Unit 5: Exponents, Radicals and Exponential Functions

Unit 5: Exponents, Radicals and Exponential Functions / Estimated Time: 4 Weeks; January 4 – February 1
CLE:
CLE 3102.2.1 Understand computational results and operations involving real numbers in multiple representations.
CLE 3102.2.2 Understand properties of and relationships between subsets and elements of the real number system
CLE 3102.3.3 Understand and apply operations with rational expressions and equations.
CLE 3102.3.9 Understand and use exponential functions to solve contextual problems.
CLE 3102.4.1 Use algebraic reasoning in applications involving geometric formulas and contextual problems.
Essential Question: Where are exponential applications evident?
Unit Vocabulary: Compound Interest, Perfect Squares, Distance Formula, Exponent, Function, Growth/Decay , Midpoint Formula, Pythagorean Theorem, Radical, Radicand, Right Triangle, Scientific Notation, Square Root, Index, Squared, Cubed, Rationalizing the Denominator
Prerequisite Skills: powers, base, non-linear, Coordinate Plane, Coordinates, Variable, Irrational Numbers, Rational Numbers
Checks for Understanding / State Performance Indicators / Assessments / Instructional Resources / Connections
ü  3102.1.1 Develop meaning for mathematical vocabulary.
ü  3102.1.2 Use the terminology of mathematics correctly.
ü  3102.1.3 Understand and use mathematical symbols, notation, and common mathematical abbreviations correctly. / SPI 3102.1.2 Write an equation symbolically to express a contextual problem. / -  Writing Expressions Worksheet: http://www.phschool.com/webcodes10/index.cfm?fuseaction=home.gotoWebCode&wcprefix=adk&wcsuffix=9901#
ü  3102.1.12 Create and work flexibly among representations of relations (including verbal, equations, tables, mappings, graphs).
ü  3102.1.13 Change from one representation of a relation to another representation, for example, change from a verbal description to a graph. / SPI 3102.1.4 Translate between representations of functions that depict real-world situations.
CLE3102.2.1
ü  3102.2.3 Operate with and simplify radicals (index 2, 3, n) and radical expressions including rational numbers and variables in the radicand.
ü  3102.2.4 Operate efficiently with both rational and irrational numbers.
ü  3102.2.5 Perform operations with numbers in scientific notation (multiply, divide, powers).
ü  3102.2.6 Use appropriate technologies to apply scientific notation to real-world problems. / SPI 3102.2.1 Operate (add, subtract, multiply, divide, simplify, powers) with radicals and radical expressions including radicands involving rational numbers and algebraic expressions.
SPI 3102.2.2 Multiply, divide, and square numbers expressed in scientific notation. / -  Radicals Worksheet: http://www.phschool.com/webcodes10/index.cfm?fuseaction=home.gotoWebCode&wcprefix=adk&wcsuffix=9901#
-  Simplifying Radicals Worksheet (with variables): http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Simplifying%20Radicals.pdf
-  Add/Subtract Radicals Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Adding+Subtracting%20Radical%20Expressions.pdf
-  Multiplying Radicals Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Multiplying%20Radical%20Expressions.pdf
-  Dividing Radicals Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Dividing%20Radical%20Expressions.pdf
-  Scientific Notation Conversions Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Writing%20Scientific%20Notation.pdf
-  Scientific Notation Operations Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Operations%20Scientific%20Notation.pdf / ACT Connections
-  Work with scientific notation.
-  Work with squares and square roots of numbers.
-  Recognize one-digit factors of a number.
-  Work with numerical factors.
-  Work problems involving positive integer exponents.
-  Work with cubes and cube roots of numbers.
CLE3102.2.2
ü 3102.2.8 Use multiple strategies to approximate the value of an irrational number including irrational square roots and including location on the real number line.
CLE3102.3.3
ü  3102.3.4 Simplify expressions using exponent rules including negative exponents and zero exponents.
CLE3102.3.9
ü  3102.3.17 Recognize “families” of functions.
ü  3102.3.19 Explore the characteristics of graphs of various nonlinear relations and functions including inverse variation, quadratic, and square root function. Use technology where appropriate.
ü  3102.3.33 Recognize data that can be modeled by an exponential function.
ü  3102.3.34 Graph exponential functions in the form y = a(bx) where b ≠ 0.
ü  3102.3.35 Apply growth/decay and simple/compound interest formulas to solve contextual problems. / SPI 3102.3.11 Analyze nonlinear graphs including quadratic and exponential functions that model a contextual situation.
CLE3102.4.1
ü  3102.4.2 Use the Pythagorean Theorem to find the missing measure in a right triangle including those from contextual situations.
ü  3102.4.3 Understand horizontal/vertical distance in a coordinate system as absolute value of the difference between coordinates; develop the distance formula for a coordinate plane using the Pythagorean Theorem.
ü  3102.4.4 Develop the midpoint formula for segments on a number line or in the coordinate plane. / SPI 3102.4.2 Solve contextual problems using the Pythagorean Theorem.
SPI 3102.4.3 Solve problems involving the distance between points or midpoint of a segment. / -  Distance Formula Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Distance%20Formula.pdf
-  Midpoint Formula Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Midpoint%20Formula.pdf / ACT Connections
-  Find the midpoint of line segment.
-  Recognize Pythagorean Triples.
Unit 6: Polynomial and Quadratic Functions / Estimated Time: 5 Weeks; February 2 – March 10
CLE:
CLE 3102.3.2 Understand and apply properties in order to perform operations with, evaluate, simplify, and factor expressions and polynomials.
CLE 3102.3.8 Solve and understand solutions of quadratic equations with real roots.
CLE 3102.3.9 Understand and use exponential functions to solve contextual problems.
CLE 3102.4.1 Use algebraic reasoning in applications involving geometric formulas and contextual problems.
Essential Question: What are the steps in performing basic operations on monomials and polynomials? How can you use quadratic functions to model real world scenarios?
Unit Vocabulary: Polynomial, Monomial, Binomials, Trinomial, Discriminant, Factor, Function, Greatest Common Factor, Quadratic, Quadratic Formula, Square Root Principle, Zeros, Quadratic Equation, Product, Quotient
Prerequisite Skills: distributive property; greatest common factor (numerical); prime factorization; like terms; square root; area; perimeter; volume; x-intercept; solution
Checks for Understanding / State Performance Indicators / Assessments / Instructional Resources / Connections
CLE3102.1.2
ü  3102.1.8 Recognize and perform multiple steps in problem solving when necessary. / SPI 3102.1.2 Write an equation symbolically to express a contextual problem.
CLE3102.3.2
ü  3102.3.5 Add, subtract, and multiply polynomials including squaring a binomial.
ü  3102.3.6 Find the quotient of a polynomial and a monomial.
ü  3102.3.7 Use various models (including area models) to represent products of polynomials.
ü  3102.3.8 Find the GCF of the terms in a polynomial.
ü  3102.3.9 Find two binomial factors of a quadratic expression. / SPI 3102.3.2 Operate with polynomials and simplify results.
SPI 3102.3.3 Factor polynomials. / -  Polynomial Puzzler (NCTM Lesson): http://illuminations.nctm.org/LessonDetail.aspx?id=L798
-  Adding/Subtracting Polynomials Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Adding+Subtracting%20Polynomials.pdf
-  Multiplying Polynomials Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Multiplying%20Polynomials.pdf
-  Multiplying Special Case Polynomials Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Multiplying%20Special%20Cases.pdf
-  Properties of Exponents Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/More%20Properties%20of%20Exponents.pdf
-  Factoring Polynomials Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Factoring%201.pdf
-  Factoring Polynomials (Special Cases) Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Factoring%20Special%20Cases.pdf / ACT Connections
-  Add, subtract, and multiply polynomials.
-  Evaluate polynomials functions, expressed in function notation, at integer values.
-  Factor simple quadratics.
CLE3102.3.8
ü  3102.3.30 Solve quadratic equations using multiple methods: factoring, graphing, quadratic formula, or square root principle.
ü  3102.3.31 Determine the number of real solutions for a quadratic equation including using the discriminant and its graph.
ü  3102.3.32 Recognize the connection among factors, solutions (roots), zeros of related functions, and x-intercepts in equations that arise from quadratic functions. / SPI 3102.3.10 Find the solution of a quadratic equation and/or zeros of a quadratic function. / -  Solving Quadratics By Factoring Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Quadratic%20Equations%20By%20Factoring.pdf
-  Solving Quadratics with Square Roots Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Quadratic%20Equations%20Square%20Roots.pdf
-  Discriminant worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/The%20Discriminant.pdf / ACT Connections
-  Identify solutions to simple quadratic equations.
CLE3102.3.9
ü  3102.3.17 Recognize “families” of functions.
ü  3102.3.19 Explore the characteristics of graphs of various nonlinear relations and functions including inverse variation, quadratic, and square root function. Use technology where appropriate. / SPI 3102.3.11 Analyze nonlinear graphs including quadratic and exponential functions that model a contextual situation.
CLE3102.4.1
ü  3102.4.1 Using algebraic expressions solve for measures in geometric figures as well as for perimeter, area, and volume. / ACT Connections
-  Compute the perimeter of simple composite geometric figures with unknown side lengths.
Unit 7: Rational Expressions / Estimated Time: 3 Weeks; March 21 – April 8
CLE:
CLE 3102.2.1 Understand computational results and operations involving real numbers in multiple representations.
CLE 3102.3.3 Understand and apply operations with rational expressions and equations.
Essential Question: What are rational expressions & how do you simplify, multiply, & divide them? How do the rules of operating with fractions correspond to operating with rational expressions?
Unit Vocabulary: Domain, Expression, Irrational Numbers, Rational Numbers, Variables, Restriction, Rational Expressions
Prerequisite Skills: simplify; like terms; domain of a function; factor; Least common denominators, fractions
Checks for Understanding / State Performance Indicators / Assessments / Instructional Resources / Connections
CLE31020.2.1
ü  3102.2.4 Operate efficiently with both rational and irrational numbers
CLE3102.3.3
ü  3102.3.10 Add, subtract, multiply, and divide rational expressions and simplify results. / SPI 3102.3.4 Operate with, evaluate, and simplify rational expressions including determining restrictions on the domain of the variables / -  Underwater Investigation: http://www.glencoe.com/sites/texas/student/mathematics/assets/interactive_lab/algebra1/A1_13/A1_13_dev_100.html
-  Simplifying Rational Expressions Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Simplifying%20Rational%20Expressions.pdf
-  Add/Subtract Rational Expressions Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Adding+Subtracting%20Rational%20Expressions.pdf
-  Dividing Rational Expressions Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Dividing%20Rational%20Expressions.pdf
-  Multiplying Rational Expressions Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Multiplying%20Rational%20Expressions.pdf
-  Domain of Rational Expressions Worksheets: http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Excluded%20Values.pdf / ACT Connections
-  Determine when an expression is undefined.
-  Find and use the least common multiple.