# STANDARDS MAP. Grade Eight - Math

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1 Program Title: Prentice Hall Algebra 1, California Edition STANDARDS MAP Grade Eight - Math IMAP/CRP Publisher Comments Meets Standard ALGEBRA I 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 SE/TE: 9-14, 19-28, 59-86, 89-97, TE: 2C-D, 52C-D SE/TE: TE: 2C, 52C-D SE/TE: , , Reteaching: 2, 4, 5, 12-18, 32 Transparencies: T11, T12 Section 2.2 Videos: 3, Properties of Real Numbers SE/TE: Mathematical Reasoning 14, 23, 28, 62, 70, 76, 118, 124, 128, 147, 179, 182, 185, 186, 248, 272, 277, 366, 512, 522, and Critical Thinking 28, 85, 92, 97, 122, 138, 208, 212, 244, 269, 409, 435 Algebra Student Tutorial CD-ROM 1

2 2.0 Students understand and SE/TE: 54-58, 82-86, 93-97, 204- SE/TE:15-18, , use such operations as 213, , , taking the opposite, finding 503 Reteaching: 3, 38, 39, the reciprocal, taking a TE: 52C-D, 202C, 480C-D root, and raising to a Transparencies: T17, fractional power. They T44, T46, T48, T49 understand and use the rules of exponents Section 5.1 Videos: 8, Exponents; 18, Introduction to Radicals; 20, Rational Exponents 3.0 Students solve equations and inequalities involving absolute values SE/TE: , TE: 112D, 398D Reteaching: 27, 76, 77 Transparencies: T13, T36-T38 Sections 3.2, Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x - 5) + 4(x - 2) =12 SE/TE: 24-28, SE/TE: , , Transparencies: T12, T15 Sections 2.2, 3.2 Videos: 4, Simplifying Algebraic Expressions Algebra Student Tutorial CD-ROM 2

3 5.0 Students solve multistep SE/TE: , , 183- SE/TE: ; problems, including word 191, "Multi-Step problems, involving linear TE: 112C-D, 170C-D 398C-D Problem" equations and linear inequalities in one variable 32, 124, 208, and provide justification 234, 295, 377, for each step 383, 384, 423, 462, 463, 556, 584, 585, 594 Reteaching: 22, 24-26, 28, 29, 35, 36, 75, 93 Transparencies: T15, T35, T36 Sections 3.2, 3.3 Videos: 5, Solving Linear Equations; 6, Solving Linear Inequalities 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) SE/TE: , , TE: 302C-D, 398D Reteaching: 60, 61, 63, 78 Transparencies: T25- T27, T39-T41 Sections 4.1, 4.3, 4.5 Videos: 7, Graphing Linear Equations; Intercepts; 8, Graphing Linear Inequalities; 15, The Slope Intercept Form Algebra Student Tutorial CD-ROM 3

4 7.0 Students verify that a point SE/TE: , SE/TE: lies on a line, given an TE: 302D Reteaching: 64, 65 equation of the line. Transparencies: T30, Students are able to derive T31 linear equations by using the point-slope formula Section 4.2 Videos: 16, The Point Slope Form 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 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 SE/TE: TE: 302D SE/TE: , TE: 356C-D SE/TE: Transparencies: T29, T32, T33 Section 4.3 SE/TE: Reteaching: 68-71, 73 Transparencies: T34, T42a, b, c, T43a, b Sections 4.4, 4.5 Videos: 17, Solving Systems of Linear Equations; 18, Systems of Linear Inequalities Algebra Student Tutorial CD-ROM 4

5 10.0 Students add, subtract, SE/TE: 26-28, 90-92, 94-97, 214- Reteaching: 40, 45-48, multiply, and divide 216, , , 58 monomials and , , 557- Transparencies: T12, polynomials. Students 569 T19, T23 solve multistep problems, TE: 202C-D, 430D including word problems, Sections 2.2, 5.2, 5.3 by using these techniques Videos: 9, Adding, Subtracting, Multiplying Polynomials; Special Products; 10, Division of Polynomials Puzzles: 74-76, Students apply basic factoring techniques to second- and simple thirddegree 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 SE/TE: TE: 260C-D SE/TE: TE: 430C Reteaching: Transparencies: T20, T21 Section 5.4 Videos: 10, The Greatest Common Factor and Factoring by Grouping; 11, Factoring Trinomials and Binomials; 12, Choosing a Factoring Strategy Puzzles: 80, 82 SE/TE: Reteaching: 79 Section 8.1 Videos: 13, Simplifying Rational Expressions Algebra Student Tutorial CD-ROM 5

6 13.0 Students add, subtract, SE/TE: , , 541, SE/TE: , 604- multiply, and divide rational expressions and TE: 430C-D 574D Reteaching: 80-84, 105 functions. Students solve both computationally and Section 8.1 conceptually challenging Videos: 13, problems by using these Multiplying and techniques Dividing Rational Expressions; Adding and Subtracting Rational Expressions; 14, Simplifying Complex Fractions; Solving Equations Containing Rational Expressions 14.0 Students solve a quadratic equation by factoring or completing the square 15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems SE/TE: , , , TE: 260D, 574C SE/TE: , , TE: 356D, 430D, 534D SE/TE:589 Reteaching: 57, 58, 101, 103, Transparencies: T23, T60 Section 6.1 Videos: 12, Solving Quadratic Equations by Factoring; 21, Solving Quadratic Equations by Completing the Square SE/TE: , , 518, , Reteaching: 72, 85 Transparencies: T56 Algebra Student Tutorial CD-ROM 6

7 16.0 Students understand the SE/TE: SE/TE: , 591- concepts of a relation and a TE: 534C-D 594 function, determine Reteaching: whether a given relation Transparencies: T50 defines a function, and give pertinent information about Section 7.1 given relations and Videos: 16, Functions 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 SE/TE: TE: 534C SE/TE: SE/TE: TE: 574D SE/TE: Transparencies: T51 Section 7.1 SE/TE:588 Reteaching: 104 Transparencies: T59, T60 Section 6.2 Videos: 21, Solving Quadratic Equations by the Quadratic Formula Algebra Student Tutorial CD-ROM 7

8 20.0 Students use the quadratic SE/TE: , Reteaching: 104, 105, formula to find the roots of TE: 574D 107 a second-degree Transparencies: T59, polynomial and to solve T60 quadratic equations Section 6.2 Videos: 21, Solving Quadratic Equations by the Quadratic Formula 21.0 Students graph quadratic functions and know that their roots are the x- intercepts SE/TE: , 576 TE: 534D SE/TE: Reteaching: 97 Transparencies: T52- T55, T57, T58, T60 Section 7.3 Videos: 22, Graphing Quadratic Equations Algebra Student Tutorial CD-ROM 8

9 22.0 Students use the quadratic SE/TE: , Transparencies: T59 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 SE/TE: , TE: 574C SE/TE: 35-37, 38-39, 44-46, , , , , , , 410, 468, TE: 39 SE/TE: , 295, , 593 Reteaching: 107 Videos: 12, Quadratic Equations and Problem Solving SE/TE: , , , , ; "Write a Convincing Argument" 39, 46, 70, 85, 86, 106, 117, 123, 146, 156, 157, 164, 195, 255, 296, 322, 332, 337, 341, 345, 379, 385, 391, 476, 579, 584, 594, 606 TE: 170D Reteaching: 8, 10, 31, 37, 67, 86 Transparencies: T9 Algebra Student Tutorial CD-ROM 9

10 24.1 Students explain the SE/TE: , TE: 170D difference between inductive and deductive reasoning and identify and provide examples of each 24.2 Students identify the hypothesis and conclusion in logical deduction SE/TE: 192TE: 170D 24.3 Students use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion 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 SE/TE: 14, TE: 14, 23 SE/TE: 35-37, , , , , , , , 486, TE: 52D, 112C SE/TE:"Counterexample" 14, 18, 76, 85, 106, 124, 146, 182, 192, 193, 208, 212, 244, 569, 597 SE/TE: , Algebra Student Tutorial CD-ROM 10

11 25.1 Students use properties of SE/TE: , , 486 SE/TE:"Write a numbers to construct TE: 14, 52D Convincing simple, valid arguments Argument" (direct and indirect) for, or formulate counterexamples 85, 106, 117, to, claimed assertions 123, 146, 156, 157, 296, 322, 332, 341, 379, 385, 391, 579, 594, 606; "Counterexampl e" exercises on pp. 14, 18, 76, 85, 106, 124, 146, 182, 192, 193, 208, 212, 244, 597 TE: 23, 39 Algebra Student Tutorial CD-ROM 11

12 25.2 Students judge the validity SE/TE: 33, 35-37, , 147 SE/TE:Additional of an argument according TE: 8, 52D "Error Analysis" to whether the properties of the real number system and 8, 18, 37, 43, 74, the order of operations 118, 129, 162, have been applied correctly 179, 182, 186, at each step 208, 224, 244, 280, 295, 322, 345, 386, 416, 435, 493, 505, 511, 569, 597, 601 TE: 8 Enrichment: Looking for Errors Puzzles: Error Analysis pages 23, 28, 49, 58, 59, 64, 78, 83, 89, 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 SE/TE: SE/TE:"Sometimes, always, never" 18, 62, 69, 76, 80, 118, 146, 147, 186, 225, 248, 317, 435, 485, 489, 541, 585, 594 TE: 18 Algebra Student Tutorial CD-ROM 12

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