Your task is to plan a trip to visit each planet at least once. You will be gone for at least 65 Araca days and no longer than 70 Araca days.

Transcription

1 In a galaxy far, far away from ours, there is a solar system called Araca with 7 planets. The aliens that live there like to travel back and forth between planets. The order of the planets goes like this: Neva is 1st, then Branto, Sentra, Callax, Dorf, Tisan, and Falba is last. The distance between each planet is 1 more day than the distance between the 2 previous planets. For example, to get from Neva to Branto it takes 1 Araca day. To get from Branto to Sentra it takes 2 Araca days, and so on. 1 Araca day is equal to 50 Earth hours. Your task is to plan a trip to visit each planet at least once. You will be gone for at least 65 Araca days and no longer than 70 Araca days. Which planets will you visit? In what order? How long will you stay at each one? How many total Earth hours will you be gone? Good luck! Remember to show all your work! 1 of 9

2 Suggested Grade Span 3 5 Task In a galaxy far, far away from ours, there is a solar system called Araca with 7 planets. The aliens that live there like to travel back and forth between planets. The order of the planets goes like this: Neva is 1st, then Branto, Sentra, Callax, Dorf, Tisan, and Falba is last. The distance between each planet is 1 more day than the distance between the 2 previous planets. For example, to get from Neva to Branto it takes 1 Araca day. To get from Branto to Sentra it takes 2 Araca days, and so on. 1 Araca day is equal to 50 Earth hours. Your task is to plan a trip to visit each planet at least once. You will be gone for at least 65 Araca days and no longer than 70 Araca days. Which planets will you visit? In what order? How long will you stay at each one? How many total Earth hours will you be gone? Good luck! Remember to show all your work! Alternative Versions of Task More Accessible Version In a galaxy far, far away from ours, there is a solar system called Araca with 4 planets. The aliens living there like to travel back and forth between planets. The order of the planets goes like this: Neva is 1st, then Branto, Sentra, and then Callax. The distance between each planet is 1 more day than the distance between the 2 previous planets. For example, to get from Neva to Branto it takes 1 Araca day. To get from Branto to Sentra it takes 2 Araca days, and so on. 1 Araca day is equal to 50 Earth hours. Your task is to plan a trip to visit each planet once, and then to go back to Neva. How many total Earth hours will you be gone? Good luck! Remember to show all your work! 2 of 9

3 More Challenging Version In a galaxy far, far away from ours, there is a solar system called Araca with 7 planets. The aliens living there like to travel back and forth between planets. The order of the planets goes like this: Neva is 1st, then Branto, Sentra, Callax, Dorf, Tisan, and Falba is last. The distance between each planet is double the distance between the 2 previous planets. For example, to get from Neva to Branto it takes 1 Araca day. To get from Branto to Sentra it takes 2 Araca days, to get from Sentra to Callax it takes 4 Araca days, and so on. 1 Araca day is equal to 50 Earth hours. Your task is to plan a trip to visit each planet at least once. How many total Earth days will you be gone? Good luck! Remember to show all your work! Context This task is part of a thematic unit I teach on the solar system. Students have been learning about the planets, facts and figures about distances, equivalent Earth hours and days. They have been doing a number of math-related activities using these concepts. This task has students apply knowledge to a new situation and review skills such as place value, regrouping and problem solving. What This Task Accomplishes This task allows students to apply knowledge learned during the unit on the solar system, such as calculating Earth hours. It also asks them to practice certain problem-solving skills such as creating representations, making connections, finding approaches and using mathematical reasoning. Finally, it has students apply regrouping and place value concepts to a problemsolving situation. What the Student Will Do Students will begin by figuring out the distance between each planet. They will represent this information in some way, such as a labeled diagram. Next, they will have to decide in what order they will visit each planet and how much time they will stay there. They will have to multiply, or they may notice some patterns which they can utilize. They will need to keep in mind the time constraints given and calculate equivalent Earth hours. They will need to explain how they solved this problem, using appropriate math language and concepts. Students will hopefully make some connections to what they have learned in our unit on the solar system. Finally, students will share their solutions with the class. 3 of 9

4 Time Required for Task Approximately two 45-minute math sessions. Interdisciplinary Links As mentioned, this task is done in conjunction with a unit on the solar system. This task helped to reinforce many of the mathematical concepts presented during this unit. In addition to the science and math involved, students wrote planet poetry, researched planets, read science fiction stories and designed their own imaginary solar system. Students could also compare distances between the planets in our solar system. Teaching Tips Encourage students to do this problem step by step. Make sure that the representations they start with are simple, labeled and easy to use. They will also need to represent their trip data in some form that is understandable. For some students this task may be too challenging. You can make the task less complex by reducing the number of planets and making the number of days required to spend traveling more open-ended. Suggested Materials A copy of the task Pencil Crayons Rulers An overhead projector for presenting the problem to class Students may want to share their solution with the class using a different format such as a poster. It is important to have materials for this on hand. Possible Solutions There are many possible solutions. A correct solution includes a labeled diagram of the planets and the correct distances in days between them. It includes a representation of data that is correct and stays within the time constraint of Araca days. It also has the trip time calculated in earth hours and includes an appropriate explanation of strategies and reasoning used for solving this problem. More Accessible Version Solution = 12 Araca days 12 Araca days x 50 Earth hours = 600 Earth hours 4 of 9

5 More Challenging Version Solution N to B = 1 B to S = 2 S to C = 4 C to D = 8 D to T = 16 T to F = Araca days x 50 hours = 3,150 Earth hours 3,150 Earth hours 24 hours in an Earth day = Earth days Task-Specific Assessment Notes Novice The Novice will have few or no parts correct, demonstrating only a rudimentary understanding of the task. Very little math language will be used, and representations will be limited to diagrams that lack accuracy with respect to the task. Apprentice The Apprentice will have a partially correct solution. The student may make calculation errors or may not stay within the day parameter. The Apprentice may also neglect to convert time to Earth hours or may make a mistake in the pattern. Some math language and representations will be used. Practitioner The Practitioner will have a correct solution and will include a well-labeled chart and diagram. The approach and reasoning will be very clear, and an explanation will include the steps followed in solving the problem. Calculations will be correct and may indicate verification of the answer in several ways. Math language and representations will be used accurately and appropriately. Expert The Expert will have a correct solution and a well-labeled chart and/or diagram. The explanation will be very clear and detailed. The Expert will utilize a pattern to solve the problem and will discuss the strategy used in detail. The Expert may verify the answer in several ways and will make a good mathematical connection or observation. 5 of 9

6 Novice 6 of 9

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9 Expert 9 of 9