Key to Algebra

Correlation with the

California

Math Content Standards

Key Curriculum Press

1150 65^th St.

Emeryville, CA 94608

1-800-338-7638

www.keypress.com

Key to Algebra was developed with the belief that anyone can learn basic algebra if the subject is presented in a friendly, non-threatening manner and someone is available to help when needed. Some teachers use Key to Algebra as the basic text for individualized algebra course, while others use it as a supplement to their regular hardbound text.

Key to Algebra shouldn’t replace group exploration of concepts, cooperative problem or class discussions.

Books 1-4 are restricted to operations on integers so that students who have not yet mastered fractions can begin their study of algebra. In Books 5-7 operations on fractions are taught as students study rational algebraic expressions. Books 8-10 cover real numbers, graphs, system of equations, square roots and quadratic equations. Together these books comprise a complete introductory algebra course.

1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable.	Book 1- Operations on Integers Adding of integers p.9 Subtracting of integers-p.18 Multiplying Integers-p.24 Dividing Integers-p.3 Book 2-Variables, Terms, and Expressions Review of operations on integers-pp1-3 Book 5-Rational Numbers Rational numbers-p.1 Dividing integers-pp2/3 Graphing integers-p.6 Graphing rational numbers-pp.7-10 Book 6-Multiplying and Dividing Rational Expression Multiplying Fractions-pp.6/7 Reciprocals-p.30 Dividing fractions and expressions- pp.31-34
1.1 Students use properties of numbers to demonstrate whether assertions are true or false.	Book 1- Operations on Integers Principle of adding zero-p.11 Commutative property for addition-p.12 Associative principle-p.13 Principle of adding opposites-p.16 Commutative property for multiplication-p.26 Associative property for multipication-p.27 Principle for multiplying by zero, one or negative one-p.28 Distributive property –pp.31-32
2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.	Book 1-Operations on Integers Opposites-p16 Book 2-Variables, Terms, and Expressions Exponents-pp6-10 Book 6-Multiplying and Dividing Rational Expression Reciprocals-pp30/31 Book 10-Square Roots and Quadratic Equations Taking a root-Square roots and more-p13 The product and quotient rules-pp13-21
3.0 Students solve equations and inequalities involving absolute values.	Book 5-Rational Numbers Absolute Value-p14 Solving inequalities-pp.18-23 Solving equations involving absolute value-pp24-26
4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.	Book 2-Variables, Terms, and Expressions Combining like terms-pp.20-24 Simplify using order of operations-pp27-28 Using the distributive principle-p29 Book 3-Equations Solving equations-pp.1-34
5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.	The Key to Algebra materials do not address this standard
6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).	Book 8-Graphs Linear equations-pp.18-19 Compute y-intercept-pp.24-25 Graphing Linear inequalities-pp.31-34
7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.	Book 8-Graphs The slope of a line-pp.20-25 Writing linear equations in the form Y = mx + b-pp.26-27 Finding the Equation of a Line-pp.28-29
8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.	The Key to Algebra materials do not address this standard
9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.	Book 9-Systems of Equations System of equations-P.1 Solving systems of equations by graphing-pp.2-7 Solving system of equations by addition or subtraction –pp.8-11 Solving system of equations by substitution-pp.12-15 Solve by any method-pp.16-17 Word problems involving systems of equations-pp.18-19 Using the multiplication principle and solve-pp.20-27 Solving more word problems-pp.28-29 Solving system of inequalities-pp.30-34
10.0 Students add, subtract, multiply and divide monomials and polynomials. Students solve multistep problems, including word problems by using these techniques. 11.0 Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.	Book 2-Variables,Terms, and Expressions Multiplying terms-pp.12-14 Areas of rectangles (word problems)-pp.16-17 Like and unlike terms-p.18 Combining like terms-pp.19-24 Perimeters (word problems)-p.25-26 Order of operations-pp.27-28 Using the distributive property-p.29 Book 4-Polynomials Adding polynomials-pp. 2 and 6 Opposites of polynomials-p.3 Subtracting polynomials-pp.5-5 The distributive principle-pp.8-10 Multiplying and factoring polynomials-pp.15-29 Book 6-Multiplying and Dividing Rational Expressions Multiplying fractions (polynomials)-pp.7-8 Simplifying fractions (dividing polynomials)-pp.15-17 Simplifying fractions(dividing by a polynomial)-pp.18-21 Dividing polynomials-pp.22-23 Simplifying multiplication problems-pp26-29 Reciprocals-p.30 Dividing fractions-pp31-32 Multiplication and division (monomials and polynomials)-pp.33-34 Book 7-Adding and Subtracting Rational Expression Ratio Problems-pp.28-29 Percent problems-pp.30-31 Time problems-pp.32-33 Problems about rational numbers-p.34 _______________________________________________________________________ Book 4-Polynomials Factoring out a common term-pp.11-14, 24 Multiplying and factoring polynomials-pp.15 Factoring the difference of two squares-pp.21, 23,29 Perfect square binomials- pp.20, 22, 25, 27 ,28, 29
12.0 Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.	Book 6-Multiplying and Dividing Rational Expressions Simplifying rational expressions-pp.18-21
13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques.	Book 6-Multiplying and Dividing Rational Expressions Multiplying fractiona-pp.6-8 Simplifying fractions (division)-pp.14-21 Rewriting fractions in simplest form-p.25 Simplifying multiplication problems-pp.27-29 Dividing –pp.31-32 Multiplication and division pp.33-34 Book 7-Adding and Subtracting Rational Expressions Adding with common denominators-pp.1-5 The opposite of a fraction-p.6 Subtraction with common denominator-pp.7-10 Adding and subtracting with different denominators-pp.11-14, 16-18 Least Common Denominators-pp. 18-22 Problems about rational numbers-p.34
14.0 Students solve a quadratic equation by factoring or completing the square.	Book 4-Polynomials The zero product rule-p.30 Quadratic equations-Factoring-pp.3132 Using quadratic equations-pp.33-34 Book 10-Square Roots and Quadratic Equations Completing the square-pp.22-25
15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.	The Key to Algebra materials do not address this Standard.
16.0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions.	Book 5-Rational Numbers Relations-pp27-28 Functions-pp.29-34
17.0 Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression.	The Key to Algebra materials do not address this Standard.
18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion.	The Key to Algebra materials do not address this Standard.
19.0 Students know the quadratic formula and are familiar with its proof by completing the square.	Book 10-Square Roots and Quadratic Equations Know the quadratic formula-p.26
20.0 Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.	Book 10-Square Roots and Quadratic Equations Quadratic formula-pp.26-29 Using the quadratic formula to solve problems-pp30-31
21.0 Students graph quadratic functions and know that their roots are the x-intercepts.	Book 10-Square Roots and Quadratic Equations Graphs of quadratic functions-pp.33-34
22.0 Students use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.	The Key to Algebra materials do not address this Standard.
23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.	The Key to Algebra materials do not address this Standard.
24.0 Students use and know simple aspects of a logical argument.	The Key to Algebra materials do not address this Standard.
25.0 Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements .	The Key to Algebra materials do not address this Standard.