Log your Progress Exponentially

In this unit the student will need to learn the following skills.

1. How to represent roots and powers using radicals and fractional exponents.

2. How to simplify roots and powers using fractional and negative exponents.

3. How to identify the graphs of exponential and power functions.

4. How to evaluate exponential and power functions involving growth or decay.

5. How to change between exponential and logarithmic functions.

Lesson and Activity Schedule

Time / Skill/
Concept / Activity / Material/ source / Tech Tools
Day 1 / Rational exponents, growth and decay functions & logarithms / Pre Test
A.9-12.A.3.1A
C.9-12.N.1.1 / Achievement Series
# 30003
# 86935 / On-line Test
Introduction to vocabulary and formulas / Note Taking / Teacher Projected information on screen / Microsoft One Note
Rational exponents and radicals / Practice problems using Windows Journal / Text Assignment* / Windows Journal &
SynChronEyes
Day 2 / Graphs of rational power functions / Teacher directed activity comparing graphs / Sample problems from text / TI Interactive
History of mathematicians who discovered logarithm and exponential functions / Voki presentations to class / Previously created Voki featuring a historical mathematician / Internet sites www.voki.com/
Projector and screen
Day 3 / Exponential growth and decay
functions / Lesson Opener
Compound Interest—
Buy a house / Worksheet / Windows Journal & graphing calculator
Exponential growth and decay
functions / Read examples and use on-line calculator for working growth and decay problems / Internet sites
Explaining exponential functions.* / Internet sites
Day
4 / Exponential growth and decay
functions / Practice Problems / Text assignment / Windows Journal & graphing calculator
Day
5 / Exponential growth and decay
graphs / Lab activity to collect data, graph and calculate equation / M & M Worksheet / TI 84 graphing calculator
Exponential growth and decay
graphs / Analyze graphs of growth and decay along with power functions / Worksheet for Fathom Program / Fathom program*
Day 6 / Introduction to logarithms / Note Taking / Teacher Projected information on screen / Microsoft One Note
Logarithmic functions / Practice problems using Windows Journal / Text Assignment* / Windows Journal &
SynChronEyes
Day 7 / Math in History
Slide Rule / Lesson Opener
Use a slide rule / Information from web site / Internet site
Properties of logarithms / Practice problems using Windows Journal / Worksheet / Windows Journal &
SynChronEyes
Day
8 / Exponential and logarithmic equations / Practice Problems / Text assignment / Windows Journal & graphing calculator
Day
9 / Exponential equation models / Lab activity to collect data, graph and calculate equation / Light Intensity with CBL &
Post information on wiki / TI 84 graphing calculator
CBL
Logger Pro*
Day 10 / Exponential equation models / Compound Interest Fathom Activity / Fathom worksheet / Fathom software program*
Day 11 / Review concepts / Teacher directed review and practice problems / Text problems / Windows Journal and TI Interactive
Day 12 / Rational exponents, growth and decay functions & logarithms / Post Test
A.9-12.A.3.1A
C.9-12.N.1.1 / Achievement Series
# 59621# 58260 / On-line Test

Internet sites

Site for calculating simple interest compared to compound interest.

http://id.mind.net/~zona/mmts/functionInstitute/exponentialFunctions/simpleInterest.html

Site for voki

www.voki.com/

Other Internet sites

Introduction to graphing functions

http://www.purplemath.com/modules/expofcns.htm

Interactive tutorial on exponential functions

http://www.analyzemath.com/expfunction/expfunction.html

Math help for exponential functions + interactive graphing applet

http://www.ucl.ac.uk/Mathematics/geomath/level1/expnb/MHexpnb.html

Sources of material

Software programs.

Fathom - Dynamic Data Software

http://www.keypress.com/x5656.xml

The Geometer's Sketchpad® - : JavaSketchpad™

http://www.dynamicgeometry.com/javasketchpad/about.php

Logger Pro 3

http://www.vernier.com/soft/lp.html

Text & Worksheet materials.

Functions, Statistics & Trigonometry by Scott Foresman

Algebra 2 by McDougal Littel

Other worksheets and information

M&M Activity and the CBL instructions and the Voki instructions are attached as word documents.

The other worksheets are all have current copyrights.










PART 1 COLLECTING DATA

1.  Empty your container of M & Ms & count them. Place them back in the glass & mix them. Pour them out on the desk, count the number that show the m and place them back in the glass. Record this number. Repeat this procedure and record the results each time.

Trial Number / Number of M & Ms

2.  Make a scatter plot graph of the data on the graphing calculator. (TI 84)

Enter the information, create the graph.

3.  Calculate the equation of the graph and write it down. It should be exponential (y = a (b)^x). ______

4.  Draw a smooth curve of your graph through the scatter plot on the calculator.

Answer the following questions.

5.  What type of graph is your exponential graph? (growth or decay)

______

6.  Is the money graph similar to the Y = 2x graph? ______

7.  What happens to the y value as the x value increases? ______

Trigonometry Power Unit 1

Voki Investigation

PROCEDURE

1. Investigate famous mathematicians by using an internet search.

2. Select a mathematician to research. Try to select one of the people who were important in the development of logarithms and exponential functions.

3. Read the information about his discoveries and select one to emphasize.

4. Use at least 3 sources and cite your sources on your completed project.

5. Prepare a presentation to inform the class about this mathematician.

6. Create a voki to represent the famous mathematician. Produce a short segment in which your voki explains his most famous mathematical concept. http://www.voki.com/

7. Go to the Math2Use wiki, join the discussion group and post a comment about the activity in which you address one of the items listed on the Trigonometry page. Reply to 1 post from another student.

https://math2use.wikispaces.com/

Trigonometry Name ______

Light Intensity

In this activity you will measure the intensity of light as the distance from the source increases. You will then analyze the data to determine what type of graph results. Calculate the equation for the graph.

Procedure

1.  Attach the CBL to the graphing calculator and select Apps

CBL/CBR

Data Logger

2.  Select Light for PROBE

Set SAMPLES to 20

And INTERVAL to .2 sec

PLOT at End

3.  Follow the DIRECTIONS on the calculator for connecting the light probe

4.  Measure the intensity of the light starting about 6 inches from the source and moving slowly away

5.  Analyze the graph to determine the type of graph. (exponential, power function, inverse, or inverse square)

6.  Determine the equation of the graph. Graph the equation to see how closely it matches your graph from the data.

7.  Go to the Math2Use wiki and write your comments. Be sure to address the topics listed on the Trigonometry page of the wiki.

https://math2use.wikispaces.com/

Lorie Johnston

Newell High School

Trigonometry, Functions & Statistics