Criteria and Performance Level Rationales
Problem Solving
Apprentice
The student's strategy of using a table to indicate the exact and rounded populations of six towns and applying addition to determine the team with the greatest combined population works to solve the first part of the task. The student's answer, "Team 3 has a greater population," is correct. The student's strategy of using a table to compare the exact and rounded populations using greater and less than symbols per student would not work to solve the second part of the task. The student's answer, "I compared every town with the > and < symbols," is not correct.
Reasoning Proof
Apprentice
The student demonstrates understanding of the first part of the task by correctly applying the concept of rounding to the nearest hundred for populations of five towns. The student's error for College Station is considered a careless error and not a flaw in the student's reasoning. The student uses addition to calculate each team's total rounded population and determines the team with the greatest combined population. The notation flaw for College Station does not lead to an incorrect answer to the question. The student does not show correct reasoning in the second part of the task. The questions require the student to compare the exact population, the rounded population, or the exact and rounded population between each teams' two home towns. This student is just comparing the exact and rounded populations per student.
Communication
Practitioner
The student correctly uses the mathematical terms population, greater/less than, symbols, number, greatest from the task. The student also correctly uses the terms table, least. The student correctly uses the mathematical symbols, < and >.
Connections
Practitioner
The student makes mathematically relevant observations about her/his solution. The student states, "I noticest that Ryan lives in Amarillo and it has the greatest number of people living there," and "His team friend lives in Grapevine and has the least people living there."
Representation
Apprentice
The student's first table is appropriate to the task but is not accurate. The student provides all necessary labels but the entered data for the rounded population for Eric from College Station is not correct. It should state 93,900. The student's second table is not appropriate to the task and has errors. The fourth column should be labeled rounded population. Eric's rounded population should read 93,900. Ryan's population should read 190,695 and his rounded population should read 190,700.