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Q
uantitative
R
easoning &
P
roblem
S
olving
268
© 2014 Pacific Crest
T
roubleshooting
Find the error and correct it!
The community was analyzing the opportunities for recycling and accepting bids for solid waste
management. Three companies presented packages for you to consider as a member of the solid waste
oversight committee. The first company presented a set of graphs of the reduction of solid waste through
their approach to recycling showing a net decrease of 78% in waste. The second company presented
a formula that showed the cost for their service based upon the composition of solid waste. The third
company presented two tables: The first table showed the current breakdown of components of solid
waste that weren’t recyclable and the associated per ton charge of the component and the calculated
costs of each component. The second table showed recyclables and the reduced charge based upon the
value of each recyclable. The other members of the committee all agreed that the 78% reduction in waste
was impressive and most clearly communicated (“Look at how big the reduction is!”). They called for a
vote of the committee and the other members voted “Yes” to a three-year contract with the first company.
The committee chairperson has turned to you and asked for your input and vote.
M
aking it Matter
Solving problems in your life
●
You have put together an analysis of your food expenses for the last year, including all grocery shopping
excursions, dining out, snacks purchased, and miscellaneous (such as bringing a bottle of wine to a
dinner party at which you were a guest). How would you represent this analysis for yourself and others
so that your budgeting process (and managing your budget!) are most effective?
L
earning to Learn Mathematics
Reflecting on and appreciating your learning
1. When you are engaged in mathematical learning, problem solving, or investigating a new situation,
what are the triggers you look for to determine if switching representations might be valuable?
2. When is the cost of changing representations greater than the benefit received?
3. Why does the symbolic representation cause many people to react with a “Uhh...no, thanks.”
A
ssessing Your Performance
Assessing your performance as a learner
Review the description of
A Successful Performance
and assess your own performance against the
standard offered there.
●
How and why was your performance
SUCCESSFUL
?
●
How can you
IMPROVE
your performance, making it more successful? What
concrete steps
do you
need to take to make each improvement?