correlated to the Washington D.C. Public Schools Learning Standards Algebra I

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1 correlated to the Washington D.C. Public Schools Learning Standards Algebra I

2 McDougal Littell Algebra correlated to the Washington DC Public Schools Learning Standards Algebra I NUMBER SENSE AND OPERATIONS INDICATORS AI.N.1 Use the properties of operations on real numbers, including the associative, commutative, identity, and distributive properties, and use them to simplify calculations. PE/TE: Lesson 1.2: Apply Order of Operations, 8-10, 11 (#19, 32-33) Lesson 2.2: Add Real Numbers, Lesson 2.3: Subtract Real Numbers, 84 (#53-56) Lesson 2.4: Multiply Real Numbers, Lesson 2.5: Apply the Distributive Property, , 101 (#9-12) Lesson 2.6: Divide Real Numbers, AI.N.2 Simplify numerical expressions, including those involving integer exponents or the absolute value (e.g., 3(2 4 1) = 45, = 14); apply such simplifications in the solution of problems. PE/TE: Lesson 1.2: Apply Order of Operations, 8-11 Lesson 1.4: Write Equations and Inequalities, 26 (#55-57) Chapter Review: 54 (#13-18) Chapter Test: 57 (#1-3) Lesson 2.1: Use Integers and Rational Numbers, 68 (#42-49) AI.N.3 Calculate and apply ratios, proportions, rates, and percentages to solve a range of consumer and practical problems. PE/TE: Lesson 3.5: Write Ratios and Proportions, 166 (#45-52), 167 (#53-55) Lesson 3.7: Solve Percent Problems, 180 (#33-36), 181 (#37-40) Lesson 3.5 Extension: Find Percent of Change, 183 (#11-14) Chapter Review: 195 (#44, 51-52) Chapter Test: 197 (# ) Lesson 4.4: Find Slope and Rate of Change, 237 (#7), 240 (#19-21), 241 (#36-37) 1

3 AI.N.4 Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers, including approximate error in measurement and the approximate value of square roots. (Reminder: This is without the use of calculators.) PE/TE: Lesson 2.7: Find Square Roots and Compare Real Numbers, 111, 114 (#15-22), 115 Lesson 3.7: Solve Percent Problems, 178 Lesson 3.7 Extension: Find Percent of Change, 182 AI.N.5 Understand the concept of nth roots of positive real numbers and of raising a positive real number to a fractional power. Use the rules of exponents also for fractional exponents. PE/TE: Lesson 8.3 Extension: Define and Use Fractional Exponents, AI.N.6 Apply the set operations of union and intersection and the concept of complement, universal set, and disjoint sets, and use them to solve problems, including those involving Venn diagrams. PE/TE: Lesson 2.1 Extension: Apply Sets to Numbers and Functions,

4 PATTERNS, RELATIONS AND ALGEBRA INDICATORS AI.P.1 Recognize, describe, and extend patterns governed by a linear, quadratic, or exponential functional relationship or by a simple iterative process (e.g., the Fibonacci sequence). PE/TE: Activity 1.3: Patterns and Expressions, 14 Activity 8.1: Products and Powers, 488 Activity 8.3: Zero and Negative Exponents, 502 AI.P.2 Use properties of the real number system to judge the validity of equations and inequalities and to justify every step in a sequential argument. PE/TE: Lesson 3.1: Solve One-Step Equations, Lesson 3.2: Solve Two-Step Equations, Lesson 3.3: Solve Multi-Step Equations: Lesson 3.4: Solve Equations with Variables on Both Sides, Lesson 6.1: Solve Inequalities Using Addition and Subtraction, , 359 (#10-21) Lesson 6.2: Solve Inequalities Using Multiplication and Division, Lesson 6.3: Solve Multi-Step Inequalities, , 372 AI.P.3 Demonstrate an understanding of relations and functions. Identify the domain, range, and dependent and independent variables of functions. PE/TE: Lesson 1.6: Represent Functions as Rules and Tables, Lesson 4.1: Plot Points in a Coordinate Plane, 207, 210 (#24-27) Lesson 4.2: Graph Linear Equations, , 219 (#26-31), 220 (#37), 221 (#40) Mixed Review of Problem Solving: 233 (#4-5) AI.P.4 Translate between different representations of functions and relations: graphs, equations, sets of ordered pairs (scatter plots), verbal, and tabular. PE/TE: Lesson 1.6: Represent Functions as Rules and Tables, Activity 1.7: Scatter Plots and Functions, 42 Lesson 1.7: Represent Functions as Graphs, Lesson 1.7 Extension: Determine Whether a Relation Is a Function, Mixed Review of Problem Solving: 51 (#8) Chapter Review: 56 (#35-40) Chapter Test: 57 (#16, 19) Standardized Test Practice: 61 (#9, 11, 17-18) Lesson 5.6: Fit a Line to Data, , 328 (#6-7), 329 (#8, 13-14), 330 (#19), 331 (#20-21) AI.P.5 Demonstrate an understanding of the relationship between various representations of a line. Determine a line s slope and x- and y-intercepts from its graph or from a linear equation that represents the line. PE/TE: Lesson 4.3: Graph Using Intercepts, Lesson 4.4: Find Slope and Rate of Change, , 239 Activity 4.5: Slope and y-intercept, 243 Lesson 4.5: Graph Using Slope-Intercept Form,

5 AI.P.6 Find a linear function describing a line from a graph or a geometric description of the line (e.g., by using the point-slope or slope y-intercept formulas). Explain the significance of a positive, negative, zero, or undefined slope. PE/TE: Lesson 4.4: Find Slope and Rate of Change, , 239 (#4-6) Lesson 5.1: Write Linear Equations in Slope-Intercept Form, , Lesson 5.2: Use Linear Equations in Slope-Intercept Form, 292, 296 (#3-8) Lesson 5.3: Write Linear Equations in Point-Slope Form, 303, 305 (#3-11), 306 (#20-22) AI.P.7 Find linear functions that represent lines either perpendicular or parallel to a given line and through a point (e.g., by using the point-slope form of the equation). PE/TE: Lesson 5.5: Write Equations of Parallel and Perpendicular Lines, AI.P.8 Add, subtract, and multiply polynomials with emphasis on 1st- and 2nd-degree polynomials. PE/TE: Lesson 9.1: Add and Subtract Polynomials, Lesson 9.2: Multiply Polynomials, AI.P.9 Demonstrate facility in symbolic manipulation of polynomial and rational expressions by rearranging and collecting terms, factoring [e.g., a 2 - b 2 = (a + b)(a - b), x x + 21 = (x + 3)(x+ 7), 5x x 3-5x 2 = 5x 2 (x 2 + 2x - 1)], identifying and canceling common factors in rational expressions, and applying the properties of positive integer exponents. PE/TE: Lesson 9.4: Solve Polynomial Equations in Factored Form, 578 (#17-25), 579 (#40-45) Lesson 9.5: Factor x 2 + bx + c, , 586 (#3-17) Lesson 9.6: Factor ax 2 + bx + c, , 599 (#1-15) Lesson 9.7: Factor Special Products, , 603 (#3-24) Lesson 9.8: Factor Polynomials Completely, , 610, 611 (#61-66) AI.P.10 Divide polynomials by monomials with emphasis on 1st- and 2nd-degree polynomials. PE/TE: Lesson 12.3: Divide Polynomials, 784, 788 (#3-6) AI.P.11 Perform basic arithmetic operations with rational expressions and functions. PE/TE: Lesson 12.2: Graph Rational Functions, Lesson 12.5: Multiply and Divide Rational Expressions, Lesson 12.6: Add and Subtract Rational Expressions, Chapter Test: 835 (#8-10, 14-19) 4

6 AI.P.12 Find solutions to quadratic equations (with real roots) by factoring, completing the square, or using the quadratic formula. Demonstrate an understanding of the equivalence of the methods PE/TE: Lesson 10.3: Solve Quadratic Equations by Graphing, 643 Activity 10.5: Completing the Square Using Algebra Tiles, 662 Lesson 10.5: Solve Quadratic Equations by Completing the Square, Lesson 10.6: Solve Quadratic Equations by the Quadratic Formula, Chapter Review: 699 (#20-30) AI.P.13 Solve equations and inequalities, including those involving absolute value of linear expressions (e.g., x 2 > 5), and apply to the solution of problems. PE/TE: Lesson 3.1: Solve One-Step Equations, Lesson 3.2: Solve Two-Step Equations, Lesson 3.3: Solve Multi-Step Equations, Lesson 3.4: Solve Equations with Variables on Both Sides, Lesson 6.1: Solve Inequalities Using Addition and Subtraction, Activity 6.2: Inequalities with Negative Coefficients, 362 Lesson 6.2: Solve Inequalities Using Multiplication and Division, Lesson 6.3: Solve Multi-Step Inequalities, Lesson 6.4: Solve Compound Inequalities, Lesson 6.5: Solve Absolute Value Equations, Lesson 6.6: Solve Absolute Value Inequalities, Chapter Review: 415 (#5-7), 416 (#8-19), 417 (#20-30), 418 (#31-36) Chapter Test: 419 (#5-25) AI.P.14 Solve everyday problems (e.g., compound interest and direct and inverse variation problems) that can be modeled using linear or quadratic functions. Apply appropriate graphical or symbolic methods to the solution. PE/TE: Lesson 4.6: Model Direct Variation, Chapter Review: 274 (#22-28) Lesson 8.5: Write and Graph Exponential Growth Functions, 523, 525 (#38), 527 (#47-50), Lesson 12.1: Model Inverse Variation, AI.P.15 Solve everyday problems (e.g., mixture, rate, and work problems) that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. PE/TE: Lesson 7.1: Solve Linear Systems by Graphing, 429 (#4-5), 432 (#31-33), 433 (#34-36) Lesson 7.2: Solve Linear Systems by Substitution, 437 (#4-5), 438 (#6), 440, 441 (#35-38) Lesson 7.3: Solve Linear Systems by Adding or Subtracting, 449, 450 (#43-45) Lesson 7.4: Solve Linear Systems by Multiplying First, 453 (#4), 456, 457 (#43-44) Mixed Review: 458 Lesson 7.5: Solve Special Types of Linear Systems, 464, 465 (#35-41) Lesson 7.6: Solve Systems of Linear Inequalities, 468 (#6), 471, 472 (#41) Mixed Review: 473 5

7 DATA ANALYSIS, STATISTICS AND PROBABILITY INDICATORS AI.D.1 Select, create, and interpret an appropriate graphical representation (e.g., scatter plot, table, stemand-leaf plots, circle graph, line graph, and line plot) for a set of data, and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data. PE/TE: Lesson 13.7: Interpret Stem-and-Leaf Plots and Histograms, 883 (#8-9), 885 (#20-22) 6

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MATHEMATICS CURRICULUM MAP

Haverhill Public Schools MATHEMATICS CURRICULUM MAP Working Document, 2008-2009 TERM 1 AUGUST/SEPTEMBER/OCTOBER TERM 2 NOVEMBER/DECEMBER/JANUARY Introduction to Algebra Graphs and Linear Equations Integers