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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
Households50,000 Households 3-Call Planjustified
time within 24-27 minute range justified time within 27-30 minute
range 5-Call Planjustified
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): Plan10,000 Households50,000 Households 3-Call Plan27 min.done
by10:4830
min.done
by10:51 5-Call Plan30 min.done
by 10:5135
min.done
by10:56 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 UNDERSTANDINGUnderstand 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 |
STRATEGYChoose 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 |
Strategywas 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 offindings 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 |
10:21-10:23 |
2 |
2 |
2 |
2 |
10:2310:25 |
4 |
4 |
6 |
3 |
10:2510:27 |
6 |
8 |
14 |
4 |
10:2710:29 |
8 |
16 |
30 |
5 |
10:2910:31 |
10 |
32 |
62 |
6 |
10:3110:33 |
12 |
64 |
126 |
7 |
10:3310:35 |
14 |
128 |
254 |
8 |
10:3510:37 |
16 |
256 |
510 |
9 |
10:3710:39 |
18 |
512 |
1,022 |
10 |
10:3910:41 |
20 |
1,024 |
2,046 |
11 |
10:4110:43 |
22 |
2,048 |
4,094 |
12 |
10:4310:45 |
24 |
4,096 |
8,190 |
13 |
10:4510:47 |
26 |
8,192 |
16,382 |
14 |
10:4710:49 |
28 |
16,384 |
32,766 |
15 |
10:3710:39 |
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 |
10:2110:25 |
4 |
4 |
4 |
2 |
10:2510:29 |
8 |
16 |
20 |
3 |
10:2910:33 |
12 |
64 |
84 |
4 |
10:3310:37 |
16 |
256 |
340 |
5 |
10:3710:41 |
20 |
1,024 |
1,364 |
6 |
10:4110:45 |
24 |
4,096 |
5,460 |
7 |
10:4510:49 |
28 |
16,384 |
21,844 |
8 |
10:4910:53 |
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 |
10:2110:27 |
6 |
6 |
6 |
2 |
10:2710:33 |
12 |
36 |
42 |
3 |
10:3310:39 |
18 |
216 |
258 |
4 |
10:3910:45 |
24 |
1,296 |
1,554 |
5 |
10:4510:51 |
30 |
7,776 |
9,330 |
6 |
10:5110:57 |
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 |
10:2110:28 |
7 |
7 |
7 |
2 |
10:2810:35 |
14 |
49 |
56 |
3 |
10:3510:42 |
21 |
343 |
399 |
4 |
10:4210:49 |
28 |
2,401 |
2,800 |
5 |
10:4910:56 |
35 |
16,807 |
19,607 |
6 |
10:5611:03 |
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 |
10:2110:29 |
8 |
8 |
8 |
2 |
10:2910:37 |
16 |
64 |
72 |
3 |
10:3710:45 |
24 |
512 |
584 |
4 |
10:4510:53 |
32 |
4,096 |
4,680 |
5 |
10:5311:01 |
40 |
32,768 |
37,448 |
6 |
11:0111:09 |
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 |
10:2110:30 |
9 |
9 |
9 |
2 |
10:3010:39 |
18 |
81 |
90 |
3 |
10:3910:48 |
27 |
729 |
819 |
4 |
10:4810:57 |
36 |
6,561 |
7,380 |
5 |
10:5711:06 |
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 |
10:2110:31 |
10 |
10 |
10 |
2 |
10:3110:41 |
20 |
100 |
110 |
3 |
10:4110:51 |
30 |
1,000 |
1,110 |
4 |
10:5111:01 |
40 |
10,000 |
11,110 |
5 |
11:0111:11 |
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 |
10:2110:33 |
12 |
12 |
12 |
2 |
10:3310:45 |
24 |
144 |
156 |
3 |
10:4510:57 |
36 |
1,728 |
1,884 |
4 |
10:5711:09 |
48 |
20,736 |
22,620 |
5 |
11:0911:21 |
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 |
10:2110:36 |
15 |
15 |
15 |
2 |
10:3610:51 |
30 |
225 |
240 |
3 |
10:5111:06 |
45 |
3,375 |
3,615 |
4 |
11:0611:21 |
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 |