EXPONENTS SIMPLIFYING MULTIPLICATION EXPRESSIONS LESSON PLAN

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## Intermediate Algebra

### Overview

Topics 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.

Introduces the standard form of a quadratic equation, reviews squareroot properties, and demonstrates the solution of quadraticequations.

Shows how to derive a general formula that can be used to solve anyquadratic equation and explores various real-worldapplications.

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.

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.