NJCTL



Progressive Mathematics Initiative Mathematics CurriculumUnit Plan # 5Title: RadicalsSubject: Algebra 2Length of Time: 3 weeksUnit Summary: The unit covers roots, radicals, complex numbers, notation, operations with, graphing and solving equations. Students learn to convert between rational exponents and radical form, write roots in simplest terms, and perform operations with roots. Students will be introduced to the imaginary number i and perform operations with it. The graphing of square roots will be done and students will graph more complicated radical functions.Learning TargetsConceptual Category: Number and Quantity Domain: The Real Number SystemsCluster: Extend the properties of exponents to rational exponents.N-RN.1Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.N-RN.2Rewrite expressions involving radicals and rational exponents using the properties of exponents.Conceptual Category: Number and Quantity Domain: The Complex Number SystemsCluster: Perform arithmetic operations with complex numbers.N-CN.1Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real.N-CN.2Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.Conceptual Category: Algebra Domain: Reasoning with Equations and InequalitiesCluster: Understand solving equations as a process of reasoning and explain the reasoningA-REI.12Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.Conceptual Category: Algebra Domain: Seeing Structure in ExpressionsCluster: Interpret the structure of expressionsA-SSE.1Interpret expressions that represent a quantity in terms of its context.Conceptual Category: Functions Domain: Interpreting FunctionsCluster: Analyze functions using different representationsF-IF.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated casesConceptual Category: Functions Domain: Building FunctionsCluster: Build a function that models a relationship between two quantitiesF-BF.1Write a function that describes a relationship between two quantities.Cluster: Build new functions from existing functionsF-BF.3Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs.Unit Essential Question:HowHow can knowing that roots and exponents are inverses, help in solving radical equations?Unit Enduring Understandings:The denominator of a rational exponent is the index of the radical.A radical cannot be in the denominator of a simplified expression.i=-1When solving a radical equation, the solutions need to be checked for extraneous answers.In the graph of fx=ab(x?c)±d, a is a vertical dilation or reflection, b is a horizontal dilation or reflection, c is a horizontal slide, and d is a vertical slide of fx=x.Unit Objectives:Students will be able to graph square roots and describe the transformation of the parent function.Students will be able to simplify radicals and radical expressions.Students will be able to simplify radicals with an index other than 2.Students will be able to convert rational exponents to and from radical form.Students will be able to solve radical equations and identify extraneous answers.Students will be able to simplify complex radical expressions using i.Evidence of LearningFormative Assessments: SMART Response questions used throughout the unit. 4 Quizzes Summative Assessment:Unit TestLesson PlanTopicsTimeframe (days)Topic #1: Graphing Square Root Functions2Topic #2: Working with Square Roots?Topic #3: Irrational Roots?Quiz 1 Graphing and Simplifying Roots?Topic #4: Adding and Subtracting Radicals1Topic #5: Multiplying Radicals1Topic #6: Rationalizing the Denominator1Quiz 2 Operations with Radicals?Topic #7: Cube Roots1Topic #8: nth Roots1Topic #9: Rational Exponents1Quiz 3 Indexes Other than Two?Topic #10: Solving Radical Equations1Topic #11: Complex Numbers1Quiz 4 Solving Radical Equations and complex numbers?Topic #12: Review and Unit Test2Curriculum Resources:courses/math/algebra2/ ................
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