August 15, 2019
Real numbers, absolute value, and
opposites
Agenda
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1) Bell work
2) Finish the syllabus overview
3) Note-taking process
4) Direct Instruction
5) Pairs/Trios Practice
6) Independent Practice
7) Homework reminder/announcements
8) Summarize the lesson
9) Exit Slip
Bell work
1) Please take a ruler off the table
2) Stand your name tag up on your desk
3) Download the August 15th presentation
on Canvas
4) Copy the Cornell notes’ template onto
pg. 7 of your composition notebook
5) Update your table of contents
6) Work on the note-taking homework
Encouraging Quotation
Table of Contents
1) Table of Contents
pgs. 1-2
2) Test Scores
pg. 3
3) Cornell notes’ template
pg. 4
4) Note-taking strategies(article and notes)
pg. 5
5) Abbreviations sheet
pg. 6
6) Real numbers, Absolute Value & Opposites pg. 7
1) The note-taking activity
Due Tuesday August 20th
Homework
Note-taking homework
 Mark the text by:
 Underlining note-taking tips
 Circling the most important words in each paragraph
 Take notes on pg.5 in your notebook while keeping the
essential question in mind (Essential Question: What are strategies I can use to take
better notes in school?)
 Answer the Text based questions (on loose leaf paper)
 Are notes considered a finished product or a work in process?
 Your brain’s action during note taking is compared to which object?
 What are four of the most important things to remember when taking notes?
Attention signal
Call and response
Math related
I state the first part
The class finishes the second part
I say, “Real numbers are”
The class says, “rational or irrational”
Learning target (Objective)/Essential
Question
Learning Target: Students will be
able to classify real numbers, find
absolute value, and find opposites.
Essential Question: How do you
classify real numbers, find absolute
value, and find opposites?
Standards
MAFS.6.NS.3.6a: Recognize opposite signs of
numbers as indicating locations on opposite sides of
0 on the number line; recognize that the opposite of
the opposite of a number is the number itself, e.g., –
(–3) = 3, and that 0 is its own opposite.
MAFS.6.NS.3.7c:Understand the absolute value of a
rational number as its distance from 0 on the
number line; interpret absolute value as magnitude
for a positive or negative quantity in a real-world
situation.
Standard
MAFS.8.NS.1.1: Know that numbers that
are not rational are called irrational.
Understand informally that every number
has a decimal expansion; for rational
numbers show that the decimal expansion
repeats eventually, and convert a
decimal expansion which repeats
eventually into a rational number.
The Real Number System
The Real Number System
Real Numbers
 Real numbers consist of all the rational and irrational numbers.
 The real number system has many subsets:
◦ Natural Numbers
◦ Whole Numbers
◦ Integers
 Rational Numbers
 Irrational Numbers
Natural Numbers
Natural numbers are the set of
counting numbers.
{1, 2, 3,…}
Whole Numbers
Whole numbers are the set of
numbers that include 0 plus the set
of natural numbers.
{0, 1, 2, 3, 4, 5,…}
Integers
Integers are the set of whole
numbers and their opposites.
{…,-3, -2, -1, 0, 1, 2, 3,…}
Rational Numbers
Rational numbers are any numbers
a
that can be expressed in thebform of
, where a and b are integers, and b ≠
0.
They can always be expressed by
using terminating decimals or
repeating decimals.
Terminating Decimals
Terminating decimals are decimals that
contain a finite number of digits.
Examples:
36.8
0.125
4.5
Repeating Decimals
 Repeating decimals are decimals that contain a infinite
number of digits.
 Examples:
 0.333…

1.9
 7.689689…
FYI…The line above the decimals indicate that number
repeats.
Irrational Numbers
 Irrational numbers are any numbers that cannot be
expressed as
.
a
b
 They are expressed as non-terminating, non-repeating
decimals; decimals that go on forever without repeating a
pattern.
 Examples of irrational numbers:
 0.34334333433334…
 45.86745893…
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(pi)
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
2
Other Vocabulary Associated with the Real
Number System
 …(ellipsis)—continues without end
 { } (set)—a collection of objects or numbers. Sets are notated
by using braces { }.
 Finite—having bounds; limited
 Infinite—having no boundaries or limits
 Venn diagram—a diagram consisting of circles or squares to
show relationships of a set of data.
Example
Classify all the following numbers as natural, whole, integer,
rational, or irrational. List all that apply.
a. 117
b. 0
c. -12.64039…
d. -½
e. 6.36
f.
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g. -3
Venn Diagram of the Real Number System
Rational Numbers
Irrational Numbers
Your Turn
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When taking the square root of any number
that is not a perfect square, the resulting
decimal will be non-terminating and nonrepeating. Therefore, those numbers are
always irrational.
FYI…For Your Information
Absolute value
Example
Practice Problems
Opposites
Examples
Practice problems
Question
How are absolute value
and opposites similar?
Exit Slip (Homework)
.
I can classify all the following numbers
as natural, whole, integer, rational, or
irrational, find their absolute value, and
find their opposites.
15, 0, -11.53148…, -1/4, 4.24, 8
Have a great day!