|
WASHINGTON
STATE MATHEMATICS COUNCIL 2000
MIDDLE SCHOOL MATH OLYMPIAD Session I PROBLEM SOLVING |
5678 |
Scoring
Guidelines:The Tiles Game
CORRECT ANSWER[Scores
of 0, 2, 3, and 4 are possible.]
Points |
Look
for the following: |
4 |
Grades
7 and 8:27/216,1/8,.125, or 12.5% Grades
5 and 6:12/64,3/16,.1875, or 18.75% |
3 |
.
If answer is in fractional form, denominator and numerator
are both correct in first form of answer, but simplified form is incorrect. .
If answer is in decimal or percent form, original
(fraction) form of answer is correct, but conversion to decimal or percentage
is incorrect. |
2 |
.
Numerator or
denominator used to identify answer is incorrect, leading to incorrect
fraction, decimal, or percent form of answer.(One of the two, numerator or
denominator --is/was originally
correct.) |
0 |
.
Answer is not correct (and would not have been with
correct calculation). |
PROBLEM
UNDERSTANDING[Scores of 0, 2, 3, and 4 are possible.]
Students were asked:Do you
understand what the problem is asking?What did you notice about patterns?How did that help you solve the problem?
Points |
Look
for the following: |
4 |
Grades
7 and 8:< /span> .
Discovers there are 6 x 6 x 6 or 216 permutations (i.e.,
shows strong understanding that there is a need to discover all possible permutations of 3 tiles). .
Discovers that there are 27 permutations resulting in a
sum of 7 or that there are 6 combinations resulting in a sum of 7 (i.e.,
shows strong understanding of need to find the permutations that will sum to
7, whether this is done by combinations first or by listing permutations). .
Shows evidence of approaching the problem in an orderly
way Grades
5 and 6: .
Discovers there are 4 x 4 x 4 or 64 permutations (i.e.,
shows strong understanding that there is a need to discover all possible permutations of 3 tiles). .
Discovers that there are 12 permutations resulting in a
sum of 5 or that there are 3 combinations resulting in a sum of 5 (i.e.,
shows strong understanding of need to find the permutations that will sum to
5, whether this is done by combinations first or by listing permutations). .
Shows evidence of approaching the problem in an orderly
way. |
3 |
Grades
7 and 8: .
Discovers there are 6 x 6 x 6 or 216 permutations (i.e.,
shows understanding of the need to discover all possible permutations of 3
tile numbers, even if method used is not completely valid). .
Shows understanding of the need to determine the number of
these permutations that result in a sum of 7, even if method for doing so is
not completely valid. .
Shows evidence of approaching the problem in an orderly
way. Grades
5 and 6: .
Discovers there are 4 x 4 x 4 or 64 permutations (i.e.,
shows understanding of the need to discover all possible permutation of 3
tile number, even if method used is not completelyvalid). .
Shows understanding of the need to determine the number of
these permutations that result in a sum of 5, even if method for doing so is
not completely valid. .
Shows evidence of approaching the problem in an orderly
way. |
2 |
.
Shows understanding that the problem has two parts
(numerator & denominator). .
Shows some evidence of approaching, or attempting to
approach -- the problem in an orderly way. |
0 |
.
No evidence that an attempt was made to understand the
problem and/or to communicate this understanding. |
STRATEGY
Students were
asked:What is your strategy for solving
the problem (e.g., table, list, etc.)?Is your strategy valid?Is it
carried out completely?
Points |
Look
for the following: |
4 |
.
A valid strategy is used: makes a table, or uses logic and
calculations. Strategy is completely carried through. |
3 |
.
A valid strategy is used, but may not be completely
carried through or may not be used for completely valid reasons (making
strategy not 100% valid). |
2 |
.
A strategy was applied, but reasoning is confused or not
logical. |
1 |
.
An attempt was made to use a strategy, but strategy was
poor (very incomplete). |
0 |
.
No evidence of a strategy |
COMMUNICATION
Students were
asked:Is your reasoning about the
problem and about your strategies clearly communicated -- using words,
pictures, tables, symbols?
Points |
Look
for the following: |
4 |
.
Described problem understanding, strategy, and solution
clearly and completely, step-by-step, with all steps included. .
Used appropriate labels, terminology, and symbols. |
3 |
.
Described problem understanding, strategy, and solution,
but steps may be missing from the explanation.The evaluator is required to infer that intermediate steps were
performed correctly. .
Used appropriate labels, terminology, and symbols (with
perhaps very minor errors). |
2 |
.
Strategy was described, but steps may be missing or out of
order. Understanding
of problem may or may not be directly communicated (but should be indirectly
communicated). |
1 |
.
An attempt was made to explain strategy, but reasoning is
confusing. Understanding
of problem is poorly communicated, directly or indirectly. |
0 |
.
No sentences or phrases were provided to explain strategy,
understanding, solution. |
Students were asked:<12/span>How did you
check that your answer was reasonable?
Points |
Look
for the following: |
4 |
There is evidence that the result was checked. |
2 |
A claim was made that the answer was checked for reasonableness, but there is no substantiating evidence of this check. |
0 |
There is no evidence of or claim about a check for reasonableness. |