Blake E. Peterson

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Math Ed 308 Assignments

Date Given
Date Due
Assignment
Aug. 30
Sept. 1
Find the roots of x^n + 1 = 0 for n = 1, 2, 3, 4, … and plot each set of roots (by hand) on a different set of axes. By generalizing the observed pattern, explain where the roots of x^20 + 1 = 0 and x^21 + 1 = 0 would lie (in detail) without actually finding and plotting the roots.
Sept. 1
Sept. 3
Cubic Tangent Line
Use the symbol manipulation capabilities of the TI-89 to prove the following:
For the function , f(x) = (x - a)(x - b)(x - c) show that the tangent line at x= (a+b)/2 intersects the graph of f(x) at the point x = c.Be sure to use complete sentences linking the algebraic and calculus phrases together.
Sept. 3
Sept. 8
Complete the attached graphing assignment on the TI-89
Sept. 8
Sept. 15
Create a spreadsheet that will compute: a) n!=n(n-1)(n-2) . . . (3)(2)(1) from n!=n(n-1)! (DO NOT USE THE BUILT IN FACTORIAL FUNCTION); and b) the Fibonacci numbers F(n), where F(1)=F(2)=1, and F(n+2)=F(n+1) + F(n), n>1. Both of these can be done on the same spreadsheet. Since one of the purposes of this assignment is to give you experience with the reset idea, please create this spreadsheet to show only 10 values at a time similar to the Harmonic Series spreadsheet. Name the file fiblastname (By lastname I mean the first three letters of your last name and the first letter of your first name. For example mine would be fibpetb.) Don’t forget to make a user-friendly format.
Sept. 10
Sept. 15
Find and read an article about using technology to teach mathematics in the Mathematics Teacher journal. You can either search online by following this link or go to the library in the periodicals (QA1.N28) Write a 1-page (double spaced) critique of the article being sure to a) briefly summarize the paper and identify the main point; b) critique the article and describe whether or not you agree with that main point.
Sept. 15
Sept. 20
Create a spreadsheet that plots 3 graphs on the same set of axes. Each graph should be of the function aCos(bx + c) + d for different entries of the parameters a, b, c, and d. Make the entries dynamic using scroll bars. The purpose of the spreadsheet is to allow students to enter different values for a, b, c and d and see the effects on the respective graphs. There may be diffrerent features of this file when compared to the cubic file because of the difference in the types for funtions being graphed. The name of this file should be COSlastname. See the file Cubic as a sample graphing spreadsheet.
Sept. 17
Sept. 24
Write an nth root spreadsheet using a variation of the divide and average method. The title of the spreadsheet should be nrootname. The spreadsheet should take as inputs: the number for which the root will be taken, n (the degree of the root), and an estimate. The spreadsheet should output the appropriate root. The format should be similar to the Square Root spreadsheet done in class. It should include at least 25 iterations but the majority should be computed in less than 10 iterations.
Sept. 20
Sept. 24
Create a model to find the Greatest Common Divisor (GCD) of two numbers using the Euclidean Algorithm. The worksheet should have input values of a and b and output values of the GCD(a, b). The output should be in a single cell and the user should not have to scan the whole spreadsheet to locate the GCD. It may be helpful to use the VLOOKUP command to find the output. The title of the spreadsheet should be eucname. You may also need the INT and MOD commands. The INT(a) command finds the integer part of number a while the MOD(a, b) command finds the remainder of a divided by b.
Sept. 22
Sept. 27
Create a spreadsheet that simulates rolling 2 dice, finds the sum of the faces and keeps a running tally of how many times each sum has occurred. The spreadsheet should include a histogram that displays the frequency of occurrences and buttons to clear and toss multiple times. Name this file Diename.
Sept. 27
Oct. 1
Create a spreadsheet that will convert a base 10 number to a base x number where x = 2, 3, 4, 5, 6, ….16. The inputs should be the number to be converted and the base, x, to which it will be converted. The output number will have a maximum of 7 places. Include some type of error message when x is too big or if the number to be converted is too big for the base. For example, 150 would yield an error message if the user tries to convert it to a base 2 number because it won’t fit in the 7 places. However, 250,000,000 would not yield an error message when converting it to a base 16 number. The symbols for numbers greater than 9 are T=10, E=11, A=12, B=13, C=14, and D=15.
Sept. 29
Oct. 6
Redo the die spreadsheet to include pictures of the two die which change depending on the random numbers generated. Make sure that any errors in the original die assignment are resolved in this new file. Submit the spreadsheet as a file named die2name.
NOTE: If a cell is highlighted to be part of the data series for a graph and sometimes the cell has a number to be graphed and other times you want the contents of the cell ignored and not graphed, put =#N/A in the cell and it will be ignored.
Sept. 29
Oct. 8
Construct a spreadsheet that will simulate the tossing of a needle onto a grid of at least 4 parallel lines. The needle should be half as long as the distance between the parallel lines. The spreadsheet should keep track of the total number of tosses as well as the number of times that the needle crossed a line. These numbers should be used to compute an approximation of PI. The spreadsheet should also include buttons to clear, toss once, and toss multiple times.
Oct 6
Oct 11
On Geometer’s Sketchpad construct the following quadrilaterals: Parallelogram, kite, rhombus, rectangle and square. Each quadrilateral should be constructed so that if a vertex of it is moved, its fundamental properties are preserved. For example, the opposite sides of a parallelogram must always be parallel. It is important, however, that each quadrilateral can take on different shapes within its class. For example, the rhombus should be constructed to allow it to be changed into a very skinny diamond shape or a square. Another example would be for a parallelogram to be reshaped into a rectangle or a rhombus or a square. All 5 of the quadrilaterals should be contained in a single file and labeled appropriately. The name of the file should be quadname.gsp.
Oct 8
Oct 18
On one sketch construct a convex pentagon and a convex hexagon with their corresponding mid-polygons (a polygon created by connecting the midpoints of the sides of a polygon). Calculate the areas of the polygons and the mid-polygons. Use these figures to determine if the ratios of the areas of the midpentagon and the pentagon are nice fixed values like the triangle and quadrilateral. If so, prove them. If not, find the upper and lower bounds of the ratios. Repeat this for the hexagon and its midhexagon. In the sketch with the pentagon and hexagon, include the proof or a description of the bounds. Submit the sketch under the name of mpolname.gsp
Oct. 11
Oct 18
Parabola: Given a focus and a directrix (use a segment instead of a line), construct the locus of a parabola. It should be constructed so the locus will change shape as the focus or the directrix are moved. Submit this file with the name Parapetb.gsp (the italicized portion is the usual name ending).
Oct 13
Oct 15
When the midquadrilateral of a quadrilateral is constructed, it is a parallelogram with an area that is half of the original parallelogram. Show that the 4 triangles outside of the parallelogram can be arranged to exactly cover the parallelogram. Draw and explain how the triangles fit together to cover the parallelogram.
Oct 18
Oct 25
The quadrilateral created by connecting the midpoints of an arbitrary convex quadrilateral is a parallelogram with area equal to one-half of the area of the original quadrilateral. The triangles outside of this parallelogram and inside the original quadrilateral will tile the parallelogram. Construct a sketch on Geometer’s Sketchpad that will display an animation of this tiling. The final sketch should contain a quadrilateral with its corresponding parallelogram created by midpoints. It should also contain two buttons, appropriately labeled, that when pressed will tile the parallelogram or reset the picture. This file should be named tilename.gsp.
Oct 20
Oct 25
Create a sketch that plots a graph of the function aSec(bx - c) + d. The parameters a, b, c, and d need to be constructed so that the display of the graph is dynamic. The purpose of the sketch is to allow students to move the points associated with a, b, c, and d and see the effects on the respective graphs. The name of this file should be Secantname.gsp.
Oct 22
Oct 27
Using tools (scripts) that you create for at least two different regular polygons, construct a full page semiregular tessellation consisting of those different types of polygons. Submit the file (tessname.gsp).
Oct 25
Oct 27

a. Describe two configurations of an hyperbolic triangles on the Poincare Half-Plane that minimize the sum of the angles.

b. Describe two configurations of an hyperbolic triangles on the Poincare Half-Plane that maximize the sum of the angles.

Oct 27
Nov. 1
Let F[m] and F[n] be the mth and nth Fibonacci numbers respectively. Find a relationship between m, n, F[m], and F[n] so that if m and n are related then F[m] and F[n] are related in the same way. Submit a handwritten description of this relationship.
Oct 29
Nov 5
Riley is on a camping trip near the McKensie River. He has taken his bucket to gather some firewood when he sees that his tent is on fire. Where should he fill his bucket in the river so that he will have to run the shortest possible total distance to get to his tent with a bucket full of water? Use calculus and Mathematica to solve this problem analytically. Submit the assignment as a Mathematica notebook file named firename.nb. Include the symbolic solutions in the file as well as written text that describes the steps to the solution.
Nov 1
Nov 5
Investigate the Taylor Polynomial approximation of Tan[x] comparing various centers of approximation and various degrees of the polynomial. Submit a file named taylorname.mws containing at least 3 graphs and a written description of your conclusions.
Nov 3
Nov 10
In Mathematica create an animation of a helix that when animated continuously will move up and down like a spring attached at the top. The helix should have at least three curves. Call this assignment springname.
Nov 5
Nov 10
Use Mathematica to construct a graph of a Helix tube.
Nov 8
Nov 15
Complete the "Name that Graph" worksheet.
Nov 10
Nov 12
Read the article "Student Interactions in Technology-Rich Classrooms" from the November, 2010 Mathematics Teacher. Be prepared to discuss this article in detail. Copies of the article can be found in the envelope outside of my office.
Nov 10
Nov 15
Prove the following theorem related to the rugby problem discussed in class.
Theorem: The point located by constructing a circle through the goal posts and tangent to the perpendicular line ( this is the line that is perpendicular to the goalline and passes through the point where the ball was downed) is the optimal (the point where the viewing angle of the goalposts is the greatest) point.
Nov 17
Nov 22
Prove that the locus of optimal kicking locations in the rugby problem is an hyperbola.
Nov 17
Dec 6
Complete one CBL activity and write an updated, less perscriptive version of the activity to be used with the TI-89. More detail about this assignment can be found in the following link.