HIGHLINE SCHOOL DISTRICT
OLYMPIAD
March 25, 2000


Circle Problem Scoring Guide

CORRECT ANSWER:
PointsLook for the following:
4The correct answer is given: 190 lines
0Answer is not correct

PROBLEM UNDERSTANDING:

What did you notice about patterns? How did that help you approach the problem?
PointsLook for the following:
4 Noticed two or more of the following patterns:
  1. The number of lines is D X (D - 1)/2 where D is the number of dots.
  2. If you draw 19 lines from point A, then 18 new lines can be drawn from point B, 17 from C, etc to form the sum 19 + 18 + 17 + ... + 1 =190
  3. The following sequence is recognized: 
    Dots =                                          4  5  6  7  8  9 10 ...  20
Lines =                                         6 10 15 21 28 36 45 ... 190
Increase in lines from previous number of dots: 4  5  6  7  8  9 10 ...  19
3 Noticed one of the patterns mentioned above
2Expressed an understanding of the problem but did not mention a pattern
1The task is misunderstood
0No attempt at response

STRATEGY:

Students were asked: What strategy did you use? Why did you choose it?
PointsLook for the following:
4A valid strategy is used: (make a table, draw lines and count, develop a sequence, or write an equation
3 A valid strategy is used, but may have breakdown in logic
2 Strategy was described, but steps may be missing or ...
Labels may be missing or directions may not have completely been followed
1Strategy was not explained according to directions, or the reasoning is confused (but there was one)
0No attempt at stragegy, just answers

COMMUNICATION:

Students were told: Explain your reasoning using sentences, pictures. or tables
PointsLook for the following:
4 Described strategy and solution clearly and completely, step-by-step, with all steps included and ...
Appropriate labels, terminology, and symbols are used
3 Described strategy and solution, but steps may be missing from the explanation.
The evaluator is required to infer that intermediate steps were performed correctly
Appropriate labels, terminology, and symbols are used
2 Strategy was described, but steps may be missing or out of order
1Strategy was not explained according to directions, or reasoning is confusing
0No attempt to explain

REASONABLE RESULT:

Student was asked: How do you know your answer was reasonable? Did you work the problem a different way?
PointsLook for the following:
4Review used a different approach to support the result
Review demonstrated correctness of work (showed work)
Explained why the result makes sense
3 The result was checked using the same approach as initially
2 A statement is make about checking the result without supporting information ("we checked our result")
1A check was done but it was not valid
0No attempt was made to demonstrate the reasonableness of the result