You and Your Group Are a Team of Research Scientists for United States Department of Education

Dimensional Analysis
Everyday Applications /

/ Introduction
According to Texas A & M University, "Dimensional Analysis (also called Factor-Label Method or the Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value."
Sounds complicated right? It doesn't have to be. In fact, dimensional analysis can be quite easy. Up to this point, you should already know a bit about rational expressions. A rational expression is an algebraic fraction whose numerator and denominator are polynomials. For example, (3x/6y) is a rational expression. We should already know how to simplify rational expressions. In the case of (3x/6y), the simplified answer is x/2y, as 3 can divided into the numerator and denominator. Also, we should know how to multiply rational expressions.
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

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:

Research a given list of sites on how dimensional analysis is used in real life;
Choose a real life dimensional analysis problem that seems particular interesting to your group;
Write a short reflection on why you think the chosen problem is interesting;
Research units and conversions for the chosen problem;
Develop your own dimensional analysis problem to class OR
Present the chosen problem to class showing how dimensional analysis was used;

Process

Day 1: Brainstorm and Research

Your first step is to determine the roles within the group.

Lead Researcher: / Will be the contact person with the Secretary of the Department of Education (the teacher).
Administrative Assistant: / Will be in charge of taking notes for the group, and makes sure everything is recorded.
Technology Professional: / Will be in charge of handling technology and doing research online.
Pubic Relations: / This person will be in charge of presenting the project to the public.

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:

Differences between area and volume:

NASA mix-up causes lost spacecraft:

and

Environmental science problems:

Various ways in which unit conversion is used:

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:

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!

EvaluationPerformance 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
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

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 pursue 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.

Teacher Page

Introduction

A perfect introduction would be a short discussion on the lost space craft by NASA dueto failed unit conversion. This will generate some interest on the topic of dimensional analysis.

The goal of this project is to show students that there are some real life instances of math in our world. Since dimensional analysis is one of the more useful and applied forms of algebra, it's a prime candidate for a small group project.

Learners

This project is intended an a cumulative project on conversion of units and performsing simple dimensional analysis. This type of project wouold most likley come at the end of years work of algebra. Ideally, this would come at the end of a unit on rational expressions. Some work on rational expressions is necessary to complete this project. Since this is aimed at algebra students, the students should be in grades 8-10.

Curriculum Standards

NCTM Algebra Standards Addressed:

use symbolic algebra to represent and explain mathematical relationships;
draw reasonable conclusions about a situation being modeled.

Students will be expected to develop some deep critical thinking skills, as well as teamwork skills. There will be some compromise when deciding which problem to choose for the group. There may be some creative problem solving depending on how difficult the students make the project.

Process

Day 1: Brainstorm and Research

Your first step is to determine the roles within the group. (This can be changed by the teacher. Students might form groups that are much stronger than other, so group formation is up to the instructor.)

Also, keep in mind that you as the teacher are the Secretary of Education. Make sure to "play the role."

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:

Differences between area and volume:

NASA mix-up causes lost spacecraft:

and

Environmental science problems:

Various ways in which unit conversion is used:

The technology assistant should be the group member 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.

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:

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.

Day 3: Presentation Day

Resources Needed

The only resources necessary will be a computer for each group. Butcher paper, and other drawing materials may be used for student demonstrations, but are not necessary.

This project only requires one teacher. Students will be working on their own a majority of the time.

Evaluation

Teachers shouldn't have to do much work for this project. Evaluation should be fairly straightforward. Students will be graded on their behavior and work ethic within their group. Students will also be graded on their short reflection. The instructor should check for grammatical and spelling errors, but more importantly, if the student put effort and attempted to analyze the problem.

For the group project, students will need to demonstrate that they understand the problem, and know where the problem is coming from. They will also be graded on the correctness of their math skills.

Credits and References

Header graphic taken from:

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.

Last updated on 10/25/02. Based on a