ALABAMA COURSE OF STUDY MATHEMATICS GRADES 9-12
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1 COURSE OF STUDY MATHEMATICS GRADES 9-12 Correlated to BASIC MATH SKILLS, ALGEBRA, GEOMETRY, ALGEBRA 2, LIFE SKILLS MATH, CONSUMER MATHEMATICS, MATH FOR THE WORLD OF WORK 4201 Woodland Road Circle Pines, Minnesota Telephone (651) or (800)
2 MATERIALS USED IN THIS ALABAMA/ CORRELATION: ALGEBRA 2004 GEOMETRY 2001 ALGEBRA LIFE SKILLS MATH 2003 CONSUMER MATHEMATICS 2003 MATH FOR THE WORLD OF WORK
3 TABLE OF CONTENTS ALGEBRA I... 3 GEOMETRY... 7 ALGEBRA II ALGEBRAIC CONNECTIONS
4 SE: Student Edition TE: Teacher Edition TRL: Teacher s Resource Library ALABAMA ALGEBRA I Number and Operations Students will: 1. Simplify numerical expressions using properties of real numbers and order of operations, including those involving square roots, radical form, or decimal approximations. Example: Express in simplified form. Applying laws of exponents to simplify expressions, including those containing zero and negative integral exponents Algebra 2. Analyze linear functions from their equations, slopes, and intercepts. Finding the slope of a line from its equation or by applying the slope formula Determining the equations of linear functions given two points, a point and the slope, tables of values, graphs, or ordered pairs Graphing two-variable linear equations and inequalities on the Cartesian plane Algebra I 3. Determine characteristics of a relation, including its domain, range, and whether it is a function, when given graphs, tables of values, mappings, or sets of ordered pairs. Finding the range of a function when given its domain Example: finding the range of f(x) = -x 2 + 2x 3 when given the domain {-4, -2, 0, 2, 4} ALGEBRA SE: pp. 4-15, 17, 28, 31-43, 46-58, , , , , , TE: pp. 4-15, 17, 28, 31-43, 46-58, , , , , , Applications: (Home, Career, Community): pp. 5, 33, 39, 58, 191, 198, 211, 215, 221, 330, 342, 343; Mental Math: pp. 17, 37, 47, 127, 132, 158, 189, 199, 335, 337; Manipulatives: pp. 5, 7, 9, 11, 51, 57, 125, 197, 201; Group Problem Solving: pp. 5, 7, 11, 13, 35, 49, 57, 130, 135, 203, 212, 331, 335, 341, 343; Learning Styles: pp. 7, 9, 11, 13, 15, 17, 33, 35, 49, 51, 57, 125, 127, 130, 132, 157, 158, , 193, , , 213, 221, 330, 333, 339, 343 TRL: Workbook Activities: 2-9, 13-17, 19-23, 46-49, 58, 73-75, ; Activities/Alternative Activities: 2-9, 13-17, 19-23, 43-46, 54, 69-70, , SE: pp , TE: pp , ; Applications: (Home, Career, Community): pp. 259, 293; Group Problem Solving: pp. 261, 264, 291; Learning Styles: pp. 260, 290, 293 TRL: Workbook Activities: 88-89, 95-96; Activities/Alternative Activities: 82-83, SE: pp TE: pp ; Group Problem Solving: pp. 264; Learning Styles: p. 266 TRL: Workbook Activities: 89-90; Activities/Alternative Activities: SE: pp , , TE: pp , , ; Applications: (Home, Career, Community): pp. 251, 281; Manipulatives: p. 305; Group Problem Solving: pp. 261, 272, 305; Learning Styles: pp. 255, 257, 260, 277, 278, 281, 282; Application Activity 9, Everyday Algebra 9 TRL: Workbook Activities/Activities: 86-88, 92-94, 100; Alternative Activities: 80-82, 86-88, 94 SE: pp TE: pp ; Learning Styles: pp. 269, 271 TRL: Workbook Activities: 91; Activities/Alternative Activities: 85 3
5 ALGEBRA I 4. Represent graphically common relations, including x = constant, y = constant, y = x, y = x, y = x 2, and y = x. Identifying situations that are modeled by common relations, including x = constant, y = constant, y = x, y = x, y = x 2, and y = x 5. Perform operations of addition, subtraction, and multiplication on polynomial expressions. Dividing by a monomial 6. Factor binomials, trinomials, and other polynomials using GCF, difference of squares, perfect square trinomials, and grouping. 7. Solve multistep equations and inequalities including linear, radical, absolute value, and literal equations. Examples: solving for x in problems such as x 4 = 0, x-4 < 2, x = 6, x + 3 > 10, and y = mx + b Writing the solution of an equation or inequality in set notation Example: finding the solution of x + 3 > 10 to be {x x > 7 or x < - 13} ALGEBRA scope of AGS Algebra. SE: pp TE: pp ; Applications: (Home, Career, Community): pp. 146, 147; Mental Math: p. 139; Manipulatives: pp. 139, 140, 145; Group Problem Solving: pp. 137, 139, 141, 147; Learning Styles: pp. 137, 139, 143, 146, 147, 149 TRL: Workbook Activities: 51-57; Activities/Alternative Activities: SE: pp TE: pp ; Applications: (Home, Career, Community): pp. 163, 165, 167, 178; Mental Math: pp. 158, 173, 176; Manipulatives: pp. 163, 165, 173, 175; Group Problem Solving: pp. 163, 167, 171, 177; Learning Styles: pp. 157, 158, 161, 163, 167, , 173, , 179 TRL: Workbook Activities: 58-65; Activities/Alternative Activities: SE: pp , 88-89, 96-97, , , , TE: pp , 88-89, 96-97, , , , ; Applications: (Home, Career, Community): pp. 312, ; Mental Math: p. 337; Manipulatives: pp. 75; Group Problem Solving: pp. 75, 89, 264, 272, 313, 341, 343; Learning Styles: pp. 77, 89, 97, , 339, 343, 347 TRL: Workbook Activities: 30-31, 36, 37, 89, 92-93, 102, ; Activities/Alternative Activities: 29-30, 34, 35, 83, 86-87, 96, SE: pp , 88-89, TE: pp , 88-89, ; Estimation Exercise 4; Community Connection 4; Applications: (Home, Career, Community): p. 102; Manipulatives: p. 75; Group Problem Solving: pp. 75, 89, 99, 103; Learning Styles: pp. 89, 97, 102 TRL: Workbook Activities: 30, 36-40; Activities/Alternative Activities: 29, Graphing the solution of an equation or inequality SE: pp , 84-89, , , , TE: pp , 84-89, , , , ; Estimation Exercise 4; Community Connection 4; Applications: (Home, Career, Community): pp. 102, 259; Manipulatives: pp. 75, 304; Group Problem Solving: pp. 75, 89, 99, 103, 261, 272, 305; Learning Styles: pp. 89, 97, 102, 255, 257, 260, TRL: Workbook Activities: 30, 36-40, 86-88, 92-93, 100; Activities/Alternative Activities: 29, 34-37, 80-82, 86-87, 94 4
6 ALGEBRA I Modeling real-world problems by developing and solving equations and inequalities, including those involving direct and inverse variation 8. Solve systems of linear equations and inequalities in two variables graphically or algebraically. Modeling real-world problems by developing and solving systems of linear equations and inequalities 9. Solve quadratic equations using the zero product property. Approximating solutions graphically and numerically Geometry 10. Calculate length, midpoint, and slope of a line segment when given coordinates of its endpoints on the Cartesian plane. Deriving the distance, midpoint, and slope formulas Measurement 11. Solve problems algebraically that involve area and perimeter of a polygon, area and circumference of a circle, and volume and surface area of right circular cylinders or right rectangular prisms. Apply formulas to solve word problems Example: finding the radius of a circle with area 75 square inches ALGEBRA The opportunity to explore this concept can be found in Problem Solving exercises in the SE/TE on pp. 5, 7, 11, 13, 35, 45, 49, 57, 67, 69, 73, 75, 83, 89, 99, 103, 105, 107, 109, 113, 115, 117, 137, 139, 141, 163, 167, 171, 177, 203, 212, 213, 229, 236, 241, 253, 262, 291, 313, 321, 331, 335, 344, 369, 379, 389, 391 and in Applications on pp. 26, 58, 90, 118, 150, 178, 214, 244, 282, 322, 350, 380, 402; Application Activities 1-13; Everyday Algebra 1-13; TE/SE: Applications of Algebra: pp SE: pp , TE: pp , ; Estimation Exercise 10; Community Connection 10; Applications: (Home, Career, Community): pp. 293, 295, 312, ; Mental Math: p. 293; Manipulatives: pp. 299, 303, 305, 323; Group Problem Solving: pp. 272, 291, 300, 305, 308, 313; Learning Styles: pp , 290, 293, , 303, 307, , 319 TRL: Workbook Activities: 92-93, ; Activities/Alternative Activities: 86-87, SE: pp , TE: pp , ; Application Activity 6; Everyday Algebra 6; Applications: (Home, Career, Community): pp. 179, 389; Mental Math: pp. 173, 176; Manipulatives: pp. 173, 175, 388, 391; Group Problem Solving: pp. 177, 389, 391; Learning Styles: pp. 173, , 389, 391 TRL: Workbook Activities: 64-65, ; Activities/Alternative Activities: 60-61, SE: pp , , , TE: pp , , , ; Applications: (Home, Career, Community): pp. 105, 259, 293, 361; Mental Math: p. 293; Group Problem Solving: pp. 104, 261, 291, ; Learning Styles: pp. 105, 261, 290, 293, TRL: Workbook Activities: 41, 88, 95-96, 116; Activities/Alternative Activities: 38, 82, 89-90, 109 SE: pp , TE: pp , 78-83; Applications: (Home, Career, Community): pp. 23, 79; Manipulatives: pp. 23, 81; Group Problem Solving: p. 83; Learning Styles: pp. 24, 79, 81 TRL: Workbook Activities: 12, 32-34; Activities/Alternative Activities: 12,
7 ALGEBRA I ALGEBRA Data Analysis and Probability 12. Compare various methods of data reporting, including SE: pp , , scatterplots, stem-and-leaf plots, histograms, box-and-whisker TE: pp , , ; Estimation Exercise 7; Community Connection 7; plots, and line graphs, to make inferences or predictions. Applications: (Home, Career, Community): pp. 186, 191, 211; Mental Math: p. 189; Determining effects of linear transformations of data Manipulatives: p. 205; Learning Styles: pp. 185, , 193, 205 Example: The mean score on an algebra test was 78. If the TRL: Workbook Activities: 66-68, 71, 73-74; Activities/Alternative Activities: 62-64, 67, 69 teacher adds five points to each student s grade, the mean score will be 83. Determining effects of outliers scope of AGS Algebra. Evaluating the appropriateness of the design of a survey The opportunity to explore this concept can be found in the SE/TE on p Identify characteristics of a data set, including measurement or SE: pp categorical and univariate or bivariate. TE: pp Estimation Exercise 7; Community Connection 7; Applications: (Home, Example: conducting a survey of 100 students to determine Career, Community): pp. 186, 191; Mental Math: pp. 189; Learning Styles: pp. 185, , whether boys and girls prefer to watch the same 193 genres of movies to get a bivariate, categorical data set TRL: Workbook Activities: 66-68; Activities/Alternative Activities: Use a scatterplot and its line of best fit or a specific line graph to scope of AGS Algebra. determine the relationship existing between two sets of data, including positive, negative, or no relationship. 15. Estimate probabilities given data in lists or graphs. Comparing theoretical and experimental probabilities SE: pp TE: pp ; Application Activity 7; Everyday Algebra 7; Applications: (Home, Career, Community): pp. 208, 211, 215; Manipulatives: pp. 201, 205, 207; Group Problem Solving: pp. 203, 209, 212; Learning Styles: pp , 205, , 213 TRL: Workbook Activities: 70-74; Activities/Alternative Activities:
8 SE: Student Edition TE: Teacher Edition TRL: Teacher s Resource Library ALABAMA GEOMETRY Algebra Students will: 1. Determine the equation of a line parallel or perpendicular to a second line through a given point. Geometry 2. Justify theorems related to pairs of angles, including angles formed by parallel and perpendicular lines, vertical angles, adjacent angles, complementary angles, and supplementary angles. Example: proving vertical angles congruent 3. Verify the relationships among different classes of polygons by using their properties. Example: showing that a square has all the properties of both a rectangle and a rhombus Determining the missing lengths of sides or measures of angles in similar polygons 4. Determine the measure of interior and exterior angles associated with polygons. Verifying the formulas for the measures of interior and exterior angles of polygons inductively and deductively 5. Solve real-life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes. Example: finding the center of a solid wooden wheel using the perpendicular bisectors of two chords GEOMETRY SE: pp TE: pp ; Learning Styles: pp. 115, 117, 118, TRL: Workbook Activities: 38-41; Additional Practice SE: pp , 68-76, 81-89, , TE: pp , 68-76, 81-89, , ; Applications: (Home, Career, Community): pp. 70, 75, 81, 84, 85, 198; Group Problem Solving: pp. 55, 71, 76; Learning Styles: pp , 69-71, 75-76, 81-82, 86-89, 169 TRL: Workbook Activities: 18, 24-28, 64-65; Additional Practice 11, 14-17, 33, SE: pp , 90, TE: pp , 90, ; Manipulatives: pp. 78, 147, 151; Applications: (Home, Career, Community): pp. 81, 151, 157; Group Problem Solving: pp. 82, 159; Learning Styles: pp , 90, 145, , 151, 153, TRL: Workbook Activities: 27, 48-54; Additional Practice 18, SE: pp TE: pp ; Learning Styles: pp. 233, 234 TRL: Workbook Activities: 77-78; Additional Practice 44 SE: pp , , , TE: pp , , , ; Manipulatives: pp. 78, 147, 151; Applications: (Home, Career, Community): pp. 81, 151 ; Group Problem Solving: pp. 82, 159 ; Learning Styles: pp , , 151, 153, , 169; TRL: Workbook Activities: 50-52, 59-60; Additional Practice 28-29, 33 The opportunity to explore this concept can be found in the SE/TE on pp , , , general Problem Solving Exercises on pp. 6, 14, 19, 27, 43, 55, 72, 89, 100, 103, 106, 118, 159, 183, 193, 199, 230, 239, 243, 265, 290, 299, 322, 355, 367, 378, and Application Skills on pp. 28, 56, 90, 128, 172, 214, 244, 278, 310, 346, 370, 386. TE: Manipulatives: pp. 78, 147, 331; Applications: (Home, Career, Community): pp. 81, 84-85, 90, 151, 321; Group Problem Solving: pp. 82, 89, 341; Learning Styles: pp , 86-90, , 151, 153, , 322, , 327, 330, , TRL: Workbook Activities: 27-29, 49-53, ; Additional Practice 16-17, 28-30,
9 GEOMETRY GEOMETRY Determining the equation of a circle given the center and radius SE: pp TE: pp ; Applications: (Home, Career, Community): p. 321; Learning Styles: pp , 321 TRL: Workbook Activities: ; Additional Practice Apply the Pythagorean Theorem to solve application problems, SE: pp , , expressing answers in simplified radical form or as decimal TE: pp , , ; Chapter Project: 8; Manipulatives: p. 264; Applications: approximations, using Pythagorean triples when applicable. (Home, Career, Community): pp. 261, 265, 278; Group Problem Solving: p. 260; Learning Styles: pp , , 261, 263, , , , TRL: Geometry On The Job 8; Community Connection 8; Chapter 8 Self-Study Guide; 7. Use the ratios of the sides of special right triangles to find lengths of missing sides. Deriving the ratios of the sides of and triangles 8. Deduce relationships between two triangles, including proving congruence or similarity of the triangles from given information, using them to solve problems and to establish other relationships. Determining the geometric mean to find missing lengths in right triangles 9. Use inductive reasoning to make conjectures and deductive reasoning to justify conclusions. Recognizing the limitations of justifying a conclusion through inductive reasoning 10. Find the missing measures of sides and angles in right triangles by applying the right triangle definitions of sine, cosine, and tangent. 11. Determine the areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. Examples: finding the area of a rectangle given the coordinates of its vertices, showing that the median of a trapezoid is half the sum of the bases Workbook Activities: 85-94, 97; Additional Practice 47-53, 56 SE: pp , 233 TE: pp , 233; Manipulatives: p. 223; Applications: (Home, Career, Community): p. 228 ; Group Problem Solving: p. 230; Learning Styles: pp , , 233 TRL: Workbook Activities: ; Additional Practice SE: pp. 138, , , 179, 184, , , TE: pp. 138, , , 179, 184, , , ; Manipulatives: p. 223; Applications: (Home, Career, Community): p. 228; Group Problem Solving: p. 230; Learning Styles: pp. 138, , , 196, , TRL: Workbook Activities: 46-47, 63-65, 72-76; Additional Practice 35-37, SE: pp , 80, , TE: pp , 80, , ; Manipulatives: p. 151; Applications: (Home, Career, Community): p. 151; Learning Styles: pp. 54, 80, 151 TRL: Workbook Activities: 18, 51-52, 65; Additional Practice 11, 29, 37 SE: pp TE: pp ; Applications: (Group Problem Solving: p. 341; Learning Styles: p. 341 TRL: Workbook Activities: 110; Additional Practice 67 SE: pp. 254, , , TE: pp. 254, , , ; Community Connection 9; Geometry on the Job 9; Chapter 9 Self-Study Guide; Manipulatives: p. 301; Applications: (Home, Career, Community): pp. 297, 303; Learning Styles: pp , 286, , , 298, 302, TRL: Workbook Activities: 86, 90, 95-99, 109; Additional Practice 48, 51, 54-58, 66 8
10 GEOMETRY 12. Apply distance, midpoint, and slope formulas to solve problems and to confirm properties of polygons. 13. Identify the coordinates of the vertices of the image of a given polygon that is translated, rotated, reflected, or dilated. Example: rotating a triangle a given number of degrees around a specific point, comparing the vertices of the image and preimage 14. Classify polyhedrons according to their properties, including the number of faces. Example: identifying a polyhedron having 6 vertices and 12 edges Identifying Euclidean solids Measurement 15. Calculate measures of arcs and sectors of a circle from given information. Examples: finding the area of a sector given its arc length and radius, finding the arc length of a sector given its area and radius, finding the area of arc length given the measure of the central angle and the radius 16. Calculate surface areas and volumes of solid figures, including spheres, cones, and pyramids. Developing formulas for surface area and volume of spheres, cones, and pyramids Calculating specific missing dimensions of solid figures from surface area or volume Determining the relationship between the surface areas of similar figures and volumes of similar figures GEOMETRY SE: pp. 103, , , 128, 198, TE: pp. 103, , , 128, 198, ; Applications: (Home, Career, Community): pp. 108, 110, 198; Learning Styles: p. 103, 109, , 128, 198, TRL: Workbook Activities: 36-37, 40, 41, 44, 91-92; Additional Practice 21, 23, SE: pp , TE: pp , ; Manipulatives: pp. 201, 205, 210; Applications: (Home, Career, Community): pp. 203, 206, 211, 242, 244; Group Problem Solving: p. 213; Learning Styles: pp , , 209, , , 241 TRL: Workbook Activities: 66-70, 79-82; Additional Practice 38-41, SE: Solid figures: pp TE: Solid figures: pp ; Community Connection 11; Geometry on the Job 11; Chjapter 11 Self-Study Guide; Manipulatives: p. 358; Applications: (Home, Career, Community): pp. 359, 362, 369; Group Problem Solving: p. 366; Learning Styles: pp , 358, 361, 370 TRL: Workbook Activities: ; Additional Practice SE: pp TE: pp ; Learning Styles: pp TRL: Workbook Activities: 108; Additional Practice 65 SE: pp TE: pp ; Community Connection 11; Geometry on the Job 11; Chjapter 11 Self-Study Guide; Manipulatives: p. 358; Applications: (Home, Career, Community): pp. 359, 362, 369; Group Problem Solving: p. 366; Learning Styles: pp , 358, 361, 370 TRL: Workbook Activities: ; Additional Practice SE: pp. 355, TE: pp. 355, ; Applications: (Home, Career, Community): p. 359; Learning Styles: pp. 355, 358 scope of AGS Geometry. 9
11 GEOMETRY Data Analysis and Probability 17. Analyze sets of data from geometric contexts to determine what, if any, relationships exist. Example: Collect data and create a scatterplot comparing the perimeter and area of various rectangles. Determine whether a line of best fit can be drawn. Distinguishing between conclusions drawn when using deductive and statistical reasoning Calculating probabilities arising in geometric contexts Example: finding the probability of hitting a particular ring on a dart board whose rings are formed by equally spaced concentric circles 18. Construct with precision a circle graph to represent data from given tables or classroom experiments. GEOMETRY The opportunity to explore this concept can be found throughout the AGS Algebra student textbook, the teacher s edition and applicable activities. SE/TE: The opportunity to explore this concept can be found on pages Community Connection 6; Geometry on the Job 6; Chapter 6 Self-Study Guide; Manipulatives: pp. 201, 205, 210Applications: (Home, Career, Community): pp. 198, 203, 206, 211, 214 ; Group Problem Solving: pp. 183, 213; Learning Styles: pp. 183, , , 196, , , 206, 209, 212 TRL: Workbook Activities: 62-71; Additional Practice SE: pp TE: pp ; Applications: Learning Styles: p. 327 TRL: Workbook Activities: 105; Additional Practice 63 Interpreting a circle graph: SE/TE: p. 346; Applications: (Home, Career, Community): p. 346 TRL: Workbook Activities:
12 SE: Student Edition TE: Teacher Edition TRL: Teacher s Resource Library ALABAMA ALGEBRA II ALGEBRA 2 Number and Operations Students will: 1. Determine the relationships among the subsets of complex numbers. Example: using Venn diagrams or tree diagrams to show how subsets of complex numbers are related 2. Simplify expressions involving complex numbers, using order of operations and including conjugate and absolute value. Examples: simplifying -8, (4-2i) i 3 i 3. Analyze families of functions, including shifts, reflections, and dilations of y = k (inverse variation), y = kx (direct x variation/linear), y = x 2 (quadratic), y = a x (exponential), and y = log a x (logarithmic). Example: comparing the graphs of y = 2 x, y = 2 x + 1, y = 2 x + 1, and y = -2 x Identifying the domain and range of a relation given its graph, a table of values, or its equation, including those with restricted domains Example: finding the domain of y = 1 or y = x 2 x - 3 Identifying real-world situations corresponding to families of functions 4. Determine approximate real zeros of functions graphically and numerically and exact real zeros of polynomial functions. Using completing the square, the zero product property, and the quadratic formula SE: pp TE: pp ; Learning Styles: p. 364 TRL: Estimation Exercise 11; Community Connection 11; Workbook Activities/Activities/Alternative Activities: 96 SE: pp , , TE: pp , , ; Applications: (Home, Career, Community): pp. 98, 181; Learning Styles: pp , 182, 184, 186, 188, , TRL: Estimation Exercise 12; Community Connection 12; Workbook Activities/Activities/Alternative Activities: 30, 49-52, SE: pp , , TE: pp , , ; Applications: (Home, Career, Community): pp. 41, 42, 50, 55, 58, 60, 115, 129, 131, 132, 140, 143, 233, 242, 244, 253, ; Group Problem Solving: pp. 50, 120, 124, 133, 138, 141, 234, 245, 250; Learning Styles: pp. 37, 38, 41, 42, 44, 46, 47, 53, 55-58, 60, 112, , , , 128, 134, 143, 145, 233, 236, 238, 240, 245, 247, 249, 251, 255, 256; TRL: Workbook Activities/Activities/Alternative Activities: 12-19, 32-40, SE: pp TE: pp ; Applications: (Home, Career, Community): p. 244; Group Problem Solving: p. 245; Learning Styles: p. 245 TRL: Workbook Activities/Activities/Alternative Activities: 70 SE: pp. 38, 42, 51, 58, 66, 121, 126, 134, 140, 144, 234, 247, 251, 253, 258 TE: pp. 38, 42, 51, 58, 66, 121, 126, 134, 140, 144, 234, 247, 251, 253, 258 Applications: (Home, Career, Community): pp. 42, 58, 140, 253; Group Problem Solving: p. 234; Learning Styles: pp. 38, 42, 58, 121, 126, 134, 247, 251 TRL: Application Activities 2, 4, 8; Community Connection 8; Workbook The opportunity to explore this concept can be found in the SE/TE on pages 43-44, Applications: (Home, Career, Community): pp. 94, 95; Group Problem Solving: p. 96; Learning Styles: pp. 15, 91, 94 TRL: Workbook Activities/Activities/Alternative Activities: 14, 28, 29 11
13 ALGEBRA II ALGEBRA 2 5. Identify the characteristics of quadratic functions from their roots, graphs, or equations. Writing an equation when given its roots or graph Graphing a function when given its equation Examples: graphing equations of the form y = a(x-h) 2 + k, graphing equations of the form y = ax 2 + bx + c SE: pp TE: pp ; Applications: (Home, Career, Community): pp. 94, 95, 98; Group Problem Solving: pp. 77, 82, 85, 86, 96, 105; Learning Styles: pp. 74, 76, 77, 80, 84, 88, 99, 100, TRL: Workbook Activities/Activities/Alternative Activities: SE: pp TE: pp ; Applications: (Home, Career, Community): pp. 115, 129, 131, 132, 140, 143; Group Problem Solving: pp. 120, 124, 133, 138, 141; Learning Styles: pp. 112, 114, 116, 117, , 125, 126, 128, 134, 138, 143, 145 TRL: Workbook Activities/Activities/Alternative Activities: Determining the nature of the solutions of a quadratic equation SE: pp TE: pp ; Applications: (Home, Career, Community): pp. 94, 95, 98; Group Problem Solving: pp. 77, 82, 85, 86, 96, 105; Learning Styles: pp. 74, 76, 77, 80, 84, 88, 99, 100, TRL: Workbook Activities/Activities/Alternative Activities: Determining the maximum or minimum values of quadratic functions both graphically and algebraically 6. Perform operations on functions, including addition, subtraction, multiplication, division, and composition. Determining the inverse of a function or a relation Performing operations on polynomial and rational expressions containing variables Example: simplifying x + 5 x 2 + 6x + 5 Constructing graphs by analyzing their functions as sums or differences The opportunity to explore this concept can be found in the SE/TE on pages Applications: (Home, Career, Community): pp. 115, 129, 131, 132, 140, 143; Group Problem Solving: pp. 120, 124, 133, 138, 141; Learning Styles: pp. 112, 114, 116, 117, , 125, 126, 128, 134, 138, 143, 145 TRL: Workbook Activities/Activities/Alternative Activities: SE: pp , TE: pp , ; Applications: (Home, Career, Community): pp. 244, 429; Group Problem Solving: pp. 245, 428; Learning Styles: pp. 245, 418, 419, 421, 422, 425, TRL: Workbook Activities/Activities/Alternative Activities: 70, SE: pp TE: pp ; Applications: (Home, Career, Community): pp. 159, 161, 168, 175, 181, 191; Group Problem Solving: pp. 155, 159, 166, 171, 193; Learning Styles: pp , , 158, 163, , 170, 173, 182, 184, 186, 188, 190 TRL: Workbook Activities/Activities/Alternative Activities: The opportunity to explore this concept can be found in the SE/TE on pages Applications: (Home, Career, Community): p. 159; Group Problem Solving: pp. 155, 159; Learning Styles: pp. 151, 152, 155, 156, 158 TRL: Workbook Activities/Activities/Alternative Activities:
14 ALGEBRA II ALGEBRA 2 7. Solve equations, inequalities, and applied problems involving absolute values, radicals, and quadratics over the complex numbers, as well as exponential and logarithmic functions. Example: solving x 2 4 > 0 or 3 x = 81 Solving equations using laws of exponents, including rational and irrational exponents Expressing the solution of an equation, inequality, or applied problem as a graph on a number line or by using set or interval notation Algebra II 8. Solve systems of linear equations or inequalities in two variables using algebraic techniques, including those involving matrices. Example: using the matrix operations of a calculator to solve a SE: pp , , , TE: pp , , , ; Applications: (Home, Career, Community): pp. 209, 211, 233, 242, 244, 253, 256, 257, 416, 429, 433; Group Problem Solving: pp. 234, 245, 250, 428; Learning Styles: pp , 211, 225, 233, 236, 238, 240, 245, 247, 249, 251, , 406, 407, , , , , , 434 TRL: Estimation Activity 8; Community Connection 8; Workbook Activities/Activities/Alternative Activities: 57-58, 64-74, SE: pp , , 226, TE: pp , , 226, ; Applications: (Home, Career, Community): pp. 211, 213; Learning Styles: pp , , , 211, 214 TRL: Application Activity 7; Workbook Activities/Activities/Alternative Activities: 54-56, This concept fall outside the scope of AGS Algebra 2. SE: pp. 1-27, 30, 61-67, TE: pp. 1-27, 30, 61-67, ; Applications: (Home, Career, Community): pp. 13, 14, 25, 65, 140; Learning Styles: pp. 3, 5, 7, 10, 13, 14, 18, 21, 23, 25, 27, 62, 63, 67 TRL: Application Activities 1, 2; Workbook Activities/Activities/Alternative Activities: 1-10, system of linear equations Evaluating the determinant of a 2x2 or 3x3 matrix This concept fall outside the scope of AGS Algebra 2. Solving word problems involving real-life situations SE: pp. 10, 14, 18, 21, 25, 30, TE: pp. 10, 14, 18, 21, 25, 30, ; Applications: (Home, Career, Community): pp. 14, 25, 140; Group Problem Solving: p. 141; Learning Styles: pp. 10, 14, 18, 21, 25 TRL: Application Activity 1; Workbook Activities/Activities/Alternative Activities: 39 Geometry 9. Solve coordinate geometry problems using algebraic techniques. Examples: finding missing coordinates of vertices of polygons, determining properties of polygons given the coordinates of their vertices, determining perpendicularity of sides of a polygon on a coordinate plane The opportunity to explore this concept can be found in the SE/TE on pages , 226. Learning Styles: pp TRL: Application Activity 7; Workbook Activities/Activities/Alternative Activities: 31 13
15 ALGEBRA II ALGEBRA 2 Data Analysis and Probability 10. Use different forms of representation to compare characteristics of data gathered from two populations. Evaluating the appropriateness of the design of an experimental study Describing how sample statistics reflect values of population parameters 11. Determine an equation of linear regression from a set of data. Examining data to determine if a linear or quadratic relationship exists and to predict outcomes 12. Calculate probabilities of events using the laws of probability. Using permutations and combinations to calculate probabilities The opportunity to explore this concept can be found in the SE/TE on pages Applications: (Home, Career, Community): p. 459; Group Problem Solving: pp. ; Learning Styles: pp , 462 TRL: Workbook Activities/Activities/Alternative Activities: This concept fall outside the scope of AGS Algebra 2. The opportunity to explore this concept can be found in the SE/TE on pages Learning Styles: pp TRL: Workbook Activities/Activities/Alternative Activities: 101 SE: pp TE: pp ; Applications: (Home, Career, Community): p. 375; Learning Styles: pp , , , 375 TRL: Workbook Activities/Activities/Alternative Activities: Calculating conditional probability This concept fall outside the scope of AGS Algebra 2. Calculating probabilities of mutually exclusive events, This concept fall outside the scope of AGS Algebra 2. independent events, and dependent events 14
16 SE: Student Edition TE: Teacher Edition TRL: Teacher s Resource Library ALABAMA ALGEBRAIC CONNECTIONS LIFE SKILLS MATH MATH FOR THE Algebra Students will: 1. Use algebraic and geometric techniques to make financial and economic decisions, including those involving banking and investments, insurance, personal budgets, credit purchases, recreation, and deceptive and fraudulent pricing and advertising. Examples: banking-determining the best choice of certificates of deposit, savings accounts, checking accounts, or loans; credit purchases-comparing the costs of fixedor variable-rate mortgage loans, comparing the costs associated with various credit cards; personal budgets-determining the best plan for long distance phone service SE: The opportunity to explore this concept can be found on pages , , and TE: The opportunity to explore this concept can be found on pages , , and ; Applications (Home, Career, Community): pp. 122, 125, 126, 214, 218, 221, 229, 235, 238; Group Problem Solving: pp. 122, 125, 216, 218, 221, 230, 232, 239; Learning Styles: pp. 121, 124, 220, 230, 232, 234, 237, 238 TRL: Workbook Activities: 39-40, 66-74; Activities/Alternative Activities: 33-35, 61-69; Chapters 8, 13, 14 Self-Study Guides WORLD OF WORK SE/TE: The opportunity to explore this concept can be found throughout the textbook: Wages: pages 6-30; Benefits: pages 32-50; Corporate Banking: pages ; Operating Expenses: pages ; Business Management: pages and refer also to pages , , , and Math At Work: pp. 19, 28, 43, 132, 152, 169, 222, 232; Applications (Home, Career, Community): pp. 14, 23, 27, 29, 38, 42, 49, 124, 127, 144, 151, 152, 165, 168, 172, 218, 219, 223, 236, 237, 240; Group Problem Solving: pp. 10, 42, 49, 130, 144, 161, 175, 224, 243; Learning Styles: pp , 13, 15, 18-19, 22, 28, 26, 35-36, 38-39, 42-44, 48, , 123, , , , 145, , , 164, , , 217, 219, 221, 223, 225, 231, 233, 236, 239, 241; TRL: Math On The Job/Business Forms: 1-2, 6-8, 11, 12; Workbook Activities: 1-11, 28-41, 50-55; Activities/Alternative Activities: 1-9, 23-34, 42-46; Chapters 1-2, 6-8, 11, 12 Self-Study Guides CONSUMER MATHEMATICS SE: The opportunity to explore this concept can be found on pages 30-52, 56-76, , , , , and TE: The opportunity to explore this concept can be found on pages 30-52, 56-76, , , , , and Applications (Home, Career, Community): pp. 33, 37-39, 43, 47, 49, 52, 59-60, 65, 69, 83, 85, 89, 93, 95, 97-98, 101, 103, 105, 113, 115, , 121, 175, 256, , 262, 269, 274, , 285, , 297; Group Problem Solving: pp. 35, 37, 51, 61, 67, 71, 74, 83, 85, 92, 101, 119, 121, , 251, 253, 272, 276, 285, 291, 293, 295; Learning Styles: pp. 32, 40, 43, 62, 64, 69, 89, 95, 97, 100, 118, 121, 173, 175, 249, 256, 261, 278, 281, 284, 291, 298 TRL: Consumer Tips/Community Connection: 2, 3, 4, 5, 9, 10; Workbook Activities: 14-54, 75-78, ; Activities/Alternative Activities: 14-54, 76-78, ; Chapters 2, 3, 4, 5, 9, 10 Self- Study Guides 15
17 ALGEBRAIC CONNECTIONS LIFE SKILLS MATH MATH FOR THE WORLD OF WORK Generating, manually or with technological tools, graphs and tables related to personal finance and economics Example: using computer software to create an amortization table for a mortgage loan or a circle graph for a personal budget 2. Solve problems using direct, inverse, and joint variation. SE: Pages , , TE: Pages , , ; Applications (Home, Career, Community): pp. 218, 229, 238, 240; Group Problem Solving: pp. 216, 218, 239; Learning Styles: pp. 220, TRL: Workbook Activities: 68-71, 74; Activities/Alternative Activities: 63-66, 69 SE/TE: The opportunity to explore this concept can be found in the Problem Solving Exercises on pages 2, 3, 4, 13, 21, 24, 41, 43, 52, 57, 59, 77, 80, 91, 96, 105, 107, 110, 112, 125, 133, 136, 139, 141, 155, 159, 161, 163, 165, 167, 169, 178, 180, 181, 183, 185, 196, 198, 201, 216, 218, 229, 238, 249, 251, 261, 279, 281, 296; and Applications: pages 14, 28, 46, 66, 82, 98, 114, 126, 148, 170, 186, 206, 222, 240, 266, 286, and 306. SE: Examples of a business budget can be found on pages and TE: Examples of a business budget can be found on pages and Group Problem Solving: p. 71 TRL: Workbook Activities: 17; Activities/Alternative Activities: 14 SE/TE: The opportunity to explore this concept can be found in the Problem Solving Exercises on pages 17, 19, 27, 36, 39, 57, 59, 65, 71, 81, 83, 88, 93, 102, 105, 108, 112, 132, 134, 136, 145, 159, 169, 174, 183, 187, 197, 199, 205, 210, 217, 224, 235, 237, 242, 251, 252, 255, 259; and Applications: pages 29, 49, 73, 95, 113, 137, 153, 175, 191, 211, 225, 243, and 263. CONSUMER MATHEMATICS SE: Pages , , , TE: Pages , , , ; Applications (Home, Career, Community): pp. 83, 85, 89, 93, 95, 97-98, 101, 103, 105, 113, 115, , 121, 133, 256, ; Group Problem Solving: pp. 83, 85, 92, 101, 119, 121, 251, 253; Learning Styles: pp. 89, 95, 97, 100, 118, 121, 249, 256, 261 TRL: Consumer Tips/Community Connection: 4, 9; Workbook Activities; 41-54, 64, ; Activities/Alternative Activities: 41-54, 64, ; Chapters 4, 9 Self-Study Guides SE/TE: The opportunity to explore this concept can be found in the Problem Solving Exercises on pages 11, 12, 49, 70, 71, 100, 101, 120, 121, 141, 146, 149, 154, 181, 185, 209, 211, 217, 253, 255, 261, 295, 305, 309, 339; and Applications: pages 26, 52, 76, 106, 134, 164, 202, 242, 262, 298, 324, and
18 ALGEBRAIC CONNECTIONS LIFE SKILLS MATH MATH FOR THE WORLD OF WORK 3. Use formulas or equations of functions to SE: Students can explore this scope of calculate outcomes of exponential growth or concept by applying pages 231- AGS Math for the World of Work. decay. 232 to exponential functions Example: problems involving compound found in the AGS Algebra 2 interest, bacterial growth, carbon-14 dating, textbook on pages depreciation, cooling point in chemistry TE: Students can explore this concept by applying pages to exponential functions found in the AGS Algebra 2 textbook on pages Group Problem Solving/ Learning Styles: p. 232 TRL: Workbook Activity: 72; Activity/Alternative Activity: 4. Determine maximum and minimum values of a function using linear programming procedures. Example: Given the boundaries x > 0, y > 0, 2x 3y + 15 > 0, and x < 9, find the maximum and minimum values of f(x,y) = 3x + 5y. 5. Approximate rates of change of nonlinear relationships from graphical and numerical data. Graphing information from tables, equations, or classroom-generated data to model consumer costs and to predict future outcomes 67 scope of AGS Life Skills Math. SE: The opportunity to explore this concept can be found on pages and pages TE: The opportunity to explore this concept can be found on pages and pages Applications (Home, Career, Community): pp. 218, 221, 259, 263, 264, 266; Group Problem Solving: pp. 216, 218, 221, 261, 265; LS: pp. 220, 263, 265; TRL: Workbook Act.: 68-70, 78-79; Activities/ Alternative Activities: 63-65, 74 scope of AGS Math for the World of Work. SE: The opportunity to explore this concept can be found pages and TE: The opportunity to explore this concept can be found pages and Applications (Home, Career, Community): pp. 218, 219, 223, 236, 237, 240; Group Problem Solving: pp. 224, 243; Learning Styles: pp. 217, 219, 221, 223, 225, 231, 233, 236, 239, 241; TRL: Math On The Job/Business Forms: 11, 12; Workbook Activities: 50-55; Activities/Alternative Activities: 42-46; Chapters SSG CONSUMER MATHEMATICS SE: Students can explore this concept by applying pages , and to exponential functions found in the AGS Algebra 2 textbook on pages TE: Students can explore this concept by applying pages , and to exponential functions found in the AGS Algebra 2 textbook on pages Applications: p. 115 TRL: Workbook Activity: 52; Activity/ Alternative Activity: 52 scope of AGS Consumer Math. SE: The opportunity to explore this concept can be found on pages and 262. TE: The opportunity to explore this concept can be found on pages and 262. Applications (Home, Career, Community): p. 262; Group Problem Solving: pp. 251, 253 TRL: Workbook Activities: ; Activities/Alternative Activities:
19 ALGEBRAIC CONNECTIONS LIFE SKILLS MATH MATH FOR THE WORLD OF WORK 6. Use the extreme value of a given quadratic SE: The opportunity to determine cost function to solve applied problems. scope of AGS Life Skills Math. needed to maximize profit can be found Example: determining the cost needed to on pages 58-69, 131, , 141- maximize profit 153, , , and TE: The opportunity to determine cost needed to maximize profit can be found on pages 58-69, 131, , , , , and Applications (Home, Career, Community): pp. 60, 61, 64, 144, , 165, 168, 172, 218, 219, 223, 240; Group Problem Solving: pp. 69, 144, 161, 175, 224, 243; Learning Styles: pp , 63-64, 68, 131, , , 145, 147, 149, , 164, 168, 169, , , 221, 223, 225, 239, 241 TRL: Math On The Job/Business Forms: 7, 8, 11; Workbook Activities: 14-16, 34-41, 50-51, 55; Activities/Alternative Activities: 11-13, 28-34, 42-43, 46; Chapters 7-8, Make predictions based upon tables or graphs from societal contexts. Example: making predictions about population change or employment rate SE/TE: The opportunity to explore this concept can be found on pages 10-13, 60-64, and Applications (Home, Career, Community): pp. 11, 64; Group Problem Solving: pp. 11, 13, 163; LS: pp. 13, 60, 62, 64; TRL: Workbook Activities: 4-5, 20-21, 49; Activities/Alternative Activities 4-5, 19-20, 44 Self-Study Guides SE: The opportunity to explore this concept can be found on pages 62-63, 67, and 236. TE: The opportunity to explore this concept can be found on pages 62-63, 67, and 236. Applications (Home, Career, Community): p. 236; Learning Styles: pp. 63, 236 TRL: Workbook Activities: 15; Activities/Alternative Activities: 12 CONSUMER MATHEMATICS scope of AGS Consumer Math. scope of AGS Consumer Math. 18
20 ALGEBRAIC CONNECTIONS LIFE SKILLS MATH MATH FOR THE WORLD OF WORK Geometry scope of 8. Determine missing information in an applicationbased scope of AGS Life Skills Math. AGS Math for the World of Work. situation by using the properties of right triangles, including trigonometric ratios. Example: application-construction or landscaping problem 9. Analyze the aesthetics of real-life situations using line symmetry, rotational symmetry, or the golden ratio. Example: identifying the symmetry found in nature, art, or architecture 10. Use arc length and sector area to solve applied problems. Measurement 11. Critique the appropriateness of measurements in terms of precision, accuracy, and approximate error. Example: determining whether one candidate has a significant lead over another candidate when given their current standings in a poll and the margin of error scope of AGS Life Skills Math. scope of AGS Life Skills Math. SE: The opportunity to explore this concept can be found on pages 20-28, 72-73, 93-95, , and TE: The opportunity to explore this concept can be found on pages 20-28, 72-73, 93-95, , and Applications (Home, Career, Community): pp. 27, 28, 73, 95, 109, 275, 277, 281; Group Problem Solving: pp. 22, 24, 25, 27, 73, 110, 273, 279, 283, 285, 286; Learning Styles: pp. 21, 22, 24, 93, 109, 277, 279, 283; TRL: Workbook Activities: 6-10, 22, 37, 80-86; Activities/Alternative Activities: 6-8, 21, 31, 76-82; Math on the Job 16, Community Connection 16, Chapter 16 SSG Guide scope of AGS Math for the World of Work. scope of AGS Math for the World of Work. SE: The opportunity to explore this concept can be found on pages and TE: The opportunity to explore this concept can be found on pages and Applications (Home, Career, Community): pp , 206, 210; Group Problem Solving: p. 203; Learning Styles: pp , , TRL: Workbook Activities: 47-49, 50; Activities/Alternative Activities: CONSUMER MATHEMATICS scope of AGS Consumer Math. scope of AGS Consumer Math. scope of AGS Consumer Math. SE: Pages TE: Pages Group Problem Solving: pp. 343, 345 TRL: Workbook Activities: ; Activities/Alternative Activities:
21 ALGEBRAIC CONNECTIONS LIFE SKILLS MATH MATH FOR THE WORLD OF WORK 12. Use ratios of perimeters, areas, and volumes of SE: Pages scope of similar figures to solve applied problems. TE: Pages ; AGS Math for the World of Work. Example: using a blueprint or scale drawing Applications: p. 277; Learning of a house to determine the amount of carpet Styles: p. 277 to be purchased for the house TRL: Workbook Activity 82; Activity/Alt. Activity 78 Data Analysis and Probability 13. Model a set of data by estimating the equation of a curve of best fit from tables of values or scatterplots. Example: predicting or analyzing election results, population change, inflation rate, employment rate, or cholesterol count 14. Estimate probabilities given a frequency distribution. Making decisions on the basis of probabilities SE: The opportunity to explore predicting can be found on page 60. TE: The opportunity to explore predicting can be found on page 60. Learning Styles: p. 60 TRL: Workbook Activity: p. 60; Activity/Alt. Activity: p. 60 SE: Pages TE: Pages Applications (Home, Career, Community): pp. 64, 66; Group Problem Solving: pp. 52, 55, 58, 65; Learning Styles: pp. 57, 60 TRL: Workbook Activities: 15-21; Activities/Alternative Activities: 14-20; Chapter 4 Self-Study Guide SE: The opportunity to explore this concept can be found on pages and 236. TE: The opportunity to explore this concept can be found on pages and 236. Applications (Home, Career, Community): pp , 236; Group Problem Solving: pp. Learning Styles: pp , 6, 236 TRL: Workbook Activities: 15-16; Activities/Alternative Activities: scope of AGS Math for the World of Work. CONSUMER MATHEMATICS SE: Pages , TE: Pages , Applications (Home, Career, Community): pp. 182, 184, 190, 195, 202; Group Problem Solving: pp. 182, 185, 187, 189, 192, 197, 199, 201, 345; Learning Styles: pp. 181, 189, 199 TRL: Workbook Activities: 79-88; Activities/Alternative Activities: scope of AGS Consumer Math. scope of AGS Consumer Math. 20
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