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FUN MATH VI Spring 2009
(unfortunately this is listed as section 1.0 in printed text).
Week 3
Lab Day. Dynagraph Activity
This lab uses Geometer’s Sketch Pad and dynagraphs. Today’s dynalab activity is available through the link after the concept prep assignment in section 2.1 of the e-book.
This activity includes linear functions in the investigation, which may be easier for students to understand initially. Be sure to work through the activities yourself before your lab. Note that students are asked to guess the function rule in several activities. Please encourage them to really try hard to come up with a conjecture with sound reasoning before clicking on the “show function” button. Discuss with them the nature of linear functions -- the rate of change is constant no matter what the initial value is or what the slope is. Compare this constant rate of change to that of the exponential functions.
Please note that the Geometers Sketch Pad software is available on computers in the main library and also in the computer labs in Bowman and White Hall, so feel free to ask students to finish the lab for homework. Make sure that students have the main idea before they leave lab today, however. You might need to help them through some of the “dynaguess” problems until they have the hang of it.
If you have comments concerning this lab or suggestions to make it better, please let me know. Thanks.
Day 1. Section 2.3. Graphs of Exponential Functions
Review the concept prep assignment with students, taking care to discuss questions a) – k) slowly and in significant detail. Contrast and compare the graph of with those of and .
After reviewing the e-book’s discussion of “The Effect of the Factor a” you might want to assign the checkpoint exercises as an in-class activity.
Continue with other suggested in class activities, closing with a discussion of concavity if time permits. The comments in the e-book about the rates of change and concavity should be understandable to students, since they worked with this idea in the dynalab activities.
SuggestedHomework:2.3, p. 48 – 49: 1-35 odd BY HAND. Students have a hard time with these.
Day 2. Finish 2.3; 2.4 Continuous Growth and Decay
Discuss concavity of exponential functions, if you didn’t have time yesterday.
I usually need this day to continue working with graphs of exponential functions, emphasizing all the translations. You might have students working at the chalkboard. Be sure to summarize, noting the effects of the different parameters on the graph of the function.
Time permitting, let students work through, on their own, the hypothetical scenario in the e-book: P = 1, r = 1,t = 1 in the compound interest formula.
Then discuss continuous compounding via the examples. Be sure to point out that the natural decay exponential function has a negative exponent. Compare this to a “regular” decay function, where the factor is less than 1 and the exponent is positive.
Be sure to discuss the graph of the natural exponential function.
You may have to postpone the entire discussion of e until tomorrow.
Suggested homework: 2.4, p. 56- 57: 1-10 all
Checkpoint 2.4, (p. 110); read and study section 2. 5.
OR ask students to redo the graphs from 2.3 Be sure to give students a quiz on this tomorrow, telling them that you will ask them to graph by hand, WITHOUT use of graphing calculator.
Day 3. Section 2.5. SolvingExponential Equations
Try to have students figure out the technique for themselves. Be sure to show them the tabular and graphical checks.
You might want to discuss some of the more difficult problems in the exercises before assigning them: especially #9, #10, or #11.
Suggested homework: 2.5, p.62-63: #1 – 4 (a, c e); #5 – 8 (a, c); 9, 11 (a,c,e), 12 (a,b,e)