Prentice Hall Algebra 1, Oklahoma Edition 2011 Algebra I C O R R E L A T E D T O, Algebra I (Updated August 2006)
PROCESS STANDARDS High School The National Council of Teachers of Mathematics (NCTM) has identified five process standards: Problem Solving, Reasoning and Proof, Communication, Connections, and Representation. Active involvement by students using these processes is likely to broaden mathematical understandings and lead to increasingly sophisticated abilities required to meet mathematical challenges in meaningful ways. Process Standard 1: Problem Solving 1. Apply a wide variety of problem-solving strategies (identify a pattern, use equivalent representations) to solve problems from within and outside mathematics. 2. Identify the problem from a described situation, determine the necessary data and apply appropriate problem-solving strategies. Process Standard 2: Communication 1. Use mathematical language and symbols to read and write mathematics and to converse with others. 2. Demonstrate mathematical ideas orally and in writing. 3. Analyze mathematical definitions and discover generalizations through investigations. Process Standard 3: Reasoning 1. Use various types of logical reasoning in mathematical contexts and real-world situations. 2. Prepare and evaluate suppositions and arguments. 3. Verify conclusions, identify counterexamples, test conjectures, and justify solutions to mathematical problems. 4. Justify mathematical statements through proofs. Process Standard 4: Connections 1. Link mathematical ideas to the real world (e.g., statistics helps qualify the confidence we can have when drawing conclusions based on a sample). SE/TE: 6, 9, 50, 73, 256, 264, 295, 296, 297, 300, 327, 476, 638 SE/TE: 146, 174, 232, 335, 408-409, 477, 481-482, 484, 552, 588, 604 SE/TE: 48, 88, 153, 179, 185, 192, 227, 316, 341, 462, 509, 524, 541, 547, 581, 605, 665, 673 SE/TE: 157, 163, 180, 249, 255, 262, 342, 367, 416, 566, 595, 716 SE/TE: 256-257, 262-263, 272, 351, 384, 568, 573, 604-605, 750 SE/TE: 28-29, 71, 97, 135, 167, 254, 282, 352, 363, 382, 385, 390, 396, 425, 442, 508, 671 SE/TE: 45, 344, 400-401, 442 SE/TE: 28-29, 69, 130, 150, 218, 282, 382, 400, 533, 692 SE/TE: 28, 29, 48, 71, 97, 137, 151, 192, 339, 401, 476, 602 SE/TE: 130-131, 297, 445, 449, 477, 575-576, 688 1
2. Apply mathematical problem-solving skills to other disciplines. 3. Use mathematics to solve problems encountered in daily life. 4. Relate one area of mathematics to another and to the integrated whole (e.g., connect equivalent representations to corresponding problem situations or mathematical concepts). Process Standard 5: Representation 1. Use algebraic, graphic, and numeric representations to model and interpret mathematical and real world situations. 2. Use a variety of mathematical representations as tools for organizing, recording, and communicating mathematical ideas (e.g., mathematical models, tables, graphs, spreadsheets). 3. Develop a variety of mathematical representations that can be used flexibly and appropriately. SE/TE: 43, 119, 220, 290, 327, 383, 411, 483, 569, 630, 754 SE/TE: 136, 139, 152-153, 157-158, 180, 295, 407-409, 421, 523, 588, 597, 685, 723 SE/TE: 76, 164, 238, 303, 373, 433, 491, 557, 616, 654, 700, 773 SE/TE: 69-74, 96, 349-353, 364, 382, 416, 426, 475, 574, 626 SE/TE: 6, 248-251, 262, 371, 405-406, 556, 579, 716 SE/TE: 68, 86, 178-179, 256-257, 484, 486, 513, 532, 678, 710-713 2
MATHEMATICS CONTENT STANDARDS Algebra I (Updated August 2006) The following skills are required of all students completing Algebra I. Major Concepts should be taught in depth using a variety of methods and applications (concrete to the abstract). Maintenance Concepts have been taught previously and are a necessary foundation for this course. The major concepts are considered minimal exit skills and districts are strongly encouraged to exceed these skills when building an Algebra I curriculum. Visual and physical models, calculators, and other technologies are recommended when appropriate and can enhance both instruction and assessment. MAJOR CONCEPTS Number Sense and Algebraic Operations - Polynomials, Exponents, Expressions Relations and Functions - Linear Functions & Slope Formulas Data Analysis, Statistics and Probability - Tables, Graphs, Charts, Scatter Plots MAINTENANCE CONCEPTS Number Sense & Algebraic Reasoning- Equations, Inequalities, Exponents, Rational Numbers Geometry Volume, Surface Area, Ratio, Proportion, Formulas Data Analysis and Statistics - Graphical Representations, Measures of Central Tendency Standard 1: Number Sense and Algebraic Operations - The student will use expressions and equations to model number relationships. 1. Equations and Formulas 2. Expressions a. Translate word phrases and sentences into expressions and equations and vice versa. b. Solve literal equations involving several variables for one variable in terms of the others. c. Use the formulas from measurable attributes of geometric models (perimeter, circumference, area and volume), science, and statistics to solve problems within an algebraic context. d. Solve two-step and three-step problems using concepts such as rules of exponents, rate, distance, ratio and proportion, and percent. a. Simplify and evaluate linear, absolute value, rational and radical expressions. b. Simplify polynomials by adding, subtracting or multiplying. SE/TE: 4-10, 33, 62, 64, 66, 70, 72, 78 SE/TE: 117-122, 127 SE/TE: 118-122, 123-124, 127, 200, 202-203, 256-258, 282, 284, 582, 667, 729, 752-756, 774 SE/TE: 111, 115, 126-127, 130-135, 138-141, 150, 157, 631, 642, 695-697 SE/TE: 28, 30, 34, 50, 52-55, 56-60, 77, 632-635, 636-639, 640-645, 655-656, 664-670, 701 SE/TE: 502-507, 508, 511-512, 513, 514-516, 517-521, 528-529 c. Factor polynomial expressions. SE/TE: 509-512, 529, 532, 533-538, 539-544, 545-550, 551-555, 558 3
Standard 2: Relations and Functions - The student will use relations and functions to model number relationships. 1. Relations and Functions a. Distinguish between linear and nonlinear data. b. Distinguish between relations and functions. c. Identify dependent and independent variables, domain and range. d. Evaluate a function using tables, equations or graphs. 2. Linear Equations and Graphs a. Solve linear equations by graphing or using properties of equality. b. Recognize the parent graph of the functions y = k, y = x, y = x, and predict the effects of transformations on the parent graph. c. Slope I. Calculate the slope of a line using a graph, an equation, two points or a set of data points. II. Use the slope to differentiate between lines that are parallel, perpendicular, horizontal, or vertical. III. Interpret the slope and intercepts within the context of everyday life (e.g., telephone charges based on base rate [yintercept] plus rate per minute [slope]). d. Develop the equation of a line and graph linear relationships given the following: slope and y-intercept, slope and one point on the line, two points on the line, x-intercept and y-intercept, a set of data points. e. Match equations to a graph, table, or situation and vice versa. 3. Linear Inequalities and Graphs a. Solve linear inequalities by graphing or using properties of inequalities. b. Match inequalities (with 1 or 2 variables) to a graph, table, or situation and vice versa. 4. Solve a system of linear equations by graphing, substitution or elimination. SE/TE: 255, 257-260, 262-264, 266-267, 304-305 SE/TE: 257, 262, 286-290, 291-294, 306 SE/TE: 255-256, 258, 260, 267, 282, 286-287, 289-290, 291-294, 304, 306 SE/TE: 270-276, 278-279, 289-290, 305-306, 475-480, 494 SE/TE: 62, 64, 69, 72, 78, 87-93, 94-100, 101-104, 105-108, 110-116, 125-127, 278-279 SE/TE: 329, OK2 3, OK4 5 SE/TE: 314-320, 330, 332-333, 345-346 SE/TE: 351, 353-354, 357-362, 374 SE/TE: 314-315, 317, 319-320, 329, 335-336, 342-343, 349 SE/TE: 329-333, 338-340, 341-344, 346, 349-350, 354 SE/TE: 70, 72, 74, 78, 256-257, 259-260, 270-271, 274-276, 280-285, 304-306, 330, 332, 334-337, 339, 341-344, 346, 350-351 SE/TE: 174-177, 178-183, 184-190, 191-196, 199-205, 206-207, 216-221, 239 SE/TE: 382-387, 388, 390-395, 396-398, 399-404, 407-411, 412-413 4
* 5. Nonlinear Functions a. Match exponential and quadratic functions to a table, graph or situation and vice versa. b. Solve quadratic equations by graphing, factoring, or using the quadratic formula. SE/TE: 476-480, 488, 494, 566-572, 573-578, 580-585, 586-590, 591-592, 601-607, 617 Standard 3: Data Analysis, Probability and Statistics - The student will use data analysis, probability and statistics to formulate and justify predictions from a set of data. 1. Data Analysis a. Translate from one representation of data to another and understand that the data can be represented using a variety of tables, graphs, or symbols and that different modes of representation often convey different messages. b. Make valid inferences, predictions, and/or arguments based on data from graphs, tables, and charts. c. Solve two-step and three-step problems using concepts such as probability and measures of central tendency. 2. Collect data involving two variables and display on a scatter plot; interpret results using a linear model/equation and identify whether the model/equation is a line best fit for the data. SE/TE: 716-721, 730-731, 733-735, 746-747 SE/TE: 718, 720-721, 732-735, 744-745, 746-747 SE/TE: 722-728, 734-735, 746, 759-760, 762-763, 767-771, 774-775 SE/TE: 364-370, 371, 374 5