Integers

1
Integers
2
Objectives

• To learn what is meant by
• the word integer.

2. To learn a visual representation of adding
integers.
3
Integers
Real Numbers
Rational numbers -6,0,-2/3, 25/7,
7 1/12

Algebraic Numbers
in theNumber System
Integers -2,-1,0,1,2,3,
Whole numbers 0,1,2,3,4,
Natural numbers 1,2,3,4,
4
Integers

• Judith has a cell phone plan that allows her to
  talk 25 anytime minutes.
• She uses her cell phone to speak to Nestor for 15
  minutes.
• She uses it again to talk 20 minutes to Markus.
• How many minutes did Judith talk on her cell
  phone?
• Does Judith have minutes left on her plan?
• Why?

5
Integers Real World Connections

• Judith has a cell phone plan that allows her to
  talk 25 anytime minutes.
• She uses her cell phone to speak to Nestor for 15
  minutes.
• She uses it again to talk 20 minutes to Markus.
• How many minutes did Judith talk on her cell
  phone?
• How many minutes are left on her plan (without
  rollover) or how many minutes did she go over her
  allowed minutes?
• How can this number be labeled on the graph?

35
10 minutes over
6
Integers Real World Connections

• Team Peitgen and Team Voss are playing a game of
  football.
• Team Peitgen throws a pass from their 5 yard line
  and the pass is completed for 40 yards.
• If their quarterback is sacked and loses 20
  yards, how many total yards were gained on the
  two plays combined?

7
Integers Real World Connections

• Team Peitgen and Team Voss are playing a game of
  football.

8
Integers Real World Connections
Team Peitgen throws a pass from their 5 yard line
and the pass is completed for 40 yards.
If their quarterback is sacked and loses 20
yards, how many total yards did they gain on the
two plays combined?

9
Integers Real World Connections

• Ana enters the elevator from the basement of the
  parking garage and takes it to the 11th floor for
  lecture.
• She takes the elevator two floors down for a
  workshop.
• On what floor will Ana be if she then goes down
  seven floors for a snack.
• How many flights did she travel in total (up and
  down)?

10
Integers Real World Connections

• Ana enters the elevator from the basement of the
  parking garage and takes it to the 11th floor for
  lecture.
• She takes the elevator two floors down for a
  workshop.
• On what floor will Ana be if she then goes down
  seven floors for a snack.
• How many flights did she travel in total (up and
  down)?

11
Adding Integers Number Line
4 4
Answer 8
12
Adding Integers Number Line
3 (-5)
Answer -2
13
Number Line - Rules

• Counter starts at zero (0)
• Counter moves right for each positive number
• Counter moves left for each negative number
• The answer is where the counter ends on the
  number line.

14
Integers Number Line

• Worksheet and Board Activities

15
(No Transcript)
16
Integers with Counter
3 (-6)
3
-6
-3
17
Counter - Rules

• Green represent positive numbers
• Red represent negative numbers
• One color cancels out the other
• Ex. One red cancels out one green
• The number of the items left is the answer and
  the color represents the sign.

18
Integers Counter

• Worksheet and Board Activities

19
Integers with Counter
20
Adding Integers Same Sign Rules

• When adding numbers of the same signs, add the
  numbers, and keep the sign.
• Example 1 3 4 7 Since the signs of both
  numbers are positive, the answer is positive.
• Example 2 (-4) (-2) -6 Since the signs
  of both numbers are negative, the answer is
  negative.

21
Adding Integers Different Sign Rules

• When adding numbers of the opposite signs, take
  their absolute values, subtract the smaller from
  the larger, and give the result the sign of the
  number with the larger absolute value.
• Example 1 7 (-4) 7 - 4 3 Since the
  larger absolute value was 7, give the result the
  same sign as 7, which is positive. Answer is 3.
• Example 2 2 (-6) 6 - 2 4 Since the
  larger absolute value was 6, give the result the
  same sign as -6, which was negative. Answer is
  -4.

22
Adding Integers

• Dynamic Worksheet Activity
• (GeoGebra)