2-1 Integers and the Number Line

1
2-1 Integers and the Number Line

• Objective To state the coordinate of a point on
  a number line, to graph integers on a number
  line, and to add integers by using a number line.

2
Drill 16

• Simplify
• 1. 6s 2r 3r s
• 2. 9(a 2b) 2a
• Evaluate if a 5, b 4, and c 3
• 3. 3ac bc
• 4. b c 2ab

3
Drills and Classwork

• Put your drills and classwork on a separate sheet
  of paper each day.
• The drills and classwork from one day will be
  collected each unit.

4
Create Groups!

• Group the following numbers together
• at least 3 different groups
• Name each group according to characteristics
• 3 -15 15.3 17 280
• -5 -12 10 11.0 -280
• ½ 0 ¾ - ¼ 6.253

5
The Number Line (1.)

• Definition A line with equal distances marked
  off to represent numbers.
• Example
• Number lines should have arrows on each end to
  indicate that they go on forever.
• We use a number line to add and subtract numbers.
  
• Number lines are a one dimensional graph.

-3
-2
-1
0
1
2
6
Use the Number Line to add and Subtract Numbers

• Show the similarity
• 5 -3
• 5 3
• Show the difference
• -6 3
• -6 3

7
Venn Diagram for Real Numbers(2.)

• Reals, R
• I irrationals
• Q rationals
• Z integers
• W wholes
• N naturals

Q
I
Z
W
N
8
Sets

• Properties of sets
• Defined by braces
• Contain numbers or objects (such as ordered
  pairs) separated by commas
• They help us group things together (they are like
  a container).

9
Natural Numbers (N)(3.)

• Definition The set of counting numbers,
  starting at 1, and including all the positive
  whole numbers. 1, 2, 3, 4, 5, 6, 7, 8, 9,
• means that it continues on to infinity.
• The natural numbers are a set of numbers.

10
Whole Numbers (W)(4.)

• Definition The set of numbers that includes all
  the Natural numbers, and 0.
• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
• What is the difference between Natural numbers
  and Whole numbers?
• Is 0 a natural number? Is 0 positive or negative?

11
Integers (Z) (5.)

• Definition The set of numbers that includes all
  the Whole numbers and all the negative Natural
  numbers.
• , -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6,
  
• The set of integers starts at negative infinity,
  and counts by ones all the way to positive
  infinity.

12
Venn Diagram for Real Numbers

• Reals, R
• I irrationals
• Q rationals
• Z integers
• W wholes
• N naturals

Q
I
Z
W
N
13
Examples
Sets Examples
Natural Numbers (N) 1, 2, 3, 4, 5, 6, 7, 8, 9,
Whole Numbers (W) 0, 1, 2, 3, 4, 5, 6, 7, 8,
Integers (Z) -4, -3, -2, -1, 0, 1, 2, 3, ...
14
Classwork (16)

• Name the set of numbers graphed. Name the set of
  numbers that each number belongs to
• 5.
• 6.

-3
-2
-1
0
1
2
-3
-2
-1
0
1
2
15
Graph and Coordinate (6., 7.)

• 6. Graph To plot a point on number line.
• 7. Coordinate The number that corresponds to a
  point on a number line.
• Name the coordinate of the point that is graphed
  on the number line below.

-3
-2
-1
0
1
2
16
Graph each set on number line ( 16)

• 7. -1, 0, 1, 2
• 8. Integers less than zero
• 9. Integers less than zero but greater than
  -6

17
Write an addition sentence

• Start at -1, add 3, subtract 5 (add negative 5)
• -1 3 5 or -1 3 -5

-5
3
-3
-2
-1
0
1
2
18
Rewind

• A number line is
• Natural Numbers are ?
• Whole Numbers are ?
• Integers are ?
• All Natural Numbers are in the set of _______ and
  _______