79. UNIT SEVEN: Process Analysis Paper (MATH or SCIENCE)

UNIT SEVEN: Process Analysis Paper

The Short Prose Reader Assignments: Chapter 6: Process Analysis (181-184) and Mark Shiffrin "Thumbs on the Wheel" (185-189) and Nora Ephron "How to Foil a Terrorist Plot in Seven Simple Steps" (190-194) and Ernest Hemingway "Camping Out" (195-202).

Short Papers: Math / Science Process Analysis Paper

Rubric: 1-51, 49-51, 57-59, 61-63 (+1 for end paragraph with a topic sentence, varied

sentence structure, active voice )

Quiz: ---

Process Analysis Paper

"Science is organized knowledge."

--Herbert Spencer

Writing Invitation

The goal in writing about math, science, or any other discrete process is to convey to the reader as clearly and simply as possible the steps that the author undertook and the results that the author obtained. We use process based writing in lab reports and math projects, of course, but also in medicine, navigation, and technical writing. When we write about a process, we want to be a specific, simple, and clear as possible.

Pre-Writing

For this project, you have the choice of encountering one of the following forms of Process Analysis Writing:

• • Mathematical Proof (in conjunction with your math class)

  • Science Lab Report (in conjunction with your science class)

  • Recipe: Write a recipe for your favorite dish to include in a class cookbook. In addition to describing the step-by-step process for preparing the food, you should also tell something about the tradition behind the food, special occasions for eating it, the first time you ate it, and so forth. The goal should be to make the process clear and reassuring, to emphasize how following these simple steps will yield a delicious meal.

Details

Your paper will:

• • Be 1-2 pages, typed, double spaced

  • Have a thesis statement that tells what the process is, and why it is a good process to know

  • Follow the appropriate form and conventions for the type of report you’re writing

  • Show evidence that you spent time thinking about issues pertaining to organization

  • Include all the essential steps, including what to avoid

  • Use definition to explain terms the reader may not know

  • Show awareness of the audience, and link the audience to the purpose of the process

Assessment

Your success will be assessed using the following rubric:

Math Process Writing:

Process Writing Guidelines:

9th Grade Algebra and 10th Grade Geometry

1. General Writing Assignment (Essay, Project, or Short Answer)

Writing in mathematics should be concise and direct (simplify, simplify, simplify!), and should utilize correct vocabulary and terminology when referring to specific mathematical operations.

When writing an essay, or when writing for a project or for short answers, students should follow the basic formal paragraph structure (topic sentence → supporting evidence → analysis). Essays should follow the 5-Paragraph format (give or take a paragraph).

Sources should always be cited. Quotes should always be cited in-text, and should credit the author or article if there is no author. All other information may be cited in a works-cited page using simple source citation (Author. “Title”. Publication/URL)

2. Writing Proofs:

Proofs follow a logical, deductive reasoning process, wherein students must use mathematical properties, postulates, and theorems to arrive, step by step, at a logical conclusion or the indicated “prove statement”. Each step (statement) must be logically derived from the given information, or from previous steps, and must also be explained using concrete known facts, mathematical properties, postulates, or theorems (reason).

I. Algebraic Proof: (Two - Column)

When writing an Algebraic Proof, students must detail each step taken in the process of simplifying an expression or solving an equation:

Example Problems:

A. Expression:

In an Algebraic, Two-Column Proof, given the following expression, simplify completely.

3(x - 5) + 4x -13

Statements (Column 1) Reasons (Column 2) Comment

B. Equation:

In an Algebraic, Two-Column Proof, given the following equation, solve for x:

2x - 2(x + 6) = x / 4 + 3

Statements (Column 1) Reasons (Column 2) Comment

II. Geometric Proof:

Similarly to Algebraic Proofs, in Geometric Proofs students must justify, step by step, each statement made in order to find a logical path towards justifying the “prove statement”. Beginning with the “given information”, students must create logical, step by step explanations (statements) and justify each step along the way (reasons). In Geometric Proof, students must not only use mathematical operations and properties of equality, but must also use Geometric definitions, postulates and theorems to justify each step.

It is always recommended to plan out a proof before you begin to write it in a formal presentation. Mark your diagram with properties, definitions, and congruences that you can see, based on the diagram and the given information. Then outline your proof to ensure each step you take follows logically from the information you already have. In writing the proof itself, steps must use the information given, as well as the the information already stated previously in the proof. Each logical jump and assumption must be justified, no matter how “obvious”.

Geometric Proofs may be presented in 3 different ways: Two-Column Proofs, Paragraph Proofs, and Flow Proofs.

A. Two - Column Proof: (used most often)

Two-column proofs follow the statement/reason structure. This is the most common format for Geometric Proofs, and will be the main focus of the proof-writing process.

Example Problem:

Using the diagram and the given information below, write a two-column proof, showing that triangle ABE is congruent to Triangle ADE

Solution:

Statements (Column 1) Reasons (Column 2) Comment

B. Paragraph Proof:

Paragraph proofs can be a more direct way to write a proof. Paragraph proofs require the student to write a complete paragraph, beginning with the “given information” and ending with the “prove statement”. Just like in the two-column proof, each statement that is written must be justified with a reason; however in a paragraph proof these statements and reasons are written in complete sentences. Attention to grammar, spelling and capitalization is expected. Paragraph proofs may use first, second, or third person voice, but also must utilize academic rhetorical devices, such as “therefore”, “we can deduce”, etc.

Example Problem:

Using the diagram and the given information below, write a two-column proof, showing that triangle ABE is congruent to Triangle ADE

Solution:

“Firstly, we are given that angle CAB is congruent to angle CAD. We can also deduce from the diagram that angles BAE and CAB are supplements, and angles DAE and CAD are supplements because of the definition of supplementary angles. Therefore, angles BAE and DAE are congruent because of the Congruent Supplements Theorem. We are also given that segment CE is perpendicular to segment BD, which, by the definition of perpendicular lines, means that the measure of angle of AEB and the measure of angle AED are both equal to 90 degrees, and therefore equal to each other. Furthermore, we can deduce that angles AEB and AED are congruent, due to the reason that all right angles are congruent to each other. Finally, we can deduce from the diagram that segment AE is congruent to itself by the Reflexive Property. These statements prove that triangle ABE and triangle ADE are congruent by the Angle - Side - Angle Congruence Postulate.”

C. Flow Proof:

Flow proofs are helpful visual tools for completing proofs. Flow proofs can also be a good way to plan for a proof and organize it into a visual presentation that outlines the “flow” of the argument and which statements lead directly to the next statement or to the prove statement.

Flow proofs are structured so that statements are presented in boxes, and the reasons for the statements are written underneath each box. Flow proofs can “flow” from left to right, or from top to bottom. In the example problem below, the “flow” moves from top to bottom.

Example Problem:

Process Writing in Math Prompt: Choose one concept that we have learned this year in class, perhaps one that you enjoyed most or one that you understood least. Developed a scholarly 2-3 page mathematical paper in which you explore this topic further. Include necessary definitions, examples, and diagrams. Example: Excerpt from “Limits at Infinity and Infinite Limits” © 2002 Donald Kreider and Dwight Lahr It may be argued that the notion of limit is the most fundamental in calculus— indeed, calculus begins with the study of functions and limits. In many respects it is an intuitive concept. The idea of one object “approaching” another, even approaching it “arbitrarily closely” seems natural enough. Our language is full of words that express exactly such actions. And in mathematics the idea of the value of x approaching some real number L, and coming as close to it as we please, does not seem to be stretching the ideas of everyday speech. It is surprising, then, that there are such subtle consequences of the concept of limit and that it took literally thousands of years to “get it right”. In the definition of , a is a real number. It would be natural to relax this to include the cases and This means that the value of increases beyond all bounds that you might name () or decreases below all (negative) bounds that you might name. Definition 1: means that the value of approaches as the value of approaches . This means that can be made as close to as we please by taking the value of sufficiently large. Similarly, means that can be made as close to as we please by taking the value of sufficiently small (in the negative direction). Example 2: . This is simply the observation that by taking sufficiently large we can make its reciprocal as close to zero as we please. Similarly . The line is approached by the graph of as and also as . It is called a horizontal asymptote of the graph. Also the vertical line is approached by the graph as. It is called a vertical asymptote of the graph. Finding such horizontal and vertical asymptotes for a graph aids in sketching the graph. Summary: In this section we extended our notion of limit to include points where the limit does not exist but where we could use the notation to provide additional information about the behavior of the function...

Science Process Writing

Inquiry Plan

Researchable Question:

Hypothesis:

Materials List:

Safety Issues:

Procedure:

• • Repeatable, repeated multiple times, controlled variable, a control, clearly explained in a list, data collected

Data and observations:

• • Reprsent data in an organized manner with labels of units and to correct precision

  • Record complete/detailed observations during procedure

Analysis:

• • Manipulate/represent data in ways to make it data patterns clearer. (graphs, averages, percents,...)

Conclusion:

• • Hypothesis supported or not and how results support the science concept/principle you are investigating

  • Error Analysis: What are some possible errors in your research and how might they have impacted results

  • Further Investigation: What further research could be done to learn more about your question?

Chemistry Lab Report Rubric

/20

Model Lab Report

Question: Do citrus fruits produce more volts and amps than non citrus fruit.

Hypothesis: The lemon and lime with citric acid will produce more volts and micro amps than the banana and potato because the banana and the potato do not have citric acid and citric acid is what dissolves the Zinc to create the Zinc ions that starts the process of the travel of electrons.

Materials List

• • (4) Banana

  • (4) lime

  • (4) lemon

  • (2) potato

  • Ruler

  • Marker

  • Copper wire (at least 3 inches long) (electrode)

  • A 1 ½ inch Zinc nail (electrode)

  • A digital Multimeter

  • Wire Leeds

(didn’t have enough bananas, limes, and lemons, so we had to flip them over)

• 1. Measure out 1.34 g of copper wire

  2. Measure out 2.62 g of a zinc nail

  3. Using your ruler and marker, mark the nail and the copper wire at an inch.

  4. Put your zinc nail inside a lime up to the mark

  5. 2 inches next to the nail, insert the copper wire up to the mark.

  6. Connect the black wire to the head of the nail

  7. Connect the red wire to the copper wire an inch from where you inserted it

  8. Hook up the wires to the corresponding colored wires.

  9. Wait for 15 seconds.

  10. Record Microamps

  11. Switch to volts.

  12. Wait 15 seconds

  13. Record volts.

  14. Repeat steps 4-13 using the same copper and zinc nail on every fruit/

Trial 1

Trial 2

Averages

Calculations:

We took the average by adding up the corresponding results and then dividing that sum by the amount of results previously added together.

Observations/Analysis:

No matter the fruit/vegetable the average volts for each fruit and the average volts for the fruits overall were all very consistent (between .71 and .79). However, the microamps were highly variable (between 18 - 106) and this is because of the amount of citric acid and the speed of the reaction.

Possible Mistakes:

Not all of the fruit was the same, weight or shape. This affects the amount of citric acid. We were only able to try a select few specimens of each fruit. This limits our results and could not be representative We only had one potato so that limited our results because that one potato could not be representative of the average potato.. The nail would be gradually degrading because of the citric acid. We didn’t have enough bananas, limes, and lemons, so we had to flip them over. We had to share the electrometer with another group and the constant jostling and and switching could have interfered with the accuracy of results.

Conclusion:

Our hypothesis was incorrect.

After the experiment, it turned out that all of the fruit/vegetables, regardless if they were citrus or not, are batteries and produced a consistent amount of volts (microamps were highly variable). When we researched further, we found this is due to the presence of H+ acids and also citric and malic acid in all of the fruits/vegetables we tested which also dissolves the Zinc, creating Zinc ions and starts the process of the flow of electrons. The banasa had a lower average microamps because they have a very low amount of citric acid so the reaction was happening very slowly.

We also found that (see the link below) all of the vegetables and fruit we have citric acid.

Further Questions:

Since bananas and potatoes don't taste citrusy, how citric acid do the have and how much citric acid is needed for a battery? I researched these questions briefly and could not find concrete answers.

WORKS CITED PAGE

http://www.hawkinswatts.com/documents/Natural%20Acids%20of%20Fruits%20and%20Vegetables.pdf