Project Title

A Cool Million!

 

Introduction

What would you do with one million dollars?  In this project, you will have the opportunity to spend one million dollars on building a swimming pool complex.  There are many factors to consider, including the price of construction and the size of the various elements of the complex.  Of course, you will need to use algebraic factoring skills to solve the problems.  Get ready for some fun with factoring!

 

Task

Working together with your group, you will design a swimming pool complex.  The total budget for the project is one million dollars.  By solving each problem algebraically, your group will determine the width of a concrete walkway, the dimensions of the kiddie pool, and the dimensions of a landscape design.  At the end of the project, you will have some money left over and will be able to make decisions about adding extra elements to the pool.

 

Instructions

Solve each problem in order keeping careful notes along the way.  Be sure to show your algebraic work completely, as it will be displayed on your final product.  Once all of the problems are solved, you will create a display of the pool complex design.

 

1                     First problem:

·                     The Adult Pool Area has a total area of 15,000 square feet.  The Adult Pool Area consists of a rectangular swimming pool and a concrete walkway of even width surrounding all four sides of the pool.  The swimming pool is 120 ft. by 70 ft.

 

Hint:  First draw a picture of the pool and the walkway surrounding it on all four sides and label the walkway of even width, x.  

 

·                     Now label your picture with an expression for the total length, including the walkway.  Then label your picture with an expression for the total width, including the walkway.

 

Hint:  How many sections of walkway are added to the length?  What about to the width?

 

·                     Using the expressions for total length and width, find an expression for the total area of the rectangular pool and walkway.  In order to solve for x, you will need to set the expression for area equal to the 15,000 square feet.  Now use your factoring skills to solve.

 

Hint:  Don’t forget to set your equation equal to zero before factoring.  Is there a GCF?

 

·                     Now that you have found the width of the concrete walkway surrounding the pool, you should be able to sketch out a quick drawing of the Adult Pool Area with all dimensions labeled.  This drawing will help you keep your measurements straight as you continue with the project.

 

2                     Second problem:

·                     The Kiddie Pool Area has a total area of 5000 square feet. The Kiddie Pool Area consists of a rectangular pool and a rectangular concrete pad. The length of the rectangular pool is 30 feet greater than the width.  The pool has a concrete pad along only one side of the pool.  The dimensions of the pad are 20 ft. by w feet, where w is the width of the pool.

 

Hint:  First draw a picture of the pool and the concrete pad.  Position the pad so that one side is along the width of the pool.

   

·                     Now label your picture with an expression for the total length, including the concrete pad.  Label your picture with an expression for the total width.

 

Hint:  Use substitution to label the length of the pool in terms of w.

 

·                     Using the expressions for total length and width, find an expression for total area of the rectangular pool and concrete pad.  In order to solve for w, you will need to set the expression for area equal to the 5000 square feet.  Now use your factoring skills to solve.

 

Hint:  You will need to distribute the w and set the equation equal to zero in order to factor.

 

·                     Now that you have found the width of the pool, solve for the length. Again, sketch out a quick drawing of the Kiddie Pool Area with all dimensions labeled.  This drawing will help you keep your measurements straight as you continue with the project.

 

3          Third Problem:

·                     A rectangular Landscape element is being added to the pool complex to beautify the grounds.  If the length is 8 more than twice the width and the total area is 960 square feet, find the length and width of the rectangular landscape element. 

 

Hint:  Follow the same process as problems one and two.  First, draw a picture and label.  Then find an algebraic expression for total area.  In this case, set that expression equal to 960 square feet.  Then set the equation equal to zero and don’t forget to factor out the GCF. 

 

·                     Sketch out a quick drawing of the Landscape element with all dimensions labeled.  This drawing will help you keep your measurements straight as you continue with the project.

 

 

4          Fourth problem:

·                     Keeping in mind the one million dollar budget, your group will now calculate the costs of each of the parts of the pool complex.

 

 

·                     The pool complex will consist of the Adult Pool Area, the Kiddie Pool Area, and the Landscape element.  The outside dimensions of the complex are 150 ft. by 200 ft.  The remaining area can be covered in grass, concrete, or landscaped.  It will be helpful to use the following table to complete your calculations.    

 

 

Hint:  Ensure that your total cost is within the one million dollar budget and check

that your total area is correct by adding the areas of each piece.  What should the areas of the pieces total? 

 

Collaboration

Get together with another group to compare your answers to each of the four problems.  Discuss what your group decided to do with the remaining area in the complex.  Some groups may have chosen to go with the cheaper grass, while some may have chosen the more expensive landscaping. 

·         What if you were able to spend any remaining money on extra elements for your pool?

·         Would that change how you finished the remaining area?

·         What elements are missing from the pool complex?

·         Do some Internet research to determine how your group would like to spend the remaining money.  Include your extras in the final product. 

 

Conclusions

Your final product will be a poster-sized display of the pool complex, including all algebra used to solve the four problems above.  You may either neatly draw the pool complex or use design software such as Google SketchUp to create a professional computer generated product.  You may want to use headings to separate your work for each of the three areas:  Adult, Kiddie, and Landscaping.  

 

Free Download: http://sketchup.google.com/

 

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.  Each of the three problems is solved algebraically by factoring.    A neat, detailed table is included to display the breakdown of the costs involved.	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.  Each of the three problems is solved algebraically by factoring.  Minor errors may be noted.    A neat table is included to display the breakdown of the costs involved.  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 attempts to answer each of the problems.  Algebraic solutions are either not shown or guess & check is used, rather than algebra.  Errors are noted.    A table is included to display the breakdown of the costs involved but may not be complete.  Errors are 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 the three problems, but little to no work is shown.  Major errors are noted.    The breakdown of the costs involved is minimal or missing.  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.