I. Curricular Framework

Concept:

Relationahips

Essential Question:

What are the relationships between amplitude and period to the sine and cosine functions?

Bridge:

Cause and Effect

Content:

Sine and Cosine Functions

Outcomes:

II. Standards Aligned

III. Instruction and Assessment

1. Connect: Connecting to the Concept Experientially

Objective: The student will be able to visualize a sinusoid graph.

Activity: The students will do the "wave" (the kinesthetic wave that is done by fans at a football game). The students will also view pictures and physical examples of the sinusoid wave in nature.

Assessment: Student participation.

2. Attend: Attending to the Connection

Objective: The students will be able to compare and contrast the examples of the waves.

Activity: The students will list descriptions that compare and contrast the different waves and establish the patterns.

Assessment: The students' ability to construct a Venn diagram comparing and contrasting the waves.

Assessment, Phase One, Level of Engagement, Fascination:

3. Image: Creating a Mental Picture

Objective: The students will describe amplitude and period and the effects they have on the sinusoid graph.

Activity: The students will help the teacher construct the sine and cosine graph with the coordinates from the circle graph. The students will work in groups with the graphing calculator and discover patterns in changing the amplitude and period. (A teacher-designed worksheet will guide the students in this activity.)

Assessment: The ability of the students to discover the effect of changing the amplitude and period of the graph.

Assessment, Phase Two, Seeing the Big Picture:

4. Inform: Receiving Facts & Knowledge

Objective: The student will be able to graph the sine and closing functions. The student will be able to determine the amplitude and period of the sine and cosine functions.

Activity: The teacher will lecture.

Assessment: The ability of the students to answer the teacher's questions.

Assessment, Phase Three, Success with Acquiring Knowledge:

5. Practice: Developing Skills

Objective: The student will be able to construct the graphs of the sinusoid functions indicating period and amplitude.

Activity: Textbook problems.

Assessment: Completion of assignment.

Assessment, Phase Four, Success with Acquiring Skills:

6. Extend: Extending Learning to the Outside World

Objective: The students will be able to determine their own sinusoid graph.

Activity: The students will work in groups to pick an area of interest to them and find an example of a sinusoid graph. Some suggestions are music, tide tables, temperature over a period of time, moon changes, oscillator, or any other area the student may notice the sinusoid occurring.

Assessment: The students' ability to find a problem.

7. Refine: Refining the Extension

Objective: The student will be able to determine the characteristics of the graph he chose to investigate.

Activity: The students will work in groups to graph their sinusoid function and to label its amplitude and period. They will make a chart depicting their investigations and results.

Assessment: The students' work.

8. Perform: Creative Manifestation of Material Learned

Objective: The student will be able to demonstrate his knowledge of the sinusoid function.

Activity: The students will present their function to the class and discuss its properties. The student will take a test on graphing the sine and cosine functions.

Assessment: Student presentation and test.

Assessment, Phase Five,Performance, Creative Use of Material Learned: