Analytic
Geometry
Unit 4: Extending the
Number System
Excerpts from Georgia Department of
Education Webinar May 8, 2013
melissa.stewart@hallco.org
May 2013
Warm-Up
Complete the following tables:
Based on the information from your chart, conjecture which of the
statements is ALWAYS true, which is SOMETIMES true, and which is NEVER
true.
• The sum of a rational number and a rational number is rational.
• The sum of a rational number and an irrational number is
irrational.
• The sum of an irrational number and an irrational number is
irrational.
• The product of a rational number and a rational number is
rational.
• The product of a rational number and an irrational number is
irrational.
• The product of an irrational number and an irrational number is
irrational.
melissa.stewart@hallco.org
May 2013
Answers:
• The sum of a rational number and a rational number is rational.
•
ALWAYS true.
The sum of a rational number and an irrational number is
irrational.
•
ALWAYS true.
The sum of an irrational number and an irrational number is
irrational.
SOMETIMES true (
•
•
The product of a rational number and a rational number is
rational.
ALWAYS true
The product of a rational number and an irrational number is
irrational.
SOMETIMES true (
•
)
)
The product of an irrational number and an irrational number is
irrational.
SOMETIMES true (
)
melissa.stewart@hallco.org
May 2013
What’s the main idea of Unit 4?
•
•
•
•
Extend the properties of exponents to rational exponents.
Use properties of rational and irrational numbers.
Perform arithmetic operations on polynomials.
Perform arithmetic operations with complex numbers.
Concepts & Skills to Maintain from Previous Grades
 number sense
 computation with whole numbers and integers, including
application of order of operations
 operations with algebraic expressions
 simplification of radicals
 measuring length and finding perimeter and area of
rectangles and squares
 laws of exponents, especially the power rule
Websites to help with the above:
http://www.crctlessons.com/
www.aplusmath.com
www.aaamath.com
melissa.stewart@hallco.org
May 2013
Enduring Understandings from this Unit
 Nth roots are inverses of power functions. Understanding the
properties of power functions and how inverses behave
explains the properties of nth roots.
 Real-life situations are rarely modeled accurately using
discrete data. It is often necessary to introduce rational
exponents to model and make sense of a situation.
 Computing with rational exponents is no different from
computing with integral exponents.
 The complex numbers are an extension of the real number
system and have many useful applications.
 Addition and subtraction of complex numbers are similar to
polynomial operations.
melissa.stewart@hallco.org
May 2013
Examples & Explanations
Problem 1:
(a)A biology student is studying bacterial growth. She was surprised to find
that the population of the bacteria doubled every hour.
Complete the following table:
(b) The student conducting the study wants to create a table with more
entries; specifically, she wants to fill in the population at each half hour.
However she forgot to make these measurements so she wants to estimate
the values.
Complete the following table:
Answer:
(c)What if the student wanted to estimate the population every 20 minutes
instead of every 30 minutes. What multiplier would be necessary to be
consistent with the population doubling every hour?
Complete the following table:
Answer:
(d) Use the population context to explain why it makes sense that we define
to be
and
to be
melissa.stewart@hallco.org
May 2013
Answer: The equation for the population
is
.
melissa.stewart@hallco.org
May 2013
Problem 2: A garden is created so that the garden bed is seven yards
more than twice the width of the bed. A walkway is created around the
garden that is 2 yards wide. Write an expression that represents the area of
the walkway surrounding the garden.
Area of large rectangle – Area of small rectangle
melissa.stewart@hallco.org
May 2013
Problem 3: Rewrite each of the following expressions involving complex
numbers in the form
where
and
are real numbers.
A.
B.
C.
D.
E.
melissa.stewart@hallco.org
May 2013
Answers:
A.
B.
melissa.stewart@hallco.org
May 2013
C.
D.
melissa.stewart@hallco.org
May 2013
 Websites to assist and enrich:
-
http://brightstorm.com/search/?k=polynomials
http://brightstorm.com/search/?k=rational+exponents
http://brightstorm.com/search/?k=complex+numbers
http://www.khanacademy.org/search?page_search_query=comp
lex+numbers
- http://www.khanacademy.org/search?page_search_query=polyn
omials
 The student edition for Unit 4 can be
found at
https://www.georgiastandards.org/C
ommon-Core/Pages/Math-9-12.aspx
On the left side, please look under
mathematics, Accelerated Geometry
B/Advanced Algebra. Then, the right
side has a pull-down menu to access
the units.
 Additional parent guides will be
posted to the parent resource page on
http://www.hallco.org/boe/index.ph
p (right hand menu) as they become
available.
melissa.stewart@hallco.org
May 2013