2-1 Integers Pg.76

Essential Question When would you need to use negative integers in the real world?

Definitions integers- the set of whole numbers and their opposites (positive or negative) opposite- two numbers that are an equal distance from zero on a number line absolute value- the distance of a number from zero on a number line; shown by l l

INTRODUCTION TO INTEGERS Integers are positive and negative numbers. …, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, … Each negative number is paired with a positive number the same distance from 0 on a number line. These numbers are called opposites. -3 -2 -1 1 2 3

Integers Numbers to the left of zero are less than zero. Numbers to the right of zero are more than zero. The numbers –1, -2, -3 are called negative integers. The number negative 3 is written –3. The numbers 1, 2, 3 are called positive integers. The number positive 4 is written +4 or 4. Zero is neither negative nor positive.

Negative numbers are used to… 1. 2. 3. The answers are on the next 3 slides 

Negative Numbers Are Used to Measure Temperature

Negative Numbers Are Used to Measure Under Sea Level 30 20 10 -10 -20 -30 -40 -50

Negative Numbers Are Used to Show Debt Let’s say your parents bought a car but had to get a loan from the bank for $5,000. When counting all their money they add in -$5.000 to show they still owe the bank.

Hint If you don’t see a negative or positive sign in front of a number it is positive. 9 = 9 +

Opposite Example 1 The opposite of a number is the same distance from 0 on a number line as the original number, but on the other side of 0. Zero is its own opposite. –4 and 4 are opposites –4 4 • • –5–4–3–2–1 0 1 2 3 4 5

Opposite Example 2 Graph the integer -7 and its opposite on a number line. 7 units 7 units 1 2 3 4 5 6 7 –7–6–5–4–3–2–1 0

Graph the integer and its opposite on a number line. Opposite Examples 3&4 Graph the integer and its opposite on a number line. 1 2 3 4 5 6 7 8 9 -9–8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0

Absolute Value Video Clip (1:30) Write down 1 fact from the clip about absolute value. http://player.discoveryeducation.com/index.cfm?guidAssetId=EE3ED6D0-96E6-4FF7-8D82-3FCD782528EB&blnFromSearch=1&productcode=US

The symbol is read as “the absolute value of The symbol is read as “the absolute value of.” For example -3 is the absolute value of -3. Reading Math

Absolute Value Example 1 Use a number line to find each absolute value. |8| 8 units 1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0 8 is 8 units from 0, so |8| = 8.

Absolute Value Example 2 Use a number line to find each absolute value. |–12| 12 units –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 –12 is 12 units from 0, so |–12| = 12.

Absolute Value Examples 3 & 4 2 1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0 7 1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0

You can compare and order integers by graphing them on a number line. Integers increase in value as you move to the right along a number line. They decrease in value as you move to the left. The symbol < means “is less than,” and the symbol > means “is greater than.” Remember!

Comparing Example 1 Compare the integers. Use < or >. > -4 -11 > -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -4 is farther to the right than -11, so -4 > -11.

Comparing Example 2 Use a number line to order the integers from least to greatest. –3, 6, –5, 2, 0, –8 1 2 3 4 5 6 7 8 –8 –7–6 –5–4 –3 –2 –1 0 The numbers in order from least to greatest are –8, –5, –3, 0, 2, and 6.

Comparing Examples 3&4 › ‹ -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 ‹

Comparing Example 5 1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0

Work Session-Together Showing off Integer WS Meaning of Integer WS Comparing and Ordering Sort Number Line WS Work Session-With your Partner Work Session- On your own

Closing When would you use negative numbers in the real world? Do the numbers increase or decrease as you move to the left of zero? < means: > means:

Homework 13.3 WS Comparing and Ordering Integers

Role of Integers Video Clip Write down 3 facts about integers from the clip. 1. 2. 3. http://player.discoveryeducation.com/index.cfm?guidAssetId=E2DCB058-17F3-41C9-A4C8-B08D1D2AACB8&blnFromSearch=1&productcode=US

Homework Workbook pg. 13 All problems

Work Session Textbook Pg. 78 16-38 even only GRADED