Brief Description

Students will solve a problem by using trigonometry. They will graph and obtain the equation of a wave. They will calculate amplitude, period, frequency, and phase-shift to determine if the wave is within certain parameters. This will determine if the skipper and first mate are responsible for the shipwreck during a storm. Meets Arizona State Standards 3 and 6.

Standards and Frameworks

Technology Standards

• 3T-P1: Communicate to a variety of audiences using professional level technology tools.
• 3T-P3: Use technology tools to publish and present information with interactive features.
• 6T-P2: Routinely and ethically use productivity tools, communication tools and research skills to solve a problem.

• 2M-P1:  Construct and draw inferences from graphs and data plots that summarize data from real-world situations
• 2M-P3: Apply curve fitting to make predictions from data
• 3M-P1: Model real-world phenomena using functions and relations (e.g., linear, quadratic, sine and cosine, and exponential)
• 3M-P5. Apply trigonometry to real-life problem situations

Academic

• Students will use their knowledge of trigonometric functions to find an equation using the given data by producing a scatter plot.
• Students will examine their findings for the data against the given specifications for the boat.
• Students will justify their solution to the problem by interpreting the data and specifications of the boat to conclude who was at fault, the weather or human error.

• Students will use technology to produce a graph to be used in their presentation.
• Students will use productivity tools to communicate the solution to a problem through a presentation.

The students need to have used some of the technology tools, such as PowerPoint and/or Publisher.

Materials

Student Handout
Assessment Rubric(s)
Computer with access to PowerPoint, Publisher, etc.
Scanner (optional)
Floppy Disk (if they will be using different computers and are unable to save to a network)
Graphing Calculator

Accommodations for Special Needs

Reach/gifted students: These students can use their knowledge and creativity in the presentation.

SEI (Sheltered English Immersion) students: Teacher will read through the handout and explain the rubric for all students at the beginning of the lesson. These students would be distributed throughout the groups.

Special Education Students:  Teacher will read through the handout and explain the rubric for all students at the beginning of the lesson. These students can sit next to or be grouped with strong readers. They can contribute verbally in their group.

Procedures

Students should be familiar with the trigonometric graphs and scatter plots.
Students should be able to use the equation of the form y = A sin (Bx – C) + D

• Put students in groups of four/five
• Students will be given the handout. This contains the background and the problem they are to solve.
• The students use the graphing calculator to plot the data and do a sine regression to find the equation of a wave. They find the amplitude, phase shift, period, frequency and vertical shift from the equation.
• They need to answer all the questions in the handout.
• They use this information to decide if the waves were within the specs of the boat (given in the handout) and hence decide whether it was the weather or maybe human error that caused the boat to capsize.
• They will produce a presentation of their findings using the rubric to make sure all the necessary information is given to the jury (peers).

The judges (peers) will assess the project using the rubric provided. Their score will be an average of all the scores.