1. 1-8 Number Lines Real #’s

2. We have numbers to represent quantities The cavemen needed a way to count. Whole Numbers: {0, 1, 2, 3, …} shorthand (W) Then they discovered debt and that they could owe quantities: Integers – {…, -3,-2,-1,0,1,2,3,…} shorthand (Z) Then they realized they could have parts of the whole: Real Numbers ie..75, ½, -8.012

3. Negative integers Z - -4 -3 -2 -1 So, is there a way to picture the distance between quantities and show order? Origin 0 Origin 0 Positive integers Z + 1 2 3 4 Negative Integers + Positive Integers + all the stuff in between = Real Numbers (R)

4. Coordinate on the Number Line A is a positive 3 units from 0? B is a negative 1.5 units from 0? C is a positive 2 units away from B? -4 -3 -2 -1 0 1 2 3 4

5. Showing order and comparing algebraically -4 -3 -2 -1 0 1 2 3 4 -Practice plotting: A(-1), B(2.5), C(7/3), D(-3.75), and E(-3) -List A-E in order of their values on the number line. -How can we write this using <? -How can we write this using >? can be used to show order on the number line.

6. Determine which ones are true: 2<5 -4<0 -3>-2 -5<1/4 -3>-4 -2 <-2.01 8>-9

7. Practice Problems Write a number to represent each situation. 10 feet below sea level. A temperature rise of 8 degrees. A profit of $20. 5 miles west A weight loss of 3 lbs.

8. 1-9 Opposites & Absolute Value Additive Inverses: A number and its opposite. -1 and 1 -3.5 and 3.5 What about 0? The sum of a number and its opposite always = 0. Describe what additive inverses look like on a number line?

9. |absolute value| The distance from 0 on a number line. |8| = |-3| =

10. Misconceptions: |-8| vs -|8| |4 – 3| vs |4| - |3|

11. Equations with absolute value. What does |x| = 3 mean? It is asking “what numbers” are 3 units from zero.

12. Examples Simplify. 1)- ( -3) 2) l -9 l3) – ( 4 + 8) 4) – l 4 + 8 l5) 10 – l -2 l6) l -2 l + l 8 l Give the solution set. 7) l x l = 48) l x l = - 1

13. Assignment: Sheet 3 Chapter 1 Quiz next class period!!!