Mathematical Explorations
Quantitative Reasoning Name _______________________________
The Problem:
Two different buyers purchased a home ten years ago. The first buyer had a30-year $150,000 loan with a
fixed interest rate of 4.5%. The second buyer had a 30-year $150,000 loan with an adjustable-rate
mortgage (ARM). The starting rate was 3%, but after 4 years the rate rose to 5.5% (it had an interest rate
of 3% for years 1, 2, 3 and 4, then the interest rate changed to 5.5% in year 5 for the remaining balance
and remaining time). Both home owners sold their house after 10 years. Which homeowner paid the
least?
Notes: Pay attention to time on the ARM.
DO NOT WRITE ON THIS SHEET. STAPLE THIS SHEET TO THE FRONT OF YOUR SOLUTION ON
YOUR OWN PAPER. YOUR WORK WILL BE SCORED ACCORDING TO THE RUBRIC ON THE REVERSE
SIDE OF THIS SHEET.
Check-off
I wrote the problem up on new paper in pencil.
I followed the order of the rubric given and did all parts.
My paper is neatly done. It has no scribbles, the writing is neat, there are no spiral shreds.
The cover sheet is stapled as the first page.
My name is on the paper.
QR9
MTH 120 QUANTITATIVE REASONING (QR) SCORING RUBRIC
MTH 120 is a course that further develops quantitative reasoning, an NMC learning objective. The first steps to
successful problem solving are getting started and being organized. Your Quantitative Reasoning (QR)
assignments will be graded using the rubric below, which emphasizes organization and getting started. Follow
the instructions carefully. Make sure to write complete sentences.
1. Gather Information (3 points)
Identify the question and all important information about the question given in the problem. Write
this in your own words and know what makes it important. Do not rewrite the entire problem.
This includes:• Identify numbers and units given.
• Write all formulas you need; write what each variable represents.
• Include any graphs, tables, or pictures drawn or given.
•Clearly write the question you must answer in your own words.
2. Write your reasonable answer (1 point)
Write a reasonable approximation as to what an answer to the question should look like. In what
range of numbers do you expect your answer to be and why? Try using simpler numbers to make
an estimate. In a few cases it might be possible to “guess” the answer at this point. If so, state your
thinking, but be aware that you still have to show work to support your guess. In other cases, with
your current background, it might be very difficult to make a reasonable guess. You are
encouraged to look up the topic to learn more, so that you can make a reasonable conjecture.
3. Solve and Communicate (5 points)
Solve the problem using an appropriate mathematical method. Make sure to show all calculations
and clearly label every calculation with words.
• If you use an algebraic equation, make sure to define a variable and clearly write and solve an
equation.
• If you logically think your way through the problem, make sure to clearly show your thinking.
• If you are using a spreadsheet or calculator, show all formulas and tables.
• Write a sentence stating why your solution is sound. This is where you compare what you thought
was a reasonable answer from Part 2 to your solution. If they do not agree make sure to tell how you
determined which is the reasonable answer and why, this will be a good time to consult another
source, like an on-line calculator. “Because I used the correct formula” or “Because I did the correct
work” is not justification that your answer is reasonable.
4. The Conclusion (1 point)
• Write a sentence conclusion (or sentences) that clearly answers all questions asked. Make sure
this is written at the end of your paper and answers all questions
asked.
5. Write-up
• Write your solution neatly on your own paper, no spiral shreds, no
scribbles, no obvious erasures
• Make sure to follow the rubric above in the order given.
• Make no marks on this paper (other than maybe check-marks) and
attach it as a cover page.
Gather Information
Reasonable Answer
Solve and Communicate
Conclusion
Layout