Criteria and Performance Level Rationales
Problem Solving
Expert
The student's strategy of using a diagram to show the number of miles between the towns, finding the total miles, and comparing the sums to determine if Brandon is correct works to solve the problem. The student's answer, "Brandon is not correct," is correct. The student uses an alternate strategy of a number line and applies prior knowledge that an odd number plus an even number equals an odd number and an odd number plus and odd number plus an odd number equals an odd number.
Reasoning & Proof
Expert
The student demonstrates correct reasoning of the underlying concepts of the problem. The student correctly shows the two sets of miles and understands that comparing the two sums is necessary to determine if Brandon's use of the less than sign/notation is correct. The student verifies her/his answer by creating a number line. The student also shows understanding that three groups of odd miles equals an odd total of miles and an odd group of miles added with an even group of miles equals an odd total of miles.
Communication
Expert
The student correctly uses the mathematical terms mile, "shortst" (shortest)from the problem. The student correctly uses the terms diagram, key, less than, greater than, 1st, 2nd, odd, even, rule, number line, total, most, more. The student correctly uses the mathematical notation <, from the problem. The student also uses the notation > and '.
Connections
Expert
The student makes the mathematically relevant Practitioner observations, "If he goes both routes it is 231 to city, 229 back home, 460 miles," "159 is the most miles but is in shortst route," and "route 1 is 2 miles more than route 2." The student applies the understanding that adding three odd numbers results in an odd total and adding an odd number and an even number results in an even number. The student states, "I know odd + even = odd rule, O + E = E." The student also extends her/his understanding of measurement by stating, "I know 5,280 ' is 1 mile to." The student verifies her/his answer by making a number line to show the total miles of each route and indicating that 231 miles is farther than 229 miles.
Representation
Expert
The student's diagram is appropriate and accurate. A key defines Brandon's town, the other towns, and miles. All other necessary labels are included. The student states, "I can do a number line to show the total miles to show I am right. The student's number line is appropriate and accurate.

Note: A student may use a printed number line as a strategy so long as she/he independently selects the number line.