Transcript 1-8 Number Lines

1-8 Number Lines
Real #’s
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
So, is there a way to picture the distance
between quantities and show order?
Negative integers
Positive integers
Z-
-4
Z+
Origin
-3
-2
-1
0
1
2
3
4
Negative Integers + Positive Integers + all the stuff in between = Real Numbers (R)
Coordinate on the Number Line
-4
-3
-2
-1
0
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?
1
2
3
4
Showing order and comparing algebraically
< and > can be used to show order on the number line.
-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 >?
Determine which ones are true:
2<5
-4<0
-3>-2
-5<1/4
-3>-4
-2 <-2.01
8>-9
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.
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?
|absolute value|
• The distance from 0 on a number line.
|8| =
|-3| =
Misconceptions:
• |-8| vs
-|8|
• |4 – 3| vs |4| - |3|
Equations with absolute value.
What does |x| = 3 mean?
It is asking “what numbers” are 3 units from
zero.
Examples
Simplify.
1) - ( -3)
2) l -9 l
3) – ( 4 + 8)
4) – l 4 + 8 l
5) 10 – l -2 l
6) l -2 l + l 8 l
Give the solution set .
7) l x l = 4
8) l x l = - 1
Assignment:
• Sheet 3
• Chapter 1 Quiz next class period!!! 