Essay #1
Due Sunday September 25.
The last day for a consultation is Thursday, September 22.
Topic: What is a function?
Some ideas you need to consider:

Write the definition of a function in your own words.

What does a function look like? Is it always a graph?

What are the attributes of a function?

What are some tips for discovering if a relationship is a function or not?

What is (and is not) a function from the viewpoint of a variety of disciplines
(anthropology, English, physics)? How are these different from but related to the functions we looked at in class?

Include multiple representations of functions (e.g. graphic, symbolic, words, mappings, etc.) and discuss which attributes are best shown in each representation.

Include a bibliography if needed; it does not count in your word count, though.
Audience: Ms. Leigh, who has suffered slight amnesia, needs to be reminded of mathematical basics. She needs to be able to read the details and supporting evidence for your statements in order to feel that what you’ve written is both relevant and accurate.
Assignment format:
This will be a 700 word descriptive essay that is typed (12 point) and double spaced with margins not larger than 1 inch per side. The Proof of Attendance form from The Writing Center must be attached at the back of the essay along with a copy of the rubrics for me to use in grading your essay.
Grading Rubric: next page, attach to essay with PoA
10% your grade
Rubrics Sheet for: Essay #1
Name:__________________
Topic Development and Task Responsiveness (5 points):

Fulfills the purpose of the essay; addresses the considerations


Includes all relevant facts; is free from factual errors


Develops the context of the topic in mathematics/other disciplines


Has a welldefined and wellsupported thesis


Demonstrates mastery of the topic

Critical Thinking (5 points):

Clear reasoning and idea development, treats the subject as complex


Good references cited and rewritten in the student’s voice


Demonstrates a high level of reflection and synthesis


Determines relevant patterns, inferences, and connections


Shows logical inquiry and reasoning

Conventions, Mechanics, and Readability (5 points):

Good grammar and proper use of math terminology throughout


Introductory paragraph is well organized and engaging


References are used appropriately and structure is evident


Good transitions between thoughts and paragraphs


Summary is concise and provides closure

______ Receipt from Writing Center (3 points)
______ Received by deadline (2 points off each day late)
Essay #2
Due Sunday, October 30.
Last day for consultation is Thursday, October 27.
Topic: Devise a visual, verbal, and algebraic way of
connecting the following three concepts.

The Euclidean distance formula

The Standard Equation of a Circle centered at (h, k)

The Pythagorean Theorem
Some ideas you need to consider:

Think of at least 2 related mathematical or real life topics that can be extended from these three topics.

Historically, what came first?

Are there graphical and symbolic connections you can illustrate?

How were these topics introduced and taught to you? Can you think of a more interesting or compelling approach? What did you learn from this topic?
Audience: Ms. Leigh, who has suffered slight amnesia, needs to be reminded of mathematical basics. She needs to be able to read the details and supporting evidence for your statements in order to feel that what you’ve written is both relevant and accurate.
Assignment format:
This will be a 700 word descriptive essay that is typed (12 point) and double spaced with margins not larger than 1 inch per side. The Proof of Attendance form from The Writing Center must be attached at the back of the essay along with the Rubrics Sheet for me to use in grading your essay.
Grading Rubric: next page, attach to essay with PoA
10% of your grade
Rubrics Sheet for_Essay #2
Name:__________________
Topic Development and Task Responsiveness (5 points):

Uses many modes of showing connections; addresses considerations


Includes all relevant facts; is free from factual errors


Develops the context of the topic fully


Has a welldefined and wellsupported thesis about the connections


Demonstrates mastery of the connections and history

Critical Thinking (5 points):

Clear reasoning and idea development; clear and precise


Good references cited and rewritten in the student’s voice


Demonstrates a high level of reflection and synthesis


Determines relevant patterns, inferences, and connections


Shows logical inquiry and reasoning

Conventions, Mechanics, and Readability (5 points):

Good grammar and proper use of math terminology throughout


Introductory paragraph is well organized and engaging


References are used appropriately; illustrations are attributed


Good transitions between thoughts and paragraphs


Summary is concise and provides closure

______ Receipt from Writing Center (3 points)
______ Received by deadline (2 points off each day late)
Essay #3
Due Sunday, November 20.
Last day for consultation is Thursday, November17.
Topic: Eccentricity of a hyperbola
Investigate the geometric significance of the eccentricity of a hyperbola by completing the three steps that follow. Then write a report telling what you have done, what patterns you have observed, and what relationship you have found between the eccentricity and the shape of the hyperbola.
A. Use the definition of eccentricity*, e, to show, for the hyperbola
that e = .
*e = c/a where c is the distance from the center to a focus point.
I want to see how you go from the definition ( e = c/a) to the formula with the square root in neat precisely written steps…almost a proof. How are a, b, c, and eccentricity related? How does the eccentricity show up in the graph or predict the graph?
B. Compute and report the eccentricity for each of the following five hyperbolas with a calculator:
Discuss the utility of these choices for illustration. Why NOT just any 5 hyperbolas? How does it help you understand eccentricity to use these specific ones? What is the relationship between eccentricity and shape?
Why is this a math experiment? What do you notice about the design of the steps you are following that makes this a welldesigned experiment?
Essay #3 continued
C. Use graphing software to show Quadrant 1 for each of these 5 on the same set of axes. Insert this picture in your essay with a cogent caption.
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