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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