f
Number and Operation Concepts: The student
compares numbers using percents.
The student
correctly used percent and converted it to dollars.
g
Number and Operation Concepts: The student
carries out proportional reasoning in cases...involving...contractions.
b
Problem Solving and Mathematical Reasoning:
Implementation. The student…
• chooses and employs effective problem
solving strategies in dealing with nonroutine and multistep problems;
• …uses mathematics to model real world situations….
The student
used an example to disprove Patrick’s conjecture. The student
applied the successive discount to show that the price of the shirt
was not zero dollars after two weeks.

c
Problem Solving and Mathematical Reasoning:
Conclusion. The student…concludes a solution process with a
useful summary of results….
The student
concluded the process by stating that Patrick will not get the shirt
for free.
The student
wrote $30, which represents 25% of the original price, therefore
concluded the correct amount of discount.
d
Problem Solving and Mathematical Reasoning:
Conclusion. The student employs forms of mathematical reasoning
including…using counter examples.
The student
disproved the conjecture by showing the shirt would never be free
but would cost $30 at the end of two weeks.
a
Mathematical Skills and Tools: The student
carries out numerical calculations….
The student
determined that $60 is 50% of $120 and that $30 is 25% of $120.
d
Mathematical Communication: The student communicates
logical arguments clearly, showing why a result makes sense and
why the reasoning is valid.
The student
specifically explained why the reasoning is valid and gave numerical
answers.
e
Mathematical Communication: The student presents
mathematical ideas effectively…in writing.
The student “explaination” [sic] clearly stated the reasoning
that the shirt would never be free.
The errors of punctuation and spelling do not detract from the
overall quality of the work.
