# Essay Topics: The History of Zero

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Essay Topics:

1. The History of Zero. Questions you might consider: When did it become a part of our number system? Where did the word “zero” come from? What are some properties that involve 0? What did ancient mathematicians think about dividing by zero? What are some other symbols for zero? What is the difference between a line with a slope of zero and a line with no slope? What does zero have to do with x-intercepts and y-intercepts? What is zero used for in the real world? Complete a problem involving zero and explain step-by-step how you arrived at your solution.

1. The History of Negative Numbers. Questions you might consider: When did they become a part of our number system? Why were they invented? What are negative numbers used for in the real world? What did ancient mathematicians think about negative numbers? What are some properties that involve negative numbers? The “-“ symbol has many different meanings—what are some of them? Complete a problem involving negative numbers and explain step-by-step how you arrived at your solution.

1. The Fibonacci sequence and the Golden Ratio. Questions you might consider: What is the Fibonacci sequence? Is there a recursive formula for it? Who discovered it? Where can you find the Fibonacci sequence in the real world? What is the Golden Ratio? How is the Golden Ratio related to the Fibonacci sequence? Where can you find the golden ratio in the real world?

1. The History of Imaginary Numbers. Questions you might consider: What are imaginary numbers? When were they invented? Why were they invented? What did ancient mathematicians think about imaginary numbers? What are some properties that involve imaginary numbers? What do imaginary numbers have to do with quadratic equations? What are imaginary numbers used for in the real world? Complete a problem involving imaginary numbers and explain step-by-step how you arrived at your solution.

1. History of the Pythagorean Theorem. Questions you might consider: What is the Pythagorean Theorem? What is it used for? Who is Pythagoras? Who are the Pythagoreans? What have the Pythagoreans discovered besides the Pythagorean Theorem? What does President Garfield have to do with the Pythagorean Theorem? Where can you find the Pythagorean Theorem in the real world? Complete a problem involving the Pythagorean Theorem and explain step-by-step how you arrived at your solution.

1. Interest Plans. Kayla is saving her money for a new \$9000 motorcycle. She currently has \$7,000 in her bank account and has two different interest plans to consider:

1. Plan A—receive 5% of her current balance each year.

2. Plan B—receive \$375 each year.

What type of growth process is being used for each plan? How do you know? For each plan, how long must she wait until she can buy her motorcycle? Include your work and explain how you arrived at your solution. If you were picking an interest plan, under what circumstances would you choose Plan A? Under what circumstances would you choose Plan B? Why?

1. Perimeter and Area. A new amusement park will be opened in 2 years. The owners have a fixed amount of fence, so the park must have a perimeter of 400 m. The owners can choose how to shape the park, as long as it is a rectangle with a perimeter of 400 m. Write the dimensions of several different rectangles, each with a perimeter of 400 m and explain how you know that they each have a perimeter of 400 m. What kind of relationship (linear, quadratic, cubic, or exponential) exists between the side lengths and the area? Draw a graph of side length (independent) versus area (dependent). What is the largest area that can be achieved with 400 m of fence? Explain how you arrived at your answer.

Important Dates:

Specifications:

• Font: Times New Roman

• Font Size: 12

• Margins: 1 inch

• Your essay should be at least 5 paragraphs in length made up of 1 introductory paragraph, at least 3 supporting paragraphs, and 1 conclusion paragraph.

• You may submit your work on printed paper or you may send it to hforsyth@laalliance.org

How you will be graded:
 Essay 4 3 2 1 Score Pre-writing activity Work is complete and organized. It looks like the student worked hard on the assignment. Work is complete. It looks like the student spent time on the assignment. Work is incomplete. It looks like the student gave the assignment a half-hearted attempt. Work is incomplete and very disorganized. It looks like the student started this yesterday/today. First Draft Work is complete and organized. It looks like the student worked hard on the assignment. Work is complete. It looks like the student spent time on the assignment. Work is incomplete. It looks like the student gave the assignment a half-hearted attempt. Work is incomplete and very disorganized. It looks like the student started this yesterday/today. Peer Revision Student provides peers with lots of quality constructive criticism. Student provides peer with some constructive criticism. Student provides peer with minimal constructive criticism. Student doesn’t provide peers with any constructive criticism. Timeliness Assignments were turned in on time. Student misses 1 deadline by 1 day. Student misses 2 deadlines by one day or misses 1 deadline by two days. Student misses several deadlines. Organization The introduction states the main topic, and provides an overview of the paper. Information is relevant and presented in a logical order. The conclusion is strong. The introduction states the main topic and provides an overview of the paper. A conclusion is included. The introduction states the main topic. A conclusion is included. There is no clear introduction, structure, or conclusion. Key Vocabulary Includes all relevant and appropriate terms for the topic. Includes all relevant information, but describes terms instead of using them.  (e.g. “flipped upside down fraction” instead of “reciprocal” Uses words incorrectly, but still clear what they meant to say. Used words so incorrectly that it is impossible to determine what they meant to say. Answers demonstrate correct understanding Answers all aspects of the question without error. The author’s extensive knowledge with the topic is evident. Main ideas are clear and are well supported by detailed and accurate information. Solid conceptual understanding, minor “work” errors. The authors knowledge with the topic is evident. Main ideas are clear but are not well supported by detailed information. Conceptual errors and or major calculation errors. The author’s knowledge of the topic is limited. Main ideas are somewhat clear. Total lack of conceptual and procedural understanding. Main ideas are not clear. Sentence Structure, Grammar, & Spelling All sentences are well constructed. The author makes no errors in grammar or spelling. Most sentences are well constructed. The author makes a few errors in grammar and/or spelling, but they do not interfere with understanding. Most sentences are well constructed. The author makes several errors in grammar and/or spelling that interfere with understanding. Sentences sound awkward, are distracting repetitive, or are difficult to understand. The author makes numerous errors in grammar and/or spelling that interfere with understanding. Total: /32

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