Correlation: California State Curriculum Standards of Mathematics for Grade 6 SUCCESS IN MATH: BASIC ALGEBRA

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1 Correlation: California State Curriculum Standards of Mathematics for Grade 6 To SUCCESS IN MATH: BASIC ALGEBRA 1

2 ALGEBRA AND FUNCTIONS 1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic equations, solve simple linear equations, and graph and interpret their results. Success in Math, Basic Algebra: See the following representative pages: 12-13, 36-49, 52-53, 86-91, 98-99, , Write and solve one-step linear equations in one variable. Success in Math, Basic Algebra: See the following representative pages: 38-39, 40-41, 42-45, 46-49, Write and evaluate an algebraic expression for a given situation, using up to three variables. Success in Math, Basic Algebra: See the following representative pages: 2-3, 12-13, 15, 16, 25, 27, 29, 31, 33, 37, 38-39, 40-41, 45, 49, 53, 55, Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions and justify each step in the process. Success in Math, Basic Algebra: See the following representative pages: 8-9, 12-13, 15, 20-21, 22-23, 24-25, 26-27, 28-29, 32-33, 37 (California Mathematics Standards Grade 6/Success in Math: Basic Algebra, cont.) 1.4 Solve problems by hand using the correct order of operations and/or using a scientific calculator. 2

3 Success in Math, Basic Algebra: pages 8-9, Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions. Success in Math, Basic Algebra: pages 46-49, 50-51, 91, , 107, Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches). Success in Math, Basic Algebra: Temperature conversion is addressed on pages 51 and Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity. Success in Math, Basic Algebra: pages 45, 46, 49, 50, 51, 56, 98-99, , 107, Solve problems involving rates, average speed, distance, and time. Success in Math, Basic Algebra: pages 45, 50, 51, 56, 96-97, 127, 129, 130, 191 (California Mathematics Standards Grade 6/Success in Math: Basic Algebra, cont.) 3.0 Students investigate geometric patterns and describe them algebraically. Success in Math, Basic Algebra: pages , 119, 124, 127, 143, , 146, 149, 150, 153, , 165, 173, , 179, 183 3

4 3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = ½ bh, C = Πd, formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively). Success in Math, Basic Algebra: See the following representative pages: 50, 51, 143, 145, 146, 150, 153, 155, 156, 165, 169, 173, 176, 179, Express simple relationships arising from geometry in symbolic form. Success in Math, Basic Algebra: See the following representative pages: 50, 51, 143, 145, 146, 150, 153, 155, 156, 165, 169, 173, 176, 179, 183 SUCCESS IN MATH: BASIC ALGEBRA California Mathematics, Grade 7 ALGEBRA AND FUNCTIONS 1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs. 4

5 Success in Math, Basic Algebra: See the following representative pages: 2-3, 12-13, 36-37, 38-39, 40-41, 42-45, 46-49, 52-53, 84-85, 86-87, , , , , , , Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A). Success in Math, Basic Algebra: See the following representative pages: 13, 37, 39, 41, 45, 49, 53, 135, 137, 139, 143, 145, 149, 165, 173, 179, 181, 187, Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5) 1/2. Success in Math, Basic Algebra: See the following representative pages: 8-9, 37, 50-51, 129, , , , (California Mathematics Standards Grade 7/Success in Math: Basic Algebra, cont.) 1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used. Success in Math, Basic Algebra: See the following representative pages: , ,

6 1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly. Success in Math, Basic Algebra: See the following representative pages: 2-3, 18-19, 24-31, 36-49, 52-53, 64-65, Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph. Success in Math, Basic Algebra: See the following representative pages: 84-85, 86-87, 88-89, 90-91, 101, , , , Students interpret and evaluate expressions involving integer powers and simple roots. Success in Math, Basic Algebra: See the following representative pages: 4-5, , , , , , (California Mathematics Standards Grade 7/Success in Math: Basic Algebra, cont.) 2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents. Success in Math, Basic Algebra: See the following representative pages: 4-5, , , , ,

7 2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent. Success in Math, Basic Algebra: See the following representative pages: 28-29, 30-31, 42-45, 46-49, , , , , , 129, 130, Students graph and interpret linear and some nonlinear functions. Success in Math, Basic Algebra: See the following representative pages: 84-85, 86-87, 88-89, 90-91, , , Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. Success in Math, Basic Algebra: See the following representative pages: , , 108 (California Mathematics Standards Grade 7/Success in Math: Basic Algebra, cont.) 3.2 Plot the values from the volumes of three-dimensional shapes for various values of the edge lengths (e.g., cubes with varying edge lengths or a triangle prism with a fixed height and an equilateral triangle base of varying lengths). Success in Math, Basic Algebra: pages 143, , 155, Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio ( rise over run ) is called the slope of a graph. 7

8 Success in Math, Basic Algebra: See the following representative pages: 84-85, 86-87, 88-89, 90-91, 96-97, Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities. Success in Math, Basic Algebra: Slope is addressed on pages 88-89, and Students solve simple linear equations and inequalities over the rational numbers. Success in Math, Basic Algebra: See the following representative pages: 37, 38-39, 40-41, 42-45, 46-49, 52-53, (California Mathematics Standards Grade 7/Success in Math: Basic Algebra, cont.) 4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. Success in Math, Basic Algebra: pages Solve multistep problems involving rate, average speed, distance, and time or a direct variation. Success in Math, Basic Algebra: See the following representative pages: 45, 50, 51, 56, 96-97, 127, 129, 130, 191 8

9 SUCCESS IN MATH: BASIC ALGEBRA California Mathematics, Algebra I Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations. Success in Math, Basic Algebra: See the following representative pages: 2-3, 36-37, 38-39, 40-41, 42-45, 46-49, 50-51, 52-53, 90-91, 98-99, , , , , , 143, 145, 149, 153, 155, 165, 169, 173, 179, 181, , , ,

10 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. Success in Math, Basic Algebra: See the following representative pages: 20-21, 22-23, 66-69, 70-71, 72-73, Students use properties of numbers to demonstrate whether assertions are true or false. Success in Math, Basic Algebra: See the following representative pages: 20-21, (California Mathematics Standards Algebra I/Success in Math: Basic Algebra, cont.) 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. Success in Math, Basic Algebra: See the following representative pages: 52, 53, 58, , , , , , , Students solve equations and inequalities involving absolute values. Success in Math, Basic Algebra: pages 62-63,

11 4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x 5) + 4(x 2) = 12. Success in Math, Basic Algebra: See the following representative pages: , 140, Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable, with justification for each step. Success in Math, Basic Algebra: See the following representative pages: 39, 51, 91, 137 (California Mathematics Standards Algebra I/Success in Math: Basic Algebra, cont.) 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., sketch the region defined by 2x + 6y < 4). Success in Math, Basic Algebra: See the following representative pages: 84-85, 86, 89, 90-91, 93, 101, 103, , Students verify that a point lies on a line, give n an equation of the line. Students are able to derive linear equations by using the point-slope formula. Success in Math, Basic Algebra: See the following representative pages: 85-87, 93, 94, , 189, 190, 191. In addition, deriving linear equations given the slope and y-intercept is addressed on pages

12 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. Success in Math, Basic Algebra: pages , 108, 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. Success in Math, Basic Algebra: pages , , , , (California Mathematics Standards Algebra I/Success in Math: Basic Algebra, cont.) 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. Success in Math, Basic Algebra: See the following representative pages: 36-37, 38-39, 40-41, 42-45, 46-49, 50-53, , , 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. Success in Math, Basic Algebra: See the following representative pages: , , , ,

13 12.0 Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms. Success in Math, Basic Algebra: The GCF of monomials is addressed on pages Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques. Success in Math, Basic Algebra: pages 42-45, 46-49, 50-55, 121, 153 (California Mathematics Standards Algebra I/Success in Math: Basic Algebra, cont.) 14.0 Students solve quadratic equations by factoring or completing the square. Success in Math, Basic Algebra: pages Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. Success in Math, Basic Algebra: See the following representative pages: 45, 48-49, 50-51, 96-97, 127, 129, 130, 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. Success in Math, Basic Algebra: Foundation skills are taught on pages

14 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. Success in Math, Basic Algebra: Independent and dependent variables are addressed on pages and 105 (California Mathematics Standards Algebra I/Success in Math: Basic Algebra, cont.) 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. Success in Math, Basic Algebra: Foundation skills are found on pages Students know the quadratic formula and are familiar with its proof by completing the square. Success in Math, Basic Algebra: pages , Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations. Success in Math, Basic Algebra: pages , Students graph quadratic functions and know that their roots are the x-intercepts. 14

15 Success in Math, Basic Algebra: pages 105, 107, 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. Success in Math, Basic Algebra: The quadratic formula and factoring are covered on pages and (California Mathematics Standards Algebra I/Success in Math: Basic Algebra, cont.) 23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. Success in Math, Basic Algebra: pages 105, Students use and know simple aspects of a logical argument. Success in Math, Basic Algebra: This opportunity arises frequently in the Write About It section of lessons. Some examples are pages 23, 123, and 173. These activities support making a logical argument Students explain the difference between inductive and deductive reasoning and identify and provide examples of each. Success in Math, Basic Algebra: Deductive reasoning is addressed on pages Students identify the hypothesis and conclusion in logical deduction. 15

16 Success in Math, Basic Algebra: N/C 24.3 Students use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion. Success in Math, Basic Algebra: N/C (California Mathematics Standards Algebra I/Success in Math: Basic Algebra, cont.) 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. Success in Math, Basic Algebra: See the following representative pages: 20-21, 22-23, 33, 42-45, 48-49, Students use properties of numbers to construct simple valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions. Success in Math, Basic Algebra: Properties of numbers are addressed on pages 20-21, 22-23, 42-45, and Students judge the validity of an argument according to whether the properties of the real number system and the order of operations have been applied correctly at each step. Success in Math, Basic Algebra: Properties of real numbers and the order of operations are addressed on pages 8-9, 20-21, 22-23, 42-45, and

17 25.3 Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, students determine whether the statement is true sometimes, always, or never. Success in Math, Basic Algebra: See the following representative pages: 36-53, 54, 56, 62-63, , ,

Correlation of Moving with Math Grade 7 to HSEE Mathematics Blueprint

Correlation of Moving with Math Grade 7 to HSEE Mathematics Blueprint Number Sense 1.0 Students know the properties of, and compute with, rational numbers expressed n a variety of forms: 1.1 Read, write