Project Title

Work it out!

 

Introduction

Solving work problems in algebra requires a solid understanding of rational equations.  By now you should be comfortable with a classic problem such as: 

 

If it takes Bob 3 hours to paint a room and it takes Jeff 5 hours to paint the same room, how many hours would it take if the two painters work together? 

 

Many students will attempt to take an average and come up with an answer of 4 hours, but 4 hours doesn’t make sense.  Why would it take longer than Bob working alone?  Surely the two painters would complete the room in less than 3 hours.  Using the algebra work model, we discover that the room should be painted in slightly less than two hours.  The work model allows us to consider each painter’s contribution as a rate and add the two rates together to calculate a time projection for the pair painting the room together.

 

Task

Working with your group, you will first solve a work problem algebraically.  Once you are comfortable with solving the problem, you will design a task for your fellow students to perform in class.  First you will time three students completing the task individually and then use the work model to determine how long it should take for the three students to complete the task while working together.  Of course models are not always perfect, so your next step will be to see how close your model comes to reality.  Get ready for some hard work! 

 

Instructions

Complete each problem in order keeping careful notes along the way.  At the conclusion, you will design a website to showcase your project.  You may want to use a camera to record video or take pictures as you are working. 

 

1                     First problem:  Solve a problem

·                     Students A, B, and C can complete a puzzle in 20 minutes, 15 minutes, and 30 minutes, respectively.  If all three students work together, how long should it take to complete the puzzle?

 

·                     First, find the rate for Student A.  Then, find the rate for Student B.  Finally, find the rate for Student C.

 

Hint:  Remember that .  The work being completed is one puzzle.

 

·                     If the students work together, their rates will need to be added together.  What is the total rate when all three students work together?

 

Hint:  Don’t forget to get common denominators.  What is the LCM of 15, 20, and 30?

 

·                     Now substitute the total rate into the work model, .  The variable W is still one because the amount of work to be completed is one puzzle.  Then, solve for t.

 

Hint:  Express your answer in terms of minutes and seconds.

 

2                     Second problem:  Collect individual data

 

·                     Now that you have successfully used the work model to solve a real-life problem, get with your group to discuss what type of activity could be timed within your classroom.  The students from the first problem completed a puzzle.  Determine what type of task your group would like to time people performing.  The task needs to take at least 2 minutes but no more that 10 minutes for a student to perform alone. 

 

Some ideas include:  shooting 50 free throws, passing out 25 papers, solving a set of math problems, building a card tower, building a figure from blocks.

 

·                     Choose a task that will highlight your group’s creativity and interests.  You may need to bring in materials from home or ask to borrow materials from your teacher.  Be sure to get approval from your teacher before continuing.

 

·                     Once your idea is approved, find three willing participants to try the task.  Time each student individually and record the time.  For simplicity, you will want to round each student’s time to the nearest ½ of a minute. 

 

Hint:  In order to have accurate data, ensure that each student has not seen the task being performed before being timed.  Don’t forget to capture video or photos during the tasks.

 

3                     Third problem:  Calculate using the work model

 

·                     Now that you have each student’s time individually, use the work model and your knowledge of rational equations to determine how long it should take the three students to complete the task if they work together.

 

Hint:  First find the rate for each student.  Then add the rates of all three together, being careful to get common denominators.  Once you have the total rate, substitute the rate into the work model: .  Remember that W will be one.  Then solve for t.

 

·                     The solution is the amount of time it should take if all three students work together to complete the task.  Do you think that the time is accurate?  Why or why not?

 

4                     Fourth problem:  Collect group data and compare 

 

·                     Gather the same three students that were timed before and ask them to work together to complete the task.  Time how long it takes for the task to be completed when the three students work together.  

 

·                     Compare the actual time to the projected time by calculating the percent error.

 

Hint:   Percent error is calculated by first finding the change between the actual time and the projected time.  The absolute value of this change is then divided by the projected or theoretical time.  The formula for percent error is as follows:

 

 

5         Fifth Problem:  Discussion

 

·                     Was the actual time to complete the task more or less than the projected time?  What factors might have contributed to that result?

 

·                     What steps might your group have taken in order to minimize the percent error of your experiment?

 

·                     When completing your task, did you allow three people to work together effectively?  Why or why not? 

 

Collaboration:

Work together with your group to write your own work model word problem. If needed use the examples from the lesson on Rational Equations to help guide your work.  On a separate piece of paper, solve the problem within your group.  Trade only problems, not solutions, with a neighboring group.  Work together within your group to find the solution to the new word problem that you got from the other group.  When your group agrees on a solution, check your solution against the original solution from the group that authored the problem.  Do the answers agree?  If not, compare the solutions and work together to determine which solution is correct and why.

 

Conclusions

Work together within your group to create a website to highlight your project.  Websites can be created for free at www.weebly.com.  Consider importing pictures or videos of the students completing your task to add a touch of creativity and interest.  The website should contain solutions to each of the five problems. 

 

Grade

Your project will be given a score of 1 to 4, with 4 being the highest score possible. You will be evaluated based on the following criteria:

Score

Content

Presentation

4

Your project appropriately answers each of the problems.  Completed data tables and step-by-step algebraic solutions are included. 

 

Evidence of careful data collection is apparent.  The chosen task effectively allows three students to work together to complete the task.

Your project contains information presented in a logical and interesting sequence that is easy to follow.

 

Your project is professional looking with graphics and attractive use of color. 

 

3

Your project appropriately answers each of the problems.  Completed data tables and algebraic solutions are included.  All steps may not be shown.

 

Evidence of careful data collection is apparent.  The chosen task effectively allows three students to work together to complete the task.  Minor errors may be noted.

Your project contains information presented in a logical sequence that is easy to follow.

 

Your project is neat with graphics and attractive use of color. 

 

2

Your project partially answers each of the problems.  Partially completed data tables and algebraic solutions are included.  All steps may not be shown.

 

Evidence of data collection is apparent although errors are present.  The chosen task allows three students to work together to complete the task, but is not ideal.  Errors may be noted.

Your project is hard to follow because the material is presented in a manner that jumps around between unconnected topics.

 

Your project contains low quality graphics and colors that do not add interest to the project.

1

Your project attempts to answer some of the problems.  Partially completed data tables and algebraic solutions are included.  Very little work is shown.

 

Evidence of data collection is apparent although errors are present.  The chosen task allows three students to work together to complete the task, but is not ideal.  Major errors are noted.

Your project is difficult to understand because there is no sequence of information.

 

Your project is missing graphics and uses little to no color.


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