WASHINGTON STATE MATHEMATICS COUNCIL

###### 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.

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