Download Chapter 3 3.1 3.2 Compare and Order Integers

Chapter 3
This study sheet provides students and parents with the basic concepts of each chapter. Students still need to apply these skills in
context. They need to know when to apply each concept, often after working through a word problem, table, chart, or graph. Some
problems may be more challenging than the ones shown here, but students first need to understand these basic concepts. There
th
are usually several ways to solve a math problem, but this guide will show you the easiest way for 6 graders. The sections are listed
in the order that I plan on teaching them, and that is subject to change. We do not use every section of the textbook.
Click on the blue links to navigate through the study guide. You can also view videos at Khan Academy and Virtual Nerd.
Section
Topic:
3.1
Understand Positive and Negative Numbers
Integers include whole numbers and their opposites. They can be positive or
negative.
Two numbers are opposites if they are the same distance from 0 on a number line,
but on opposite sides of 0.
Example: What is the opposite of -3?
Step 1 Graph the integer
-3 is a negative number so we must graph it 3 steps to the left of zero.
Step 2 Now, graph the number’s opposite on a number line.
Common errors to
avoid:
Try this problem
on another sheet
of paper:
Be sure to use the
correct words. The
number -2 is read
“negative two” not
“minus two.”
Name the
integer that
represents the
following
situation.
Using words such as
minus and plus to
describe negative
and positive
numbers can
become confusing
when subtracting,
adding and
comparing negative
and positive
numbers.
“Sam lost 7 lbs.
after two
months of
dieting. “
Practice
more at
these
websites:
Integers
and
Number
Lines
IXL.com
Graph this
number and its
opposite on a
number line.
Since -3 is three places to the left of 0, its opposite (3) will
be three places to the right of zero.
Answer
Number lines can also be vertical, like this
On a vertical number line, positive numbers are located at the top
and negative numbers are located at the bottom.
Section
Topic:
3.2
Compare and Order Integers
To compare integers and order integers, place them on a number line.
Integers to the right are greater, and integers to the left are less.
Compare the following numbers on a number line.
3, -6, 1, 5, -9, -2
We can see the correct least-to-greatest order is
-9 < -6 <-3 < -2 < 1 < 3 < 5
On a vertical number line, the numbers located at the bottom
are less and the numbers located at the top are greater.
Common errors to
avoid:
Don’t forget to
look at the sign of
each number when
comparing
integers.
-4 < 3
Negative 4 is less
than 3.
Try this problem
on another sheet
of paper:
Practice
more at
these
websites:
Space
Race
Order the
following
integers from
greatest to least.
15, -20, 0, -2, -6
Answer
IXL.com
Section
Topic:
3.4
Compare and Order Rational Numbers
In the same way we can compare and order Integers with a number line
(Lesson 3.2), you can also use a number line to compare and order rational
numbers. Rational numbers include decimals and fractions.
-
-
-
Common errors to
avoid:
Try this problem
on another sheet
of paper:
When comparing
and ordering
rational numbers,
don’t forget to
look at the signs
for each number.
Negative numbers
will always be less
than positive
numbers.
1. Compare.
Write < or >
Practice
more at
these
websites:
Compare
Jeopardy
Math Games
IXL.com
2. Order the
numbers from
least to greatest.
1.3, -4 , -
Answer
Section
Topic:
3.5
Absolute Value
Absolute value is a number’s distance from zero on a number line.
For example, the absolute value of -2 is 2, since -2 is 2 steps from zero.
The absolute value of +3 is 3, since +3 is 3 steps from zero.
Common errors to
avoid:
The absolute value
of a number is
always positive.
Do not simply find
the opposite of a
number when
finding the
absolute value.
Try this problem
on another sheet
of paper:
Find the
absolute value.
1.|-3
| = ____
2.|8.56|= ____
Practice
more at
these
websites:
Absolute
Value
Millionaire
Absolute
Value
Balloons
Common Error:
| |≠Correct Answer:
Answer
| |=
Section
Topic:
3.6
Compare Absolute Value
We can use absolute value to compare many situations in the real world.
The table below shows the weight changes of three dogs.
If we take the absolute value of each weight change, we can compare the
changes and find which dog’s weight changed the most, no matter if it’s a
gain or a loss.
Duffy |1.3| = 1.3 lbs. Buddy |-1.1| = 1.1 lbs. and Dinah |-1.4| = 1.4 lbs.
So, Dinah’s weight changed the most (1.4 lbs.).
Common errors to
avoid:
Try this problem
on another sheet
of paper:
Practice
more at
these
websites:
Write down the
actual value of
each number in
order to compare
them!
A school of fish
were swimming at
the same depth.
Fish #1 dove to a
depth of -15 feet.
Fish #2 rose 18
feet toward the
surface and Fish #3
dove to a depth of
-19 feet. Which
fish had the
greatest change in
depth?
Compare
Absolute
Values
Answer
Absolute
Value
Boxes
Section
Topic:
3.7
Rational Numbers and the Coordinate Plane
Common errors to
avoid:
Try this problem
on another sheet
of paper:
An ordered pair is a pair of numbers such as (5, -2).
To plot the ordered pair (5, -2):
First, start at 0 on the x-axis and
because 5 is a positive number,
we will count 5 units to the right.
Remember,
x-coordinate is
graphed first, then
the y-coordinate is
graphed.
Graph and label
the following
ordered pairs.
Practice
more at
these
websites:
Coordinate
Soccer
Find the
Alien
A (-3, 6)
B (1.5, -2.5)
Second, starting at 5 on the
x-axis we will count down 2 units
because our y-coordinate is a
negative number (-2).
Answer
(5, -2)
Sometimes we can take a
fraction of a step, such as a half
step.
Section
Topic:
3.8
Ordered Pair Relationships
Common errors to
avoid:
Try this problem
on another sheet
of paper:
Practice
more at
these
websites:
Quadrant
Basketball
There are four regions in a coordinate plane. They are separated by the
x-axis and y-axis.
These four regions are called quadrants. Quadrants are numbered using
Roman numerals I, II, III and IV. (1, 2, 3 and 4).
We say that the point (1, 4) is
located in Quadrant I and the
point (3, -4) is located in
Quadrant IV.
Quadrant I starts in
the top right of the
coordinate grid
and moves
counterclockwise
until you reach
Quadrant IV.
Draw a giant Cshape on the grid,
and you will pass
through the
quadrants in order.
Name the
quadrants that
the following
coordinate pairs
are in.
A (-3, -2)
B (2, 5)
C (-4, 1)
D (3, -5)
Answer
IXL.com
Section
Topic:
3.9
Distance on the Coordinate Plane
We can use a coordinate plane as a map to find distance between two
points.
Common errors to
avoid:
The easiest way to
find distance is to
draw in each step
and count them.
Try this problem
on another sheet
of paper:
Find the distance
between (-3,5)
and (4,5).
Example: Find the distance between (4, -2)
and (4, 3).
Step 1: Graph the points.
Step 2: Count the distances between the two
points along a straight line.
Step 3: Double check!
Answer
Practice
more at
these
websites:
Distance
Game
IXL.com
Section
Answer
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3.1
Sam lost 7 lbs. So the integer that would
represent the situation is -7. The opposite
of -7 is 7.
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Section
Answer
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3.2
Order the following integers from greatest to least.
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15 > 0 > -2 > -6 > -20
(Remember it said “greatest to least” not “least
to greatest”.)
Section
Answer
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3.4
1. Compare. Write < or >
<
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because - is farther to the right on a
number line.
2. Order the numbers from least to greatest.
- 4 < - < 1.3
Section
Answer
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3.5
Find the absolute value.
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1.|-3
|= 3
2.|8.56|= 8.56
Section
Answer
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3.6
A school of fish were swimming at the same depth. Fish #1 dove to a depth
of -15 feet. Fish #2 rose 18 feet toward the surface and Fish #3 dove to a
depth of -19 feet. Which fish had the greatest change in depth?
Click to return to the study guide.
Fish
Fish #1
Fish #2
Fish #3
|-15| = 15
|18| = 18
|-19| = 19
Change in depth (ft.)
-15
18
-19
Fish #3 had the greatest change in depth (19 ft.).
Section
Answer
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3.7
Graph and label the following ordered pairs.
A (-3, 6)
B (1.5, -2.5)
A (-3, 6)
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B (1.5, -2.5)
Section
Answer
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3.8
Name the quadrants that the following coordinate pairs are in.
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A (-3, -2) – Quadrant III (3)
B (2, 5) – Quadrant I (1)
C (-4, 1) – Quadrant II (2)
D (3, -5) – Quadrant IV (4)
Section
Answer
Return to Study Guide
3.9
The distance between (-3, 5) and (4, 5) is 7 units.
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