Module 3 Project

 

Module 3 Project: Spray Park

 

Towards the end of each lesson, under Project Connection, you are prompted to complete a part of the Module 3 Project. You can access the entire project from this page at any time. Before you get started on any part of the Module 3 Project, read about the entire project here. That way, you will get a sense of what is expected of you.

 

You will submit your Module 3 Project to your teacher at the end of Module 3.

Introduction

 

 

 

Spray parks are popular recreation environments designed with various types of equipment that spray, squirt, mist, and dump water on children. Aside from offering great joy to children, spray parks also offer delight to the mathematician who marvels at the multiple examples of the parabola. These marvels include the trajectory (path) of the water being sprayed from various pipes and fountains and some of the metallic structures carrying the water.

 

In the Module 3 Project you will design a spray park for a playground. You will use quadratic functions to model the paths of the water sprays.

 

As you progress through the module, your skill with quadratic functions will increase. With each lesson, you will use your new skills to add detailed characteristics of the trajectories and functions to your design. Your creative side will flourish, but you will also need your organizational ability.

To start those creative juices flowing, think about how you might use the following kinds of spray equipment.

 

 

Activity 1

 

Part 1

 

It is time to start designing your own spray park. Your first task is to choose five different pieces of equipment from the image shown. For each piece of equipment, do the following:

1. On a labelled grid or using a graphing tool, draw the graph of the parabola showing the trajectory of the sprayed water.
   
   
2. Justify the shape of your parabola.
   
   
   • Decide on the units for the x- and y-axes. Choose units with which you are familiar, and clearly state the units you are using.
     
     
   • The y-intercept should be at the source of the spraying water, and the x-axis should signify ground level. Therefore, only the first quadrant of your graph will be considered (positive x-values and positive y-values), although you should include all quadrants on your graph.
     
     
   • The water in your spray park should be squirted from a variety of heights and travel a variety of distances. This will make your park exciting for your guests. The trajectory of the water should approximate the shape of the water flow in the pictures of the various pieces of equipment. You must justify the heights and lengths of the trajectories you choose—state why you made each choice and who will be using each piece of equipment.

Part 2

3. For each of the five pieces of spray equipment you chose, write the equation of the parabola showing the trajectory of the sprayed water. Show all of your work for obtaining the equation.
   
   Two samples are provided to help you get started. In the samples, the unit for the x-and y-axes is feet. The equations for the parabolas have not been included; however, you are required to include equations in your work.
   
   The first sample is a low-powered cannon designed for infants. The low water pressure ensures no one is injured. This cannon shoots water from a height of only 1 ft and the stream travels 1 ft horizontally.
   
   
    
   
   

The second sample is the water trajectory from one of the fountains being squirted from a Silly Serpent. This version of the Silly Serpent will be constructed quite low to the ground, so the water will spray from a height of 1 ft but will reach a peak height of 2 ft. This will allow infants to get fully wet and will also allow younger children to get their lower torso and legs wet before moving onto more advanced equipment. The water will spray a horizontal distance of a little more than 2.25 ft.

 

 

Activity 2

 

Now that you have chosen five pieces of equipment for your spray park and planned the water trajectories for them, you are going to design two custom pieces of spray equipment. This will make your park unique.

4. Name and draw a sketch of each of your custom-designed pieces of equipment.
   
   
5. For each of your custom pieces, write the equation of the parabola showing the trajectory of the sprayed water and draw the graph on a labelled grid. You can use a graphing tool if you prefer.
   
   
6. Explain why your parabolas accurately model the trajectories.

Activity 3

 

© Water Odyssey™ by Fountain People, Inc.

 

You should now have seven pieces of equipment for your spray park. It is time to strategically arrange the seven pieces. Develop a layout of the spray park showing where each piece of equipment is located and the distance between each piece. Justify your choices of locations by explaining the advantages your choices have over other possible layouts.

 

You can present your layout as a colour drawing, 3-D model, or computer image of your spray park. The spray trajectories (especially the distances travelled) should be shown and made fairly close to scale, as should the distances between the various pieces of equipment.

 

Examples of factors that may affect the placement of each piece of equipment include the space needed for the water spray, safety concerns, grouping by age of intended users, the popularity of individual pieces of equipment, and aesthetic appeal.

 

Conclusion

 

Write a brief conclusion to your Module 3 Project. Include a personal reflection of how you felt about the project during and after completion. Be sure to explain why you felt the way you did.

 

Assessment Guidelines

 

Your Module 3 Project will be evaluated by your teacher using the following evaluation guidelines. Read the rubric carefully. Make sure you have completed the requirements for each of the categories.

 

MODULE 3 PROJECT: SPRAY PARK RUBRIC
Score	Graphs, Diagrams, and/or Models	Mathematical Concepts: Quadratic Functions and Their Characteristics in Corresponding Graphs	Mathematical Calculations	Completion	Communication: Final Presentation	Written Explanations
3 Meets the Standard	Graphs, diagrams, and/or models are clear and greatly add to the reader's understanding of the procedure(s).	Math work shows complete understanding of quadratic functions in the form y = a(x − p)2 + q and y = ax2 + bx + c and their characteristics in corresponding graphs used to solve the problem(s).	All required mathematical representations are completed and correct.	All aspects of the project are completed.	The work is presented in a neat, clear, organized fashion that is easy to read and/or see.	Written explanations are detailed and clear.
2 Approaches the Standard	Graphs, diagrams, and/or models are clear and easy to understand.	Math work shows substantial understanding of quadratic functions in the form a(x − p)2 + q and y = ax2 + bx + c and their characteristics in corresponding graphs.	There may be some serious math and/or calculation errors or flaws in reasoning.	All but one aspect of the project are completed.	The work is presented in an organized fashion but may be hard to read and/or see at times.	Written explanations are clear.
1 Below the Acceptable Standard	Graphs, diagrams, and/or models are somewhat difficult to understand.	Math work shows some understanding of quadratic functions and their characteristics in corresponding graphs.	There are major math and/or calculation errors or serious flaws in reasoning.	All but two aspects of the project are completed.	The work appears sloppy and/or disorganized. It is hard to know what information goes together.	Written explanations are a little difficult to understand but include critical components.
INC Does Not Meet the Minimum Standard	Graphs, diagrams, and/or models are difficult to understand or are not used.	Math work shows very limited understanding of the underlying concepts needed to solve the problem(s) or is not present.	There is no understandable attempt at using mathematical representations.	Several aspects of the project are not completed.	There is no understandable presentation of project work.	Written explanations are difficult to understand and are missing several components or were not included.
Total Score /	/3	/6	/3	/3	/3	/3

Don’t forget to submit your completed Module 3 Project to your teacher at the end of Module 3!

Mathematics 20-1 Learn EveryWare © 2011 Alberta Education