Prentice Hall Mathematics: Algebra Correlated to: Michigan Merit Curriculum for Algebra 1

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1 STRAND 1: QUANTITATIVE LITERACY AND LOGIC STANDARD L1: REASONING ABOUT NUMBERS, SYSTEMS, AND QUANTITATIVE SITUATIONS Based on their knowledge of the properties of arithmetic, students understand and reason about numbers, number systems, and the relationships between them. They represent quantitative relationships using mathematical symbols, and interpret relationships from those representations. L1.1 Number Systems and Number Sense L1.1.1 Know the different properties that hold in SE/TE: 56-62, 70-76, 79-91, , 112, different number systems, and recognize that the , 192, 194, 241, , 608, 610 applicable properties change in the transition from the positive integers, to all integers, to the rational numbers, and to the real numbers. TE: 57, 59, 62, 71-72, 75, 80, 84, 87, 89, 144, 147, 573, 575 Guide: 2-1, 2-3, 2-4, 3-4, 4-6, 10-4; Vocabulary and Study Skills Worksheets (English and Spanish): 2-1, 2-3, 2-4, 2-5, 3-4, 4-6, 10-4; Activity Labs: 2-1, 2-4, 3-4; Technology Activities: 2-3, 3-4, 4-6; Checkpoint Quiz (English and Spanish): 2-4; Quiz Show CD-ROM; TI 83/84 Plus Activities: 2-3; Web Code: atg- 9041, ate-0201, ata-0201, ate-2032, ate- 0203, ata-0203, ate-0204, ata-0204, ate- 0205, ata-0205, ate-0304, ata-0304, ate- 0406, ata-0406, ate-1004, ata-1004 L1.1.2 Explain why the multiplicative inverse of a number has the same sign as the number, while the additive inverse of a number has the opposite sign. SE/TE: 56-62, 72-76, 1

2 TE: 57, 59, 62, 71-72, 75 Worksheets (English and Spanish): 2-1, 2-3; Activity Labs: 2-1; Technology Activities: 2-3 Quiz Show CD-ROM; TI 83/84 Plus Activities: 2-3; Web Code: atg- 9041, ate-0201, ata-0201, ate-2032, ate- 0203, ata-0203 L1.1.3 Explain how the properties of associativity, commutativity, and distributivity, as well as identity and inverse elements, are used in arithmetic and algebraic calculations. SE/TE: 56-62, 70-76, 79-91, , 112 TE: 57, 59, 62, 71-72, 75, 80, 84, 87, 89 Guide: 2-1, 2-3, 2-4; Vocabulary and Study Skills Worksheets (English and Spanish): 2-1, 2-3, 2-4, 2-5; Activity Labs: 2-1, 2-4; Technology Activities: 2-3; Checkpoint Quiz (English and Spanish): 2-4 2

3 Quiz Show CD-ROM; TI 83/84 Plus Activities: 2-3; Web Code: atg- 9041, ate-0201, ata-0201, ate-2032, ate- 0203, ata-0203, ate-0204, ata-0204, ate- 0205, ata-0205, L1.1.4 Describe the reasons for the different effects of multiplication by, or exponentiation of, a positive number by a number less than 0, a number between 0 and 1, and a number greater than 1. SE/TE: 69-76, 110, 112, , 485, 488 TE: 71, , 434 Worksheets (English and Spanish): 2-3, 8-1; Technology Activities: 2-3 Quiz Show CD-ROM; TI 83/84 Plus Activities: 2-3; Web Code: ate- 0203, ata-0203, ate-0801, ata

4 L1.1.5 Justify numerical relationships (e.g., show that the sum of even integers is even; that every integer can be written as 3m +k, where k is 0, 1, or 2, and m is an integer; or that the sum of the first n positive integers is n (n +1)/2). SE/TE: 516(#55), 542, 544 Worksheets (English and Spanish): 9-4 Web Code: ate-0904, ata-0904 L1.2 Representations and Relationships L1.2.2 Interpret representations that reflect absolute value relationships (e.g. l x - a l b, or a ± b ) in such contexts as error tolerance. SE/TE: , TE: 237, 239 Worksheets (English and Spanish): 4-6; Technology Activities: 4-6 4

5 Web Code: ate-0406, ata-0406 L1.2.4 Organize and summarize a data set in a table, plot, chart, or spreadsheet; find patterns in a display of data; understand and critique data displays in the media. SE/TE: 33-39, 42-45, 49-50, , TE: 34, 36, 42, 44, 351, 355 Worksheets (English and Spanish): 1-5, 1-6, 6-7; Activity Labs: 6-7; Checkpoint Quiz (English and Spanish): 1-5, 6-7 Web Code: ate-0105, ata-0105, ate-0106, ata- 0106, ate-2122, ate-0607, ata

6 STANDARD L2: CALCULATION, ALGORITHMS, AND ESTIMATION Students calculate fluently, estimate proficiently, and describe and use algorithms in appropriate situations (e.g., approximating solutions to equations.) They understand the basic ideas of iteration and algorithms. L2.1 Calculation Using Real and Complex Numbers L2.1.1 Explain the meaning and uses of weighted averages (e.g., GNP, consumer price index, grade point average). L2.1.2 Calculate fluently with numerical SE/TE: , , , 488 expressions involving exponents; use the rules of exponents; evaluate numerical expressions involving rational and negative exponents; transition easily between roots and exponents. TE: , 434, , 446, , 452, 455, 458 Worksheets (English and Spanish): 8-1, 8-3, 8-5; Checkpoint Quiz (English and Spanish): 8-4 Web Code: ate-0801, ata-0801, ate-0803, ata- 0803, ate-0775, ate-0804, ata-0804, ate- 0775, ate-0805, ata-0805 L2.1.3 Explain the exponential relationship between a number and its base 10 logarithm, and use it to relate rules of logarithms to those of exponents in expressions involving numbers. 6

7 L2.1.4 Know that the complex number i is one of two solutions to x 2 = -1. L2.1.5 Add, subtract, and multiply complex numbers; use conjugates to simplify quotients of complex numbers. L2.1.6 Recognize when exact answers aren t always possible or practical; use appropriate algorithms to approximate solutions to equations (e.g., to approximate square roots). SE/TE: , TE: 177, 179 Worksheets (English and Spanish): 3-8; Checkpoint Quiz (English and Spanish): 3-8 L3.1 Measurement Units, Calculations, and Scales L3.1.2 Describe and interpret logarithmic relationships in such contexts as the Richter scale, the ph scale, or decibel measurements (e.g., explain why a small change in the scale can represent a large change in intensity); solve applied problems. Web Code: ate-0308, ata-0308, ate-1002, ata STANDARD L3: MEASUREMENT AND PRECISION Students apply measurement units and calculations, and understand the concept of error. 7

8 STRAND 2: ALGEBRA AND FUNCTIONS STANDARD A1: EXPRESSIONS, EQUATIONS, AND INEQUALITIES Students recognize, construct, interpret, and evaluate expressions. They fluently transform symbolic expressions into equivalent forms. They determine appropriate techniques for solving each type of equation, inequality, or system of equations, apply the techniques correctly to solve, justify the steps in the solutions, and draw conclusions from the solutions. They know and apply common formulas. A1.1 Construction, Interpretation, and Manipulation of Expressions (linear, quadratic, polynomial, rational, power, exponential, logarithmic, and trigonometric) A1.1.1 Give a verbal description of an expression SE/TE: 4-8, 10-15, 48, 50 that is presented in symbolic form, write an algebraic expression from a verbal description, and evaluate expressions given values of the variables. TE: 5, 7, 11-12, 14 Worksheets (English and Spanish): 1-1 Web Code: ate-0101, ata-0101, ate-0775, ate- 0102, ata-0102 A1.1.2 Know the definitions and properties of exponents and roots, transition fluently between them, and apply them in algebraic expressions. SE/TE: 9-15, 48, 50, , , , , 655, 658 TE: 11-12, 14, 177, 179, , 446, , 452, 455, 458, , 620 8

9 Worksheets (English and Spanish): 3-8, 8-3, 8-5, 11-1; Checkpoint Quiz (English and Spanish): 3-8, 8-4 Web Code: ate-0775, ate-0102, ata-0102, ate- 0308, ata-0308, ate-0803, ata-0803, ate- 0775, ate-0804, ata-0804, ate-0775, ate- 0805, ata-0805, ate-1101, ata-1101 A1.1.3 Factor algebraic expressions using, for example, greatest common factor, grouping, and the special product identities (e.g., differences of squares and cubes). SE/TE: , , TE: 501, 503, 520, 522, 525, 527, , 532, , 538 Worksheets (English and Spanish): 9-2, 9-5, 9-8; Activity Labs: 9-7; Checkpoint Quiz (English and Spanish): 9-7 9

10 Web Code: ate-0902, ata-0902, ate-0905, ata- 0905, ate-0906, ata-0906, ate-0907, ata- 0907, ate-0775, ata-0908, ate-0908, ate A1.1.6 Transform exponential and logarithmic expressions into equivalent forms using the properties of exponents and logarithms including the inverse relationship between exponents and logarithms. A1.2 Solutions of Equations and Inequalities (linear, quadratic, polynomial, rational, power, exponential, logarithmic, and trigonometric) A1.2.1 Write equations and inequalities with one or two variables to represent mathematical or applied situations, and solve. SE/TE: , , , , 194, , , 244, 246 TE: 121, 123, , 131, , 138, 208, 210, 214, 216, , 224 Worksheets (English and Spanish): 3-1, 3-2, 4-2, 4-4; Activity Labs: 3-3; Technology Activities: 3-3; Checkpoint Quiz (English and Spanish):

11 Quiz Show CD-ROM; TI 83/84 Plus Activities: 3-1, 4-4; Web Code: ate- 0301, ata-0301, ata-0302, ate-0302, ate- 0303, ata-0303, ata-0402, ate-0402, ate- 0403, ata-0403, ate-0775, ate-0404, ata A1.2.2 Associate a given equation with a function whose zeros are the solutions of the equation. SE/TE: , 608, 610 TE: 566, 569 Guide; Technology Activities: 10-3; Checkpoint Quiz (English and Spanish): 10-3 Web Code: ate-1003, ata-1003 A1.2.3 Solve (and justify steps in the solutions) linear and quadratic equations and inequalities, including systems of up to three linear equations with three unknowns; apply the quadratic formula appropriately. SE/TE: , , 244, 246, , , , , 424, , , ,

12 TE: 208, 210, 214, 216, , 224, , 378, 383, 386, , 392, , 401, 566, 569, 573, 575, 581, 583, 587, 589 Worksheets (English and Spanish): 4-2, 4-4, 7-1, 7-2, 7-3, 10-4, 10-6; Activity Labs: 10-5; Technology Activities: 7-1, 7-3, 10-3; Checkpoint Quiz (English and Spanish): 4-3, 7 2, 10-3 Quiz Show CD-ROM; TI 83/84 Plus Activities: 4-4, 7-1, 10-4; Web Code: ata-0402, ate-0402, ate-0403, ata- 0403, ate-0775, ate-0404, ata-0404, ate- 0701, ata-0701, ata-0702, ate-0702, ate- 0775, ate-0703, ata-0703, ate-1003, ata- 1003, ate-1004, ata-1004, ate-0775, ate- 1005, ata-1005, ate-0775, ate-1006, ata A1.2.4 Solve absolute value equations and inequalities, (e.g. solve l x - 3 l 6), and justify steps in the solution. SE/TE: , TE: ,

13 Worksheets (English and Spanish): 4-6; Technology Activities: 4-6 Web Code: ate-0406, ata-0406 A1.2.6 Solve power equations (e.g., (x + 1) 3 = 8) and equations including radical expressions (e.g., = 7), justify steps in the solution, and explain how extraneous solutions may arise. SE/TE: , 656, 658 TE: , 633 Worksheets (English and Spanish): 11-3; Technology Activities:

14 Web Code: ate-0775, ate-1103, ata-1103 A1.2.8 Solve an equation involving several variables (with numerical or letter coefficients) for a designated variable, and justify steps in the solution. SE/TE: STANDARD A2: FUNCTION Students understand functions, their representations, and their attributes. They perform transformations, combine and compose functions, and find inverses. Students classify functions and know the characteristics of each family. They work with functions with real coefficients fluently. A2.1 Definitions, Representations, and Attributes of Functions A2.1.1 Recognize whether a relationship (given in SE/TE: 29-32, 48, 50, , 300, 302 contextual, symbolic, tabular, or graphical form) is a function; and identify its domain and range. TE: 29, 31, 259, 261 Worksheets (English and Spanish): 1-4, 5-2; Activity Labs: 5-2; Checkpoint Quiz (English and Spanish):

15 Web Code: ata-0104, ate-0104, atb-2031, ate- 0502, ata-0502 A2.1.2 Read, interpret, and use function notation, and evaluate a function at a value in its domain. SE/TE: , 300, 302 TE: 259, 261 Worksheets (English and Spanish): 5-2; Activity Labs: 5-2; Checkpoint Quiz (English and Spanish): 5-2 Web Code: ate-0502, ata-0502 A2.1.3 Represent functions in symbols, graphs, tables, diagrams, or words, and translate among representations. SE/TE: , , 300, 302 TE: , 267, ,

16 Worksheets (English and Spanish): 5-4; Activity Labs: 5-4; Technology Activities: 5-3 Quiz; Student Express CD-ROM; TI Navigator, Instant Check System; Success Tracker TM Online Quiz Show CD-ROM; TI 83/84 Plus Activities: 5-3; Web Code: ate- 0775, ate-0503, ata-0503, ate-0504, ata A2.1.4 Recognize that functions may be defined by different expressions over different intervals of their domains; such functions are piecewisedefined (e.g., absolute value and greatest integer functions). A2.1.5 Recognize that functions may be defined recursively, and compute values of and graph simple recursively defined functions (e.g., f (0) = 5, and f (n ) = f (n -1) + 2 ). SE/TE: 296, TE: 297 Guide; Technology Activities:

17 Quiz; Student Express CD-ROM; TI Navigator, Instant Check System; Success Tracker TM Online Web Code: ata-0507, ate-0507, ate-2032 A2.1.6 Identify the zeros of a function and the intervals where the values of a function are positive or negative, and describe the behavior of a function, as x approaches positive or negative infinity, given the symbolic and graphical representations. SE/TE: , 608, 610 TE: 566, 569 Guide; Technology Activities: 10-3; Checkpoint Quiz (English and Spanish): 10-3 Web Code: ate-1003, ata-1003 A2.1.7 Identify and interpret the key features of a function from its graph or its formula(e), (e.g. slope, intercept(s), asymptote(s), maximum and minimum value(s), symmetry, average rate of change over an interval, and periodicity). SE/TE: , , , , 368, , , , 715, 718 TE: , 314, , 334, , 555, ,

18 Worksheets (English and Spanish): 6-1, 6-2, 6-4, 10-1, 12-1; Activity Labs: 6-2; Technology Activities: 6-1, 6-2, 12-1; Checkpoint Quiz (English and Spanish): 6-4 Quiz; Student Express CD-ROM; TI Navigator, Instant Check System; Success Tracker TM Online Quiz Show CD-ROM; TI 83/84 Plus Activities: 6-2, 12-1; Interactive Textbook Online: 6-2; Web Code: ate-0775, ate-0601, ata-0601, ata-0602, ate-0602, ate- 2032, ate-0604, ata-0604, ate-1001, ata- 1001, ate-1201, ata-1201 A2.2 Operations and Transformations A2.2.1 Combine functions by addition, subtraction, multiplication, and division. An opportunity to address this standard can be found on: SE/TE: , 541, 544 TE: 496, 498 Guide; Activity Labs: 9-1; Technology Activities:

19 A2.2.2 Apply given transformations (e.g., vertical or horizontal shifts, stretching or shrinking, or reflections about the x - and y -axes) to basic functions, and represent symbolically. Web Code: ate-0901, ata-0901 SE/TE: , 192, 194, , TE: 151, 154, 360, 362, Guide; Checkpoint Quiz (English and Spanish): 3-5 Quiz Show CD-ROM; TI 83/84 Plus Activities: 6-8; Web Code: ate- 0305, ata-0305, ate-0608, ata-0608 A2.2.3 Recognize whether a function (given in tabular or graphical form) has an inverse and recognize simple inverse pairs (e.g., f (x ) = x 3 and g (x ) = x 1/3 ). 19

20 A2.3 Families of Functions (linear, quadratic, polynomial, rational, power, exponential, logarithmic, and trigonometric) A2.3.1 Identify a function as a member of a family of functions based on its symbolic, or graphical representation; recognize that different families of functions have different asymptotic behavior at infinity, and describe these behaviors. SE/TE: , 715, 718 TE: 669 Worksheets (English and Spanish): 12-1; Technology Activities: 12-1; Quiz Show CD-ROM; TI 83/84 Plus Activities: Web Code: ate- 1201, ata-1201 A2.3.2 Describe the tabular pattern associated with functions having constant rate of change (linear); or variable rates of change. SE/TE: , 365, 368 TE: , 314 Worksheets (English and Spanish): 6-1; Activity Labs: 6-1; Technology Activities:

21 Quiz; Student Express CD-ROM; TI Navigator, Instant Check System; Success Tracker TM Online Web Code: ate-0775, ate-0601, ata-0601 A2.4 Lines and Linear Functions A2.4.1 Write the symbolic forms of linear functions SE/TE: , , 366, 368 (standard [i.e., Ax + By = C, where B 0 ], pointslope, and slope-intercept) given appropriate information, and convert between forms. TE: , 322, 332, 334, , 340 Worksheets (English and Spanish): 6-2, 6-4; Activity Labs: 6-2; Technology Activities: 6-2, 6-5; Checkpoint Quiz (English and Spanish): 6-4 Quiz; Student Express CD-ROM; TI Navigator, Instant Check System; Success Tracker TM Online Quiz Show CD-ROM; TI 83/84 Plus Activities: 6-2; Interactive Textbook Online: 6-2, 6-5; Web Code: ate-0602, ata-0602, ate-2032, ate-0604, ata-0604, ate- 0605, ata-0605 A2.4.2 Graph lines (including those of the form x = h and y = k ) given appropriate information. SE/TE: , , 366,

22 TE: , 322, , 328, 332, 334, , 340 Worksheets (English and Spanish): 6-2, 6-4; Activity Labs: 6-2; Technology Activities: 6-2, 6-5; Checkpoint Quiz (English and Spanish): 6-4 Quiz; Student Express CD-ROM; TI Navigator, Instant Check System; Success Tracker TM Online Quiz Show CD-ROM; TI 83/84 Plus Activities: 6-2; Interactive Textbook Online: 6-2, 6-5; Web Code: ate-0602, ata-0602, ate-2032, ate-0603, ata-0603, ate- 0604, ata-0604, ate-0605, ata-0605 A2.4.3 Relate the coefficients in a linear function to the slope and x - and y -intercepts of its graph. SE/TE: , 366, 368 TE: , 322 Worksheets (English and Spanish): 6-2; Activity Labs: 6-2; Technology Activities:

23 Quiz Show CD-ROM; TI 83/84 Plus Activities: 6-2; Web Code: ate- 0602, ata-0602, ate-2032 A2.4.4 Find an equation of the line parallel or perpendicular to given line, through a given point; understand and use the facts that non-vertical parallel lines have equal slopes, and that nonvertical perpendicular lines have slopes that multiply to give -1. SE/TE: , TE: , 348 Worksheets (English and Spanish): 6-6; Technology Activities: 6-6 Quiz; Student Express CD-ROM; TI Navigator, Instant Check System; Success Tracker TM Online Web Code: ate-0775, ate-0606, ata-0606 A2.5 Exponential and Logarithmic Functions A2.5.1 Write the symbolic form and sketch the graph of an exponential function given appropriate information. (e.g., given an initial value of 4 and a rate of growth of 1.5, write f (x ) = 4 (1.5) x ). SE/TE: , TE: 469,

24 Worksheets (English and Spanish): 8-7; Checkpoint Quiz (English and Spanish): 8-7 Quiz Show CD-ROM; TI 83/84 Plus Activities: 8-7; Web Code: ate- 0807, ata-0807 A2.5.4 Understand and use the fact that the base of an exponential function determines whether the function increases or decreases and understand how the base affects the rate of growth or decay. SE/TE: , TE: , 481 Guide; Activity Labs:

25 A2.5.5 Relate exponential and logarithmic functions to real phenomena, including half-life and doubling time. Web Code: ate-0808, ata-0808 SE/TE: , , TE: 469, 472, , 481 Worksheets (English and Spanish): 8-7; Activity Labs: 8-8; Checkpoint Quiz (English and Spanish): 8-7 Quiz Show CD-ROM; TI 83/84 Plus Activities: 8-7; Web Code: ate- 0807, ata-0807, ate-0808, ata-0808 A2.6 Quadratic Functions A2.6.1 Write the symbolic form and sketch the graph of a quadratic function given appropriate information (e.g., vertex, intercepts, etc.). SE/TE: , 607, 610 TE: , 555, ,

26 Worksheets (English and Spanish): 10-1, 10-2; Technology Activities: 10-2 Web Code: ate-1001, ata-1001, ate-1002, ata A2.6.2 Identify the elements of a parabola (vertex, axis of symmetry, direction of opening) given its symbolic form or its graph, and relate these elements to the coefficient(s) of the symbolic form of the function. SE/TE: , 607, 610 TE: , 555, , 562 Worksheets (English and Spanish): 10-1, 10-2; Technology Activities:

27 Web Code: ate-1001, ata-1001, ate-1002, ata A2.6.3 Convert quadratic functions from standard to vertex form by completing the square. SE/TE: , 608, 610 TE: 581, 583 Guide; Activity Labs: 10-5 Web Code: ate-0775, ate-1005, ata-1005 A2.6.4 Relate the number of real solutions of a quadratic equation to the graph of the associated quadratic function. SE/TE: , 608, 610 TE: 566,

28 Guide; Technology Activities: 10-3; Checkpoint Quiz (English and Spanish): 10-3 Web Code: ate-1003, ata-1003 A2.6.5 Express quadratic functions in vertex form to identify their maxima or minima, and in factored form to identify their zeros. SE/TE: , 608, 610 TE: 573, 575 Worksheets (English and Spanish): 10-4 Quiz Show CD-ROM; TI 83/84 Plus Activities: 10-4; Web Code: ate- 1004, ata

29 A2.7 Power Functions (including roots, cubics, quartics, etc.) A2.7.1 Write the symbolic form and sketch the SE/TE: 605, , , graph of power functions. TE: 639, 642 Worksheets (English and Spanish): 10-8; Activity Labs: 10-8; Technology Activities: 10-8; Checkpoint Quiz (English and Spanish): 11-4 A2.7.2 Express direct and inverse relationships as functions (e.g., y = kx n and y = kx -n, n > 0) and recognize their characteristics (e.g., in y = x 3, note that doubling x results in multiplying y by a factor of 8). Web Code: atg-9041, ate-1008, ata-1008, ate- 1104, ata-1104 A2.7.3 Analyze the graphs of power functions, noting reflectional or rotational symmetry. SE/TE: 605, , , TE: 639,

30 Worksheets (English and Spanish): 10-8; Activity Labs: 10-8; Technology Activities: 10-8; Checkpoint Quiz (English and Spanish): 11-4 Web Code: atg-9041, ate-1008, ata-1008, ate- 1104, ata-1104 A2.8 Polynomial Functions A2.8.1 Write the symbolic form and sketch the graph of simple polynomial functions. SE/TE: , 541, 544 TE: , 498 Worksheets (English and Spanish): 9-1; Activity Labs: 9-1; Technology Activities:

31 Web Code: ate-0901, ata-0901 A2.8.2 Understand the effects of degree, leading SE/TE: , 541, 544 coefficient, and number of real zeros on the graphs of polynomial functions of degree greater than 2. TE: , 498 Worksheets (English and Spanish): 9-1; Activity Labs: 9-1; Technology Activities: 9-1 Web Code: ate-0901, ata-0901 A2.8.3 Determine the maximum possible number of zeros of a polynomial function, and understand the relationship between the x -intercepts of the graph and the factored form of the function. SE/TE: , 608, 610 TE: 566,

32 Guide; Technology Activities: 10-3; Checkpoint Quiz (English and Spanish): 10-3 Web Code: ate-1003, ata-1003 STANDARD A3: MATHEMATICAL MODELING Students construct or select a function to model a real-world situation in order to solve applied problems. They draw on their knowledge of families of functions to do so. A3.1 Models of Real-world Situations Using Families of Functions. A3.1.1 Identify the family of function best suited SE/TE: , , , , for modeling a given real-world situation (e.g., , quadratic functions for motion of an object under the force of gravity; exponential functions for compound interest; trigonometric functions for periodic phenomena. In the example above, recognize that the appropriate general function is exponential (P = P 0 a t ) TE: 477, 478, 481, 552, 555, , 562, ,

33 Worksheets (English and Spanish): 10-1, 10-2, 10-8; Activity Labs: 8-8, 10-8; Technology Activities: 10-2, 10-8 Web Code: ate-0808, ata-0808, ate-1001, ata- 1001, ate-1002, ata-1002, atg-9041, ate- 1008, ata-1008 A3.1.2 Adapt the general symbolic form of a function to one that fits the specifications of a given situation by using the information to replace arbitrary constants with numbers. In the example above, substitute the given values P 0 = 300 and a = 1.02 to obtain P = 300(1.02) t. SE/TE: , , , TE: , 481, 552, 555, , 562 Worksheets (English and Spanish): 10-1, 10-2; Activity Labs: 8-8; Technology Activities:

34 Web Code: ate-0808, ata-0808, ate-1001, ata- 1001, ate-1002, ata-1002 A3.1.3 Using the adapted general symbolic form, draw reasonable conclusions about the situation being modeled. In the example above, the exact solution is , but for this problem an appropriate approximation is 365. SE/TE: , TE: , 481 Guide; Activity Labs: 8-8 Web Code: ate-0808, ata-0808 *A3.1.4 Use methods of linear programming to represent and solve simple real-life problems. 34

35 STRAND 4: STATISTICS AND PROBABILITY STANDARD S2: BIVARIATE DATA EXAMINING RELATIONSHIPS Students plot and interpret bivariate data by constructing scatterplots, recognizing linear and nonlinear patterns, and interpreting correlation coefficients; they fit and interpret regression models, using technology as appropriate. S2.1 Scatterplots and Correlation S2.1.1 Construct a scatterplot for a bivariate data SE/TE: 33-37, 49-50, , set with appropriate labels and scales. TE: 34, 36, 351, 355 Worksheets (English and Spanish): 1-5, 6-7; Activity Labs: 6-7; Checkpoint Quiz (English and Spanish): 1-5, 6-7 Web Code: ate-0105, ata-0105, ate-2122, ate- 0607, ata-0607 S2.1.2 Given a scatterplot, identify patterns, clusters, and outliers; recognize no correlation, weak correlation, and strong correlation. SE/TE: 34-37, TE: 34, 36 35

36 Worksheets (English and Spanish): 1-5; Checkpoint Quiz (English and Spanish): 1-5 S2.1.3 Estimate and interpret Pearson s correlation coefficient for a scatterplot of a bivariate data set; recognize that correlation measures the strength of linear association. Web Code: ate-0105, ata-0105 SE/TE: , TE: 351, 355 Worksheets (English and Spanish): 6-7; Activity Labs: 6-7; Checkpoint Quiz (English and Spanish):

37 S2.1.4 Differentiate between correlation and causation; know that a strong correlation does not imply a cause-and-effect relationship; recognize the role of lurking variables in correlation. Web Code: ate-2122, ate-0607, ata-0607 SE/TE: 34-37, TE: 34, 36 Worksheets (English and Spanish): 1-5; Checkpoint Quiz (English and Spanish): 1-5 Web Code: ate-0105, ata-0105 S2.2 Linear Regression S2.2.1 For bivariate data which appear to form a linear pattern, find the least squares regression line by estimating visually and by calculating the equation of the regression line; interpret the slope of the equation for a regression line. SE/TE: , TE: 351,

38 Worksheets (English and Spanish): 6-7; Activity Labs: 6-7; Checkpoint Quiz (English and Spanish): 6-7 Web Code: ate-2122, ate-0607, ata-0607 S2.2.2 Use the equation of the least squares regression line to make appropriate predictions. SE/TE: , TE: 351, 355 Worksheets (English and Spanish): 6-7; Activity Labs: 6-7; Checkpoint Quiz (English and Spanish): 6-7 Web Code: ate-2122, ate-0607, ata

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