Integers

= **Integers** =

Depict segment addition and subtraction.
(a) Drawing two segments that can be subtracted to give a natural number. (b) Drawing two segments that cannot be subtracted to give a natural number.
 * 1. Illustrate at what it means to say that the integers are //closed// under addition by depicting segment addition (example: 3+5=8).
 * You may draw your segments 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 segments 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. ||

Additive Identity and Inverse:
Answer the following questions in the rightmost cells below. Identify group members participating in this section of the lesson.
 * //a//+ __additive identity__ = //a// || What is the additive identity? ||
 * //a// + __additive inverse__ = __additive identity__ || What is the additive inverse? ||
 * In the cell at right, define the additive inverse operation using addition with the additive inverse. ||  ||

Write 3 Problems:
Write at least 3 problems arising from the additive inverse operation. Identify group members participating in this section of the lesson. In the cells at right, write two subtraction problems whose differences are not natural number ||  ||   ||
 * In the cell at right, write one subtraction problem whose difference is a natural number. ||||  ||
 * Zero and negative numbers are not natural numbers.

Zero as a Placeholder [[image:mayan_babylonian_zero.jpg width="224" height="146"]]
Research the history of zero as a placeholder. Consider using the following site: http://www-history.mcs.st-and.ac.uk/ At a minimum, answer the following questions in the space below:
 * 1) How did Babylonians determine place value before inventing a placeholder?
 * 2) About when did the Babylonians first use a placeholder?
 * 3) About when did the Mayans first use a placeholder?

Create an attractive illustration (8.5"x11") of the emergence of zero in Babylonian numeration 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.

Roman and Arabic Numeration: The Influential //Liber Abaci//
Research the title //Liber Abaci//.Consider using the following site: http://www-history.mcs.st-and.ac.uk/ At a minimum, answer the following questions in the space below:
 * 1) Who wrote it?
 * 2) When and where was it published?
 * 3) Whom did it influence?

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 author of //Liber Abaci// 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.