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WASHINGTON STATE MATHEMATICS COUNCIL 2001
MIDDLE SCHOOL MATH OLYMPIAD Session I ~ Problem Solving
Phone Trees |
5-8 |
The score for each team for
Session I is the average of
the 5 scores below (maximum 4 points).
|
Points |
CORRECT ANSWER |
|
4 |
·
Accurately shows and
explains the following times
ending within a round (i.e.,
clearly showing that the last full round is not needed): Plan 10,000
Households 50,000 Households 3-Call Plan justified
time within 24-27 minute range justified time within 27-30 minute
range 5-Call Plan justified
time within 25-30 minute range justified
time within 30-35 minute range 10:53 ® 7/8
only: Shows correct times within
rounds for a third phone
tree plan. ·
Shows that a complete round of calls does not have to be
made to complete the phone calls In all cases. ·
Indicates that neither 10,000 nor 50,000 households can be
reached in 15 minutes under either plan. |
|
3 |
·
Accurately shows the following times (ending time end of round): Plan 10,000 Households 50,000 Households 3-Call Plan 27 min. done
by 10:48 30
min. done
by 10:51 5-Call Plan 30 min. done
by 10:51 35
min. done
by 10:56 ® 7/8
only: Shows correct times for a third phone tree plan. ·
One or two calculation or reasoning errors in Rubric level
4 time answers/reasoning. ·
May not recognize that whole rounds are needed for the
last round. ·
Indicates that neither 10,000 nor 50,000 households can be
reached in 15 minutes under either plan. |
|
2 |
·
One or two calculation errors in Rubric level 3 times
shown above. ·
Does or may not recognize that whole rounds are needed for
the last round. ·
May have data but does not reach (or state) decision
regarding 15 minute goal. |
|
0 |
·
Answer other than one of the above. |
|
Points |
PROBLEM UNDERSTANDING Understand the problem – patterns, concepts, and approach |
|
4 |
·
Correctly understands all required responsibilities. ·
Uses all
necessary information and data. |
|
3 |
·
Understands how to develop table or diagram, but does not
use this for recommendation. ·
Uses necessary information and data. |
|
2 |
·
Understands that the time required to alert households is
of central importance. ·
May have neglected to use necessary information. |
|
1 |
·
The task is incorrectly understood. ·
Information is incorrectly used or inaccurate. |
|
0 |
·
No attempt at a response. |
|
Points |
STRATEGY Choose and apply a valid
strategy for each part of the problem solution. |
|
4 |
·
Chose a valid strategy to develop tables/diagrams,
summary, and recommendations. ·
Applied the strategy correctly, consistently, and
completely. |
|
3 |
·
Chose a valid strategy to develop tables/diagrams and make
recommendations. ·
Applied the strategy correctly, but some breakdown in
reasoning or logic. |
|
2 |
·
Strategy was only
partly fit for the task. ·
Strategy was partially or incorrectly completed. |
|
1 |
·
Strategy did not apply to the task. |
|
0 |
·
No attempted strategy. |
|
Points |
COMMUNICATION Explain all requested
components of the final solution, using tables, symbols, labels, and correct
vocabulary. |
|
4 |
Using appropriate methods (tables, diagrams, terminology, symbols): ·
Communicated table/diagram, summary, and
recommendations clearly. ·
Communicated strategy clearly and completely for
table/diagram, summary, and recommendations. ·
Grammatical construction is basically correct. |
|
3 |
Using appropriate methods
(tables, diagrams, terminology, symbols): ·
Communicated table/diagram, summary, and
recommendations clearly, BUT may have
omitted reasoning connections, requiring the reader to make inferences. ·
Communicated strategy clearly and completely for
table/diagram, summary, and recommendations,
BUT
may have omitted reasoning connections, requiring the reader to make
inferences. ·
May include awkward grammar. |
|
2 |
·
Communicated table/diagram, summary, recommendations,
and strategy, but reasoning connections may be missing and inferences
cannot be made. ·
Labels may be missing or directions may not have been
completely followed. |
|
1 |
·
Table/diagram, summary, recommendations, and strategy
are not explained according to directions. |
|
0 |
·
No evidence of explanation. |
|
Points |
CHECK
FOR REASONABLENESS Demonstrate that entire solution has
been reasoned through. |
|
4 |
·
Discussed strongly valid reasons for time findings and
recommendations. ·
Demonstrated (or inferred) through above discussion that
findings and recommendations were checked for reasonableness. |
|
3 |
·
Discussed valid reasons for time findings and
recommendations. ·
Demonstrated (or inferred) through above discussion that
findings and recommendations were checked for reasonableness. |
|
2 |
·
(Reasonableness/Reasoning level between 3 and 1.) |
|
1 |
·
Reasons for time findings and recommendations were not
supported by evidence. ·
Demonstration (or
inference) of
check for reasonableness of findings and recommendations is not clearly
evident. |
|
0 |
·
Reasons for time findings and recommendations were not
provided. ·
No evidence of demonstration (or inference) of check for
reasonableness of findings and
recommendations. |
7/8 Additional Phone Tree Tables
2-Person Tree
|
Round Number |
Time of Round |
Total Minutes at End of Round |
Total # of Calls Made During Round |
Cumulative # of Calls at End of Round |
|
1 |
10:21 ¾ 10:23 |
2 |
2 |
2 |
|
2 |
10:23 ¾ 10:25 |
4 |
4 |
6 |
|
3 |
10:25 ¾ 10:27 |
6 |
8 |
14 |
|
4 |
10:27 ¾ 10:29 |
8 |
16 |
30 |
|
5 |
10:29 ¾ 10:31 |
10 |
32 |
62 |
|
6 |
10:31 ¾ 10:33 |
12 |
64 |
126 |
|
7 |
10:33 ¾ 10:35 |
14 |
128 |
254 |
|
8 |
10:35 ¾ 10:37 |
16 |
256 |
510 |
|
9 |
10:37 ¾ 10:39 |
18 |
512 |
1,022 |
|
10 |
10:39 ¾ 10:41 |
20 |
1,024 |
2,046 |
|
11 |
10:41 ¾ 10:43 |
22 |
2,048 |
4,094 |
|
12 |
10:43 ¾ 10:45 |
24 |
4,096 |
8,190 |
|
13 |
10:45 ¾ 10:47 |
26 |
8,192 |
16,382 |
|
14 |
10:47 ¾ 10:49 |
28 |
16,384 |
32,766 |
|
15 |
10:37 ¾ 10:39 |
30 |
32,768 |
65,534 |
4-Person Tree
|
Round Number |
Time of Round |
Total Minutes at End of Round |
Total # of Calls Made During Round |
Cumulative # of Calls at End of Round |
|
1 |
10:21 ¾ 10:25 |
4 |
4 |
4 |
|
2 |
10:25 ¾ 10:29 |
8 |
16 |
20 |
|
3 |
10:29 ¾ 10:33 |
12 |
64 |
84 |
|
4 |
10:33 ¾ 10:37 |
16 |
256 |
340 |
|
5 |
10:37 ¾ 10:41 |
20 |
1,024 |
1,364 |
|
6 |
10:41 ¾ 10:45 |
24 |
4,096 |
5,460 |
|
7 |
10:45 ¾ 10:49 |
28 |
16,384 |
21,844 |
|
8 |
10:49 ¾ 10:53 |
32 |
65,536 |
87,380 |
6-Person Tree
|
Round Number |
Time of Round |
Total Minutes at End of Round |
Total # of Calls Made During Round |
Cumulative # of Calls at End of Round |
|
1 |
10:21 ¾ 10:27 |
6 |
6 |
6 |
|
2 |
10:27 ¾ 10:33 |
12 |
36 |
42 |
|
3 |
10:33 ¾ 10:39 |
18 |
216 |
258 |
|
4 |
10:39 ¾ 10:45 |
24 |
1,296 |
1,554 |
|
5 |
10:45 ¾ 10:51 |
30 |
7,776 |
9,330 |
|
6 |
10:51 ¾ 10:57 |
36 |
46,656 |
55,986 |
7-Person Tree
|
Round Number |
Time of Round |
Total Minutes at End of Round |
Total # of Calls Made During Round |
Cumulative # of Calls at End of Round |
|
1 |
10:21 ¾ 10:28 |
7 |
7 |
7 |
|
2 |
10:28 ¾ 10:35 |
14 |
49 |
56 |
|
3 |
10:35 ¾ 10:42 |
21 |
343 |
399 |
|
4 |
10:42 ¾ 10:49 |
28 |
2,401 |
2,800 |
|
5 |
10:49 ¾ 10:56 |
35 |
16,807 |
19,607 |
|
6 |
10:56 ¾ 11:03 |
42 |
117,649 |
137,256 |
8-Person Tree
|
Round Number |
Time of Round |
Total Minutes at End of Round |
Total # of Calls Made During Round |
Cumulative # of Calls at End of Round |
|
1 |
10:21 ¾ 10:29 |
8 |
8 |
8 |
|
2 |
10:29 ¾ 10:37 |
16 |
64 |
72 |
|
3 |
10:37 ¾ 10:45 |
24 |
512 |
584 |
|
4 |
10:45 ¾ 10:53 |
32 |
4,096 |
4,680 |
|
5 |
10:53 ¾ 11:01 |
40 |
32,768 |
37,448 |
|
6 |
11:01 ¾ 11:09 |
48 |
262,144 |
299,592 |
9-Person Tree
|
Round Number |
Time of Round |
Total Minutes at End of Round |
Total # of Calls Made During Round |
Cumulative # of Calls at End of Round |
|
1 |
10:21 ¾ 10:30 |
9 |
9 |
9 |
|
2 |
10:30 ¾ 10:39 |
18 |
81 |
90 |
|
3 |
10:39 ¾ 10:48 |
27 |
729 |
819 |
|
4 |
10:48 ¾ 10:57 |
36 |
6,561 |
7,380 |
|
5 |
10:57 ¾ 11:06 |
45 |
59,049 |
66,429 |
10-Person Tree
|
Round Number |
Time of Round |
Total Minutes at End of Round |
Total # of Calls Made During Round |
Cumulative # of Calls at End of Round |
|
1 |
10:21 ¾ 10:31 |
10 |
10 |
10 |
|
2 |
10:31 ¾ 10:41 |
20 |
100 |
110 |
|
3 |
10:41 ¾ 10:51 |
30 |
1,000 |
1,110 |
|
4 |
10:51 ¾ 11:01 |
40 |
10,000 |
11,110 |
|
5 |
11:01 ¾ 11:11 |
50 |
100,000 |
111,110 |
12-Person Tree
|
Round Number |
Time of Round |
Total Minutes at End of Round |
Total # of Calls Made During Round |
Cumulative # of Calls at End of Round |
|
1 |
10:21 ¾ 10:33 |
12 |
12 |
12 |
|
2 |
10:33 ¾ 10:45 |
24 |
144 |
156 |
|
3 |
10:45 ¾ 10:57 |
36 |
1,728 |
1,884 |
|
4 |
10:57 ¾ 11:09 |
48 |
20,736 |
22,620 |
|
5 |
11:09 ¾ 11:21 |
60 |
248,832 |
271,452 |
15-Person Tree
|
Round Number |
Time of Round |
Total Minutes at End of Round |
Total # of Calls Made During Round |
Cumulative # of Calls at End of Round |
|
1 |
10:21 ¾ 10:36 |
15 |
15 |
15 |
|
2 |
10:36 ¾ 10:51 |
30 |
225 |
240 |
|
3 |
10:51 ¾ 11:06 |
45 |
3,375 |
3,615 |
|
4 |
11:06 ¾ 11:21 |
60 |
50,625 |
54,240 |
1-Person Tree
|
Round Number |
Time of Round |
Total Minutes at End of Round |
Total # of Calls Made During Round |
Cumulative # of Calls at End of Round |
|
10,000 |
10:21 + 10,000 min. |
10,000 |
1 |
10,000 |
|
50,000 |
10:21 + 10,000 min. |
50,000 |
1 |
50,000 |