In this instructional video series of 26 half-hour programs on high school/college algebra, host Sol Garfunkel clearly explains baffling algebraic concepts while demonstrating how algebra is used for solving real-world problems. Graphic illustrations and on-location examples make concrete connections between mathematics and daily life. The series also has applications to geometry and calculus.

Produced by the Consortium for Mathematics and Its Applications and Chedd-Angier. 1991.

Exponents and radicals: definitions, rules, and applications to positive numbers. Using Rules for Exponents to simplify expressions. Discussion of the O-ring failure of the Challenger Space Shuttle.

This program defines polynomials and describes how the distributive property is used to multiply common monomial factors with the FOIL method. It covers factoring, the difference of two squares, trinomials as products of two binomials, the sum and difference of two cubes, and regrouping of terms.

This is the first program in which equations are solved. It shows how solutions are obtained, what they mean, and how to check them using one unknown. Concepts are worked out in an application problem involving a modern sewage plant near Los Angeles, where a linear equation is set up and solved to determine how long to keep open an inlet pipe.

To the sets of numbers reviewed in previous lessons, this program adds complex numbers — their definition and their use in basic operations and quadratic equations. Students will learn how to combine like terms, apply the FOIL method, and rationalize the denominator for finding the product or quotient of two complex numbers.

This program reviews the quadratic equation and covers standard form, factoring, checking the solution, the Zero Product Property, and the difference of two squares. Environmental and aviation examples provide realistic problems, and the method of Completing the Square is used to solve them.

8. Inequalities

This program teaches students the properties and solution of inequalities, linking positive and negative numbers to the direction of the inequality. The program presents three applications of inequalities: modeling problems of the U.S. Postal Service, finding the cheapest way to travel, and conducting market research in the pizza industry.

In this program, the concept of absolute value is defined, enabling students to use it in equations and inequalities. One application example involves systolic blood pressure, using a formula incorporating absolute value to find a person’s “pressure difference from normal.” The recipe for making fireworks offers another example.

10. Linear Relations

This program looks at the linear relationship between two variables, expressed as a set of ordered pairs. Students are shown the use of linear equations to develop and provide information about two quantities, as well as the applications of these equations to the slope of a line.

The circle and parabola are presented as two of the four conic sections explored in this series. The circle, its various measures when graphed on the coordinate plane (distance, radius, etc.), its related equations (e.g., center-radius form), and its relationships with other shapes are covered, as is the parabola with its various measures and characteristics (focus, directrix, vertex, etc.). An earthquake epicenter provides a real-life illustration.

The ellipse and hyperbola, the other two conic sections examined in the series, are introduced. The program defines the two terms, distinguishing between them with different language, equations, and graphic representations. Architecture and surgery provide interesting application examples.

13. Functions

This program defines a function, discusses domain and range, and develops an equation from real situations. The cutting of pizza and encoding of secret messages provide subjects for the demonstration of functions and their usefulness.

Graphics are used to introduce composites and inverses of functions as applied to calculation of the Gross National Product. One-to-one functions and the horizontal line test are introduced, and more encoded messages and the hazards of “the bends” in scuba diving provide instructive applications of the functions discussed.

15. Variation

In this program, students are given examples of special functions in the form of direct variation and inverse variation, with a discussion of combined variation and the constant of proportionality. These are explored in relation to polynomials and assorted equations, with applications from chemistry, physics, astronomy, and the food industry.

This program explains how to identify, graph, and determine all intercepts of a polynomial function. It covers the role of coefficients; real numbers; exponents; and linear, quadratic, and cubic functions. This program touches upon factors, x-intercepts, and zero values. These terms are demonstrated with the baking of pizza.

A rational function is the quotient of two polynomial functions. The properties of these functions are investigated using cases in which each rational function is expressed in its simplified form. The relationship between numerator and denominator is clarified, and sign and other graphs are used to determine intercepts, symmetry, and asymptotes.

Students are taught the exponential function, as illustrated through formulas. The population of Massachusetts, the “learning curve,” bacterial growth, and radioactive decay demonstrate these functions and the concepts of exponential growth and decay.

This program covers the logarithmic relationship, the use of logarithmic properties, and the handling of a scientific calculator. How radioactive dating and the Richter scale depend on the properties of logarithms is explained. Many rules and tests from previous programs are also incorporated into the lesson.

The case of two linear equations in two unknowns is considered throughout this program. Elimination and substitution methods are used to find single solutions to systems of linear and nonlinear equations. Consistent, inconsistent, and dependent systems are also explored through examples from ship navigation and garment production.

Elimination and substitution are used again to solve systems of linear inequalities. Linear programming is shown to solve problems in the Berlin airlift, production of butter and ice cream, school redistricting, and other situations while constraints, corner points, objective functions, the region of feasible solutions, and minimum and maximum values are also explored.

When the growth of a child is regular, it can be described by an arithmetic sequence. This program differentiates between arithmetic and nonarithmetic sequences as it presents the solutions to sequence- and series-related problems. Definitions include sequence, arithmetic sequence, arithmetic series, fixed number, and common difference.

This program provides examples of geometric sequences and series (f-stops on a camera and the bouncing of a ball), explaining the meaning of nonzero constant real number and common ratio. Finite and infinite geometric series and the sequence of partial sums are also defined in the discussion.

Mathematical proofs applied to hypothetical statements shape this discussion on mathematical induction. This segment exhibits special cases, looks at the development of number patterns, relates the patterns to Pascal’s triangle and factorials, and elaborates the general form of the theorem.

How many variations in a license plate number or poker hand are possible? This program answers the question and shows students how it’s done. Techniques for counting the number of ways in which collections of objects can be arranged, ordered, and combined are demonstrated.

26. Probability

In this final program, students see how the various techniques of algebra that they have learned can be applied to the study of probability. The program shows that games of chance, health statistics, and product safety are areas in which decisions must be made according to our understanding of the odds. It also shows how the subject of probability has evolved to support such fields as genetics, social science, and medicine.

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The videos linked to below are availabe from **Prentice Hall** at . . .

Lesson 1: Variables and Expressions

Lesson 2: Order of Operations

Lesson 3: Evaluating Expressions

Lesson 4: Integers and Absolute Value

Lesson 5: Adding Integers

Lesson 6: Subtracting Integers

Lesson 7: Inductive Reasoning

Lesson 8: Reasoning Strategy: Look for a Pattern

Lesson 9: Multiplying and Dividing Integers

Lesson 10: The Coordinate Plane

Lesson 1: Properties of Numbers

Lesson 2: The Distributive Property

Lesson 3: Simplifying Variable Expressions

Lesson 4: Variables and Equations

Lesson 5: Using Models with Equations

Lesson 6: Solving Equations by Multiplying/Dividing

Lesson 7: Reasoning Strategy: Try, Check, and Revise

Lesson 8: Data and Graphs

Inequalities and Their Graphs

Lesson 9: Solving One-Step Inequalities by Adding or Subtracting

Lesson 10: Solving One-Step Inequalities by Multiplying or Dividing

Lesson 1: Rounding and Estimating

Lesson 2: Estimating Decimal Products and Quotients

Lesson 3: Mean, Median, and Mode

Lesson 3A: Mean and Median on a Graphing Calculator

Lesson 4: Using Formulas

Lesson 4A: Formulas in a Spreadsheet

Lesson 5: Solving Equations by Adding or Subtracting Decimals

Lesson 6: Solving Equations by Multiplying or Dividing Decimals

Lesson 7: Using the Metric System

Lesson 7A: Precision and Significant Digits

Lesson 8: Reasoning Strategy: Simplify a Problem

Lesson 1: Divisibility and Factors

Lesson 2: Exponents

Lesson 3: Prime Factorization and Greatest Common Factor

Lesson 3A: Venn Diagrams

Lesson 4: Simplifying Fractions

Lesson 5: Reasoning Strategy: Account for All Possibilities

Lesson 6: Rational Numbers

Lesson 7: Exponents and Multiplication

Lesson 8: Exponents and Division

Lesson 9: Scientific Notation

Lesson 9A: Scientific Notation with Calculators

Lesson 1: Comparing and Ordering Fractions

Lesson 2: Fractions and Decimals

Lesson 3A: Estimating with Fractions and Mixed Numbers

Lesson 3: Adding and Subtracting Fractions

Lesson 4: Multiplying and Dividing Fractions

Lesson 5: Using Customary Units of Measurement

Lesson 5A: Greatest Possible Error

Lesson 6: Reasoning Strategy: Work Backward

Lesson 7: Solving Equations by Adding or Subtracting Fractions

Lesson 8: Solving Equations by Multiplying Fractions

Lesson 9: Powers of Products and Quotients

Lesson 1: Ratios and Unit Rates

Lesson 1A: Converting Between Measurement Systems

Lesson 2: Proportions

Lesson 3: Similar Figures and Scale Drawings

Lesson 3A: Dilations

Lesson 4: Probability

Lesson 5: Fractions, Decimals, and Percents

Lesson 6: Proportions and Percents

Lesson 7: Percents and Equations

Lesson 8: Percent of Change

Lesson 9: Markup and Discount

Lesson 10: Reasoning Strategy: Make a Table

Lesson 1: Solving Two-Step Equations

Lesson 2: Solving Multi-Step Equations

Lesson 3: Multi-Step Equations with Fractions and Decimals

Lesson 4: Reasoning Strategy: Write an Equation

Lesson 5: Solving Equations With Variables on Both Sides

Lesson 6: Solving Two-Step Inequalities

Lesson 6A: Compound Inequalities

Lesson 7: Transforming Formulas

Lesson 8: Simple and Compound Interest

Lesson 1A: Relating Graphs to Events

Lesson 1: Relations and Functions

Lesson 2: Equations With Two Variables

Lesson 2A: Direct Variation

Lesson 3: Slope and y-intercept

Lesson 3A: Graphing Lines

Lesson 4: Writing Rules for Linear Functions

Lesson 5: Scatter Plots

Lesson 6: Reasoning Strategy: Solve by Graphing

Lesson 7: Solving Systems of Linear Equations

Lesson 8: Graphing Linear Inequalities

Lesson 8A: Graphing Inequalities

Lesson 1: Points, Lines, and Planes

Lesson 2A: Drawing and Measuring Angles

Lesson 2: Angle Relationships and Parallel Lines

Lesson 3: Classifying Polygons

Lesson 3A: Angles of a Polygon

Lesson 4: Reasoning Strategy: Draw a Diagram

Lesson 5: Congruence

Lesson 6: Circles

Lesson 7: Constructions

Lesson 8: Translations

Lesson 8A: Matrices and Translations

Lesson 9: Symmetry and Reflections

Lesson 10: Rotations

Lesson 10A: Tessellations

Lesson 1: Area: Parallelograms

Lesson 2: Area: Triangles and Trapezoids

Lesson 3: Area: Circles

Lesson 4A: Three Views of an Object

Lesson 4: Space Figures

Lesson 5A: Cross Sections of Space Figures

Lesson 5: Surface Area: Prisms and Cylinders

Lesson 6: Surface Area: Pyramids, Cones, and Spheres

Lesson 7: Volume: Prisms and Cylinders

Lesson 8: Reasoning Strategy: Make a Model

Lesson 9: Volume: Pyramids, Cones, and Spheres

Lesson 1: Square Roots and Irrational Numbers

Lesson 2: The Pythagorean Theorem

Lesson 2A: The Pythagorean Theorem and Circles

Lesson 3: Distance and Midpoint Formulas

Lesson 4: Reasoning Strategy: Write a Proportion

Lesson 5: Special Right Triangles

Lesson 5A: Square Roots of Expressions with Variables

Lesson 6: Sine, Cosine, and Tangent Ratios

Lesson 6A: Finding the Angles of a Right Triangle

Lesson 7: Angles of Elevation and Depression

Lesson 1: Frequency Tables and Line Plots

Lesson 1A: Making Histograms

Lesson 2: Box-and-Whisker Plots

Lesson 2A: Stem-and-Leaf Plots

Lesson 3: Using Graphs to Persuade

Lesson 4: Counting Outcomes and Theoretical Probability

Lesson 5: Independent and Dependent Events

Lesson 6: Permutations and Combinations

Lesson 7: Experimental Probability

Lesson 8: Random Samples and Surveys

Lesson 9: Reasoning Strategy: Simulate the Problem

Lesson 9A: Using Random Numbers

Lesson 1: Patterns and Sequences

Lesson 2: Graphing Nonlinear Functions

Lesson 3: Experimental Growth and Decay

Lesson 3A: Non-Linear Functions and Graphing Calculators

Lesson 4: Polynomials

Lesson 4A: Degree of a Polynomial

Lesson 5: Adding and Subtracting Polynomials

Lesson 6: Multiplying a Polynomial by a Monomial

Lesson 7: Multiplying Binomials

Lesson 7A: Binomial Factors of a Trinomial

Lesson 8: Reasoning Strategy: Use Multiple Strategies