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:

         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 completely valid).

         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.


REASONABLE RESULT

Students were asked: 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.