Introduction
Dimensional analysis is simply converting numbers of one type of unit to another type of unit through polynomial multiplication and simplification. For example, say we were going 50 miles per hour. How many kilometers per hour would this be? This is just one of the many questions dimensional analysis can answer for us. In this WebQuest, we are going to see how algebra, in particular, dimensional analysis can be useful in real life. Later, you'll create your own problems using dimensional analysis.
Task
A WebQuest for 8-10th Grade (Algebra) |
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Task You and your group are a team of research scientists for United States Department of Education. Students often feel that math doesn't apply to real life, and that algebra is useless after high school. Your job is to work in groups of four to change the student outlook of algebra. In order to complete this task, you must do the following:
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Process
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Process Day 1: Brainstorm and Research Your first step is to determine the roles within the group.
The Department of Education already has a collection of websites with real life problems. Your first step is to browse these links: Different standards of units in different countries: NASA Mix Up: http://www.cnn.com/TECH/space/9909/30/mars.metric/ Differneces between area and volume: http://www.differencebetween.net/science/difference-between-volume-and-area/ Environmental science problems: http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/49184.html Various ways in which unit conversion is used: http://www.ck12.org/algebra/Dimensional-Analysis/rwa/Baking-Cookies/?referrer=concept_details
http://www.wyzant.com/resources/lessons/math/elementary_math/measurement Practice: http://www.alysion.org/dimensional/fun.htm The technology assistant should be the groupmember doing the research, while the rest of the group offers advice and helps out. The administrative assistant should make sure to take notes on which sites were visited, as these notes will be turned in today. It is expected that you do a bit of research outside of these sites. "dimensional analysis," and "unit conversion" are great search terms to start with in Google. From these links, your group should be getting an idea of how dimensional analysis applies to real life. After your group has looked researched the various sites, your next step is to decide if your group would like to present a problem you saw on a website, or create one of your own. If you chose a problem, make sure it is interesting to your group. Feel free to find your own real world problems online, however, be careful of time. At the end of the day, the Lead Researcher will report to the Department of Education Secretary on the problem the group found most interesting. If your group chose to make its own problem, you'll need to decide what it will be about. This will also need to be reported to the Secretary of Education. This problem will be used for the next days assignment. Your homework for the night is to write a few paragraphs on why you thought the problem was interesting. If your group is making their own problem, be sure write why you chose this problem. Day 2: Work on Problem and Presentation The first step today is to turn in the short write up on your chosen problem. Good news! The department of education has discovered a wonderful website that contains many kinds of unit conversion. You'll be using this site throughout the day: http://www.onlineconversion.com/ As a group, you've already made a choice. You must either: Present the problem you chose yesterday to the public on day 3 or Create a new problem on your own based on yesterdays chosen problem and present it to class on day 3. As you can see, both have different challenges to overcome. The problem you researched might have math that is hard to understand, and as such, you'll need to understand it to present. However, it might be more work to create your own problem and make sure the math is correct in order to present it. In either case you'll need to explain to the public what is going on with your problem. You'll need to tell the public how it relates to everyday life. You'll also need to explain the math involved in the problem. Finally, you'll need to explain why you chose this particular problem. You'll be given butcher paper for posters. You can also use the chalkboard for demonstrations. Day 3: Presentation Day The Department of Education has made a formal public announcement on the importance of math in real life. The Public Relations person will do most of the presenting, although the Department of Education will be asking questions of the whole group. This serves to show the public that the group has been competent in it's research, and to generally impress the public! |
Evaluation
Evaluation
Performance for this project will be evaluated using the following rubric. Look closely at the guidelines so that you are not surprised when receiving your grade. I would look only at the Exemplary column for the best work.
| Beginning 1 | Developing 2 | Accomplished 3 | Exemplary 4 | Score | |
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| Group Work | Student was not filling their role within the group. Student was not on task. | Student filled their role at times. Student was sometimes on task. | Student mostly filled their role within the group. Student was mostly on task. | Student was consistent in filling their group role. Student was always on task. | |
| Day 1 Reflection | Student did not complete the assignment, or showed minimal effort. | Student completed the assignment, but showed some effort. | Student has done fair amount of thinking and reflecting about their chosen problem. | Student has done much thinking about their chosen problem and explains the problem thoroughly | |
| Relation of Problem to Real Life | Problem does not relate to real life. | Problem may or may not pertain to real life, although some explanation is given. | Problem pertains to real life. Explanation given is adequate. | Problem pertains to real life. Explanation given is thorough. | |
| Explanation of Math for chosen problem | Little or no explanation of math given. | Some explanation of math given, although may contain numerous errors. | Math presented is clear; may contain few errors. | Math presented is clear and is flawless. | |
| Explanation of problem choice | No explanation given. | Little or insufficient explanation given. | Some explanation given; some members might not understand why problem was chosen. | Group can explain why they chose their particular problem and apparent thought has gone into problem. | |
| Difficulty of Problem | No problem. | Problem contains one conversion. | Problem contains no more than three conversions. | Problem contains more than three conversions. |
Conclusion
Conclusion
As you can see, Dimensional Analysis is important to many of us. Unit conversion is not limited to your math classes, but is used for all kinds of real life applications and problems. This is especially true if you want to persue a career in the sciences.
From this project, I hope we learned to apply our algebraic skills. Most of all, I hope we had some fun exploring some of the ways we can use algebra.
Credits
Credits and References
Header graphic taken from: http://www.physicalscienceseries.com/images/dimanyl.gif
We all benefit by being generous with our work. Permission is hereby granted for other educators to copy this WebQuest, update or otherwise modify it, and post it elsewhere provided that the original author's name is retained along with a link back to the original URL of this WebQuest. On the line after the original author's name, you may add Modified by (your name) on (date). If you do modify it, please let me know and provide the new URL.