Transcript The Number Line……

Integers
Integers
• Consist of positive and negative whole
numbers
The Number Line……
• A number line consists of positive numbers
(right of 0) and negative numbers (left of 0).
• A real life example of a number line is a
temperature thermometer.
Negative
Positive
0
For example…..
• -5 would represent 5 degrees below zero.
• +4 would represent 4 degrees above zero.
Make the Comparison……
• 7 degrees below 0 is (warmer/colder) than 4
degrees above 0.
• 7 degrees below 0 is a (lower/higher)
temperature than 4 degrees above 0.
Coordinates on a Graph….
• Find the best estimate of the point.
a. -2
b. 2 c. -1.75 d. -1.5

2
1
0
1
2
Sets and Subsets……
• A set is a group of numbers.
Example: Set A = {1,2,3,4,5}
• A subset is a group of numbers in which every member
is in another set.
Example: Set B = {1,2,3}
• So, B is a subset of A.
Which of the following would represent a
subset of integers?
• States Sales Tax Rate
• Amount of Gas in a Car
• Number of Students in Class
• A Dinner Receipt
You Try…Which of the following would
represent a subset of integers?
• Costs of a TV
• # of miles on the odometer of a car
• A person’s weight
• Number of residents in South Carolina
Inequalities…..
• We use inequalities to compare numbers.
• The following are inequalities:




Examples…….
• “4 is less than 7” - 4  7
• “9 is greater than or equal to 5” -
95
You Try……Insert the
appropriate inequality sign.
1. -5
-2
2. -7
2
3. 4
-12
We have the Yellow Team
and the Red Team….
Assign the left side of the room to the red team and right side to
the yellow team.
Who is favored & by how
much if we have…
So…how can I represent: -7 + 3
Start with:
Which Leaves:
Add 3:
Use the counters….
6 8
Use the counters….
5  2
Use the counters….
3  4
Use the counters….
6  2
Use the counters….
58
No Counters!
100 150
No Counters
220 170
So…How do I add signed
numbers?
How close were you?
• Same Signs
• Add the numbers
• Take their sign
• Different Signs
• Subtract the numbers
• Take the sign of the number with largest absolute
value
Opposites:
• The opposite of 5 is -5.
• What is –(-2)?
Use the counters….
3  ( 2)
Use the counters….
12  ( 20)
Do the following:
• 9–8=
• -6 – (-9)=
• -14 + 3 =
• 10 – 19 =
Do the following:
• 29 - 32 =
• -82 – 12 =
• -45 + 78 =
• 16- (-27) =
What’s 4 x -3?
=
Let’s Multiply:
 2 5
Let’s Multiply:
3 2
So…How do I explain -3 x -4?
• I like to think of this as – (3 x -4) and think
of it as the opposite of (3 x -4).
• Can you develop a rule for Multiplication?
Let’s Multiply:
3  2
So…what’s the rule for
multiplying integers?
Division:


8 2 
Divide:

6 3 
So..what’s the rule for
Dividing integers
Multiplying & Dividing:
• Like signs – positive
• Unlike signs - Negative
Homework
• Worksheet