The Great Kayak Expedition

Transcription

1 The Great Kayak Expedition Ethan went on a kayaking expedition down the Ottauquechee River last week. He left school at 2:35 and paddled downstream 3 miles until he hit the sewage treatment plant at 3:05. He decided to get out of the river at that point (wise decision) and went across the street to Pizza Chef. He then headed back up the river in his boat and it took him 90 minutes to paddle back to school. What is Ethan s rate of paddling in miles per hour? How fast is the river current? TM The Great Kayak Expedition - Page 1-

2 Grade Level 6 8 The Great Kayak Expedition Ethan went on a kayaking expedition down the Ottauquechee River last week. He left school at 2:35 and paddled downstream 3 miles until he hit the sewage treatment plant at 3:05. He decided to get out of the river at that point (wise decision) and went across the street to Pizza Chef. He then headed back up the river in his boat and it took him 90 minutes to paddle back to school. What is Ethan s rate of paddling in miles per hour? How fast is the river current? Context This task was given to students while studying ratios and rates. They had previously used dimensional analysis to convert units of measurement. What This Task Accomplishes This task allows students to see a real life situation where dimensional analysis and rates can be used. The situation was one with which students could identify, as names and places were familiar to them. They were quickly engaged in the task. Time Required for Task Most students completed the task within the 45 minute class period. Interdisciplinary Links The students were able to use this problem as a refresher for doing science labs involving rate and dimensional analysis. Teaching Tips It is essential that students understand that a ratio is a comparison of two quantities by division and a rate is a ratio that compares two different types of quantities (in this case miles and minutes). There should also be some previous work with current problems (river or air current) with discussion about what happens when you are traveling downstream (the river - Page 2-

3 helps you go faster) and what happens when you are traveling upstream ( the river works against you and slows you down). This problem could be modified for special needs students by changing the question to: What was Ethan s rate, in miles per hour on his trip to Pizza Chef and what was his rate on the trip back to school? Suggested Materials Calculators Possible Solutions Ethan s rate of paddling is 4 miles per hour and the river current rate is 2 miles per hour. Most students will correctly identify the combined rates (downstream Ethan goes 3 miles in 30 minutes, upstream he goes 3 miles in 90 minutes) and, using dimensional analysis, will convert them to 6 miles per hour downstream and 2 miles per hour upstream. Depending upon skill level, the student will use either a system of algebraic equations or guess and test to solve for Ethan s rate and the river current s rate. Benchmark Descriptors Novice The novice will not have a strategy for finding the rates asked for in the task. S/he will most likely state that Ethan went 3 miles in 30 minutes downstream and 3 miles in 90 minutes upstream. The novice will not be able to use dimensional analysis to convert those rates to miles per hour. Apprentice The apprentice will have a strategy for solving part of the problem but will be unable to complete the task successfully. S/he will successfully find the rate in miles per hour for the trip downstream and upstream but will not have a strategy for continuing the task. Practitioner The practitioner will have a strategy for successfully completing the task. The answers will be correct. S/he will most likely use guess and test to find the individual rates and will use appropriate and accurate math language to explain the solution. There may be an accurate and appropriate math representation included. - Page 3-

4 Expert The expert will have a strategy for successfully completing the task, and the answers will be correct. S/he will most likely assign variables for Ethan s rate and the rate of the current, and use a system of algebraic equations to find those rates. These steps will be clearly explained with accurate and appropriate math language and representation. There will also be a relevant mathematical connection. Author Nancy Harlow Pejouhy teaches 8th grade at Woodstock Union Middle School in Woodstock, Vermont. She is a math network leader for the Vermont Department of Education and serves on various state committees for math assessment. - Page 4-

5 Novice The student does not have a strategy to successfully complete the task. - Page 5-

6 Apprentice The student is unable to continue with the solution. S/he does not understand the need to find the rate of paddling and the rate of current. Some math language is used. - Page 6-

7 Practitioner The student successfully uses dimensional analysis to convert miles per minute to miles per hour. The student needed only two guesses to find a correct solution. All work is shown. - Page 7-

8 Expert A correct answer is achieved. The student has an appropriate representation. Accurate math language is used throughout. The student creates rules to solve the problem. Use of linear combinations to solve for Ethan s rate of paddling is appropriate. - Page 8-