BASIC ALGEBRA LESSONS

Whether needing help with basic algebra homework or reviewing for tests, Mr. X can help you, your child or your students better understand Basic Algebra. Our lessons are designed to reinforce the instructor's message. We also have a library of sample algebra problems with examples of solved problems for each basic algebra lesson. Check out our free samples below, as well as the basic algebra curriculum.
Basic Algebra Sample Lesson 1
Basic Algebra Sample Lesson 2
Basic Algebra Sample Lesson 3

Basic Algebra Curriculum

Algebraic Expressions

Title Description
 Pineapples Classic Lesson A Classic Lesson in learning how to write Algebraic Expressions. Cake and Pie Classic Lesson A Classic Lesson in learning how to write Algebraic Expressions.We may use either two variables or just one. Algebraic Notation You need a good understanding of a variable, as x. Dr. X no Longer Operates At some point we need to leave the symbol for the operation of multiplication behind, as "X" has become a variable, and not a symbol to multiply. A Bridge from Arithmetic to Algebra Part II Some simple problems lend themselves to solutions with both Arithmetic and Algebra. Visualizing these type of problems provide a bridge into the world of Basic Algebra. Learning how to Setup an Algebraic Equation Our suggestion is to pick letters that represent something easily understood. In this example M represents the number of pineapples Mike begins with. L represents the number of pineapples that Laura has. Equal Parts mean Equal Fractions These word problems can be solved with either Arithmetic or Algebra. Practice with fractions in word problems to learn how to write algebraically. A Bridge from Arithmetic to Algebra Part I Some simple problems lend themselves to solutions with both Arithmetic and Algebra. Visualizing these type of problems provide a bridge into the world of Basic Algebra. Adding Like Terms Terms combine when they have the same variables to the same powers. Coefficients Add Efficiently To do algebra easily and effectively, understand that coefficients add efficiently. Like Terms Reinforcement on combining like terms.Terms combine when they have the same variables to the same powers. Negative Multiplication A Lesson on Handling Negative Multiplication with Algebraic Terms. Sum Groups are Worth Joining Grouping terms according to the Associative Law is exceptionally easy to see. Ignorance of the Law is No Excuse The Commutative Law and the Distributive Law are discussed. Using Algebraic Notation A lesson in using Algebraic Notation and Evaluating Algebraic Expressions.Understanding how to work with variables and equations is a key skill to succeed in an Algebra course. X is Handy, In (or Out) We evaluate algebraic expressions whether x is inside or outside parenthesis.We use the distributive property when x is inside parenthesis.

Basic Skills

Title Description
 A Bridge from Arithmetic to Algebra Part I Some simple problems lend themselves to solutions with both Arithmetic and Algebra. Visualizing these type of problems provide a bridge into the world of Basic Algebra. A Bridge from Arithmetic to Algebra Part II Some simple problems lend themselves to solutions with both Arithmetic and Algebra. Visualizing these type of problems provide a bridge into the world of Basic Algebra. Learning how to Setup an Algebraic Equation Our suggestion is to pick letters that represent something easily understood. In this example M represents the number of pineapples Mike begins with. L represents the number of pineapples that Laura has. Algebraic Notation You need a good understanding of a variable, as x. Equal Parts mean Equal Fractions These word problems can be solved with either Arithmetic or Algebra. Practice with fractions in word problems to learn how to write algebraically. Dr. X no Longer Operates At some point we need to leave the symbol for the operation of multiplication behind, as "X" has become a variable, and not a symbol to multiply. Pineapples Classic Lesson A Classic Lesson in learning how to write Algebraic Expressions. Cake and Pie Classic Lesson A Classic Lesson in learning how to write Algebraic Expressions.We may use either two variables or just one. Arithmetic Operators We introduce the operators of arithmetic, the signs (or symbols) for addition, subtraction, multiplication, and division.These are generally read "plus," "minus," "times," and "divided by," respectively.We also officially introduce the equal sign. Using Algebraic Notation A lesson in using Algebraic Notation and Evaluating Algebraic Expressions.Understanding how to work with variables and equations is a key skill to succeed in an Algebra course. X is Handy, In (or Out) We evaluate algebraic expressions whether x is inside or outside parenthesis.We use the distributive property when x is inside parenthesis. Like Terms Reinforcement on combining like terms.Terms combine when they have the same variables to the same powers. Negative Multiplication A Lesson on Handling Negative Multiplication with Algebraic Terms. Ignorance of the Law is No Excuse The Commutative Law and the Distributive Law are discussed. Adding Like Terms Terms combine when they have the same variables to the same powers. Sum Groups are Worth Joining Grouping terms according to the Associative Law is exceptionally easy to see. Coefficients Add Efficiently To do algebra easily and effectively, understand that coefficients add efficiently. Percent of Change 2 Practice with the concepts of Percents and Percentages as we build a bride to Basic Algebra. Percent of Change 1 A lesson that emphasizes building a bridge from Arithmetic to Algebra with an understanding of Percentage Calculations.

Equations

Title Description
 X is the Unknown We begin with a variable representing a "fill-in-the-blank" to make a statement true. Cancel my Policy, Please We may subtract the same value from each side of an equality and maintain the equality.We may divide the same value (a factor) from each side of an equality and maintain the equality. X Fills in the Blank Don't let the concept of a variable throw you.You just "fill in the blank" with what you already know.Each "x" is unique to a math statement.We do not use different values of x "in the same problem." One Good Idea Top to Bottom Dividing a fraction with like coefficients in the numerator and the denominator simplifies to unity.This is used frequently when solving equations. X Can Be Anything The value that x stands for can be any value.Typically, we seek the value for x the makes a statement true. One-Step Equations with Fractions, Lesson 1 We explain the logic and the procedures associated with moving fractions and a variable in an Algebraic Expression.It's easy. Anything Goes with X Variables can be negative, positive, irrational, rational...all kinds of things.Anything goes...Try to make the statement true.A statement that is always true is called an identity.

Equations

Title Description
 X is the Unknown We begin with a variable representing a "fill-in-the-blank" to make a statement true. X Fills in the Blank Don't let the concept of a variable throw you.You just "fill in the blank" with what you already know.Each "x" is unique to a math statement.We do not use different values of x "in the same problem." Cancel my Policy, Please We may subtract the same value from each side of an equality and maintain the equality.We may divide the same value (a factor) from each side of an equality and maintain the equality. One Good Idea Top to Bottom Dividing a fraction with like coefficients in the numerator and the denominator simplifies to unity.This is used frequently when solving equations. X Can Be Anything The value that x stands for can be any value.Typically, we seek the value for x the makes a statement true. Anything Goes with X Variables can be negative, positive, irrational, rational...all kinds of things.Anything goes...Try to make the statement true.A statement that is always true is called an identity. One-Step Equations with Fractions, Lesson 1 We explain the logic and the procedures associated with moving fractions and a variable in an Algebraic Expression.It's easy. Square Roots and Absolute Values A review of square roots and absolute values. Solving Proportions We use all five types of proportion problems from Math-Aids.com.Solve for the value of the unknown (or variable) that makes the statement true. A Lesson in Concentrations Parts per Million and Parts per Billion are explained in a way to let it soak in, as it were.It is a very fluid idea.

Exponents

Title Description
 An Overview of Rules for Exponents We take a look at the Math-Aids handout for rules of exponents. An Introduction to Negative Exponents An introduction to negative exponents.We reference reciprocals without detail about them. A Lesson in Evaluating Exponential Functions We examine the nature of functions before we jump into the evaluation of Exponential Functions. A Lesson with Functions Decreasing Exponentially Two basic problems for functions decreasing exponentially. Multiplying with Exponents An introductory lesson for multiplication of terms with exponents. Scientific Notation with Positive Exponents 2 This lesson in Scientific Notation uses only Positive Powers of Ten. Scientific Notation with Negative Exponents 2 This lesson in Scientific Notation uses only Negative Powers of Ten. Scientific Notation with Positive and Negative Powers A lesson in Scientific Notation discusses the difference between Positive Exponents and Negative Exponents. Scientific Notation, Positive and Negative Exponents A lesson in Scientific Notation discusses the difference between Positive Exponents and Negative Exponents. Scientific Notation with Positive and Negative Exponents A lesson where we multiply numbers in Scientific Notation with a little multiplication and a smidgen of addition. Scientific Notation with both Positive and Negative Exponents We raise values expressed in Scientific Notation to both Positive Exponents and Negative Exponents. Scientific Notation and Operations Mr. X does the HARD Long Division and the student gets the EASY Long Division. Scientific Notation Operations We show all answers and work toward them.As we do we emphasize that reliance on a calculator may not be entirely helpful.

General Topics

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Inequalities

Title Description
 Properties of Inequalities An overview of the Inequality Properties Handout and some notions about one-variable inequalities.

Inequalities

Title Description
 Properties of Inequalities An overview of the Inequality Properties Handout and some notions about one-variable inequalities. Compound Inequalities with the Conjunction "OR" We solve two inequalities in one variable joined with the conjunction OR. Compound Inequalities with the Conjunction "AND" We solve two inequalities in one variable joined with the conjunction AND. Inequality in One Variable with Absolute Value We solve a single variable inequality that includes an absolute value. Square Roots and Absolute Values A review of square roots and absolute values.

Linear Equations & Inequalities

Title Description
 Finding Slope from a Graphed Line Lesson 2 A lesson in Slope.We can read slope from a graph, or calculate it from given coordinates. Finding Slope from a Graphed Line Lesson 1 A lesson in Slope.We can read slope from a graph, or calculate it from given coordinates. Finding Slope from a Pair of Points Problem Set 1 Simple calculations for Slope using a pair of Ordered Pairs. A Fast Lesson in Slope A visual demonstration and lesson on slope.We use Cartesian coordinates for this demonstration. Graphing Lines Given Y-Intercept and an Ordered Pair Given two points, where one point is the y-intercept, write the equation of the line as y = mx + b; and graph the line (segment) on the 10 x 10 grid. Graphing Two Linear Inequalities What if we have two inequalities? In this lesson we address this scenario by graphing the intersection of two linear inequalities. Square Roots and Absolute Values A review of square roots and absolute values.

Linear Functions

Title Description
 Finding Slope from a Graphed Line Lesson 2 A lesson in Slope.We can read slope from a graph, or calculate it from given coordinates. Finding Slope from a Graphed Line Lesson 1 A lesson in Slope.We can read slope from a graph, or calculate it from given coordinates. Finding Slope from a Pair of Points Problem Set 1 Simple calculations for Slope using a pair of Ordered Pairs. A Fast Lesson in Slope A visual demonstration and lesson on slope.We use Cartesian coordinates for this demonstration. Graphing Two Linear Inequalities What if we have two inequalities? In this lesson we address this scenario by graphing the intersection of two linear inequalities.

Monomial and Polynomials

Title Description
 Negative Multiplication A Lesson on Handling Negative Multiplication with Algebraic Terms. Multiplying Polynomials When we multiply polynomials we sum individual products.We multiply each term in one polynomial times each term in the other polynomial, then add the products. An Interesting Relationship, with Algebra From our multiplication table, an interesting relationship between arithmetic and algebra.We observe that x² - 1 = (x-1)(x+1), or, x² = (x-1)(x+1) + 1. Dividing Polynomials (Simplifying) We show how being able to factor terms allows to divide polynomials.The result is akin to simplifying the rational expression. An Interesting Relationship It turns out that x² = (x-1)(x+1) + 1.We look at this algebraic relationship with the standard multiplication table.If you prefer, equivalently, x² - 1 = (x-1)(x+1). Dividing Polynomials with Long Division Lesson Quotients and remainders result from these division problems where both dividend and divisor are polynomials in one variable.

Monomials and Polynomials

Title Description
 An Interesting Relationship It turns out that x² = (x-1)(x+1) + 1.We look at this algebraic relationship with the standard multiplication table.If you prefer, equivalently, x² - 1 = (x-1)(x+1). Multiplying Polynomials When we multiply polynomials we sum individual products.We multiply each term in one polynomial times each term in the other polynomial, then add the products. Negative Multiplication A Lesson on Handling Negative Multiplication with Algebraic Terms.

Title Description
 Graphing a Parabola Graph a Parabola As y = f(x), we have a simple quadratic that graphs to a parabola.We employ y = a(x-h)Â² + k. Graphing a Sideways Parabola We look at a "sideways" function with the relation x = f(y) instead of our usual y = f(x). Graphing Quadratic Functions We solve for the zeroes (roots) of a polynomial by factoring and by graphing, with assistance from the good folks at desmos.com. Graphing a Simple Parabola We walk through a simple sketch of a graph of y = xÂ² - 5.The parabola is a conic section. Solving Roots of Quadratics by Completing the Square We solve for the zeroes (roots) of a polynomial with C.T.S.(Completing the Square), by use of the Quadratic Formula, then by Factoring.No words, just fast writing and nice music.

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Rational Expressions

Title Description
 Dividing Polynomials (Simplifying) We show how being able to factor terms allows to divide polynomials.The result is akin to simplifying the rational expression. How to Divide Rational Expressions Dividing Rational Expressions is made easier by changing the operator to multiplication.Multiply the First Fraction by the Reciprocal of the Second Fraction.

Systems of Equations

Title Description
 Systems of Equations - Substitution Method Isolate one variable by itself. Then re-write the other equation with the Substitution. Systems of Equations - Graphing Method When we graph two lines, the point of intersection of those lines is the simultaneous solution to both linear equations. Systems of Equations - Cramer's Rule Cramer's Rule is a handy way to solve systems of linear equations.We use determinants of square matrices for the top-and-bottom of a fraction. Systems of Equations - Elimination Method We may eliminate a variable by adding two linear equations with opposite coefficients on the same variable. So you "look ahead a bit" to figure out how to get those opposite coefficients. Solving System of Equations Example 2 We solve for the simultaneous solution to two linear equations.We find where the lines intersect. Solving System of Equations Example 1 We solve two linear equations and examine the graph of their intersection.

Systems of Equations

Title Description
 Systems of Equations - Substitution Method Isolate one variable by itself. Then re-write the other equation with the Substitution. Systems of Equations - Graphing Method When we graph two lines, the point of intersection of those lines is the simultaneous solution to both linear equations. Systems of Equations - Cramer's Rule Cramer's Rule is a handy way to solve systems of linear equations.We use determinants of square matrices for the top-and-bottom of a fraction. Systems of Equations - Elimination Method We may eliminate a variable by adding two linear equations with opposite coefficients on the same variable. So you "look ahead a bit" to figure out how to get those opposite coefficients. Solving System of Equations Example 2 We solve for the simultaneous solution to two linear equations.We find where the lines intersect. Solving System of Equations Example 1 We solve two linear equations and examine the graph of their intersection.

Trigonometry

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