Going Airborne

Overall Achievement Level:

expert

Student Number:

Anchor Papers:

Problem Solving

expert

Problem Solving Rationale

The student’s strategy of using the relationship between distance, rate, and time (D = R x T) to find the unit rate of distance traveled around the world per hour for each character works to solve the task. The student correctly determines that Peter Pan will travel $sf text (4)/sf text(7)$ (.57) of the distance around the world in an hour, Aladdin will travel $sf text (5)/sf text (8)$ (.625) of the distance in an hour, and the Wicked Witch will travel $sf text (2)/sf text(3)$ ( $sf(.6bar6)$ ) of the distance in an hour. The student correctly determines that the Wicked Witch will travel around the world the fastest. The student then uses an alternative to find the time it would take each character to travel around the world.

Reasoning and Proof

expert

Reasoning Proof Rationale

The student demonstrates correct understanding of unit rates associated with ratios of fractions. The student correctly applies the formula of D &#247 T = R to determine the rate (distance traveled per hour) each character is traveling as a fraction of one hour. The student converts fractional amounts to decimals for easier comparison. As an alternative strategy to compare the speed of each character, the student converts the rate per hour to actual time to complete the entire race in hours and minutes. The calculations support the solution given.

Communication Level

expert

Communication Rationale

The student uses an organized, sequenced, and label response to communicate work. The student identifies the problem to be solved, explains the steps to the solution process, and explicitly states the solution. The student verifies his/her solution by explaining a second solution strategy. Formal math language and symbolic notation, including rate, formula, per, and equations is used to consolidate math thinking and to communicate ideas. The work is clear and easy to follow.

Connections Level

expert

Connections RationaleGoing Airborne

The student extends his/her solution of the problem by determining who won the race using two strategies. The student also generalizes the solution process for determining the rate of travel with the algebraic equation $sf text(D)/text(T)$ = R and the time required to travel the entire distance around the world with the equation $sf text (D)/text(R)$ = T.

Representation

expert

Representation Rationale

The student utilizes algebraic equations to provide a symbolic representation to analyze the relationships between distance, time, and rate. The student utilizes two algebraic equations $sf text(D)/text(T)$ = R and $sf text(D)/text(R)$ = T. The student then determines that comparing both rates and times show that the Wicked Witch is the fastest cartoon. Finally, the student constructs double number lines to compare the time that each character needs to complete one trip around the world.