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