Rational+Numbers

=Rational Numbers=

==**Depict segment addition and subtraction.** == (a) Drawing a rectangular area that can be divided to give an integer. (b) Drawing a rectangular area that cannot be divided to give an integer. ==**Multiplicative Identity and Inverse:** == Answer the following questions in the rightmost cells below. Identify group members participating in this section of the lesson.
 * 1. Illustrate at what it means to say that the integers are //closed// under multiplication by depicting rectangular areas (example: 3*5=15).
 * You may draw your area by hand, scan your drawing, and upload the file into the cell below.
 * Include the names of group members participating in this section of the lesson. ||
 * 2. Illustrate at what it means to say that the integers are //not closed// under subtraction by:
 * 2. Illustrate at what it means to say that the integers are //not closed// under subtraction by:
 * You may draw your areas by hand, scan your drawing, and upload the file into the cell below.
 * Include the names of group members participating in this section of the lesson. ||
 * //a*// __multiplicative identity__ = //a// || What is the multiplicative identity? ||
 * //a//* __multiplicative inverse__ = __multiplicative identity__ || What is the multiplicative inverse? ||
 * In the cell at right, define the multiplicative inverse operation using multiplication by the multiplicative inverse. ||  ||

**Write 3 Problems:**
Write at least 3 problems arising from the multiplicative inverse operation. Identify group members participating in this section of the lesson. ==**The Pythagorean School and the Golden Ratio, Phi, ** == Research the Pythagorean School and their interest in the ratios evident in the pentagon. Consider using the following site: [] At a minimum, answer the following questions in the space below:
 * In the cell at right, write one division problem whose quotient is an integer. ||||  ||
 * In the cells at right, write two division problems whose quotients are not integers. ||  ||   ||


 * 1) What did the Pythagoreans have to say about ratio and proportion?
 * 2) About when did the Pythagorean School exist?
 * 3) What place(s) are associated with the Pythagorean School?

Create an attractive illustration (8.5"x11") representing the Pythagorean School to add to the class timeline/map on the back wall of the classroom. Cite any sources used and identify group members participating in this section of the lesson. ==**Rational Boundaries for π: Archimedes or Liu Hui ** == Working separately, Archimedes and Liu Hui both sought to find rational numbers bounding the value of pi. Consider using the following site: [] At a minimum, answer the following questions about either Archimedes or Liu Hui:
 * 1) When and where did he live?
 * 2) What did he say about the value of pi?
 * 3) When did someone prove that pi is actually irrational?

Use the guidelines provided in class to collaborate using Google Docs to create an attractive trading card (half of an 8.5"x11" sheet of paper) including a picture of the mathematician you selected and a brief synopsis of his life, including significant dates and locations. Cite any sources used and identify group members participating in this section of the lesson.