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MATH HONORS 2: Mathematical Exploration For this assignment, you will be given the opportunity to gain an appreciation for mathematics as it pertains to your life. You will do so in the context of learning about the Mathematical Exploration component of your IB Mathematics course for next year. While you will not be performing a complete Mathematical Exploration until next year, this assignment will give you an opportunity to go through the process of choosing and developing an area of mathematics to research which will help you complete a Mathematical Exploration next year. Your task is to write an introduction and outline for a possible Mathematical Exploration that could be ready for you to continue next year. Part 1 - Outline Write an outline of a full Mathematical Exploration that includes: 1. 2. 3. 4. 5. A clear choice of topic An outlined plan of how you will investigate your topic At least one source for the mathematics involved in this topic One short example of the relevant mathematics A rough draft of a thesis statement Note: The outline should not exceed 1 side of 1 page. Part 2 - Introduction Use your outline and further research to help you to write a well thought out introduction which you could use for a Mathematical Exploration next year. The introduction will include a fully revised thesis statement. Note: The introduction should not exceed 1 side of 1 page. Part 3 – Peer Feedback Provide constructive feedback for your peers on their introduction and outline using the criteria provided to you in the rubric. Ask any relevant questions you had after reading the introduction. Keep in mind that your peer may want to use this task as their Mathematical Exploration next year, and your honest feedback will help make it better! Part 4 – Reflection Write a short reflection on the process of finding and researching a mathematical idea relevant to your life. Your reflection could answer some of the following questions: 1. Did you feel you were successful in developing a topic you could carry forward and explore further next year? Why or why not? 2. Did you feel you were successful in finding a topic you were truly interested in? Why or why not? 3. Did you feel the process helped you for next year? Why or why not? 4. Did you feel your peers provided valuable feedback regarding your introduction and outline? Why or why not? Note: The reflection should be between 200 – 250 words. Sample Outline Topic: Exponential Growth - Investments that could make me a millionaire Outlined plan of approach: I. How much do investments grow over time? a. find a specific investment that I could make - see what it would be worth in 5, 10, 25, and 50 years b. find another investment that I could make - see what it would be worth in 5, 10, 25, and 50 years II. What if I continue to deposit money into the investment, rather than just a one-time deposit? a. Find out and explain how the mathematics of this works b. Use my investment from part ‘a’ above as an example in my explanation III. How could I be a millionaire when I’m 55? a. Investigate two different approaches to investing that would earn me a million dollars by the time I’m 55. The Relevant Mathematics: I know the mathematics of exponential growth, for example, $4000 invested at 8% interest per year, for 20 years would be 4000(1.08)20. Also, from this website (http://www.fool.com/investing/brokerage/how-to-invest-20-100-and-1000-andmore.aspx), I found this: Say you've got 40 years to retirement. If you start with $1,000 and invest an additional $1,000 each year, and your money earns 10% annually, then when you're ready to retire at age 65, you'll have $532,111.07 I will have to do further research to understand the mathematics of this, but it seems interesting to me. Thesis: Becoming a millionaire is possible, and there’s more than one way to do it. Sources: you will list at least one good source here