Scary Reunion

Overall Achievement Level:

practitioner

Student Number:

Anchor Papers:

Problem Solving

practitioner

Problem Solving Rationale

The student’s strategy of using a coordinate grid helps them recognize they need “to find the diagonal distance for each shark.” The student uses the Pythagorean Theorem to calculate the diagonal distance of each shark at 2 pm, the formula for speed = $sf ((Distance)/(Time))$ to calculate the shark’s speed, and then “you double the sharks speed because the vessel goes the same distance at half the time.” The students answer that “for shark #1 the vessel must go 30 mph whist the vessel would have to go 34 mph to reach shark #2” is correct.

Reasoning and Proof

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Reasoning Proof Rationale

The student’s arguments are constructed with adequate mathematical basis. The student correctly applies the Pythagorean Theorem to calculate the distance traveled by each shark, “602 + 452 = c2, c = 75 miles” and “362 + 772 = c2, c = 85 miles.” The student correctly justifies the speed of each shark, “75 miles $-:$ 5 hours = 15 mph, 85 miles $-:$ 5 hours = 17 mph.” The student also shows correct reasoning for how fast the boat would need to travel by doubling the shark’s speed over 5 hours to catch up with the shark in 10 hours.

Communication Level

practitioner

Communication Rationale

A sense of purpose is communicated by the student in the original Question section, “If they wanted to pull up the anchor a 2 pm and end up near one of the sharks, how fast would the vessel have to average?” The student’s approach is provided within the Explanation, “First I had to find the Diagonal distance for each shark” and “I then used the formula for speed = D/T to find each SHARKS speed.” Appropriate formal math language such as average, location, speed, distance, time, “diagonal distance”, “pathgarum therum”, right triangle, formula, double, mph are used to share and clarify ideas.

Connections Level

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Connections RationaleScary Reunion

The student solves the tasks and notes the pattern “the sharks distance forms a right triangle.” The student explores the relationship “the vessel needs to travel double the speed the sharks go.”

Representation

practitioner

Representation Rationale

The student’s use of a coordinate grid and compass rose to illustrate the position of each shark after 5 hours is appropriate and accurate. All necessary labels are provided and the information is correct.