Going Airborne

Overall Achievement Level:

apprentice

Student Number:

Anchor Papers:

Problem Solving

apprentice

Problem Solving Rationale

The student’s strategy of scaling up the fractional amount of distances traveled in a given time to reach a sum of 1 trip around the world to determine how long it takes each character to travel around the world and which character is traveling the fastest could work to solve the task. The student incorrectly organizes the data for Aladdin, switching the values for time and distance, resulting in an incorrect conclusion that Aladdin will complete the trip in the smallest amount of time.

Reasoning and Proof

apprentice

Reasoning Proof Rationale

The student demonstrates some correct understanding of unit rates associated with ratios of fractions. The student uses incorrect reasoning when they defined Aladdin’s ratio of Distance traveled : Time spent traveling, which is the opposite ratio order used for Peter Pan and the Wicked Witch. The student uses repeated addition to scale up the fractional distances traveled by each character to equal one full trip around the world. The values determined for Peter Pan and the Wicked Witch are correct, while Aladdin’s is incorrect.

Communication Level

apprentice

Communication Rationale

The student attempts an organized, sequenced, and labeled response to communicate his/her work. The student explains the steps to the solution process and explicitly states the solution even though it is incorrect. The use of formal math language is limited, yet appropriate. The student uses incorrect symbolic notation when showing the relationship between distance traveled and the time it takes for each of the characters. The student shows this relationship as $sf text (2)/sf text (7)$ = $sf text (1)/sf text (2)$ instead of $sf text (2)/sf text (7)$ : $sf text (1)/sf text (2)$ . The student inconsistently includes labels for units of measure (distance, hours, minutes).

Connections Level

apprentice

Connections RationaleGoing Airborne

The student explores the use of rates within the task with additional opportunities to utilize rates to make mathematically based decisions concerning speed of airplanes and the cost of travel.

Representation

apprentice

Representation Rationale

The student attempts to organize the data in a grid for the story and his/her calculations. No categories for the table are provided. The relationships between distances traveled and elapsed time are written incorrectly (ex. $sf text(2)/sf text (7)$ = $sf text (1)/sf text(2)$ instead of $sf text (2)/sf text(7)$ : $sf text (1)/sf text(2)$ ). Unit labels (ex. hours, distance) are missing throughout.