HIGHLINE SCHOOL DISTRICT MATH OLYMPIAD March 25, 2000

1

Circle Problem Scoring Guide

CORRECT ANSWER:

Points	Look for the following:
4	The correct answer is given: · 190 lines
0	· Answer is not correct.

PROBLEM UNDERSTANDING

What did you notice about patterns? How did that help you approach the problem

Points

Look for the following:

4

Noticed two of the following patterns

· The number of lines is D * (D-1) / 2 where D is the number of dots

· 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

· 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	...	19

3

· Noticed one of the patterns mentioned above

2

· Expressed an understanding of the problem but did not mention a pattern

1

· The task is misunderstood

0

· No attempt at response.

STRATEGY

Students were asked: What strategy did you use? Why did you choose it?

Points	Look for the following:
4	· A 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 · Labels may be missing or directions may not have completely been followed
1	· Strategy was not explained according to directions, or the reasoning is confused (but there was one)
0	· No attempted strategy, just answers

COMMUNICATION

Students were told: Explain your reasoning using sentences, pictures. or tables

Points	Look for the following:
4	· Described strategy and solution clearly and completely, step-by-step, with all steps included · 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
1	· Strategy was not explained according to directions, or reasoning is confusing
0	· No attempt to explain

REASONABLE RESULT

Student was asked: How do you know your answer was reasonable? Did you work the problem a different way?

Points	Look for the following:
4	· Review 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
1	· A check was done but it was not valid
0	· No attempt was made to demonstrate the reasonableness of the result