Scary Reunion

Overall Achievement Level:

expert

Student Number:

Anchor Papers:

Problem Solving

expert

Problem Solving Rationale

The student’s strategy of drawing a diagram using the provided directional information works to find the distance traveled by the sharks in 5 hours and 10 hours. The student uses their diagram to show that there would be two congruent triangles creating a doubling of the distance traveled. The student’s alternate strategy uses the Pythagorean Theorem to calculate the distance the shark traveled in the first 5 hours and then doubling it to find its distance at 7 pm. The student’s answer of the boat needing to travel 30 mph to catch shark 1 and 34 mph to catch shark 2 is correct. The student recognizes that the shark is likely to travel twice the distance in twice the time to determine how far the shark will have traveled by 7 pm.

Reasoning and Proof

expert

Reasoning Proof Rationale

The student demonstrates correct reasoning by using Pythagorean theorem to find distance traveled on a coordinate grid, a2+ b2 = c2. The student also uses the speed formula to find the correct speed the boat will need to travel to catch both sharks in 5 hours, “Shark 1: $sf text(150)/sf text(5) = sf30$ , 30 miles per hour to catch the shark” and “Shark 2: $sf text(170)/sf text(5) = sf34$ , 34 miles per hours to catch the shark. The student utilizes their diagram as evidence to support their conclusion of the distance traveled by the shark at 5 hours and 10 hours.

Communication Level

expert

Communication Rationale

The student uses a methodical, organized and sequenced response to communicate their approach. The student correctly identifies the problem, describes the steps to the solution, and states a correct conclusion. Insight is communicated about an efficient strategy when the student states “The sharks will double their distance by 7 pm.” The student utilizes their insight to construct the congruent triangles and to move from “x = 75 miles” to “2x = 150 miles” to find the total distance needed to travel. Appropriate math language, such as diagram, location, difference, double, distance, Pythagorean Theorem, hypotenuse, miles, time, miles per hour, speed is used rigorously to share and clarify ideas.

Connections Level

expert

Connections RationaleScary Reunion

The student uses several alternative strategies for finding the distance traveled and the speed required to make a mathematically relevant math connection. The student explains the phenomena that “the boat has to travel at double the speed of the sharks, because it travels double the distance in the same amount of time.”

Representation

expert

Representation Rationale

The student analyzes the relationships between the distance the sharks travel in 5 hours and 10 hours by using congruent triangles to show the total distance traveled. The student uses the diagram to clarify that doubling the time doubles the distance traveled.