1. The document provides instructions and tasks for students to complete mathematical expressions, homework questions, and a lesson on reversible and non-reversible operations. 2. Students are asked to simplify expressions, complete homework problems, and determine whether example operations are reversible by considering if the starting number can be determined. 3. The document demonstrates how to "backtrack" through a multi-step operation to find the original starting number using reversible operations.

1. Opener: Put your homework questions on the back board before
starting the opener. Also, if you had a homework
presentation, please put that up BEFORE starting the
opener.
You will need your
calculator next class Simplify the following expressions:
period.
1.
Please make sure you
bring it and have
working batteries.
2.
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2. Homework Questions:
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3. Section 2.6: Getting Started
Task #1: Complete #1‐5 on page 117. Raise your hand when
you are done.
Task #2: If you finish #1 early, start to work on #9 with
your group. (It's the first question of your
homework tonight!)
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4. Section 2.7: Reversing Operations
Reversible Operations Non‐Reversible Operations
‐ opening or closing a ‐ jumping out of a plane
window ‐ compacting trash
‐ setting a clock forward ‐ taking a test
an hour ‐
‐ putting on and taking
off clothes ‐
‐
‐
‐
‐
‐
‐
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5. Is this Operation If you can come up with only one possible starting
Reversible? number, the operation is reversible. You should be
able to explain a way to reverse it if that's the case.
If you can't come up with a way to reverse the
operation, provide a counterexample ‐ 2 or more
numbers which would result in the same ending
number.
1. Adding 17 to a number results in 25.
2. Multiplying a number by ‐3 results in 21.
3. Squaring a number results in 25.
4. Changing the order of the digits of a number results in
320.
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6. Why does it matter
if something is Spiro is up to his number tricks again. Write the expression
reversible??? that results from this number trick.
1. Choose a number.
2. Multiply the number by 7.
3. Subtract 5.
Joey tells Spiro that the result of the number trick is 44.
We want to figure out how to undo Spiro's number trick
so we can know what his starting number is.
In what order should we undo the steps?
Step 1: Make a list, in the correct order, of the steps
that will undo each of the steps in Spiro's
trick.
Step 2: Apply your steps to the final number to
"backtrack" to Spiro's starting number.
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7. Ex. of backtracking: Charlie says, "I take a number, add 10, and multiply by ‐7.
My final result is 14."
We need to find Charlie's starting number.
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8. Another way to
think about reversible
and non‐reversible
operations...
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