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