EMAT 4500/6500
Connections in Secondary School Mathematics
Spring 2005

 Instructors:

 Dr. John Olive  Dr. Brad Findell

 Classroom

 233 Aderhold  111/113 Aderhold

 Offices

 105F, Aderhold   109B Aderhold

 Telephone

 706 - 542 - 4557  706-583-8155

 email

jolive@coe.uga.edu  bfindell@coe.uga.edu

Assistant: Samuel Obara < sobara@coe.uga.edu >

Office: 502 Aderhold, Phone: 542-7715


Syllabus ||| Assignments | Links


Office Hours : By appointment. Please phone or email


Assignments

Assignments should be placed in the EMAT 4500 Drop Box on Dr. Olive's G5 computer. You can access his computer via IP address: 128.192.22.117 or via the AppleTalk Network when on-campus. You should always email Dr. Olive a notification that you have dropped an assignment in the Drop Box. From off-campus, you can try emailing your assignment as an attachment (this doesn't always come through intact).

NOTE: You should use the following filename structure for all of your files:

<first intitial><last name><assignment #>.<file type>

For example: bandreas2.html would be the file name for Brandy to use for her second assignment using the SimCalc Java MathWorlds.

If you decide to submit a revised assignment BEFORE the due date then append a lower case letter (starting with "b") to your updated assignment. For example, Brandy would submit bandreas2b.html as her updated SimCalc file for the second assignment.

 

Click on a number in the following table to go to that assignment.

These will be updated periodically
1 2 3 4 5 6 7 8 9 10
11 12 13 14

Final Project


#1 . Introduction to SimCalc Java MathWorlds (portfolio)

Download the Java MathWorlds program for your computer and Package 3 curriculum materials from the SimCalc Web site.

Explore the activities described in: CLASSROOM DISCUSSION 3.2.1:MYSTERY TRIPS-MAKING AND SOLVING EQUATIONS, page 17 of JMWPkg3Unit3.pdf (click on this link to download this PDF file)

Complete the activities in: STUDENT ACTIVITY 3.2.2: MYSTERY TRIPS-MAKING AND SOLVING EQUATIONS FOR VARIABLE VELOCITIES AND RATES, page 19 of JMWPkg3Unit3.pdf

Following are some suggestions for solving problems when installing on a Windows machine:

1. When downloading the SimCalc Mathworlds program installation file for Windows (with the JV machine included), make sure you select the SAVE option rather than OPEN. Even so, I encountered a Security Warning regarding the Install Anywhere installation program. This locked up my computer and I had to use the CTRL-Alt_Delete sequence of keys to End the Task.

2. You should see an "Install" program icon on your desktop. Double-click this to install the JavaMathWorlds program on your computer. It installed in the PROGRAMS folder on my machine but I could not find the JavaMathworlds folder so had to do a search! It was there but not showing up.

3. Once I had located the folder and program file I created a shortcut on the desktop (Right Button option). Double clicking the shortcut icon did run the program with the default MathWorld (Clown only).

4. When downloading the Package 3 curriculum package, I again SAVEd the file to the desktop. The folder created is a zipped archive named JMWPkg3.

5. Right click on the zippered folder and select "Expand All." This creates a folder inside the zippered folder also named JMWPkg3. I was able to open the pdf files from this inner folder.

6. DO NOT try and double click the MathWorld files inside the Unit folders. These MUST be opened from within the Default MathWorlds file (the Clown) once MathWorlds is running.

7. With MathWorlds running, go to the FILE menu and select OPEN. Browse to the Desktop and the JMWPkg3 folder and then find the appropriate file inside the appropriate Unit folder to open. I tested several and they worked!

Good Luck!

Due: For Dr. Olive on 01/18

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#2. Activities from SimCalc Java MathWorlds (10pts)

Download Package 4 of the SimCalc curriculum materials.

Work through the following student activities from JMWPkg4Unit2PartA.pdf (click on this link to download this PDF file)

STUDENT ACTIVITY 2.1.2: GIVEN A VELOCITY GRAPH, MAKE A POSITION GRAPH TO
MATCH on page 5

STUDENT ACTIVITY 2.1.3: GIVEN A POSITION GRAPH, MAKE A VELOCITY GRAPH TO
MATCH, page 7

STUDENT ACTIVITY 2.2.2: MOVING AROUND AND DELIVERING PIZZA ON JERKY
ELEVATORS USING BOTH VELOCITY AND POSITION GRAPHS, page 15

Turn in ONE of these for your graded assignment (your choice).

Due: For Dr. Olive on 01/20

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#3. Activities from Connected Mathematics, Variables and Patterns (portfolio)

1. Write a paragraph about the relationship between average speed, the mean value theorem, and the intermediate value theorem.  Be sure to describe how or why you know that the bicycle racing context satisfies the theorems' conditions. 

2. For problem 2.1, part C on page 34, bring at least 3 different solutions with 2 different answers for Rocky's Cycle Shop and at least 2 different solutions for Adrian's Cycle shop.

3. We might describe the Popcorn problem as presenting "cumulative data" because the data represents sales that accumulate over the course of a day.  How might you describe the data in the Soda Sales problem?  And is there a way in which the Day 2 data (p. 13) is cumulative?

Due: for Dr. Findell on 01/18, For Dr. Olive on 01/25

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#4. Tangent and Secant lines to a Quadratic Function Graph (10pts)

Complete Assignment 11.1 from page 6 of Chapter 11 of Transforming Mathematics with The Geometer's Sketchpad.

You can download the chapter (MS Word document) by clicking on the link above (or this link to bring up a web version) and also the following GSP sketches to work on this assignment or produce your own following the directions in Chapter 11:

Secant_tangent.gsp and tan_to_function.gsp.

Assignment 11.1: Create the expression for the derivative of your quadratic f'(x)=2ax+b (or ask GSP for the derivative of your function) and plot its graph. Does the value of f'(x) equal the slope of the secant line for any x? Prove (algebraically) that the secant line through the points ((x-dx/2), f(x-dx/2)) and ((x+dx/2), f(x+dx/2)) will always be parallel to the tangent at the point (x, f(x)) for any quadratic function! [HINT: Might this have something to do with the Mean Value Theorem?]

You can type your proof in a text box in your GSP sketch (use the special mathematical characters available in GSP) or in a Word document. Use the Equation Editor if you have access to one. Turn in either your GSP sketch with the proof or your word-processing document.

Due: February 1, 2005

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#5. Extra Assignment for Students in Dr. Olive's EMAT 6500 (10 pts)

Create a GSP sketch for a generic cubic function f(x) = ax^3 + bx^2 + cx + d. Use sliders for a, b, c, d and a small non-zero parameter, h. Find how the slope of the secant line between (x - h, f(x - h)) and (x + h, f(x + h)) differs from the slope of the tangent line at (x, f(x)) for some variable point x on your x-axis. Prove your result algebraically, and explain how you can see this result in your GSP sketch.

Due: February 3, 2005

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#6. Exploring Integration (portfolio)

These ideas are from Dr. Findell. You can download the GSP sketch from his page by clicking here.


The sketch Integration.gsp has six pages and many suggestions in the "What to Do" boxes.  Explore with the given function and also with other functions of your choice. 
 
On the page called "Definite Integral," try left, right, and midpoint rectangles and trapezoids.  Compare and contrast.  Is there a way you can tell whether a particular method will estimate low or high?  Which of the methods are best, in general?  Pay attention to area of each rectangle and add them up.  Add up the individual area calculations.  What do each of the sum calculations mean? 
 
On the "More Rectangles" page, explore precision.  Why does increasing the number of rectangles improve the precision of the measurement?  Explore limits, such as when the number of rectangles approaches infinity or the width of rectangles approaches zero.  How do limits help us talk about the exact area? 
 
If a function represents the velocity of an object, describe how the accumulation of area between the graph and the x-axis represents distance.  Include an interpretation of area below the x-axis.
 

Due: February 10, 2005

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#7. The Definite Integral of a Quadratic Function (10 pts)

Using either the Integration.gsp or the Quad_Riemann_area.gsp sketch from the EMAT 4500 folder, investigate the value of the area between the x-axis and the function graph when the upper limit (UL) of the definite integral is the opposite value to the lower limit (LL). That is LL = -UL or UL = -LL (remember that in either case UL>LL must be true). Prove algebraically, that in this situation, the definite integral (or "directed" area between graph and x-axis) is not affected by the value of "b" in the function expression for the quadratic: f(x)=ax^2+bx+c. You may use the "First" Fundamental Theorem of Calculus to begin your proof. A more detailed explanation of this exploration can be found in my Chapter 11, pp. 17-18, Varying the coefficient of the x-term (b) for area under a quadratic.

Due: February 15, 2005

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#8. What are the big ideas in calculus? (portfolio)

Write up the results of your discussion in class on February 15, 2005. Click here to download the Word file containing the discussion questions developed by Dr. Findell.

Due: February 17, 2005

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#9. Quick Questions and Adding It Up (portfolio)

Answer the 20 quick questions given out for homework and bring your answers to class on Tuesday, February 22 for discussion. Do not spend more than half an hour on the 20 questions. Read chapter 3 from "Adding It Up" (Kilpatrick, Swafford and Findell, 2001) and be prepared to discuss the "big ideas" in this chapter.

Due: February 22, 2005

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#10. The "Arithmetic of Functions" (10 pts)

Answer the questions on the Assignment 10 homework sheet (download by clicking here). You may hand in a hand-written copy or drop an electronic copy in the Drop Box. Please retain a copy for your portfolio.

Also answer the questions on the sheet "What is a number?" and bring to class on Tuesday.

Due: Tuesday, March 1, 2005

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#11. From Fractions to Decimals (portfolio)

Experiment with the Colour Calculator developed by Dr. Nathalie Sinclair. This is a web-based tool on the Alive Maths web site. Click here to go to the web page.

Write up four interesting things that you discovered by investigating the patterns of repeating (or non-terminating) decimal representations of fractions (e.g. which fractions give you solid blocks of color? How is the period of fractions 1/n related to n? How do these patterns compare to representations of irrational numbers using the Colour Calculator?).

You can also download Nathalie's PME-25 paper (click here) in which she describes her study using the Colour Calculator with middle grades students and raises some interesting questions concerning the role of aesthetics in teaching and learning mathematics.

Due: Thursday, March 10, 2005

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#12. Sequences and Series (10 pts)

Complete problems 1, 2, 3, 5, and 6 from the handout: Sequences, Combinations, Limits by S.I. Gelfand, M.L. Gerver, A.A. Kirillov, N.N. Knostantinov, and A.G. Kushnirenko, translated from the Russian by Leslie Cohen and Joan Teller, Dover Publications, NY.

Due: Tuesday, April 5, 2005

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#13. Sequences and Series continued (10 pts)

Complete problems 17, 18, 20 and 30 from the handout: Sequences, Combinations, Limits by S.I. Gelfand, M.L. Gerver, A.A. Kirillov, N.N. Knostantinov, and A.G. Kushnirenko, translated from the Russian by Leslie Cohen and Joan Teller, Dover Publications, NY.

Due: Tuesday, April 19, 2005

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#14. Reflection and Feedback on EMAT 4500 (evaluation form)

Your assignment is to complete the evaluation form that can be downloaded as a MS Word document from the above link. You can type on the form and then print it out. This will be completely anonymous. Samuel will collect the forms and cross your name off his list as you place it in the envelope before the presentations of your Final Project on your Final Exam morning. This is your chance to reflect on YOUR contribution to EMAT 4500, the effort you put into it, the results you got out of it, how it was taught, offer suggestions, point out assignments, technologies or readings that were helpful to you, say something nice, be critical etc... Your feedback is very valuable to us and to this department!!

Due: Final Exam Day

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Final Project

Click here for details on this final assignment

Due: 5:00 p.m. on Monday May 2 (last day of classes)

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