HIGHLINE SCHOOL DISTRICT                                                          MATH OLYMPIAD  March 25, 2000

 1

Circle Problem Scoring Guide

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

PROBLEM UNDERSTANDING

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

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