Download Graphing Integers, Opposites, Absolute Value

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INTEGERS AND RATIONAL NUMBERS: GRAPHING, OPPOSITES, ABSOLUTE VALUE, AND COMPARING
Opening Problem:
Directions: Represent each phrase as a positive or negative number. Put each of the numbers on the number line
below. Label each number with its corresponding letter.
A. a gain of 5 yards ______
B. a profit of $10 ______
C. 5 ft. below sea level ______
D. 20 ft. above sea level ______
E. a loss of 15 pounds ______
F. 10° below zero ______
0
What is an integer?
Graphing Integers
Directions: Graph the following integers on a number line. Label each point.
1. A: 0, B: – 6, C: 4, D: – 2, E: 1
2. A: – 8, B: 6, C: 0, D: –14, E: 10
3. A: 5, B: –10, C: 25, D: –5, E: 15
Graphing Rational Numbers
1
1
3
4. A: – 6 , B: – 6 , C: – 6 , D: – 6
4
2
4
5. A: – 6.2, B: – 6.4, C: – 6.8, D: – 6.7
What does it mean to graph a number?
Comparing
Directions: Compare each set of numbers below using <, >, or =.
1. 9 ___ 4
9. –
1
3
___–
2
4
10. –
7
6
___–
8
7
2. 8 ___ 0
3. – 9 ___ 4
4. – 8 ___ – 7
5. –14 ___–16
6. 0 ___ – 4
7. – 9.1___– 9
11. – 4.1 ___ – 4.01
12. – 3 ___ – 3.1
13. – 8.7 ___ – 8.77
14. – 9.08 ___ – 9.008
1
8. – 6 ___– 6
4
Ordering
Directions: Put the following numbers in order from least to greatest.
1. – 6, – 4, – 10, 0, – 3
__________________________
2. – 3, 5, – 9, – 8, 2, 0
__________________________
3. – 10.8, – 10.3, – 10, – 10.1, – 10.01, – 10.9
__________________________
4.
7 1 3 5 3
, , , ,
8 2 4 6 8
__________________________
5. –
7
1
3
5
3
,– ,– ,– ,–
8
2
4
6
8
__________________________
Opposites
Directions: Find the opposite of each number.
1. – 6
2. 10
3. 15
4. –100
5. 0
How do you find the opposite of an integer?
Absolute Value
Directions: Find the absolute value of each number.
1.
9
2.
3
3.
7
4.
0
Comparing Part 2
11.  15 ___ 15
12.  1 ___ 1
5. 15
13.  4 ___– 4
6. –  9
7.
68
8.
x  y when x = 5 and y = 2
9.
y  4 when y = 2
10. a  b when a = 0 and b = 5
14. 8  2 ___ – 6
Word Problems
1. Put the following locations in order from highest elevation to lowest elevation.
Granite Peak, MT: 12,799 feet above sea level
New Orleans, LA: 8 feet below sea level
Death Valley, CA, 282 feet below sea level
Long Island Sound, CT, sea level
Answer:
Bonus #1: What are the names of the abbreviated states above?
The following is a list of the lowest recorded temperatures in 5 U.S. Cities during the month of January.
Chicago: – 27°
Salt Lake City: – 22°
Anchorage: – 34°
St. Cloud: – 43°
Columbus: – 22°
2. Which city has the lowest temperature ever recorded? _____________________________
3. Which city has the warmest temperature? ___________________________
4. What is the mode of the temperatures? _______
5. What is the median of the temperatures? ______
Bonus #2: What state is each city in?
6. A plane flew from a city at 30° N latitude to a city at 30° S latitude. How many degrees did it fly? _____
Bonus #3: What is the latitude of Salt Lake City?
Bonus #4: What city has the opposite latitude of Salt Lake City?
7. On a certain day, the temperature in Snowville went from 6° below zero to 3° above zero. What is the
difference in these two temperatures?
8. A neutral atom of nitrogen has _____ protons and _____ electrons. Express these charges as integers.
Protons: _____
Electrons: _____
9. Hikers climbed from 100 ft. below sea level to 275 feet above sea level. How many feet did they climb?