Download Algebra 2 Real and Complex Numbers

HARNETT COUNTY HIGH SCHOOLS
Course: Algebra 2
Title of Unit: Real and Complex Numbers
Timeframe: 5-7 days
Content Area Standard(s): CC.9-12.N.RN.3, CC.9-12.N.RN.1, CC.9-12.N.RN.2,
CC.9-12.N.CN.1, CC.9-12.N.CN.2, CC.9-12.N.CN.3(+), CC.9-12.N.CN.7, CC.912.A.REI.4, CC.9-12.A.REI.4b
Reading Standard(s): 3, 4, 5, 7, 9
Writing Standard(s): 1, 4, 5, 10
Math Practice(s): 3, 6, 7,
Technology Standard(s): HS.TT.1, HS.SE.1
Learning Experiences: cooperative learning, discovery, vocabulary
write/talk/draw, internet research, story writing
Project Goals and Description of Unit: In this unit, you will take a closer look at
the set of real numbers by investigating closure properties of its two subsets,
rational and irrational numbers. You will also learn different ways to express
irrational numbers using radical notation and rational exponents. By defining  1
as a new type of number called the imaginary unit, you will create a new set of
numbers called the imaginary numbers. Just as rational and irrational numbers
together form the set of real numbers, imaginary numbers and real numbers
together form the set of complex numbers. You will learn how to perform
operations with complex numbers, and you will see how complex numbers allow
you to solve quadratic equations that you weren’t able to solve in Algebra 1.
Essential Questions:
In which subset of real numbers does the sum or product of a rational number and
an irrational number belong?
How are radicals and rational exponents related?
How do you add, subtract, and multiply complex numbers?
How can you use conjugates to find the absolute value of a complex number and
to divide complex numbers?
When does a quadratic equation have imaginary solutions, and how do you find
them?
Vocabulary: properties of real numbers, closed, indirect proof, radical expression,
properties of rational exponents, imaginary unit, complex number, imaginary
number, pure imaginary number, conjugate, absolute value, discriminant, quadratic
formula
Instructional Resources (print materials, technology):
Students compose a story that uses the properties of the complex number system,
Complex Numbers Webquest: CC.9-12.N.RN.3, CC.9-12.N.RN.1, CC.912.N.RN.2, CC.9-12.N.CN.1, CC.9-12.N.CN.2, CC.9-12.N.CN.3(+), CC.912.N.CN.7, CC.9-12.A.REI.4, CC.9-12.A.REI.4b
https://sites.google.com/site/complexnumberswebquest/home
TI Activity Complex Numbers: CC.9-12.N.CN.1, CC.9-12.N.CN.2
http://education.ti.com/calculators/downloads/US/Activities/Detail?id=10887
Imaginary Numbers Lesson Plan: CC.9-12.N.RN.3, CC.9-12.N.RN.1, CC.912.N.RN.2, CC.9-12.N.CN.1, CC.9-12.N.CN.2, CC.9-12.N.CN.3(+), CC.912.N.CN.7, CC.9-12.A.REI.4, CC.9-12.A.REI.4b
http://alex.state.al.us/lesson_view.php?id=26396
http://alex.state.al.us/lesson_view.php?id=11364
Applications of Imaginary Numbers to the Real World: CC.9-12.N.CN.1, CC.912.N.CN.2, CC.9-12.N.CN.3(+), CC.9-12.N.CN.7, CC.9-12.A.REI.4, CC.912.A.REI.4b
http://www.picomonster.com/
On Core Activity Generator – Algebra 2 – 9-12.N.RN.1 – A2 6.1 Exploring Roots
and Rational Exponents A, B, C
On Core Activity Generator – Algebra 2 – 9-12.N.RN.1 – A2 6.2 Algebra Game
On Core Activity Generator – Algebra 2 – 9-12.N.RN.2 – A2 6.6 Solving Radical
Equations A, B, C
Many more available in On Core Activity Generator
Khan Academy Videos
Facilitator’s Role: lecture, guided instruction, assign cooperative group job
responsibilities, monitor student progress, facilitate learning
Assessment:
Teacher made quizzes and tests (On Core Mathematics – Examview),
Matching activity for number types,
Activity Generator - Performance Assessment: Algebra 2 – Rational Exponents
and Radical Functions Journal Activity
Notes and Additional Information: Pending initial instruction of unit