WASHINGTON STATE MATHEMATICS COUNCIL

2001 MIDDLE SCHOOL MATH OLYMPIAD

 
Session I ~ Problem Solving

Phone Trees

5-8

 

Rubric/Scoring Guidelines

 

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 10:23

2

2

2

2

10:23 10:25

4

4

6

3

10:25 10:27

6

8

14

4

10:27 10:29

8

16

30

5

10:29 10:31

10

32

62

6

10:31 10:33

12

64

126

7

10:33 10:35

14

128

254

8

10:35 10:37

16

256

510

9

10:37 10:39

18

512

1,022

10

10:39 10:41

20

1,024

2,046

11

10:41 10:43

22

2,048

4,094

12

10:43 10:45

24

4,096

8,190

13

10:45 10:47

26

8,192

16,382

14

10:47 10:49

28

16,384

32,766

15

10:37 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 10:25

4

4

4

2

10:25 10:29

8

16

20

3

10:29 10:33

12

64

84

4

10:33 10:37

16

256

340

5

10:37 10:41

20

1,024

1,364

6

10:41 10:45

24

4,096

5,460

7

10:45 10:49

28

16,384

21,844

8

10:49 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 10:27

6

6

6

2

10:27 10:33

12

36

42

3

10:33 10:39

18

216

258

4

10:39 10:45

24

1,296

1,554

5

10:45 10:51

30

7,776

9,330

6

10:51 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 10:28

7

7

7

2

10:28 10:35

14

49

56

3

10:35 10:42

21

343

399

4

10:42 10:49

28

2,401

2,800

5

10:49 10:56

35

16,807

19,607

6

10:56 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 10:29

8

8

8

2

10:29 10:37

16

64

72

3

10:37 10:45

24

512

584

4

10:45 10:53

32

4,096

4,680

5

10:53 11:01

40

32,768

37,448

6

11:01 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 10:30

9

9

9

2

10:30 10:39

18

81

90

3

10:39 10:48

27

729

819

4

10:48 10:57

36

6,561

7,380

5

10:57 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 10:31

10

10

10

2

10:31 10:41

20

100

110

3

10:41 10:51

30

1,000

1,110

4

10:51 11:01

40

10,000

11,110

5

11:01 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 10:33

12

12

12

2

10:33 10:45

24

144

156

3

10:45 10:57

36

1,728

1,884

4

10:57 11:09

48

20,736

22,620

5

11:09 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 10:36

15

15

15

2

10:36 10:51

30

225

240

3

10:51 11:06

45

3,375

3,615

4

11:06 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