 ## Department of Mathematics Education

for

Shannon Umberger

Send me an e-mail at umbie51698@aol.com

## EMAT 6680 Write-ups (Fall 2000)

Write-up # 1 - The sum, product, quotient, and composite functions of two linear functions

Write-up # 2 - Given the quadratic equation y = ax2 + bx + c: when two values are fixed, and the third value varies, what happens to the graph?

Write-up # 3 - Some different ways to examine ax2 + bx + c = 0

Write-up # 4 - The construction of the nine-point circle and a proof to support the construction

Write-up # 5 - A library of Geometer's SketchPad scripts

Write-up # 6 - Some constructions of parabolas, ellipses, and hyperbolas on Geometer's SketchPad

Write-up # 7 - The construction of some tangent circles and a proof to support the construction

Write-up # 8 - A circumscribed triangle and the relationships among the arcs of the circle, the angles of the triangle, and the angle bisectors of the triangle

Write-up # 9 - A construction and proof of the Simson Line of a pedal triangle, plus some conjectures using the Simson Line

Write-up # 10 - The parametric equations x = acos(t) and y = bsin(t), x = acos(t) + hsin(t) and y = bsin(t) + hcos(t), when a = b, a < b, and a > b

Write-up # 11 - The polar equations r = a + bcos(kq) and r = a + bsin(kq), as a, b, and k vary

Write-up # 12 - An analysis of a set of data, using a Microsoft Excel spreadsheet

Final Write-up

## EMAT 6690 Essays (Summer 2001)

Essay # 1 - Fractals on The Geometer's Sketchpad

Essay # 2 - Spirals

Essay # 3 - Some "Mean" Trapezoids

Essay # 4 - The Arbelos and the Salinon

Essay # 5 - Constructing Polar Graphs on The Geometer's Sketchpad

## EMAT 6690 Unit Plan - Graphing Trigonometric Functions (Summer 2001)

Day 1 - Graphs of the Sine and Cosine Functions

Day 2 - Amplitude and Period

Day 3 - Phase Shift and Vertical Shift

Day 4 - Putting It All Together

Day 5 - Graphs of the Tangent and Cotangent Functions

Day 6 - Graphs of the Secant and Cosecant Functions

Day 7 - Graphing by Addition of Ordinates

Day 8 - TEST

## MATH 7200 : Foundations of Geometry I (Fall 2000)

Final Project - A presentation of Heron's Formula, including proofs and related topics