Download Integers and the Coordinate Plane

Name ________________________________________ Date __________________ Class__________________
SECTION
9A
Integers and the Coordinate Plane
SECTION A Family Letter: Understanding Integers
Dear Family,
Vocabulary
The student will begin the study of an important set of
numbers called integers.
These are the math
words we are learning:
Integers are the set of numbers that include all positive and
negative whole numbers. The student will learn how to graph
integers on a number line.
Name a positive or negative number to represent
each situation.
A. a gain of 2 points in the stock market
Positive numbers can represent gains or increases.
2
B. a 15 yard penalty in football
Negative numbers can represent losses or decreases.
15
The student will graph integers and their opposites on a
number line.
Opposites are two numbers that are an equal distance from
zero on a number line.
Graph the integer 6 and its opposite on a number line.
© Houghton Mifflin Harcourt Publishing Company
6 is the same distance from 0 as 6.
Absolute value represents the distance from zero an integer
is on a number line. The absolute value of a number is always
positive because it reflects a distance, which is always a
positive value. Therefore, opposites always have the same
absolute value.
absolute value an
integer’s distance from
0 on a number line; the
symbol for absolute
value is | |.
coordinates the
numbers in an ordered
pair that locate a point
on a coordinate plane
integers the set of all
whole numbers and
their opposites
negative number
integer less than zero
opposites two
numbers that are an
equal distance from
zero on a number line
origin the point where
the x-axis and y-axis
intersect on the
coordinate plane
positive number
integer greater than
zero
quadrants the four
areas created by the
axes on a coordinate
plane
Use the number line to find the absolute value of 3.
3 is 3 units from 0, so |3|  3.
9-1
Holt McDougal Mathematics
Name ________________________________________ Date __________________ Class__________________
SECTION
9A
Integers and the Coordinate Plane
SECTION A Family Letter: Understanding Integers continued
The student will also learn to compare and order integers.
It is important to remember that negative numbers are
ALWAYS less than positive numbers.
Use the number line to compare each pair of integers.
Write  or .
5 ___ 3
5 is to the left of 3 on the number line.
5  3
This is just the beginning of the student’s involvement with integers.
Understanding the concept of positive and negative values is
important as the student continues in mathematics.
© Houghton Mifflin Harcourt Publishing Company
Sincerely,
9-2
Holt McDougal Mathematics
Name ________________________________________ Date __________________ Class__________________
SECTION
9A
Integers and the Coordinate Plane
SECTION A At-Home Practice: Understanding Integers
Name a positive or negative number to represent each situation.
1. a loss of 15 yards in football ________
2. an increase of 52 points ________
Graph each integer and its opposite on a number line.
3. 10
4. 8
________________________________
______________________________
Use the number line to find the absolute value of each integer.
5. |4|
________________________
6. |6|
7. |9|
________________________
______________________
Use the number line to compare each pair of integers. Write  or .
8. 0 _________ 5
9. 3 _________ 5
10. 2 _________ 4
Order, the integers in each set from least to greatest.
© Houghton Mifflin Harcourt Publishing Company
11. 6, 2, 4
______________________________________________________________________________________
12. 0, 5, 7
______________________________________________________________________________________
13. 9, 8, 1, 1
______________________________________________________________________________________
Answers: 1. 15 2. 52 3.
4.
5. 4 6. 6, 7. 9 8.  9. 
10.  11. 6, 4, 2 12. 7, 5, 0 13. 9, 1, 1, 8
9-3
Holt McDougal Mathematics
Name ________________________________________ Date __________________ Class__________________
SECTION
9A
Integers and the Coordinate Plane
SECTION A Family Fun: Integer Game
Objective
The objective is to collect all of the cards in the deck.
Materials
Deck of cards
Directions
Deal out the entire deck. Make sure the cards are face down.
Every round is played the same way: each player turns over the top
card in his or her hand. The player who has the card with the
greatest value takes all the cards played that round.
However…
• Each black card holds a positive value with the aces being the
least value and the kings being the greatest value.
• Each red card holds a negative value with the aces having the
greatest value and the kings having the least value.
If there is a tie or a round where two cards with the same value are
played, each player deals out 3 cards face down. The last card dealt
is turned over. The player with the card with the greatest value takes
all the cards that round.
The winner is the player who ends up with all the cards or who has
the greatest number of cards at the end of the game.
9-4
Holt McDougal Mathematics
© Houghton Mifflin Harcourt Publishing Company
For example: If a red 7 and a black 2 are turned over, the player with
the black 2 will win that round because 2  7.
Name ________________________________________ Date __________________ Class__________________
SECTION
9B
Integers and the Coordinate Plane
SECTION B Family Letter: Understanding Integers
Dear Family,
Vocabulary
Now that the student has a basic understanding of integers,
he or she will be introduced to the coordinate plane. The
student will graph or name points in all four quadrants of the
coordinate plane.
These are the math
words we are learning:
Give the coordinates of point D.
coordinates the
numbers in an ordered
pair that locate a point
on a coordinate plane
axes the two number
lines in a coordinate
plane
coordinate plane
formed by two number
lines in a plane that
intersect at right angles
at zero on each number
line
origin the point where
the x-axis and y-axis
intersect on the
coordinate plane
From the origin, D is three units to the right and 2 units down.
(3, 2)
quadrants the four
areas created by the
axes on a coordinate
plane
© Houghton Mifflin Harcourt Publishing Company
x-axis the horizontal
axis on the coordinate
plane
x-coordinate the first
number in an ordered
pair
y-axis the vertical axis
on the coordinate plane
y-coordinate the
second number in an
ordered pair
9-21
Holt McDougal Mathematics
Name ________________________________________ Date __________________ Class__________________
SECTION
9B
Integers and the Coordinate Plane
SECTION B Family Letter: Understanding Integers continued
When a polygon is graphed in the coordinate plane, the student can find the
length of the sides of the polygon using the units of the grid for any sides that are
parallel to either axes.
In the graph below, the vertices of the polygon are at A(–3, 4), B(2, 4), C(2, –1)
and D(–3, –1).
A
B
D
C
The length of AB is 5 units. The length of DC is 5 units.
The length of AD is 5 units. The length of BC is 5 units.
By knowing the lengths of the sides of the polygon graphed, the student can now
classify the polygon as a square because all four sides have the same length. The
student is also able to find the perimeter of the square by adding the lengths of the
sides, 5 + 5 + 5+ 5 = 20. Square ABCD has a perimeter of 20 units.
Sincerely,
9-22
Holt McDougal Mathematics
© Houghton Mifflin Harcourt Publishing Company
Because segments AB and DC are horizontal lines (parallel to the x-axis and
segments AD and BC are vertical lines (parallel to the y-axis), their lengths are
found by counting the units.
Name ________________________________________ Date __________________ Class__________________
SECTION
9B
Integers and the Coordinate Plane
SECTION B At-Home Practice: Understanding Integers
Graph each set of vertices on a coordinate plane and answer the questions.
1. A polygon has vertices at (2, 0), (6, 0), (3,
6), and (6, 6). What type of polygon is this?
What is its perimeter?
© Houghton Mifflin Harcourt Publishing Company
2. A polygon has vertices at (–2, –2), (4, –2),
(–2, 4), and (4, 4). What type of polygon is
this? What is its perimeter?
Answers: 1.
rectangle; 14 units 2.
square; 24 units.
9-23
Holt McDougal Mathematics
Name ________________________________________ Date __________________ Class__________________
SECTION
9B
Integers and the Coordinate Plane
SECTION B Family Fun: Graphing the Living Room
After you have made a graph of the living room, have everyone in the house go to the
living room and sit down. Now, mark the location of each person on your graph using an
X and the name of the ordered pair. Label each ordered pair with a letter for that
person’s name.
9-24
Holt McDougal Mathematics
© Houghton Mifflin Harcourt Publishing Company
Use the coordinate plane to make a diagram of the living room in
your house. Include a rectangle for a couch, a square for a chair, and
either a rectangle or a square for any tables.