Supporting Material: Lesson Plan

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Trigonometric Ratios in Right Triangles

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Developed as part of the Math Circles of Inquiry project, this five to six day activity is designed to help students understand trigonometric ratios, by building on their understanding of similar triangles and ratios of corresponding sides. The purpose of this module is for students to spend time and energy developing the reasons the sine, cosine and tangent ratios are effective tools for solving right triangles, by analyzing patterns that emerge when the trig table is compiled from class generated data, and to understand the numbers stored in their calculator before they start using it to problem solve. An optional...

Intergenerational Wealth

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Students will gather data on median household incomes from three towns across Connecticut (including their own town) and will calculate potential future wealth using exponential modeling. Students will compare outcomes of these models and discover factors that impact a household’s ability to accumulate and transfer wealth. Students will understand the complexity and interconnectivity of social issues. Note that this lesson is closer to a 1-week mini-unit, but that teachers may choose certain sections to focus on for a smaller 1-2 day exploration.

A Problem Fit for a Princess: Apollonian Gaskets in History

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The examination of an MTC logo takes us on a journey starting over 2,000 years ago in ancient Greece, passing through seventeenth century Bohemia, moving through twentieth century fractals, and ultimately forming the focus of this problem-solving session. Explore the Circles of Apollonius, the question posed by Princess Elisabeth of Bohemia to René Descartes, and Apollonian Gaskets.

This session is also suitable for a high school math circle or classroom.

Grid Power

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“When I grew up in the Soviet Union, all we used for math was grid paper. Grid paper leads to discovery.” This is how Tatiana Shubin, San Jose State University, begins her lesson demonstrating the myriad of wonderful math questions arising from a simple sheet of grid paper. Attempting to count all squares of any size on a limited grid will require participants to persevere, organize their thinking and construct viable arguments.

Flipping Pancakes

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The Pancake Problem, first posed in 1975, is a sorting problem with connections to computer science and DNA rearrangements, which leads to discussions of algorithms, sequences, and the usefulness of approximations and bounds.

The original problem was first posed by mathematician Jacob Goodman under the pen name “Harry Dweighter” (read it quickly) in 1975, and it has delighted math enthusiasts (including undergraduate Bill Gates) ever since!