California Algebra I Content Standards 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: 1.1 Students use properties of numbers to demonstrate whether assertions are true or false. 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. 3.0 Students solve equations and inequalities involving absolute values. 4.0* Students simplify expressions before solving linear equations and inequalities in one variable. 5.0* Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. 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 inequalities (e.g., they sketch the region defined by 2x 6y 4). 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. 8.0 Students understand the concepts of parallel lines and perpendicular lines and how their slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. 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. 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. 12.0* Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms. 13.0* Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques. 14.0* Students solve a quadratic equation by factoring or completing the square. * Indicates a key standard as identified in Chapter 3 of Mathematics Framework for California Public Schools. xiv
15.0* Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. 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. 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. 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. 19.0* Students know the quadratic formula and are familiar with its proof by completing the square. 20.0* Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations. 21.0* Students graph quadratic functions and know that their roots are the x-intercepts. 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. 23.0* Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. 24.0 Students use and know simple aspects of a logical argument: 24.1 Students explain the difference between inductive and deductive and recognize that a single counterexample is sufficient to refute reasoning and identify and provide examples of each. 24.2 Students identify the hypothesis and conclusion in logical deduction. 24.3 Students use counterexamples to show that an assertion is false. 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: 25.1 Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions. 25.2 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. 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. * Indicates a key standard as identified in Chapter 3 of Mathematics Framework for California Public Schools. xv
Correlation to California Acknowlegments Algebra I Content Standards CA Standard Introduced Practiced Taught to Mastery 1.0 2.1 (99), 4.4 (243), 9.1 (499) 4.4 (245), 9.1 (500), Chapter 9 Review (548) 2.1 (99), 2.7 (135), 4.4 (243), 9.1 (499) 1.1 0.4 (27) 2.2 (107), 2.7 (140), 4.4 (245), Chapter 6 Review (384), 8.6 (480), 9.3 (512 513), 9.4 (519), Chapter 9 Review (545) 4.4 (243 244) 2.0* 2.1 (97), 2.8 (144 147), 3.6 (196, 201), 6.2 (343), 7.6 (425 426), 9.1 (498 499), 9.8 (537), 10.1 (552), 10.5 (580) 3.6 (201), 6.3 (352 354), 6.4 (357), 6.5 (363 365), 6.6 (370 371), 6.7 (373 377), Chapter 6 Review (383 384), 7.4 (417), 7.6 (428), 10.3 (564 565), 10.4 (571 572), 10.5 (580), 10.6 (588), Chapter 10 Review (592), MPYS 3.6 (26), MPYS 6.3 (44), MPYS 6.4 (45), MPYS 6.5 (46), MPYS 6.6 (47), MPYS 10.5 (73) 3.6 (196), 6.3 (350 352), 6.5 (360 363), 6.6 (366 368), 6.8 (382), 7.6 (425 426), 9.7 (532 535), 10.1 (552), 10.5 (574 580) 3.0 7.5 (420 421) 7.5 (421 423), 7.6 (426 428), Chapter 7 Review (431), MPYS 7.5 (53), MPYS 7.6 (54) 7.5 (420 421) 4.0* 3.6 (197), Chapter 3 Review (209) 4.7 (263), Chapter 4 Review (269), 5.2 (284 285), 5.5 (309), 7.3 (411), Chapter 7 Review (432), 8.1 (442), 8.6 (482), MPYS 3.6 (26), MPYS 4.4 (30), MPYS 5.5 (39) 4.4 (240 244) 5.0* 3.4 (183 184), 3.6 (197 198), 5.5 (304 306) 3.6 (200 202), Chapter 3 Review (206), 4.1 (224), 4.4 (245 246), 4.5 (251), Chapter 4 Review (269), 5.2 (281, 284 288), 5.3 (292 295), 5.5 (308 310), Chapter 5 Review (329), 8.1 (442), 8.6 (482), MPYS 4.4 (30), MPYS 4.7 (33), MPYS 5.5 (39) 3.6 (198), 4.4 (241 244), 5.5 (306 308) 6.0* 2.4 (120), 3.2 (165 171), 3.4 (179), 5.6 (312 313) 3.4 (182 184), 3.5 (188 189, 192, 194), 3.7 (204 205), 4.4 (246), 4.5 (250), 5.6 (316 318), 5.7 (324 326), Chapter 5 Review (329), MPYS 4.5 (31), MPYS 5.6 (40), MPYS 5.7 (41) 3.4 (178 182), 5.6 (313 315) 7.0* 4.3 (234 236) 4.1 (217), 4.3 (236 239), 4.4 (246), 4.5 (248 251), 4.7 (263), Chapter 4 Review (268), 5.1 (276), 5.2 (285), 6.1 (340), 7.5 (422), MPYS 4.5 (31), MPYS 5.1 (34), MPYS 5.2a (35) 4.3 (234 236) 8.0 4.3 (237), 10.1 (551) 10.1 (555 556), 10.2 (560 561), 10.6 (586), Chapter 10 Review (589 590), MPYS 10.1 (69), MPYS 10.2 (70) 10.1 (551 552, 554 555), 10.2 (558 559) 9.0* 5.1 (273 276), 5.7 (320 321) 5.1 (276 279), 5.2 (285 288), 5.3 (292 295), 5.4 (296 300), 5.7 (324 327), Chapter 5 Review (328 329), 7.2 (403), 7.5 (423), Chapter 7 Review (432), 8.2 (452), Chapter 9 Review (548), MPYS 5.2a (35), MPYS 5.3 (37), MPYS 5.7 (41) 5.2 (281 284), 5.3 (289 292), 5.7 (321 323) 10.0* 3.6 (197), 6.3 (351 352), 9.3 (508 509) 6.3 (352 354), 6.4 (357), 6.5 (363), 6.6 (370), 6.7 (377), Chapter 6 Review (383), 7.1 (395), 7.6 (428), 8.6 (481 482), 9.3 (511 513), 9.4 (515 516, 521), 9.6 (530), 9.7 (536), 9.8 (543 544), 10.1 (556), 10.4 (573), MPYS 3.6 (26), MPYS 6.3 (44), MPYS 6.4 (45), MPYS 6.5 (46), MPYS 9.3 (63) 6.5 (361 362), 8.6 (477 479), 9.3 (509 511), 9.4 (517) 11.0 4.4 (245), 9.3 (509 511), 9.8 (541) 9.4 (519 521), 9.6 (527 530), 9.7 (536), 9.8 (544), Chapter 9 Review (547), MPYS 9.4a (64), MPYS 9.4b (65), MPYS 9.8 (68) 9.4 (515 518, 521) 12.0* 8.6 (477 478), 9.4 (518) 8.6 (480 482), Chapter 8 Review (493), 9.4 (521), 9.7 (536), 9.8 (544), MPYS 9.4b (65) 8.6 (477 478), 9.4 (518 519) 2.1 (99) indicates Lesson 2.1, page 99. * indicates a key standard. MPYS stands for More Practice Your Skills. xvi
CA Standard Introduced Practiced Taught to Mastery 13.0* 8.6 (474 479), 9.8 (540 541) 8.4 (470), 8.6 (482), Chapter 8 Review (493), 9.4 (521), 9.8 (544), Chapter 9 Review (548), Chapter 10 Review (591), MPYS 9.4b (65) 8.6 (477 479) 14.0* 9.4 (516) 9.4 (519), 9.6 (528 530), Chapter 9 Review (546), 10.6 (587), Chapter 10 Review (594), MPYS 9.4a (64), MPYS 9.6 (66) 9.6 (525 528) 15.0* 3.2 (166 167), 3.4 (182 183, 186), 4.5 (252), 4.7 (264 265), 5.2 (283 284) 5.2 (288), 5.4 (301), 5.7 (327), Chapter 5 Review (329), 8.6 (481), Chapter 9 Review (548), Chapter 10 Review (591), MPYS 5.2a (35), MPYS 5.2b (36) 4.5 (252), 4.7 (264 265), 5.2 (283 284), Chapter 7 Review (431), 8.6 (475 476) 16.0 7.1 (388 390), 7.4 (412 413), 8.6 (474 475) 7.1 (392 395), 7.2 (400 403), 7.3 (409), MPYS 7.1 (49), MPYS 7.2 (50), MPYS 7.4 (51) 7.1 (390 391), 7.2 (396 399), 7.3 (405 407) 17.0 7.1 (388 390) 7.1 (393 394), 7.2 (402 403), 7.3 (409 410), 7.4 (412 417), 7.6 (425), 9.1 (498), 9.2 (505 506), 9.3 (512), MPYS 7.4 (52) 7.1 (390 391), 7.3 (404 405) 18.0 7.1 (391) 7.1 (392 395), 7.2 (400 403), 7.3 (409), 9.3 (513), MPYS 7.1 (49), MPYS 7.2 (50) 7.2 (397 399) 19.0* 9.7 (531 532) 9.7 (534 535), 9.8 (541), Chapter 9 Review (547), 10.6 (584), MPYS 9.7 (67) 9.7 (531 533) 20.0* 9.7 (533) 9.7 (534 535), Chapter 9 Review (547), 10.6 (584), MPYS 9.7 (67) 9.7 (533) 21.0* 9.1 (497 498) 9.1 (500 501), 9.2 (505 507), 9.3 (512 513), 9.4 (519 521), 9.8 (538 540), Chapter 9 Review (546 547), Chapter 10 Review (593), MPYS 9.2 (62), MPYS 9.4a (64) 9.2 (502 505), 9.4 (515 517) 22.0 9.1 (500), 9.4 (521) 9.6 (529), 9.7 (534 535), Chapter 9 Review (547), 10.5 (581), Chapter 10 Review (590), MPYS 9.7 (67) 9.6 (527 528), 9.7 (533 535) 23.0* 9.1 (496 498) 9.1 (500 501), 9.2 (505 507), 9.3 (512 514), 9.5 (522 523), 9.6 (529), 9.7 (534 535), Chapter 9 Review (547), MPYS 9.1 (61) 9.1 (496 498) 24.0 10.1 (556), 10.6 (587), Chapter 10 Review (590) 24.1 10.1 (556), 10.2 (561), 10.4 (569), 10.5 (581), 10.6 (588), Chapter 10 Review (590) 24.2 10.1 (556), Chapter 10 Review (590) 24.3 7.2 (401) 7.2 (401), Chapter 9 Review (548), 10.1 (556), Chapter 10 Review (590) 7.2 (401) 25.0 2.7 (135 139) 2.7 (140), Chapter 3 Review (209), 4.4 (245), 5.1 (276), 9.3 (513), 9.4 (519), Chapter 9 Review (548) 2.7 (139), 10.5 (580) 25.1 2.7 (135 143) 4.4 (244 245), 6.6 (371), 9.7 (551 553), 10.5 (580) 4.4 (243 244), Chapter 9 Review (548) 25.2 0.4 (27), 2.7 (135) 2.2 (107), 2.7 (139 140), 2.8 (144 146), 4.4 (244), 6.3 (351) 4.4 (243 244), 9.3 (510) 25.3 Chapter 3 Review (210), 5.1 (279), 5.5 (309) Chapter 3 Review (210), 5.5 (309), Chapter 5 Review (328), Chapter 6 Review (384), Chapter 10 Review (590) Chapter 3 Review (210), Chapter 10 Review (590) 2.1 (99) indicates Lesson 2.1, page 99. * indicates a key standard. MPYS stands for More Practice Your Skills. xvii
California Grade Seven Standards Reinforced Number Sense 1.2 Number Sense 1.3 Number Sense 2.2 Algebra and Functions 2.1 Algebra and Functions 3.3 Algebra and Functions 3.4 Algebra and Functions 4.1 Algebra and Functions 4.2 Geometry 1.1 Geometry 1.3 Geometry 3.3 and Probability 1.1 and Probability 1.2 and Probability 1.3 Mathematical Reasoning 1.1 Mathematical Reasoning 1.2 Mathematical Reasoning 2.4 Mathematical Reasoning 2.5 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers. Convert fractions and percents and use these representations in estimations, computations, and applications. Add and subtract fractions by using factoring to find common denominators. 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. Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always that same and know that the ratio ( rise over run ) is called the slope of a graph. Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an items, 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. 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. Solve multistep problems involving rate, average speed, distance, and time or a direct variation. Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters). Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., persondays) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer. Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement. Know various forms of display for data sets, including a stem-and-leaf plot or box-and-whisker plot; use the forms to display a single set of data or to compare two sets of data. Represent two numerical variables on a scatterplot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level). Understand the meaning of, and be able to compute, the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set. Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns. Formulate and justify mathematical conjectures based on a general description of the mathematical questions or problem posed. Make and test conjectures by using both inductive and deductive reasoning. Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. xviii