Morgan County School District Re-3 August What is algebra? This chapter develops some of the basic symbolism and terminology that students may have seen before but still need to master. The concepts of variables, expressions, and equations are presented in meaningful examples in an intuitive manner. This in turn leads to an introduction to algebraic problem solving that will be the basis for problem solving throughout the course. Standard 1 - (1.1, 1.2, 1.5, 1.6) Standard 3 - (3.6) Standard 4 - (4.1, 4.5) Standard 5 - (5.1,5.4, 5.6) Standard 6 - (6.2, 6.3, 6.4) Math Algebra Grade 8 Students will be able to simplify numerical expressions and evaluate algebraic expressions. (M) Students will be able to simplify expressions with or without grouping symbols. (M) Students will be able to calculate and identify solution sets of equations over a given domain. (M) Students will be able to translate phrases into variable expressions, translate word sentences into equations, and translate simple word problems into equations. (R) September Working with real numbers - Working with real numbers - This chapter focuses on using the four operations and properties of real numbers to simplify numerical and algebraic expressions. Standard 1 - (1.1, 1.5, 1.6) Standard 6 - (6.2, 6.3, 6.4) Students will be able to analyze number properties in order to simplify expressions. (M) Students will be able to demonstrate and calculate the addition of real numbers using a number line or properties about opposites. (R) Students will be able to demonstrate and calculate the addition of real numbers using rules of addition. (R) Students will be able to demonstrate and calculate the subtraction of real numbers. (M)
Students will be able to simplify and analyze expressions involving differences, using the distributive property to simplify expressions. (R) October Working with real numbers - (cont.) Students will be able to analyze and calculate multiplication problems involving real numbers. (R) Students will be able to construct and apply equations to represent relationships among integers. (M) November Solving Equations and Problems - Algebraic methods of solving equations are developed using the properties of equality. Multistep solutions require the use of many properties from earlier in the year. Standard 1 - (1.5, 1.6) Standard 4 - (4.5) Standard 5 - (5.1, 5.4) Standard 6 - (6.2, 6.3, 6.4) Students will be able to simplify expressions involving reciprocals, and evaluate problems involving the division of real numbers and solving expressions involving quotients. (M) Students will analyze and solve equations using addition, subtraction, multiplication and division by applying more than one transformation. (R) Students will create and apply a fivestep plan to solve work story problems. (I) Students will solve equations with variables on both sides of an equation. (M) Students will solve problems involving cost, income, and value. (M) Polynomials The concept of an exponent and the first rules of exponents are introduced. The addition, subtraction, and multiplication of polynomials are Students will solve, convert, and simplify expressions involving
developed and applied in conjunction with additional rules of exponents. See December for Standards. exponents. (R) Students will solve polynomials through means of addition, subtraction, multiplication, and division. (I) December Polynomials (con't) The concept of an exponent and the first rules of exponents are introduced. The addition, subtraction, and multiplication of polynomials are developed and applied in conjunction with additional rules of exponents. Students will also be expected to evaluate problems by multiplying monomials, and determine the powers of monomials. (I) (con't) - Students will be able to analyze and solve problems by multiplying a polynomial by a monomial. (R) Students will be able to analyze and solve problems by multiplying polynomials. (I) Standard 1 - (1.1, 1.2, 1.3, 1.5, 1.6) Standard 3 - (3.6) Standard 4 - (4.1, 4.5) Standard 5 - (5.1, 5.4) Standard 6 - (6.2, 6.3, 6.4) Students will be able to transform formulas. (I) Students will solve word problems using uniform motion. (I) Factoring Polynomials This chapter develops the factorization of composite numbers, monomials, and polynomials. Division of monomials is presented as a related skill along with the rule of exponents for division. Several lessons are devoted to special techniques of factoring polynomials, and one lesson provides practice in multiplying Students will be able to analyze and solve word problems involving area and recognize problems with no solutions. (I) Students will factor integers and determine the Greatest Common Factor (GCF) of integers. (R) Students will simplify quotients of monomials and demonstrate the GCF of several monomials. (M)
binomials mentally. The last part of the chapter uses factoring and the zero-product property to solve polynomial equations and application problems. See January for Standards. Students will divide polynomials by monomials and record monomial factors of polynomials. (I) Students will calculate the product of two binomials mentally. (I) Students will factor the difference of two perfect squares and find their products. (I) Students will find the squares of binomials and factor perfect square trinomials. (I) January Factoring Polynomials (Con't) This chapter develops the factorization of composite numbers, monomials, and polynomials. Division of monomials is presented as a related skill along with the rule of exponents for division. Several lessons are devoted to special techniques of factoring polynomials, and one lesson provides practice in multiplying binomials mentally. The last part of the chapter uses factoring and the zero-product property to solve polynomial equations and application problems. Students will factor quadratic trinomials whose quadratic coefficient is 1 and whose constant term is positive. (I) Students will factor quadratic trinomials whose quadratic coefficient is 1 and whose constant term is negative. (I) Students will factor general quadratic trinomials with integral coefficients. (I) Students will factor a polynomial by grouping terms, factor polynomials completely, and solve problems by factoring quadratic equations. (I) Standard 1 - (1.3) Standard 2 - (2.3)
Standard 4 - (4.1, 4.5) Standard 5 - (5.1, 5.4) Standard 6 - (6.4) February Fractions A thorough treatment of algebraic fractions and operations with fractions and mixed expressions is presented in this chapter. Emphasis is placed on expressing fractions in simplest form and on dividing polynomials using the long division form. Standard 1 - (1.2, 1.3, 1.4, 1.5, 1.6) Standard 4 - (4.3, 4.5) Standard 6 - (6.2, 6.4) Students will simplify algebraic fractions, and multiply and divide algebraic fractions. (M) Students will express two or more fractions with their least common denominator, and add and subtract algebraic fractions. (R) Students will construct mixed expressions as fractions in simplest form. (R) Students will simplify problems by dividing polynomials. (M) March CSAP Awareness Developing methods geared towards Students will investigate data collection and analysis, statistics, and Individual class time, teacher observation, discussion, and individual work. CSAP released items, sample problems, and problems collected by the teacher needed to address
understanding, interpreting, and answering CSAP type questions using released items and practice tests. In addition, due to the specificity of the algebra class, other topics such as geometry, statistics and probability, graphing data, and data analysis will be covered. Standard 1 - (1.1, 1.2, 1.4, 1.5, 1.6) Standard 2 - (2.1, 2.2, 2.3, 2.5) Standard 3 - (3.1, 3.2, 3.3, 3.4, 3.5, 3.7) Standard 4 - (4.2, 4.4, 4.6) Standard 5 - (5.2, 5.3, 5.5) Standard 6 - (6.1) probability in problem solving situations and interpret the reasoning used in solving these problems. (R) Students will apply geometric concepts, properties, and relationships in problem solving situations and analyze the reasoning used in solving these problems. (R) standards not covered in the text. Applying Fractions This chapter presents a wide variety of equations and word problems related to algebraic fractions. Ratios are introduced and proportions are solved as a special case of fractional equations. Extensive treatment is given to solving equations with fractional coefficients and fractional equations. Percents, decimals, mixture problems, and scientific notation are also specifically covered. Students will solve problems involving ratios and proportions. (M) Students will solve equations with fractional coefficients. (M) Students will solve fractional equations. (M) Students will convert problems involving percents and decimals. (M) Students will analyze mixture and word problems. (I) Standard 1 - (1.1, 1.2, 1.4, 1.5, 1.6) Standard 2 - (2.2, 2.3) Standard 4 - (4.3) Standard 5 - (5.2) Standard 6 - (6.1, 6.2, 6.3, 6.4) April Introduction to Functions Students will solve equations with two
This chapter introduces the basic tools for working with linear equations in two variables. Solution sets of linear equations are represented graphically using the coordinate plane. The slope of a line is defined, and the standard and slope-intercept forms of a line's equation are examined. Lines are graphed from given equations, and equations are determined from given facts about a line. Functions are defined by tables, graphs, and equations. Special attention is given to linear and quadratic functions. Standard 2- (2.1, 2.2, 2.3, 2.4, 2.5) Standard 6- (6.2, 6.3) variables over given domains of the variables. (R) Students will graph ordered pairs and linear equations. (R) Students will determine the slope of a line using the slope, y-intercept form of a linear equation. (M) Given the slope of a line and one point, or given two points of a line, students will determine the equation of a line. (I) Students will identify a function, define a function by using tables and graphs, and equations. (R) Students will graph both linear and quadratic functions. (M, I) May Systems of Linear Equations This chapter shows how to find the solutions that are common to two linear equations in two variables. Three methods of solving a system of linear equations are introduced: the graphing method, the substitution method, and the addition and subtraction method. Problem solving skills are extended to include many types of problems associated with systems of linear equations such as wind and water current problems, age, digit, and fraction puzzle problems. Standard 2- (2.1, 2.2, 2.3, 2.4, 2.5) Students will use graphs to solve systems of linear equations. (R) Students will use the substitution method to solve systems of linear equations. (I) Students will use the addition or subtraction method with multiplication or division to solve systems of linear equations. (I) Students will use the multiplication with the addition or subtraction method to solve systems of linear equations. (I) Students will use systems of equations to solve wind and water current Test, quizzes, and homework.
Standard 6- (6.2, 6.4) problems, and using systems of equations to solve digit, age and fraction puzzle problems. (I) Inequalities The introduction to inequality symbols from Chapter 1 provides the background for a more formal study of inequalities in this chapter. The order of the real numbers leads to the study of inequalities with one variable and their graphs. Techniques for solving inequalities are developed. Methods for solving simple inequalities are extended to include conjunctions, disjunctions, and absolute value. Linear inequalities in two variables and systems of such inequalities are investigated with emphasis on their graphs. Standard 1- (1.2, 1.5, 1.6) Standard 2- (2.1, 2.2, 2.3, 2.4, 2.5) Standard 6- (6.2) Students will determine the relative value of real numbers by placing them on a number line. (R) Students will solve absolute value problems and absolute values of products in an open sentence. (I) Students will graph linear inequalities and systems of linear inequalities. (M) Test, quizzes, and homework Rational and Irrational numbers Rational numbers and their properties are defined and then examined in both the decimal and square root form. Irrational numbers are then introduced in terms of irrational square roots. Finding the square root of a variable expression leads to the Pythagorean Theorem and its Students will examine and demonstrate the properties of rational numbers, decimal forms of rational numbers, rational square roots, irrational square roots, square roots with variable expressions, the Pythagorean theorem, and multiplying,
applications. dividing, and simplifying radicals. (I, R, M) Quadratic Functions Students will be introduced to the quadratic equation as an alternative method of solving quadratic equations. Final Comprehensive Test Students will be able to solve quadratic equations by using the quadratic equation. (I) Summary of yearly content Test, quiz, and homework Final Test