Download Chapter 6: Integers and the Coordinate Plane

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Hour _____________________________
Date given_________________________
Chapter 6:
Integers and the Coordinate Plane
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Chapter 6 Score Tracker
Lesson
6.1
Integers
6.2
Comparing and Ordering Integers
6.4
Absolute Value
6.5
The Coordinate Plane
6.5
Ext
Reflecting Points in the Coordinate
Plane
Assessment
1
Quiz
2
Unit Test
HW Score
Score
Lesson 6.1 – Integers
Positive Numbers = __________________________________________________________
They can be written with or without a _____________________ sign ( ______ )
Words used to stand for positive numbers:
_____________________________________________________________________________
_____________________________________________________________________________
Negative numbers = ________________________________________________________
They are written with a _______________________ sign ( _______)
Words used to stand for negative numbers:
_______________________________________________________________________
_______________________________________________________________________
The number zero is not ______________________ or ______________________.
Numbers are opposites if they are the same __________________________ from zero, but on
___________________________ sides of zero.
Examples of opposites:
______ and ______
or
______ and ______
Integers are the set of ________________ numbers and their ______________________.
Example 1: Writing Positive and Negative Integers
Write a positive or negative integer that represents the situation.
a.
A contestant gains 250 points on a game show.
_____________
b.
Gasoline freezes at 40 degrees below zero. _____________
Your Turn:
Write a positive or negative integer that represents the situation.
1. A hiker climbs 900 ft up a mountain.
2. You have a debt of $24.
3. A student loses 5 points for being late
to class.
4. A savings account earns $10.
Example 2: Graphing Integers
Graph the integer and its opposite.
a.
3
–5
–4
b.
–3
–2
–1
0
1
2
3
4
5
-2
–5
–4
–3
–2
–1
0
1
2
3
4
5
Example 3: Real-Life Application
Your turn:
Graph the integer and its opposite.
5. 6
6. -4
–10 –8
–6
–4
–2
0
2
4
6
8
10
7. -12
–14 –12 –10 –8 –6 –4 –2
8.
0
2
4
6
8 10 12 14
–5
–4
–3
–2
–1
0
1
2
3
4
5
–5
–4
–3
–2
–1
0
1
2
3
4
5
1
9. What If? In Example 3, you go up 9 floors to make the second delivery. Write an
integer that represents how you return to ground level.
Lesson 6.2 – Comparing and Ordering Integers
Symbol
What it means
An inequality means the math statement ____________________________________
Example 1: Comparing Integers on a Horizontal Number Line
Compare 2 and -6.
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
2 is to the _________________ of -6. So, 2 ______ -6.
Example 2: Comparing Integers on a Vertical Number Line
Compare -5 and -3.
-5 is ____________________ -3. So, -5 _______ -3.
Your Turn:
Copy and complete the statement using < or >.
1.
2.
3.
0 ______ -4
-8 ______ -7
-5 ______ 5
Example 3: Ordering Integers
Order -4, 3, 0, -1, -2 from least to greatest.
Graph each integer on a number line.
–5
–4
–3
–2
–1
0
1
2
3
4
5
Write the integers as they appear on the number line from left to right.
So, the order from least to greatest is ____________________________________.
Example 4: Reasoning with Integers
A number is greater than -8 and less than 0. What is the greatest possible integer value of this
number?
A. -10
B.
-7
C.
-1
D.
2
The number is great than -8 and less than 0. So, the number must be to the _____________ of
-8 and to the ______________ of 0 on a number line.
–9
–8
–7
–6
So, the correct answer is ___________.
–5
–4
–3
–2
–1
0
1
Example 5: Real Life Application
Your Turn:
4. Order the integers from least to greatest.
-2, -3, 3, 1, -1
5. Order the integers from least to greatest.
4, -7, -8, 6, 1
6. In Example 4, what is the least possible integer value of the number?
7. In Example 5, Norfolk recorded a new record low last night. The new record low is
greater than the record low in Lynchburg. What integers can represent the new record low
in Norfolk?
Lesson 6.3 – Note Taking Guide p.262
Fractions and Decimals on the Number Line
Lesson 6.4 – Absolute Value
The ________________________ ____________________ of a number is the
_____________________ between the number and ______on a number line.
absolute value
**Because distance is always positive, absolute value is always _______________________ !
Example 1: Finding Absolute Value
a.
Find the of 3.
–5
–4
–3
–2
–1
0
1
2
3
4
5
So |3| = ___________
b.
Find the absolute value of −2
–5
–4
–3
1
2
–2
–1
0
1
2
3
4
5
1
So |−2 | = ___________
2
Your Turn:
Find the absolute value.
|3|
1.
4.
1
| |
4
2.
|−6|
5.
|−7 |
1
3
3.
|0|
6.
|−12.9|
Example 2: Comparing Values
Compare 2 and |−5|.
–5
–4
–3
–2
–1
0
1
2
3
4
5
So, 2 ______|−5|
Example 3: Real-Life Application
Your Turn:
7.
Is the seagull or the shrimp closer to sea level? Explain your reasoning?
Lesson 6.5 – Coordinate Plane
A ___________________________ _________________ is formed by the intersection of a
horizontal number line (___-_____________) and a vertical number line (____-_________).
The number lines intersect at the __________________ and separate the coordinate plane
into four regions called __________________________.
An ___________________ _______________ is used to locate a point in a coordinate plane.
The first number in the ordered pair is called the _____-coordinate. It tells you to move
on the _____ axis.
The second number in the ordered pair is called the _____-coordinate. It tells you to
move on the _____ axis.
Example 1: Identifying an Ordered Pair
Point T is 3 units to the _____________ of the origin and
3 units ________________. So, the x-coordinate is _______
And the y-coordinate is ______.
Your Turn:
Use the graph in Example 1 to write an ordered pair corresponding to the point.
1. Point P
2. Point Q
3. Point R
4. Point S
Example 2: Plotting Ordered Pairs
Plot (a) (-2, 3) and (b) (0, -3.5) in a coordinate plane. Describe the location of each point.
a.
b.
Your Turn:
Plot the ordered pair in a coordinate plane. Describe the location of the point.
5. (3, −1)
6. (−5, 0)
7. (−2.5, −1)
1
1
2
2
8. (−1 ,
)
Example 3: Finding Distances in the Coordinate Plane
An archaeologist divides an area using a coordinate plane in which each unit represents 1
meter. The corners of a secret chamber are shown in the graph. What are the dimensions of
the secret chamber?
Length: _____________
Width: _____________
The secret chamber is ______ meters long and _______ meters wide.
Your Turn:
9. In Example 3, the archaeologist finds a gold coin at (−1, 4), a silver coin at (−4, 2),
and pottery at (−4, 4). How much closer is the pottery to the silver coin than to the
gold coin?
You can use line graphs to display data that is collected over a period of time. Graphing and
connecting the ordered pairs can show patterns or trends in the data. This type of line graph is
also called a time series graph.
Example 4: Real-Life Application
Write the ordered pairs:
Your Turn:
In Example 4, the blizzard hits another town at noon. The table shows the hourly
temperatures from noon to 6:00 pm.
a. Display the data in a line graph.
b. Make three observations from the graph.
Lesson 6.5 Extension –
Reflecting Points in the Coordinate Plane
You can ______________________ a point in the x-axis, in the y-axis, or in both axes.
Example 1: Reflecting Points in One Axis
Example 2: Reflecting a Point in Both Axes