EXPONENTS SIMPLIFYING MULTIPLICATION EXPRESSIONS LESSON PLAN

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## Mathematics 125 | ## Intermediate Algebra |

## IntermediateAlgebra | |

## OverviewTopics include laws of exponents, radicals, equations in onevariable (linear, quadratic, and some of higher degree), systems ofliner equations, imagineries, grraphical representations, logarithms,binomial theorem. | |

## Video Lesson Descriptions (Lessons 1-13)Lesson 1- The Power of Algebra Offers a basic overview of algebra and its components, and reviews thecomutative, associative, and distributive properties for addition andmultiplication. Lesson 2- Polynomials Introduces the basic terminology of polynomials, the procedures forsimplifying a polynomial, and methods for adding, subtracting, andmultiplying polynomials. Lesson 3- Solving and GraphingEquations Demonstrates the four problem-solving techniques—verbal, symbolic,numeric, and graphic. Lesson 4- Linear Equations Reviews the general strategy for solving linear equations andintroduces formulas used for solving word problems involvingconsecutive integers, consecutive even integers, and consecutive oddintegers. Lesson 5- Solving by Factoring Introduces the rate-time-distance formula and describes some commonstrategies for solving applied problems involving rates andtimes. Lesson 6- Inequalities andAbsolute Values Explains and demonstrates how to formulate and solve linearinequalities by offering two scenarios: how to determine the exam scoreneeded in order to receive an A in the class, and how to choose thebest alternative between two salary plans. Lesson 7- Graphs of Equationsand Functions Explains the Cartesian coordinate systme and introduces the interceptmethod for graphing linear equations. Lesson 8- Systems of Equations Describes systems of linear equations and their solution throughsubstitution or elimination method. Lesson 9- Graphing Inequalities Illustrates the steps of graphing a linear inequality in theplane. Lesson 10- Introduction toQuadratic Equations Introduces the standard form of a quadratic equation, reviews squareroot properties, and demonstrates the solution of quadraticequations. Lesson 11- The Quadratic Formula Shows how to derive a general formula that can be used to solve anyquadratic equation and explores various real-worldapplications. Lesson 12- Graphing QuadraticEquations Presents three methods for graphing a quadratic equation in twovariables: plotting points using a table of values, finding the vertexand the intercepts, and applying geometric transformations. Lesson 13- Rational Expressions Explains the procedures for working with fractions involvingpolynomials. | ## Video Lesson Descriptions (Lessons 14-26)Lesson 14- The Algebra ofFunctions Illustrates the different ways that functions can be specified: by atable, a set of ordered pairs, a graph, or an equation. Lesson 15- Graphing Functions Includes examples of how to graph linear, quadratic, and higher degreefunctions. Lesson 16- Exponents and RadicalExpressions Explains how exponents help student manage very large numbers and verysmall numbers using scientific notation. Lesson 17- Exponential Functions Discusses mathematical models of exponential growth anddecay. Lesson 18- Logarithmic Functions Demonstrates how logarithms can be used to solve for an unknown thatappears in an exponent. Lesson 19- Properities ofLogarithms Introduces the five key properties of logarithms, which are derivedfrom the properties of exponents. Lesson 20- Exponential andLogarithmic Equations Reviews the properties and methods used in solving exponential andlogarithmic equations. Lesson 21- Systems of LinearEquations and Matrices Teaches students how to solve sets of three equations in three unknownsusing linear equations and matrices. Lesson 22- Operations on Matrices Introduces the algebraic operations on matrices. Lesson 23- Conic Sections Defines the properties and graphs of the many shapes—circles, ellipses,parabolas, and hyperbolas—that originate as sections of acone. Lesson 24- Sequences and Series Offers an overview of numerical sequences and the sum of their terms,known as series. Lesson 25- The Binomial Formulaand Counting Introduces counting principles required in computingprobabilities. Lesson 26- Permutations,Combinations & Probability Explains the calculation of probability using permutations andcombinations. |