## Communicating Mathematics

Problems and tasks from a variety of sources intended to illustrate the way mathematics arises in life and work.

Explaining Mathematics. Write instructions so that someone who has forgotten how could add three common fractions (e.g., 2/3 + 5/7 + 1/2) and reduce the answer to lowest terms. How could you find the fractional answer by using an ordinary four-function calculator?

Pythagorean Theorem. Explain the Pythagorean Theorem to a younger student and give two different examples of where it is used.

Kite Tiles. Use a collection of Penrose (non-periodic) tiles to explore the rules for laying them down. Write an explanation that will tell a tile-layer how to set the tiles to cover a large area without gaps.

Explaining a Design. An artist friend is making a poster for a school club, and needs to incorporate the club logo, which is a geometric design consisting of several lines at different angles inside a circle. For lack of a fax machine, you need to explain the logo over the telephone so that the friend can reproduce it perfectly.

Verbalizing Graphs. You are discussing your mathematics homework over the telephone with a friend, trying to decide whether you both got the same graph for a particular function. Describe to a classmate over the telephone the graph of y = (x^2 + 2x + 1)/(x^2 - 4).