Basic HTML Version
© 2014 Pacific Crest
81
H
ardest Problem
How hard
can
it be? Can you still use what you’ve learned?
Based on the Models, the information, and the Demonstrate Your Understanding (DYU) problems in
this activity, create the
hardest
problem you can. Start with the hardest DYU problem in this experience
and by contrasting and comparing it with the other DYU problems, play “What if” with the different
conditions and parameters in the various problems.
Can you still solve the problem? If so, solve it. If not, explain why not.
What are the conditions and parameters that make a problem involving logical reasoning a difficult
problem to solve?
T
roubleshooting
Find the error and correct it!
Identify the error and provide a correction:
Haley finished the proof and put down her pencil. Either she’d made a mistake somewhere or had
accidentally managed to disprove the entire field of mathematics. Can you figure out where she took
a wrong turn?
Steps
Explanation
x = y
Initial assumption
x
2
= xy
Multiply both sides by x
x
2
– y
2
= xy – y
2
Subtract y
2
from both sides
(x – y)(x + y) = y(x – y) Factor the left side and factor a y out of the right side
(x + y) = y
Divide both sides by (x – y)
y + y = y
Substitute y in for x because y = x
2y = y
Simplification
2 = 1
Divide both sides by y
M
aking it Matter
Solving problems in your life
●
Identify three situations where logic was used to make an argument, create a mathematical or logical
proof, and derive a formula. These situations could be from a class, this book or another book, or in
an area of interest. For each of the situations, explain the logic that was used, step-by-step.
1. To make an argument
2. To create a mathematical or logical proof
3. To derive a formula
2.2 Logical Reasoning