Criteria and Performance Level Rationales
Problem Solving
Novice
The student's strategy of using table to indicate the population stated in the task for each student and replacing the ones, tens, and hundreds places with zeros in the "round number" column does not work to solve the first part of the task. The student's answer, "Amy has the most population because she has 3 nines 99,940 on my table," is not correct. The student does not provide a strategy to solve the second part of the task. The student's statement, "Amy is > everyone," is not correct.
Reasoning Proof
Novice
The student is able create a table to list the six students and scribe the correct population from the task but demonstrates no understanding of the underlying concepts of the task. The student does not demonstrate understanding that the six students form three teams. The student does not demonstrate understanding of the mathematical concept of rounding to the hundreds place. The student replaces all the ones, tens, and hundreds place value numbers with zeros. The student is not comparing numbers by place value but by the magnitude of the first numbers reading from left to right. Therefore, 99,940 is considered the greatest population. The student does not demonstrate understanding of the concept of using greater than and less than to compare the exact and rounded town populations between two students.
Communication
Practitioner
The student correctly uses the mathematical terms population, greater than, symbol from the task. The student also correctly uses the term table. The student does not use the mathematical symbol, >, correctly.
Connections
Novice
The student solves the task and does not attempt to make a mathematically relevant observation about her/his solution.
Representation
Apprentice
The student's table is appropriate to part of the task but is not accurate. The third column should be a labeled rounded number of population. All the entered data for the third column is not accurate.