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Algebra DVDs

In this introductory lesson, students will learn that algebra is a branch of mathematics which involves much more than simple counting and measuring of quantities. They will understand that algebra requires one to examine the relationships between quantities and that these relationships are most often expressed as equations. They will see that using letters and symbols is a logical method for representing unknown quantities.

Specifically, this video will concentrate on the meaning of sets, integers, prime numbers, coefficients, axioms, natural numbers, equalities, inequalities and the number line. Students will gain proficiency in the following: evaluating an expression by substituting given values; establishing the order of operations; multiplying and dividing algebraic expressions; combining like terms by addition and subtraction; manipulation of algebraic expressions involving fractions; and using reciprocals.

This video provides students with the basic skills and information needed to continue their study in algebra. The solutions and explanations for each problem in the lesson is presented in a straightforward manner without overwhelming extraneous details. [color, 30 minutes] $39.95 ALGI01

This video algebra lesson concentrates on the concept of equations. Students will understand that an equation, if true, is a statement affirming that two expressions are equal to the same number. They will see how the distributive axiom is used in the multiplication and division processes to simplify expressions. They will gain proficiency in the principles of substitution and see how a systematic approach can make the solving of equations simple. The lesson shows how the following steps can be taken to solve for unknowns: Use the multiplication rule, wherein both sides of the equation are multiplied by a number that will help simplify the expression. Eliminate parentheses by using the distributive axiom. Combine all like terms by using the commutative and associative axioms. Add or subtract from both sides whatever number or term is required to convert the equation to the ab=x form. Divide both sides by the numerical coefficient of the variable, the unknown.

The solutions and explanations to all problems are provided in an easy-to-understand format. This basic treatment of equations will prepare your students for more advanced topics to come. [color, 37 minutes] $39.95 ALGI02

This video algebra lesson is devoted primarily to the translation of word problems into algebraic equations and expressions. After an introduction, the lesson begins by asking students to write expressions for simple problems and then moves on to more involved problems. All problems are followed by a very detailed and logical explanation as to how and why the equations are setup the way that they are. After viewing this video, students should no longer be puzzled and confused in making the conceptual leap from words to equations to solutions. [color, 36 minutes] $39.95 ALGI03

The Golden Rule, H2O, the recipe for chocolate brownies, or pi r squared. They are all formulas and most students are quite familiar with them. In this video mathematics lesson, we will direct their attention to specific types of formulas, the kind commonly used in algebra. Students will understand that a formula is, in reality, an equation, and, as such, may be manipulated and rearranged to allow for the solution of any unknown it contains. Considerable time, is devoted to the logic, as well as to the mechanics of term rearrangement and to the solving of unknowns.

Students are also taught how to solve equations . They will understand how and why exponents are added, and how they are raised to other powers. They will learn what is meant by the term dependent variable. Then they will actually see what an equation looks like as they learn to generate ordered pairs and graph them on a coordinate system.

The explanation for each subtopic is followed by illustrative problems, which are solved in a step-by-step logical fashion. This video make equations, exponents and graphing easy to understand. [color, 43 minutes] $39.95 ALGI04

In this video algebra lesson, students will learn how to simplify expressions containing fractions. They will see that basic mathematics operations such as finding the lowest common denominator and using the distributive and associative properties are as easily applied in algebra as they are in general mathematics. Making this association helps students see the logic in manipulating abstract symbols. Thus it becomes evident that solving fractions in algebra is no more difficult than it is in mathematics. Since the process of simplifying an expression most often results in an identity, the lesson begins with a brief review to distinguish the differences between the three types of equalities: equations, formulas and identities.

Then specific problems, chosen to illustrate important algebraic operations, are discussed. Every problem is solved on-screen, and each step of the solution is explained so that the student will understand the “why” behind the procedure. The student will also learn to translate word problems into equations.

This video enhances basic logic and thinking skills, while providing the student with the essential fundamentals of algebra, so important in later studies. [color, 30 minutes] $39.95 ALGI05

This video algebra lesson presents students with methods for solving for two or more unknowns within the same problem. It teaches the student why, in problems such as these, the equations to be solved are equal to each other. They see how this commonality and the power of algebra allows them to find the value of the unknowns, even when the value of neither one is given. The video teaches students how to solve problems with unknowns, using three different methods: graphical, substitution, and elimination or simultaneous equations. Each method is meticulously explained and illustrated so that the student should have no uncertainties about how the problems are solved. Finally, this video lesson teaches how solving equations with two unknowns may be very helpful in solving word problems.

This lesson reveals the logic underlying the solution of simultaneous equations and dispels the confusion and frustration often associated with this topic in algebra. [color, 41 minutes] $39.95 ALGI06

Solving problems in algebra requires that students manipulate letters and symbols according to established axioms, primarily the distributive, commutative, and associative laws of mathematics. In most cases, the first step in working with polynomials involves reducing the expression to a more manageable size...simplifying. In this lesson students see how these axioms may be used to do just that. They will learn how to combine like terms by applying them to the operations of addition, subtraction, division, and multiplication.

After a few basic definitions, the lesson begins with problems involving the combining of like terms and then moves on to multiplying and dividing monomials. Next comes the combining of polynomials, including proper operations with parentheses, exponents and positive and negative signs. Solutions to problems are presented in a step-by-step manner. Logic replaces mystery to enhance student comprehension and retention. Students will quickly realize that rather complex-looking problems may be simplified quite easily by following a logical approach.

This video math lesson is a comprehensive treatment of basic manipulations with monomials and more complex polynomials. [color, 32 minutes] $39.95 ALGI07

This video algebra lesson deals with a process which may be considered the inverse of the distributive property. It’s called factoring. If applying the distributive property involves multiplication, then factoring must involve the inverse of multiplication…division.

Students will learn in this video why certain terms may be removed from, or factored out, of an expression, and, conversely, why others may not be removed. They will understand how to calculate what’s left of the original expression as a result of the factoring process. This video lesson works methodically through a number of different problem types to ensure that the student has a thorough comprehension of the factoring process.

The lesson stresses that factoring is a most useful procedure to use in the overall simplifying of particular types of algebraic expressions. [color, 35 minutes] $39.95 ALGI08

In this lesson students will learn the definition of a quadratic equation is one which includes a single variable to the second degree, that is, to the second power. They learn that it usually is written in the form ax squared + bx + c = 0, where x is the variable and a,b, and c are the constants.

They see that graphing a second-order equation produces a parabola and that, by examining it closely, it is possible to determine the relationships variables have to one another. For instance, for what values of y are x positive...does the point (x, y) lie on the graph. Students will also learn to solve word problems, applying both the factoring and graphical approach.

This video is supplementary to another lesson in this series which deals with the solution of quadratic equations by completion of the square and substitution in the quadratic formula. [color, 36 minutes] $39.95 ALGI09

This video lesson teaches students how to solve for the roots of quadratic equations by the method of completion of the squares and by substitution in the quadratic formula.

It begins by reminding students what constitutes a quadratic equation, and, reviews the four general methods used to solve them. Students are also reminded that it is important to arrange the terms of the expression in the form of the general quadratic equation before applying these methods.

Next the lesson reviews the basics of factoring quadratic equations, and, how graphical analysis may also be used to solve for roots of quadratics. Then it launches into a very comprehensive discussion of the methods involved in determining the roots of quadratics by completing the square and by substitution in the quadratic formula. These two methods are illustrated by presenting solutions to numerous problems. Each one is meticulously and clearly explained, which should result in a high degree of student comprehension and retention.

Although this lesson concentrates on completing the square and substitution in the quadratic formula, students will gain a sense of continuity as they see how all four methods may be used to solve for roots of quadratic equations.

This video is supplementary to another lesson in this series which deals with solving quadratic equations by factoring and graphic analysis. [color, 31 minutes] $39.95 ALGI10

Mathematicians call them complex fractions, those long, complicated expressions which contain fractions within fractions...so imagine how daunting problems containing them likely appear at first glance to first-year algebra students.

But the fear factor is removed by this video lesson, which teaches them how to cut such problems down to size by simplification. In teaching students the basic operations, they quickly learn that a seemingly imposing expression may be simplified by performing a few standard algebraic steps. Then, they realize how completing the problem, that is, performing additional indicated operations, may be accomlished in one or two steps.

After mastering the mechanics of complex-fraction-simplifying, students are taught how to apply them to solving word problems. [color, 35 minutes] $39.95 ALGI11

This video lesson begins by comparing rational and irrational numbers, using numerous examples to illustrate the difference. This presentation should enable students to quickly and readily distinguish between the two. The video then briefly reviews important related terms such as squares, square root, cube, cube root, radical sign, coefficient, radicand, and index.

At this point, students are ready to begin learning basic mathematical and algebraic operations with irrational numbers. They will become familiar with the steps involved in multiplication, division, addition and subtraction and learn how, and under what circumstances, terms under the radical sign may be combined. Each of the four fundamental operations is clearly illustrated by on-screen solutions to various problems, all presented in an easy-to-understand and logical step-by-step format.

Finally the lesson demonstrates how this knowledge may be applied in solving word problems which have irrational numbers as one or more of their components. [color, 27 minutes] $39.95 ALGI12


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