Session 3, Part A

See solutions for Problems: A1 | A2 | A3

Problem A1

The inputs 12 and 8 each lead to the output 4. If you only knew that the output was 4, it would be impossible to determine which of 12 and 8 was the correct input.

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Problem A2

Some examples:


Driving directions. Telling someone how to get somewhere usually allows them to figure out how to get back (if there are no one-way streets involved). In particular, to drive back you must take each road the opposite direction, and in reverse order (last road first).


Packing and unpacking. Especially with commercially shipped packages, it can be difficult to re-pack a box without knowing where things were located before you unpacked it.


In mathematics, many algebra problems involve "undoing" steps. For example, if 3x = 12, you can find x by undoing the multiplication step.

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Problem A3

Lots of things can't be undone easily, like throwing a water balloon, using gasoline in a car engine, or exploding fireworks.

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