I. Curricular Framework

Concept:

Growth

Essential Question:

Explain the role of exponents in the growth process.

Bridge:

Rising/Falling

Content:

Exponential Equations

Outcomes:

II. Standards Aligned

III. Instruction and Assessment

1. Connect: Connecting to the Concept Experientially

Objective: To see examples of exponential/logarithmic growth in everyday life.

Activity: Video depicting exponential growth and decay.

Assessment: Attentiveness.

2. Attend: Attending to the Connection

Objective: To analyze the video.

Activity: Teacher leads discussion about video. What kind of things were shown? How did they feel?

Assessment: Quality of and participation in discussion.

Assessment, Phase One, Level of Engagement, Fascination:

3. Image: Creating a Mental Picture

Objective: To hear, feel, and express changes in sound.

Activity: Listen to a selection from "Return to Snowy River" soundtrack. Do analog of how the music makes each student feel. Display and discuss analogs.

Assessment: Depth and quality of analogs; ideas generated by discussion.

Assessment, Phase Two, Seeing the Big Picture:

4. Inform: Receiving Facts & Knowledge

Objective: To teach unit on logarithms.

Activity: Discuss the roles of exponents in mathematics. Teach the following concepts: Review fractional exponents and exponential equations; teach meaning of logarithms, laws of logos, solve logarithm equations, use table of logs, find antilogs.

Assessment: Quality of response and understanding of concepts taught.

Assessment, Phase Three, Success with Acquiring Knowledge:

5. Practice: Developing Skills

Objective: To practice concepts being taught.

Activity: Students will work in cooperative groups for review and peer tutoring. Students will play MATHO*, do worksheets, write summaries for tests, and take quizzes and tests.

Assessment: Participation in group activities and performances on quizzes and tests. * MATHO board attached. List at least 40 answers on board or overhead. Ask students to copy 24 answers (random) onto their gamesheets. Write a problem on board or overhead. Students work problem and place a square over the answer. Continue to play as BINGO.

Assessment, Phase Four, Success with Acquiring Skills:

6. Extend: Extending Learning to the Outside World

Objective: To allow students to personalize the material.

Activity: Give students project options and due dates. Discuss options with students.

I. RESEARCH PAPER suggested topics:

*Business applications of exponents or logarithms
*Use of exponents and logarithms in carbon dating
*Development of the Richter Scales
*History of logarithms (Napier)
*Another pre-approved topic

II. WORK OUT A LOGARITHMIC OR EXPONENTIAL FUNCTION — This project involves the application of an established function using logs or exponents. You will supply data for each type of problem and show the result in a change in data. For example, show how different interest rates yield different returns on the same investment. For added clarity, results could be graphed or illustrated. Some suggestions include:

*Growth and Decay
*Compound Interest
*Appreciation/Depreciation
*Decibel Computation

III. ILLUSTRATING EXPONENTIAL GROWTH — This project involves graphically and/or artistically representing some sort of exponential or logarithmic growth. This growth is not limited to established logarithmic functions. Examples include:

*Since the invention of the airplane our ability to go higher and higher into space has grown exponentially. In the few short years since the invention we have traveled millions and millions of miles into space. This growth could easily be graphed using interesting pictures or drawings.
*The number of hamburgers served in the U.S. by major restaurant chains has increased dramatically. This could also be illustrated graphically. *Your own pre-approved idea.

IV. CREATIVE IDEAS (Limited only by your imagination and our approval. Think of fun and exciting ways to illustrate logs and exponents.) Suggestions include:

*A poem about logs and/or exponents
*Song or rap about logs and/or exponents
*Video showing exponents and logs in use
*"Sales ad" showing the many uses of logs.


Assessment: Commitment to project choice.

7. Refine: Refining the Extension

Objective: To transfer understanding of personal choices to real life situations. To improve understanding through additional practice.

Activity: Submit written explanation of chosen project. Continue teacher and evaluating concepts.

Assessment: Level of student involvement.

8. Perform: Creative Manifestation of Material Learned

Objective: To allow students to share what has been learned regarding logarithms.

Activity: Students complete their contracted projects and present, explain, and display them to their classmates.

Assessment: Enjoyment and participation in the experience.

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