ModuMath Algebra Lesson Listing

 

Following is a list of the lessons for Algebra along with the educational objectives for each lesson.

 

1      Getting Acquainted with Algebra

        A.    “Translate” words into the language of algebra.

        B.     Evaluate algebraic expressions.

        C.    Evaluate formulas and other expressions.

2      Order of Operations

        A.    Use the standard order of operations to simplify and evaluate algebraic expressions.

        B.     Simplify and evaluate numerical and algebraic expressions that contain parentheses.

3      Adding and Subtracting Algebraic Expressions

        A.    Identify the terms in algebraic expressions.

        B.     Identify like terms in algebraic expressions.

        C.    Identify the special kinds of polynomials called monomials, binomials, and trinomials.

4      Multiplying Polynomials

        A.    Multiply any two polynomials.

        B.     Apply the FOIL method as a shortcut in multiplying two binomials.

        C.    Use Formulas to obtain special products of the form (a + b)2, (a – b)2 and (a + b)(a – b).

5      Laws of Algebra

        A.    Recognize five basic laws of algebra

                1.     The Commutative Law for Addition

                2.     The Commutative Law for Multiplication

                3.     The Associative Law for Addition

                4.     The Associative Law for Multiplication

                5.     The Distributive Law of Multiplication Over Addition (usually referred to as the Distributive Law)

        B.     Apply these laws to certain algebraic operations.

6      Solving Equations I

        A.    Recognize the identities of addition and multiplication.

        B.     Recognize the inverses for addition and multiplication.

        C.    Use the identities and inverses in solving equations.

7      Solving Equations II

        A.    Solve multiple step first degree equations.

        B.     Use some shortcuts to solve equations.

        C.    Understand and work with literal equations.

8      Using Equations to Solve Problems

        A.    When you complete this lesson, you will be able to use equations, tables, and diagrams to solve practical problems.

9      Solving Practical Problems

        A.    Find formulas to describe relationships between quantities in practical problems.

        B.     Use formulas to organize the information in problems and to identify the variables.

        C.    Use formulas and organized information to develop equations.

        D.    Use formulas and organized information to check solutions.

10    Inequalities

        A.    Identify inequality symbols and use them to write algebraic statements.

        B.     Identify the solution sets of inequalities on a number line.

        C.    Combine two inequalities into one compound inequality.

        D.    Solve inequalities.

        E.     Solve word problems using inequalities.

11    Linear Equations and Graphs I

        A.    Identify linear equations.

        B.     Identify linear equations that produce vertical or horizontal lines.

        C.    Use graphs, equations and ordered pairs to examine the relationships between variables.

        D.    Plot points and draw lines on the coordinate plane.

12    Linear Equations and Graphs II

        A.    Use the term “slope” to describe lines and rates of change.

        B.     Find the slope of lines on graphs.

        C.    Find the slope of a line when given two of its points.

        D.    Define the slope of horizontal and vertical lines.

13    Linear Equations and Graphs III

        A.    Fine the slope of a line from its equation.

        B.     Write any linear equation in slope-intercept form.

        C.    Use an equation in slope-intercept form to find the slope and y-intercept of its line.

        D.    Graph a line from its equation using the slope and y-intercept.

        E.     Determine if two lines are parallel by comparing their slopes.

14    Linear Equations and Graphs IV

        A.    Write an equation for a line with a given slope and y-intercept.

        B.     Write an equation for a line with a given slope and through a given point.

        C.    Write an equation for a line through two points.

15    Systems of Equations I

        A.    Solve a system of two linear equations by graphing.

        B.     Solve a system of two linear equations by substitution.

        C.    Determine how many solutions a system of linear equations has.

        D.    Explain how the number of solutions to a system can be determined from a graph.

        E.     Solve word problems using systems of two linear equations.

16    Systems of Equations II

        A.    Solve systems of equations using the elimination method.

        B.     Solve simple word problems using systems of equations.

17    Systems of Equations III

        A.    Use the elimination method to solve systems in which the terms have no additive inverses.

        B.     Use the elimination method to solve systems that have terms with coefficients that are fractions.

        C.    Use the elimination method to solve systems in which one or both of the coordinates in the solution are fractions.

18    Systems of Equations IV

        A.    Determine whether a given problem can be solved with one variable and/or two variables.

        B.     Define the two unknowns in a word problem using a single variable and using two variables.

        C.    Write equations to solve word problems both when the unknowns have been identified using one variable and when the unknowns have been identified using two variables.

        D.    Solve a given word problem with either one equation or with a system of equations.

19    Exponents

        A.    Identify expressions in simplified standard form.

        B.     Use the rules for exponents to simplify expressions.

        C.    Use the rules of exponents to divide a polynomial by a monomial.

20    Factoring I

        A.    Find the greatest common factor of a polynomial

        B.     Factor the greatest common factor from a polynomial.

21    Factoring II

        A.    Factor a polynomial with four terms by grouping.

        B.     Factor a perfect square trinomial.

        C.    Factor a binomial that is the difference of two perfect squares.

22    Factoring III

        A.    Factor a quadratic trinomial.

        B.     Factor a trinomial in quadratic form.

23    Roots and Radicals I

        A.    Use appropriate radical notation for expressions involving square roots.

        B.     Find the square roots of perfect squares.

        C.    Reduce and simplify square roots of integers that are not perfect squares.

        D.    Find or simplify the square root of monomials.

        E.     Write radicals with rational exponents and vice-versa.

24    Roots and Radicals II

        A.    Multiply or divide two radicals.

        B.     Add or subtract two radicals.

        C.    Rationalize the denominator.

25    Quadratic Equations I

        A.    Identify quadratic equations in standard form.

        B.     Solve quadratic equations by taking the square root of each side of the equation.

        C.    Solve quadratic equations by factoring.

        D.    Solve word problems that include quadratic equations.

26    Quadratic Equations II

        A.    Solve quadratic equations using the quadratic formula.

        B.     Solve word problems that include quadratic equations.

27    Rational Expressions I

        A.    Identify rational expressions and determine if there are any excluded values.

        B.     Evaluate rational expressions for given values fo the variables in the expression.

        C.    Fully reduce a rational expression.

        D.    Multiply two rational expressions and give the product in its fully reduced form.

        E.     Divide two rational expressions and give the quotient in its fully reduced form.

28    Rational Expressions II

        A.    Add or subtract two rational expressions that have the same denominator.

        B.     Add or subtract two rational expressions that have different denominators.

        C.    Simplify complex fractions.

29    Rational Expressions III

        A.    Solve equations that include rational expressions.

        B.     Check the solutions to the equations.

        C.    Solve word problems that involve equations which include rational expressions.

30    Rational Expressions IV

        A.    Solve word problems that involve writing equations that include rational expressions.

        B.     Solve “work” and “rate-time-distance” problems that involve writing equations that include rational expressions.

31    Pythagorean Theorem and Other Formulas

        A.    Identify the hypotenuse of right triangles.

        B.     Use the Pythagorean Theorem to find the missing side of a right triangle, when the lengths of two sides are known.

        C.    Use the Pythagorean Theorem to determine if a given triangle is a right triangle.

        D.    Use right triangles to solve some simple applications.

        E.     Use the Distance Formula to find the distance between two points on a plane.

        F.     Use the Midpoint Formula to find the point that is midway between two points on a line.

32    Proportion and Variation

        A.    Write ratios as fractions or decimals.

        B.     Write and solve proportions.

        C.    Use proportions to solve practical problems.

        D.    Write formulas for direct and inverse variation.

        E.     Use the formula to solve variation problems.

 

 

 

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Produced by David Schmidtke, Blackhawk Technical College, dschmidtke@blackhawk.edu    12/2002