Criteria and Performance Level Rationales
Problem Solving
Practitioner
The student's strategy of using a table to indicate the exact and rounded populations of six towns and applying addition works to solve the first part of the task. The student's strategy of using number lines and the greater than and less than symbols works to solve the second part of the task. The student's answers, "Ryan and Brody have the most population rounded total. They are team 3" "99,940 < 113,383," "99,200 > 93,900," "46,334 < 190,695," and "46,300 < 190,700," are correct.
Reasoning Proof
Practitioner
The student demonstrates correct understanding of the first part of the task by applying the concept of rounding to the nearest hundred for the population of six towns. The student uses addition correctly to calculate each team's total rounded population and determines the team with the greatest rounded combined population. The student shows correct reasoning of the second part of the task by comparing the exact and/or rounded town populations for each team and using the greater than and less than symbols correctly in stating the comparisons.
Communication
Practitioner
The student correctly uses the mathematical terms population, greatest, symbols from the task. The student also correctly uses the terms most, total, number lines, table, 100 thousands place, place value, least. The student correctly uses the mathematical symbols, < and >.
Connections
Practitioner
The student makes mathematically relevant observations about her/his solution. The student states, "You donâ€™t have to add team 2 because they have no 100 tousands place and I can see they can't go past 1 in the 100 thousands total," "Ryan's town has greatest population," "I counted by 20,000 on team 3 number lines," and "Brody has least population."
Representation
Practitioner
The student's use of a table is appropriate to the task and accurate. The student provides all necessary labels and the entered data is correct. The student's four number lines are appropriate to the task and accurate. Each number line has the team labeled, numbers labeled as either exact population or rounded population, and the intervals on the number lines are accurate and labeled correctly.