Gold Seal Lesson:
Wet And Wild Water Fountain

Copernicus Education Gateway

 

Subject:

 

Mathematics

Grade:

 

 

9-12

 

 

 

ICLE Standards:

 

 

Mathematical Reasoning: Make and test conjectures.

Functions: Model real-world phenomena with a variety of functions.

Algebra: Appreciate the power of mathematical abstraction and symbolism.

 

 

 

Performance Task:

 

 

This task requires you to work as a member of a four-person cooperative group to design a creative water fountain. Your fountain must include two intersecting parabolic water arcs which meet the following criteria.

  1. The maximum height reached by the water must be greater than 20 feet, but less than 60 feet.

  2. The speed of the water must be greater than 5 ft/sec, but less than 75 ft/sec.

  3. The angle of the nozzle must be at least 20 o , but less than 80 o .

When your team has completed its task, write a brief report describing your team's fountain. Include a mathematically accurate drawing of the parabolic arcs of your fountain. Show all mathematical work that your team needed to do to complete the task. Include anything else that you feel would be of interest to the reader.

Note to the teacher: The equation that students use to determine speed (v) and angle (a) of their parabolas is:

y = ___16____   x2   +   (tan a)x
       v2(cos a)2

Note to the teacher: If students are not familiar with this formula or do not have access to it, you should spend
time developing it in class prior to having the students do the task.

 

 

 

Knowledge / Skills:

 

 

Know the basic trigonometric functions and ratios.  (m18)

Be able to prove trigonometric identities and solve equations (linear and quadratic).  (m58)

Know how to graphically sketch basic conic sections (e.g., circles and parabolas) using their equations, and graphically solve systems of equations.  (m86)

Use expository writing skills in subjects other than English language arts.  (ela58)

 

 

 

Rubric:

 

 

4 Points  =  Team members are cooperative and share equally in performing the task. All mathematical measurements, equations, and computation correspond to the description and drawing. The fountain is realistically possible. The drawing is accurately and neatly drawn on coordinate paper. The written description is clear and complete, and it displays a high level understanding of the concepts involved in the task.

 

 

3 Points  =  Team members are cooperative, but do not share equally in performing the task. The group needs some assistance from the teacher while performing the task. Not all the mathematical measurements, equations, and computations correspond to the description and drawing. The fountain is, however, realistically possible. The drawing is either inaccurate or not neat. The written description lacks clarity and displays only a partial understanding of the concepts involved in the task.

 

 

2 Points  =  Although the team members are cooperative, either one or two students dominate the activity or one or two contribute very little. Even with much assistance from the teacher, the team has difficulty completing the task. Several errors occur in their work. Students are hazy about what they have to do and how to go about doing it. They do not demonstrate sufficient mathematical knowledge needed to do the task. Hence, the design is not realistic. The written description is neither clear nor complete and displays little understanding of the concepts involved in the task.

 

 

1 Point  =  The students are uncooperative and do not work as a team. They show very little understanding of the mathematics necessary to do the task. There are many errors in their work, and they are unable to arrive at a reasonable product. Written description, if attempted, displays no understanding of the concepts involved in the task.

 

 

 

Keywords:

 

 

ALGEBRA
GRAPHS
PARABOLA    
EQUATIONS
PROBLEM SOLVING
TRIGONOMETRY IN DAILY LIFE

 

 

 

Grades:

 

 

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [] - 6 [] - 7 [] - 8 [] - 9 [X] - 10 [X] - 11 [X] - 12 [X]

 

 

 

ICLE Application:

 

 

D

 

 

 

 

 

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