Criteria and Performance Level Rationales
Problem Solving
Expert
The student's strategy of using tables to show "Team 1 answer, Team 2 answer, and Team 3 answer" for crab walk teams, works to solve the first part of the task. The student correctly uses the less than, greater than, and equal sign to compare the three teams to solve the second part of the task. The student's answer, "I know 42.1 = 42.1, I know 42.1 > 41.7 seconds, 41.7 < 42.1 seconds," and "in seconds-team 2 > team 1, team 3 > team 1, team 1 < team 2, team 1 < team 3," is correct. The student brings prior knowledge of range, average, percent, outcome to her/his solution.
Reasoning Proof
Expert
The student demonstrates understanding that Mr. Fair requires three possible teams of four students that are as equally matched as possible. The student demonstrates understanding of correctly using the less than, greater than, and equal symbols to compare the three crab walk teams. The student brings the conceptual understanding of range and outcomes to her/his solution. The student applies the concept of average and percent to support her/his reasoning that when using Mr. Fair's data, you can not have three equally timed crab walk teams.
Communication
Expert
The student correctly uses the mathematical terms time, seconds (sec), equally, total from the task. The student also correctly uses the terms range, average, more than, fair, even, remainder, outcome, difference, per, thousandths place. The student correctly uses the notation 8.7, 8.9, 9.1, 9.9, 10.3, 10.5, 10.9, 11.0, 11.1, 11.4, 11.9, 12.2 from the task. The student also correctly uses the notation 3.5, 17.6, 19.0, 31.7, 45.4, 125.9, 41.966, 42.3, 42.1, 41.5, 41.7, 0.4, 1/12, 10.425, 10.525, 0.100, >, <, 100%.
Connections
Expert
The student makes the mathematically relevant Practitioner observations, "I notest that the fastest crabwalker is Amy," "I notest that the four slowest crabwalkers are all boys and Harry is the slowest." The student makes Expert connections by extending her/his solution to other mathematical concepts. The student states, "3.5 sec is the range." The student states, "I can find the average to get an idea from my table," and concludes, "The teams can't be exactly even because there is a remainder." The student justifies how adjusting the time would make the three teams equal. The student states, "Since team 1 41.7 is fastest team I think they should win by 0.4 seconds less than their actual time in the race," "I think that is the only way to make it 100% equal and fair because of the remainder." The student extends her/his thinking to finding outcomes. The student states, "The outcome for Harry is 1/12 students has a crabwalk of time in 12 seconds range and that is Harry." The student finds the "averages in seconds for each teams members." The student finds 10.425 for team one and 10.525 for teams two and three. The student states, "1/10 of a second difference in average per team. You have to go to thousandths place so no remainder."
Representation
Expert
The student's three tables are appropriate to the task and accurate. Each tabled is titled, the columns are correctly labeled and all entered data is correct. The student uses the data on her/his tables to extend her/his thinking to range, average, and percent.