minnesota academic standards mathematics grades...

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MINNESOTA ACADEMIC STANDARDS

MATHEMATICS GRADES 6-12

Correlated to

BASIC MATH SKILLS, MATHEMATICS PATHWAYS, MATHEMATICS: CONCEPTS, ALGEBRA, GEOMETRY,

ALGEBRA 2, LIFE SKILLS MATH AND CONSUMER MATHEMATICS

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MATERIALS USED IN THIS MINNESOTA/AGS PUBLISHING CORRELATION: BASIC MATH SKILLS ©2003 MATHEMATICS PATHWAYS ©2004 MATHEMATICS: CONCEPTS ©2005 CONSUMER MATHEMATICS ©2003 LIFE SKILLS MATH ©2003 ALGEBRA ©2004 ALGEBRA 2 ©2004 GEOMETRY ©2005

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TABLE OF CONTENTS

GRADE 6 ............................................................................................................................................ 4

GRADE 7 ............................................................................................................................................ 8 GRADE 8 .......................................................................................................................................... 18 GRADES 9, 10, 11 ............................................................................................................................ 28

GRADES 11-12................................................................................................................................. 47

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MINNESOTA MATHEMATICS AGS PUBLISHING

GRADE 6 BASIC MATH SKILLS I. MATHEMATICAL REASONING Standard: Apply skills of mathematical representation, communication and reasoning throughout the remaining four content strands. The student will: 1. Assess the reasonableness of a solution by comparing the solution to appropriate

graphical or numerical estimates or by recognizing the feasibility of a solution in a given context.

Pages xv, and estimating/reasonableness on pages 5, 7, 150, 166, 201, 226, 265, 293. Refer also to all problem-solving and application activities for the opportunity to recognize the feasibility of a solution in a given context. Please also refer to Mental Math activities in the Teacher’s Edition.

2. Appropriately use examples and counterexamples to make and test conjectures, justify solutions and explain results.

The opportunity to create examples and counterexamples, to make and test conjectures, and to justify solutions can be found throughout the AGS Basic Math Skills textbook. Explain results: refer to Learning Styles: Auditory/ Visual; Interpersonal/Group Learning, and Group Problem Solving in the Teacher’s Edition.

3. Translate a problem described verbally or by tables, diagrams or graphs, into suitable mathematical language, solve the problem mathematically and interpret the result in the original context.

Translating written problem-solving into suitable mathematical language: pages 10, 14, 20, 26, 28, 71, 73, 74, 76, 78, 84, 85, 94, 98, 100, 102, 105, 109, 115, 129, 131, 133, 145, 146, 150, 152, 157, 164, 200, 203, 205, 208, 231, 246, 250, 298, 316, 329 and Applications: pages 32, 54, 86, 118, 134, 166, 186, 212, 238, 256, 284, 302, 338.

4. Support mathematical results by explaining why the steps in a solution are valid and why a particular solution method is appropriate.

The opportunity to explore this concept can be found on pages 10, 14, 20, 26, 28, 71, 73, 74, 76, 78, 84, 85, 94, 98, 100, 102, 105, 109, 115, 129, 131, 133, 145, 146, 150, 152, 157, 164, 200, 203, 205, 208, 231, 246, 250, 298, 316, 329 and Applications: pages 32, 54, 86, 118, 134, 166, 186, 212, 238, 256, 284, 302, 338.

5. determine whether or not relevant information is missing from a problem. Pages xv; and exploring this concept: pages 10, 14, 20, 26, 28, 71, 73, 74, 76, 78, 84, 85, 94, 98, 100, 102, 105, 109, 115, 129, 131, 133, 145, 146, 150, 152, 157, 164, 200, 203, 205, 208, 231, 246, 250, 298, 316, 329 and Applications: pages 32, 54, 86, 118, 134, 166, 186, 212, 238, 256, 284, 302, 338.

6. Use accurately common logical words and phrases such as “and,” “or,” “if…then…,” “unique,” “only if.”

Logical/Mathematical vocabulary is used throughout the AGS Basic Math Skills textbook. New vocabulary appears in bold type in the text and they are defined in the text left column and in the glossary. Common logical vocabulary is also reinforced through the Teacher’s Resource Library activities as an integral portion of the entire program.

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GRADE 6 BASIC MATH SKILLS II. NUMBER SENSE, COMPUTATION AND OPERATIONS A. Number Sense Standard: Use positive and negative rational numbers, represented in a variety of ways, to quantify information and to solve real-world and mathematical problems. The student will: 1. Order and compare integers, fractions, decimals and mixed numbers with >, <, and =.

Locate and compare positive and negative rational numbers on a number line.

Pages 2-6, 35-53, 56-67, 83-92, 95-98, 109-111, 114-115, 118-127, 131-137, 141-147, 306-323, 328

2. Use rounding and estimation with integers, decimals and fractions to solve real-world and mathematical problems.

Pages 4, 5, 7, 20, 29, 95-98, 116-117, 143-147, 150, 160-166, 201, 226, 264, 265, 269, 293

B. Computation and Operation Standard: Compute fluently and make reasonable estimates with positive and negative rational numbers in real-world and mathematical problems. Understand the meanings of arithmetic operations and factorization, and how they relate to one another. Appropriately use calculators and other technologies to solve problems. The student will: 1. Determine the prime factorization of positive integers.

Pages 15, 38, 40-43, 46-54

2. Determine the least common multiple and the greatest common divisor of whole numbers.

Pages 50-53

3. Use addition, subtraction, multiplication and division of multi-digit whole and decimal numbers to solve multi-step real-world and mathematical problems.

Pages 8-32, 38-54, 90-118

4. Multiply and divide, without a calculator, numbers containing up to three digits by numbers containing up to two digits, such as 347 / 83 or 4.91 x 9.2.

Pages 15-24, 26, 30-32, 38-54, 103-113, 118, 160-165

5. Find quotients with remainders and be able to express the remainder in various ways depending on the context of the problem.

Pages 25-26, 28, 32, 74, 105, 109, 111, 113, 115, 118, 268-269

6. Use the relationship between moving the decimal point and the operations of multiplication or division by powers of ten to simplify calculations.

Pages 106-107, 115

7. Add, subtract, multiply and divide common fractions and mixed numbers as well as fractions where the common denominator equals one of the denominators.

Pages 58-86, 141-147

8. Find, represent and use percentages in real-world and mathematical problems, including percentages greater than 100% and less than 1%.

Pages 138-166

9. Apply the correct order of operations and grouping symbols when using calculators and other technologies.

Defined: page 31, 319-321; This concept can be applied through the calculator practices on pages 29, 39, 65, 113, 127, 147, 183, 204, 233, 248, 268-269, 293, 333, & 376-377. Specific calculator instructions can be found on pages 376-377.

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GRADE 6 BASIC MATH SKILLS 10. Know, use and translate calculator notational conventions to mathematical notation. Specific calculator instructions can be found on pages 376-377 and can be

applied on pages 29, 39, 65, 113, 127, 147, 183, 204, 233, 248, 268-269, 293, 333, & 376-377.

11. Understand the use of a calculator requires appropriate mathematical reasoning and does not replace the need for mental computation.

Specific mental calculations and reasoning can be found through Mental Math activities in the Teacher’s Edition. These activities combined with calculator activities and exercises give the student a solid foundation in the necessity of mental computation.

III. PATTERNS, FUNCTIONS AND ALGEBRA A. Patterns And Functions Standard: Demonstrate understanding of the rectangular coordinate system. The student will: 1. Demonstrate understanding of the four quadrants in a rectangular coordinate system

by writing and plotting ordered pairs.

Page 325

B. Algebra (Algebraic Thinking) Standard: Apply arithmetic operations in the correct order to simplify and evaluate numeric expressions in real-world and mathematical problems. The student will: 1. Apply the correct order of operations including addition, subtraction, multiplication,

division and grouping symbols to simplify and evaluate numeric expressions.

Pages 31, 60-73, 84-86, 106-107, 115, 132-134, 151-166, 223-225, 308-321, 336-337

IV. DATA ANALYSIS, STATISTICS AND PROBABILITY A. Data and Statistics Standard: Represent data and use various measures associated with data to draw conclusions and identify trends. The student will: 1. Collect, organize and represent categorical and numerical data with tables and bar

graphs.

Pages 260-276, 278-279, 284

2. Understand the differences and appropriate use of mean, median and mode. This concept falls outside the scope of AGS Basic Math Skills. 3. Find the median and possible outliers. This concept falls outside the scope of AGS Basic Math Skills. B. Probability Standard: Calculate and express probabilities numerically, and apply probability concepts to solve real-world and mathematical problems. The student will: 1. Generate and display data in graphs and tables to estimate experimental probabilities.

This concept falls outside the scope of AGS Basic Math Skills.

2. Represent all possible outcomes for a probability problem with tables, grids and tree diagrams to calculate probabilities and draw conclusions from the results.


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GRADE 6 BASIC MATH SKILLS V. SPATIAL SENSE, GEOMETRY AND MEASUREMENT A. Spatial Sense Standard: Recognize the relationship between different representations of two- and three-dimensional shapes. Understand the effect of various transformations. The student will: 1. Create models of three-dimensional geometric shapes from two-dimensional

representations.

The opportunity to explore this concept can be found on pages 184-186, (drawing geometric figures including solids can be found on page 186) 201-204, and 207-208.

2. Predict the position and orientation of simple geometric shapes under transformations such as reflections, rotations and translations.


3. Identify symmetries in three-dimensional shapes. This concept falls outside the scope of AGS Basic Math Skills. B. Geometry Standard: Identify a variety of simple geometric figures by name, calculate various quantities associated with them and use appropriate tools to draw them. The student will: 1. Use facts about angles including the relationship between complementary angles,

supplementary angles and the angles within triangles to solve real-world and mathematical problems.

Pages 70-186

2. Classify triangles as equilateral, isosceles or scalene, and right, acute or obtuse. Pages 174-175, 181-186 3. Find the area and circumference of a circle given the radius or diameter using

common approximations of pi where appropriate. Pages 242-250

4. Measure, identify, and draw perpendicular and parallel lines, angles and rectangles by using appropriate tools such as straightedge, ruler, compass, protractor or software.

Pages 170-179, 182-183, 186

C. Measurement Standard: Make calculations of time, length, area and volume within standard measuring systems, using good judgment in choice of units. The student will: 1. Solve problems requiring conversion of units within the U.S. customary system, and

within the metric system.

Pages 196-200, 206-208, 200, 218-219, 222-225, 234-238

2. Express measures of time and distance as fractions, mixed numbers and decimals to solve real-world and mathematical problems.

Pages 299-301

3. Find the area and perimeter of rectangles, squares, triangles and parallelograms by measuring, using a grid or using a formula.

Pages 198-200, 226-238, 296

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SE: Student Edition TE: Teacher Edition TRL: Teacher’s Resource Library

MINNESOTA MATHEMATICS AGS PUBLISHING AGS PUBLISHING GRADE 7 MATHEMATICS PATHWAYS MATHEMATICS: CONCEPTS

I. MATHEMATICAL REASONING Standard: Apply skills of mathematical representation, communication and reasoning throughout the remaining four content strands. The student will: 1. Assess the reasonableness of a solution by comparing the

solution to appropriate graphical or numerical estimates or by recognizing the feasibility of a solution in a given context.

Pages xviii-xix, 5, 28-29, 34-35, 37, 65, 77, 117, 141, 187, 221, 245, 246-247, 291, 341, 365, 403, 413 Please also refer to Mental Math, Modeling, and Manipulative activities in the Teacher’s Edition.

SE/TE: pages xvi, xvii, 12, 26-27, 53, 95, 111, 161, 185, 204-205, 221, 257, 283, 301, 332, 379, 345, 378; Problem solving strategies: pages 15, 42, 51, 91, 99, 123, 155, 163, 193, 197, 228, 231, 252, 267, 283, 287, 309, 317, 351, 357, 389; Applications: pages 30, 64, 100, 130, 170, 206, 232, 268, 290, 334, 358, 398; Problem Solving: pages 7, 15, 23, 27, 42, 47, 51, 75, 89, 91, 99, 123, 150, 155, 163, 169, 181, 184, 193, 197, 199, 202, 205, 228, 231, 252, 267, 283, 287, 309, 317, 351, 357, 373, 378, 389, 391 TE: Manipulatives: pages 3, 5, 9, 13, 37, 39, 45, 47, 53, 56, 61, 71, 107, 113, 115, 117, 121, 137, 143, 147, 153, 157, 161, 181, 191, 223, 239, 255, 257, 279, 281, 299, 303, 307, 353, 387, 393; Mental Math: pages 4,6, 20, 41, 44, 48, 52, 53, 56, 76, 77, 80, 91, 122, 128, 129, 138, 144, 154, 156, 160, 164, 167, 179, 180, 190, 193, 199, 216, 222, 249, 256, 258, 260, 262, 264, 276, 302, 304, 308, 314, 345, 351, 356, 370, 377, 380, 382; Modeling: pages 7, 17, 41, 87, 115, 138, 154, 185, 227, 228, 248, 275, 303, 347, 371 TRL: How To Use This Book 3-4

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MINNESOTA MATHEMATICS AGS PUBLISHING AGS PUBLISHING

GRADE 7 MATHEMATICS PATHWAYS MATHEMATICS: CONCEPTS 2. Appropriately use examples and counterexamples to make

and test conjectures, justify solutions and explain results. Pages 314-323; Explain results: refer to Learning Styles: Auditory/ Visual; Interpersonal/Group Learning, and Group Problem Solving in the Teacher’s Edition.

Reasoning skills/processes, conjectures, and argumentation are applied throughout in exercises at the end of each lesson and in Problem Solving and Application exercises listed above, and in Chapter Reviews. The student is given the opportunity to explain results in the TE: Learning Styles: Auditory/Verbal activities on pages 3, 11, 18, 22, 27, 47, 50, 75, 82, 95, 99, 108, 109, 127, 129, 141, 155, 158, 162, 177, 184, 206, 214, 218, 225, 228, 245, 251, 279, 286, 308, 317, 321, 329, 331, 343, 345, 347, 366, 369, 375, 378, 388, 396; Interpersonal/Group Learning: pages 7, 15, 22, 41, 43, 51, 58, 63, 75, 88, 91, 94, 107, 111, 118, 123, 139, 151, 159, 163, 181, 196, 219, 228, 243, 245, 252, 257, 289, 301, 316, 328, 333, 357, 369, 375, 381, 383, 389, 396; Teaching Strategies: Group Problem Solving: pages 45, 51, 85, 95, 119, 151, 165, 168, 177, 183, 187, 196, 199, 201, 221, 247, 260, 265, 282, 299, 301, 305, 317, 332, 349, 357, 373, 385, 391, 397 TRL: Estimation Exercises 1-12; Application Activities 1-12; Everyday Math 1-12; Community Connection 1-12

3. Translate a problem described verbally or by tables, diagrams, or graphs, into suitable mathematical language, solve the problem mathematically and interpret the result in the original context.

Translating written problem-solving into suitable math lang.: pp. 7, 9, 25, 27, 31, 33, 53, 57, 61, 63, 67, 79, 81, 87, 91, 101, 105, 111, 115, 125, 131, 145, 151, 159, 161, 169, 173, 175, 177, 185, 191, 197, 207, 209, 215, 219, 223, 225, 239, 241, 249, 252, 269, 273, 281, 283, 297, 301, 305, 321, 323, 327, 347, 369, 377, 411, 413, 417; Math In Your Life on pp. 2, 33, 59, 90, 119, 149, 183, 206, 235, 287, 319, 371, 420; and Apps: pp. 18, 42, 70, 94, 132, 162, 198, 226, 260, 308, 352, 394, 428.

Translating written problem-solving into suitable math. Lang.: SE/TE: pp. 7, 15, 23, 27, 30, 42, 47, 51, 64, 75, 89, 91, 99, 100, 123, 130, 150, 155, 163, 169, 170, 181, 184, 193, 197, 199, 202, 205, 206, 228, 231, 232, 252, 267, 268, 283, 287, 290, 309, 317, 334, 351, 357, 358, 373, 378, 389, 391, 398; Math in Your Life: pp. 25, 49, 82, 125, 159, 197, 226, 241, 282, 317, 331, 343, 367; TRL: Est. Ex. 1-12; App. Act. 1-12; Everyday Math 1-12; Com. Con. 1-12

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GRADE 7 MATHEMATICS PATHWAYS MATHEMATICS: CONCEPTS 4. Support mathematical results by explaining why the steps

in a solution are valid and why a particular solution method is appropriate.

The opportunity to explore this concept can be found on pages 7, 9, 25, 27, 31, 33, 53, 57, 61, 63, 67, 79, 81, 87, 91, 101, 105, 111, 115, 125, 131, 145, 151, 159, 161, 169, 173, 175, 177, 185, 191, 197, 207, 209, 215, 219, 223, 225, 239, 241, 249, 252, 269, 273, 281, 283, 297, 301, 305, 321, 323, 327, 347, 369, 377, 411, 413, and 417; Math In Your Life on pages 2, 33, 59, 90, 119, 149, 183, 206, 235, 287, 319, 371, and 420; and Applications: pages 18, 42, 70, 94, 132, 162, 198, 226, 260, 308, 352, 394, 428.

The opportunity to explore this concept can be found in the SE/TE on pages xvi, xvii, 12, 26-27, 53, 95, 111, 161, 185, 204-205, 221, 257, 283, 301, 332, 379, 345, 378; Problem solving strategies: pages 15, 42, 51, 91, 99, 123, 155, 163, 193, 197, 228, 231, 252, 267, 283, 287, 309, 317, 351, 357, 389; Applications: pages 30, 64, 100, 130, 170, 206, 232, 268, 290, 334, 358, 398; Problem Solving: pages 7, 15, 23, 27, 42, 47, 51, 75, 89, 91, 99, 123, 150, 155, 163, 169, 181, 184, 193, 197, 199, 202, 205, 228, 231, 252, 267, 283, 287, 309, 317, 351, 357, 373, 378, 389, 391 TE: Manipulatives: pages 3, 5, 9, 13, 37, 39, 45, 47, 53, 56, 61, 71, 107, 113, 115, 117, 121, 137, 143, 147, 153, 157, 161, 181, 191, 223, 239, 255, 257, 279, 281, 299, 303, 307, 353, 387, 393; Mental Math: pages 4,6, 20, 41, 44, 48, 52, 53, 56, 76, 77, 80, 91, 122, 128, 129, 138, 144, 154, 156, 160, 164, 167, 179, 180, 190, 193, 199, 216, 222, 249, 256, 258, 260, 262, 264, 276, 302, 304, 308, 314, 345, 351, 356, 370, 377, 380, 382; Modeling: pages 7, 17, 41, 87, 115, 138, 154, 185, 227, 228, 248, 275, 303, 347, 371 TRL: How To Use This Book 3-4

5. Determine whether or not relevant information is missing from a problem.

Pp. xviii; exploring this concept: pp. 7, 9, 25, 27, 31, 33, 53, 57, 61, 63, 67, 79, 81, 87, 91, 101, 105, 111, 115, 125, 131, 145, 151, 159, 161, 169, 173, 175, 177, 185, 191, 197, 207, 209, 215, 219, 223, 225, 239, 241, 249, 252, 269, 273, 281, 283, 297, 301, 305, 321, 323, 327, 347, 369, 377, 411, 413, 417; Math In Your Life pp. 2, 33, 59, 90, 119, 149, 183, 206, 235, 287, 319, 371, 420; App. pp. 18, 42, 70, 94, 132, 162, 198, 226, 260, 308, 352, 394, 428.

SE/TE: pages xvi-xvii, 15, 42, 163, 193, 267, 283, 287, 309, 317 TE: Learning Styles: pages 15, 42, 163, 193, 267, 287, 309, 317; Applications: pages 42, 283, 309; Mental Math: page 193

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GRADE 7 MATHEMATICS PATHWAYS MATHEMATICS: CONCEPTS 6. Use accurately common logical words and phrases such as

“and,” “or,” “if…then…,” “unique,” “only if.” Logical/Mathematical vocabulary is used throughout the AGS Mathematics Pathways textbook. New vocabulary appears in bold type in the text and they are defined in the text left column and in the glossary. Common logical vocabulary is also reinforced through the Teacher’s Resource Library activities as an integral portion of the entire program.

Logical/Mathematical vocabulary is used throughout the AGS Mathematics Pathways textbook. New vocabulary appears in bold type in the text and they are defined in the text left column and in the glossary. Common logical vocabulary is also reinforced through the Teacher’s Resource Library activities as an integral portion of the entire program. Additional: TE: Logical/mathematical: pages 5, 14, 15, 23, 47, 53, 59, 63, 73, 77, 79, 89, 94, 98, 100, 111, 113, 117, 122, 123, 127, 145, 149, 162, 169, 188, 195, 205, 213, 229, 249, 252, 263, 277, 289, 307, 312, 320, 332, 343, 355, 367, 378, 383, 389, 397 TRL: How To Use This Book 3-4

II. NUMBER SENSE, COMPUTATION AND OPERATIONS A. Number Sense Standard: Use positive and negative rational numbers, represented in a variety of ways, to quantify information and to solve real-world and mathematical problems. The student will: 1. Represent rational numbers as fractions, mixed numbers,

decimals or percents and convert among various forms as appropriate.

Pages 62-67, 98-132, 166-169, 178-193, 420-421

SE/TE: pages 86-100, 134-139, 149, 164-170, 180-193, 197, 199-203, 226-231, 368-371 TE: Applications: pages 93, 94, 169, 185, 192, 201, 203, 231, 369, 370; Learning Styles: pages 88, 89, 91, 94, 95, 97-100, 138, 139, 149, 165, 181, 183, 184, 188, 189, 192, 193, 199, 202, 227-229, 231, 369; Mental Math: pages 138, 164, 167, 169, 170, 190, 193, 199; Manipulatives: pages 137, 181, 191; TRL: Estimation Exercise 5; Community Connection 5; Everyday Math: 3, 5; Application Activity 3, 5; Activities 28-31, 40, 48, 49, 52-55, 57, 58, 102; Workbook 28-31, 40, 48, 49, 52-55, 57, 58, 112, 113

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GRADE 7 MATHEMATICS PATHWAYS MATHEMATICS: CONCEPTS 2. Use scientific notation with positive powers of 10, with

appropriate treatment of significant digits, to solve real-world and mathematical problems.

Pages 4-5, 54-55, 58-59, 74-75, 92-93 SE/TE: pages 76-79 TE: Learning Styles: pages 77, 79; Applications: page 79; Mental Math: pages 76, 77 TRL: Activities 24, 25; Workbook 24, 25

3. Locate and compare positive and negative rational numbers on a number line.

Pages 214-225, 312-333 SE/TE: pages 74-75, 148-151, 242-243, 321 TE: Learning Styles: pages 75, 149-151, 243, 321; Applications: page 243 TRL: Activities 23, 44, 68; Workbook 23, 44, 68

B. Computation and Operation Standard: Compute fluently and make reasonable estimates with rational numbers in real-world and mathematical problems. Understand the meanings of the basic operations, including the use of integer exponents and square roots, and how the operations relate to one another. Appropriately use calculators and other technologies to solve problems. The student will: 1. Add, subtract, multiply and divide fractions and mixed numbers.

Pages 98-99, 102-132, 143-145, 148-162, 166-177, 188-198, 278-285

SE/TE: pages 142-170 TE: Learning Styles: pages 144, 145, 149-151, 155, 158, 159, 162, 163, 165, 169, 170; Applications: pages 145, 147, 159, 169; Mental Math: pages 144, 154, 156, 160, 164, 167; Manipulatives: pages 147, 153, 157, 161; TRL: Activities 42-49; Workbook 42-49

2. Use the inverse relationship between extracting square roots and squaring positive integers to solve real-world and mathematical problems.

Pages 242-260 SE/TE: pages 280-283 TE: Learning Styles: page 281; Applications: page 283; Manipulatives: page 281; TRL: Activities 81; Workbook 83, 84

3. Calculate the percentage of increase and decrease of a quantity in real-world and mathematical problems.

Pages 185, 190-193 SE/TE: pages 190-193 TE: Learning Styles: pages 192, 193; Mental Math: pages 190, 193; Manipulatives: page 191; TRL: Activities 55; Workbook 55

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GRADE 7 MATHEMATICS PATHWAYS MATHEMATICS: CONCEPTS 4. Convert among fractions, decimals and percents and use

these representations for estimations and computations in real-world and mathematical problems.

Pages 62-67, 178-193 SE/TE: pages 86-100, 134-139, 149, 164-170, 180-193, 197, 199-203, 226-231, 368-371 TE: Applications: pages 93, 94, 169, 185, 192, 201, 203, 231, 369, 370; Learning Styles: pages 88, 89, 91, 94, 95, 97-100, 138, 139, 149, 165, 181, 183, 184, 188, 189, 192, 193, 199, 202, 227-229, 231, 369; Mental Math: pages 138, 164, 167, 169, 170, 190, 193, 199; Manipulatives: pages 137, 181, 191; TRL: Estimation Exercise 5; Community Connection 5; Everyday Math: 3, 5; Application Activity 3, 5; Activities 28-31, 40, 48, 49, 52-55, 57, 58, 102; Workbook 28-31, 40, 48, 49, 52-55, 57, 58, 112, 113

5. Understand and compute positive integer powers of nonnegative integers and express examples as repeated multiplication such as 3∧4 = 3 x 3 x 3 x 3 = 81.

Pages 4-5, 10-11, 14-15, 89, 230-237, 240-241

SE/TE: pages 76-77, 272-279 TE: Learning Styles: pages 77, 275, 277, 279; Mental Math: pages 76, 77, 276; Manipulatives: page 279; TRL: Estimation Exercise 9; Community Connection 9; Activities 24, 78-80; Workbook 24, 80-82


Pages 9, 25, 57, 61, 127, 140 SE/TE: pages 11, 22, 122, 215, 223, 229 TE: 10, 215, 229; Learning Styles: pages 11, 22, 122, 123; Applications: page 215; Mental Math: pages 122

7. Know, use and translate calculator notational conventions to mathematical notation.

This concept can be specifically found on pages 492-493. The opportunity to use this concept can be found on pages 9, 16, 41, 53, 57, 61, 90, 109, 127, 140, 155, 189, 193, 213, 215, 233, 241, 244, 256, 280, 291, 301, 305, 333, 343, 346, 379, 411.

This concept can be specifically found on pages 462-463. The opp. to use this concept can be found: SE/TE: pages 11, 22, 43, 55, 59, 77, 79, 94, 122, 127, 145, 151, 159, 181, 196, 205, 215, 223, 229, 255, 261, 265, 275, 282, 286, 325, 329, 351, 373, 379, 391; TE: pp. 10, 49, 57, 85, 98, 109, 110, 130, 139, 145, 147, 151, 165, 197, 205, 215, 225, 229, 255, 257, 263, 275, 287, 313, 325, 350, 371, 398

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GRADE 7 MATHEMATICS PATHWAYS MATHEMATICS: CONCEPTS 8. Understand that use of a calculator requires appropriate

mathematical reasoning and does not replace the need for mental computation.

The opportunity to explore this concept can be found through Mental Math and calculator activities in the Teacher’s Edition. Additional calculator activities are found in the student edition on pages 9, 16, 41, 53, 57, 61, 90, 109, 127, 140, 155, 189, 193, 213, 215, 233, 241, 244, 256, 280, 291, 301, 305, 333, 343, 346, 379, 411.

This concept can be specifically found on pages 462-463. The opportunity to use this concept can be found on pages SE/TE: pages 11, 22, 43, 55, 59, 77, 79, 94, 122, 127, 145, 151, 159, 181, 196, 205, 215, 223, 229, 255, 261, 265, 275, 282, 286, 325, 329, 351, 373, 379, 391; Problem Solving Strategies: pages 15, 42, 51, 91, 99, 123, 155, 163, 193, 197, 228, 231, 252, 267, 283, 287, 309, 317, 351, 357, 389 TE: pages 10, 49, 57, 85, 98, 109, 110, 130, 139, 145, 147, 151, 165, 197, 205, 215, 225, 229, 255, 257, 263, 275, 287, 313, 325, 350, 371, 398 TE: Mental Math: pages 4,6, 20, 41, 44, 48, 52, 53, 56, 76, 77, 80, 91, 122, 128, 129, 138, 144, 154, 156, 160, 164, 167, 179, 180, 190, 193, 199, 216, 222, 249, 256, 258, 260, 262, 264, 276, 302, 304, 308, 314, 345, 351, 356, 370, 377, 380, 382

III. PATTERNS, FUNCTIONS AND ALGEBRA A. Patterns and Functions Standard: Demonstrate an understanding of rate of change graphically and numerically. The student will: 1. Demonstrate, numerically and graphically, an

understanding that rate is a measure of change of one quantity per unit change of another quantity in real-world and mathematical problems.

Pages 176-177, 198

SE/TE: pages 182-185 TE: Learning Styles: pages 183, 184; Applications: page 185 TRL: Activities 53; Workbook 53

2. Plot points on the graph of a linear function and identify the slope or rate of change.

Pages 340-351 This concept falls outside the scope of AGS Mathematic: Concepts.

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GRADE 7 MATHEMATICS PATHWAYS MATHEMATICS: CONCEPTS B. Algebra (Algebraic Thinking) Standard: Apply arithmetic operations in the correct order to generate equivalent algebraic expressions and to solve simple formulas in real-world and mathematical problems. The student will: 1. Apply the correct order of operations including addition,

subtraction, multiplication, division and grouping symbols to generate equivalent algebraic expressions.

Pages 6-9, 24-25, 40-41, 54-65, 68-69, 84-87, 112-115, 119-123, 126-131, 136-151, 156-162

SE/TE: pages 216-232 TE: Learning Styles: pages 217-219, 223, 225, 227-229, 231, 232; Applications: pages 219, 231; Mental Math: pages 216, 222; Manipulatives: page 223; TRL: Activities 61-66; Workbook

2. Use the facts that the sum of a number and its opposite is zero and the product of a number and its reciprocal is one to generate equivalent algebraic expressions.

Pages 128-131 SE/TE: pages 48-51, 216-219, 222-229 TE: Learning Styles: pages 51, 51, 217-219, 225, 227-229; Mental Math: pages 48, 216, 222; Manipulatives: page 223; TRL: Activities 16, 61, 63-65; Workbook 16, 61, 63-65

3. Solve simple formulas with up to three variables, when the values of two of the variables are given.

Formulas defined: pages 52-53; put to use: pages 176-177, 192-193, 198, 238-245, 250-260, 264-291, 294-308, 344-347

SE/TE: pages 38-39, 56-59, 314-317, 326-333 TE: Learning Styles: pages 39, 58, 59, 315-317, 327-329, 331-333; Mental Math: page 314; Manipulatives: pages 39, 56; TRL: Activities 12, 19, 93, 94; Workbook 12, 19, 98-101

IV. DATA ANALYSIS, STATISTICS AND PROBABILITY A. Data and Statistics Standard: Represent data and use various measures associated with data to draw conclusions and identify trends. The student will: 1. Construct and analyze simple scatter plots.

Pages 408-409

SE/TE: pages 382-385 TE: Learning Styles: page 383; Mental Math: page 382; TRL: Activities 107; Workbook 118

2. Understand the meaning of, and be able to compute minimum, maximum, range, median, mean and mode of a data set.

Pages 410-419 SE/TE: pages 372-379 TE: Learning Styles: pages 373, 375, 378, 379; Applications: page 377; Mental Math: page 377; TRL: Activities 103-105; Workbook 114-116

16


GRADE 7 MATHEMATICS PATHWAYS MATHEMATICS: CONCEPTS B. Probability Standard: Calculate and express probabilities numerically and apply probability concepts to solve real-world and mathematical problems. The student will: 1. Express probabilities as percentages, fractions, proportions and decimals.

Pages 420-425

SE/TE: pages 392-397 TE: Learning Styles: pages 393, 395-397; Manipulatives: page 393; TRL: Activities 110-111; Workbook 121-122

2. Use a variety of experiments to explore the relationship between experimental and theoretical probabilities.

Pages 420-425 This concept falls outside the scope of AGS Mathematic: Concepts.

V. SPATIAL SENSE, GEOMETRY AND MEASURMENT A. Spatial Sense Standard: Recognize the relationship between different representations of two- and three-dimensional shapes. Understand the effect of various transformations. The student will: 1. Recognize a view of a three-dimensional shape, given a

view from a different orientation.

Pages 292-308

SE/TE: pages 326-333 TE: Learning Styles: pages 327-329, 331-333 TRL: Activities 93-94; Workbook 98-101

2. Use visual representations of transformations such as reflections, rotations, translations and change of scale in one and two dimensions to solve real-world and mathematical problems.

Pages 382-394 SE/TE: pages 348-357 TE: Learning Styles: pages 350, 353, 355-357; Mental Math: pages 351, 356; Manipulative activities: page 353; TRL: Activities 98-100; Workbook 106-109

B. Geometry Standard: Use basic geometric principles and proportional reasoning to solve real-world and mathematical problems. The student will: 1. Calculate the radius, diameter, circumference and area of a

circle given any one of these.

Pages 56, 251-253, 288-291, 297, 299-301, 306-307

SE/TE: pages 318-325, 379 TE: Learning Styles: pages 319-321, 379 Applications: pages 319, 323; TRL: Activities 90-92; Workbook 94-97

2. Calculate the area and perimeter of a sector of a circle given its angle and radius.

This concept falls outside the scope of AGS Mathematics Pathways.

This concept falls outside the scope of AGS Mathematic: Concepts.

17


GRADE 7 MATHEMATICS PATHWAYS MATHEMATICS: CONCEPTS 3. Use ratios and proportions to interpret map scales and scale drawings.

Pages 194-197 SE/TE: pages 200-203 TE: Learning Styles: page 202; Applications: pages 201, 203; TRL: Activities 58; Workbook 58

4. Classify quadrilaterals as squares, rectangles, rhombi, parallelograms, kites, trapezoids or none of these.

Pages 267, 270-287, 378-381 SE/TE: pages 306-309 TE: Learning Styles: pages 307-309; Applications: pages 309, 310; Mental Math: page 308; Manipulatives: page 307; TRL: Activities 87; Workbook 91

C. Measurement Standard: Make calculations of time, length, area and volume within standard measuring systems using good judgment in choice of units. The student will: 1. Choose appropriate units to calculate, measure, and record

length, weight, area and volume in both U.S. customary and metric systems.

Pages 194-197, 238-246, 248-260, 264-291, 294-307

SE/TE: pages 19, 24-27, 54-55, 80-83, 89, 162, 165, 201-203, 280-286, 290, 294-333 TE: Learning Styles: pages 25, 27, 55, 81, 82, 89, 162, 165, 202, 281, 282, 285, 286, 297, 299-301, 303, 304, 307-309, 311-313, 315-317, 319-321, 327-329, 331-333; Applications: pages 25, 55, 81, 83, 201, 203, 283, 297, 305, 309, 311, 312, 319, 323; Mental Math: pages 54, 80, 302, 304, 308, 314; Manipulatives: pages 281, 299, 303, 307; TRL: Everyday Math 9; Application Activity 9; Activities 8, 9, 18, 26, 81, 82, 84-94; Workbook 8, 9, 18, 26, 83-86, 88-101

18


MINNESOTA MATHEMATICS AGS PUBLISHING GRADE 8 MATHEMATICS PATHWAYS

I. MATHEMATICAL REASONING Standard: Apply skills of mathematical representation, communication and reasoning throughout the remaining four content strands. The student will: 1. Assess the reasonableness of a solution by comparing the solution to appropriate

graphical or numerical estimates or by recognizing the feasibility of a solution in a given context.

SE: pages xviii-xix, 5, 28-29, 34-35, 37, 65, 77, 117, 141, 187, 221, 245, 246-247, 291, 341, 365, 403, 413; Build A Model: pages 17, 38, 51, 93, 130, 147, 180, 213, 257, 281, 351, 393, 424 TE: pages xviii-xix, 5, 28-29, 34-35, 37, 65, 77, 117, 141, 187, 221, 245, 246-247, 291, 341, 365, 403, 413; Build A Model: pages 17, 38, 51, 93, 130, 147, 180, 213, 257, 281, 351, 393, 424 Mental Math: pages 3, 7, 8, 11, 31, 37, 42, 55, 69, 90, 95, 119, 132, 144, 161, 171, 185, 187, 189, 196, 211, 218, 244, 249, 272, 333, 387, 405, 417, 424; Manipulatives: pages 3, 5, 11, 25, 27, 41, 51, 81, 83, 85, 89, 101, 103, 111, 113, 117, 121, 125, 127, 149, 151, 173, 184, 213, 215, 217, 221, 225, 235, 237, 239, 241, 243, 261, 275, 321, 323, 331, 341, 387, 421 Modeling: pages 17, 33, 67, 93, 95, 133, 141, 195, 207, 239, 293, 342, 377, 407, 409


SE: pages 314-323 TE: pages 314-323; Additional Teacher’s Edition activities: Explain results: Learning Styles: Auditory/Verbal: pages 5, 29, 33, 49, 69, 77, 86, 104, 122, 129, 144, 157, 169, 205, 218, 237, 255, 275, 289, 317, 335, 345, 365, 377, 379, 391, 405, 413, 425; Interpersonal/Group Learning: pages 7, 9, 29, 37, 65, 69, 86, 108, 118, 122, 149, 187, 193, 209, 225, 235, 257, 277, 285, 289, 304, 318, 321, 331, 350, 359, 373, 415; Group Problem Solving: pages 9, 12, 27, 31, 51, 53, 57, 61, 67, 71, 79, 81, 87, 91, 101, 105, 111, 115, 125, 131, 145, 151, 159, 163, 173, 175, 176, 181, 185, 189, 191, 193, 207, 209, 215, 219, 225, 239, 241, 247, 251, 255, 269, 273, 281, 283, 300, 305, 321, 323, 347, 377, 392, 403, 411, 413, 415, 417, 425

19


GRADE 8 MATHEMATICS PATHWAYS 3. Translate a problem described verbally or by tables, diagrams, or graphs, into suitable

mathematical language, solve the problem mathematically and interpret the result in the original context.

Translating written problem-solving into suitable mathematical language: SE/TE: pages 7, 9, 25, 27, 31, 33, 53, 57, 61, 63, 67, 79, 81, 87, 91, 101, 105, 111, 115, 125, 131, 145, 151, 159, 161, 169, 173, 175, 177, 185, 191, 197, 207, 209, 215, 219, 223, 225, 239, 241, 249, 252, 269, 273, 281, 283, 297, 301, 305, 321, 323, 327, 347, 369, 377, 411, 413, and 417; Math In Your Life on pages 2, 33, 59, 90, 119, 149, 183, 206, 235, 287, 319, 371, and 420; and Applications: pages 18, 42, 70, 94, 132, 162, 198, 226, 260, 308, 352, 394, 428. Additional TE: Applications (Home, Career, Community): pages 3, 12, 19, 33, 39, 41, 43, 51, 59, 63, 67, 81, 90, 93, 111, 123, 130, 147, 151, 154, 159, 173, 177, 180, 185, 191, 193, 195, 196, 223, 226, 239, 245, 252, 253, 257, 261, 271, 287, 293, 296, 303, 315, 326, 343, 353, 368, 373, 375, 381, 384, 387, 391, 395, 401, 409, 419, 421, 424


The opportunity to explore this concept can be found in the SE and TE on pages 7, 9, 25, 27, 31, 33, 53, 57, 61, 63, 67, 79, 81, 87, 91, 101, 105, 111, 115, 125, 131, 145, 151, 159, 161, 169, 173, 175, 177, 185, 191, 197, 207, 209, 215, 219, 223, 225, 239, 241, 249, 252, 269, 273, 281, 283, 297, 301, 305, 321, 323, 327, 347, 369, 377, 411, 413, and 417; Math In Your Life on pages 2, 33, 59, 90, 119, 149, 183, 206, 235, 287, 319, 371, and 420; and Applications: pages 18, 42, 70, 94, 132, 162, 198, 226, 260, 308, 352, 394, 428. Additional TE activities: Applications (Home, Career, Community): pages 3, 12, 19, 33, 39, 41, 43, 51, 59, 63, 67, 81, 90, 93, 111, 123, 130, 147, 151, 154, 159, 173, 177, 180, 185, 191, 193, 195, 196, 223, 226, 239, 245, 252, 253, 257, 261, 271, 287, 293, 296, 303, 315, 326, 343, 353, 368, 373, 375, 381, 384, 387, 391, 395, 401, 409, 419, 421, 424; Mental Math: pages 3, 7, 8, 11, 31, 37, 42, 55, 69, 90, 95, 119, 132, 144, 161, 171, 185, 187, 189, 196, 211, 218, 244, 249, 272, 333, 387, 405, 417, 424;

20


GRADE 8 MATHEMATICS PATHWAYS 5. Determine whether or not relevant information is missing from a problem. SE/TE: Pages xviii; and exploring this concept: pages 7, 9, 25, 27, 31, 33,

53, 57, 61, 63, 67, 79, 81, 87, 91, 101, 105, 111, 115, 125, 131, 145, 151, 159, 161, 169, 173, 175, 177, 185, 191, 197, 207, 209, 215, 219, 223, 225, 239, 241, 249, 252, 269, 273, 281, 283, 297, 301, 305, 321, 323, 327, 347, 369, 377, 411, 413, and 417; Math In Your Life on pages 2, 33, 59, 90, 119, 149, 183, 206, 235, 287, 319, 371, and 420; and Applications: pages 18, 42, 70, 94, 132, 162, 198, 226, 260, 308, 352, 394, 428. Additional Applications in the TE: (Home, Career, Community): pages 3, 12, 19, 33, 39, 41, 43, 51, 59, 63, 67, 81, 90, 93, 111, 123, 130, 147, 151, 154, 159, 173, 177, 180, 185, 191, 193, 195, 196, 223, 226, 239, 245, 252, 253, 257, 261, 271, 287, 293, 296, 303, 315, 326, 343, 353, 368, 373, 375, 381, 384, 387, 391, 395, 401, 409, 419, 421, 424;

6. Use accurately common logical words and phrases such as “and,” “or,” “if…then…,” “unique,” “only if.”

Logical/Mathematical vocabulary is used throughout the AGS Mathematics Pathways Student textbook. New vocabulary appears in bold type in the text and they are defined in the text left column and in the glossary. Common logical vocabulary is also reinforced through the Teacher’s Resource Library activities as an integral portion of the entire program. Applications (Home, Career, Community): pages 3, 12, 19, 33, 39, 41, 43, 51, 59, 63, 67, 81, 90, 93, 111, 123, 130, 147, 151, 154, 159, 173, 177, 180, 185, 191, 193, 195, 196, 223, 226, 239, 245, 252, 253, 257, 261, 271, 287, 293, 296, 303, 315, 326, 343, 353, 368, 373, 375, 381, 384, 387, 391, 395, 401, 409, 419, 421, 424; Logical/Mathematical: pages 7, 15, 31, 63, 78, 104, 161, 169, 223, 247, 307, 327, 339, 369, 383, 427

II. NUMBER SENSE, COMPUTATION AND OPERATIONS A. Number Sense Standard: Use rational and irrational numbers, represented in a variety of ways, to quantify information and to solve real-world and mathematical problems. The student will: 1. Represent and compare rational and irrational numbers symbolically and on a number

line.

SE: pages 62-67, 98-132, 166-169, 178-193, 214-225, 246-249, 312-333, 420-421 TE: pages 62-67, 98-132, 166-169, 178-193, 214-225, 246-249, 312-333, 420-421; Applications (Home, Career, Community): pages 63, 67, 111, 123, 130, 180, 185, 191, 193, 223, 315, 326; Mental Math: pages 119, 132, 185, 187, 189, 218, 249; Manipulatives: pages 101, 103, 111, 113, 117, 121, 125, 127, 184, 215, 217, 221, 225, 321, 323, 331; Group Problem Solving: pages 67, 101, 105, 111, 115, 125, 131, 185, 215, 219, 225, 321, 323; TRL: Estimation Exercise 5, 7, 11; Community Connection 5, 7, 11; Application Activity 5; Everyday Math 5; Activities: 24-26, 34-43, 53, 58-63, 69-73, 80-81, 98-104; Workbook Activities: 25-27, 35-45, 55, 60-66, 72-77, 84-85, 103-110

21


GRADE 8 MATHEMATICS PATHWAYS 2. Use rational and irrational numbers to solve real-world and mathematical problems. SE: pages 62-67, 98-132, 166-169, 178-193, 214-225, 246-249, 312-333,

420-421 TE: pages 62-67, 98-132, 166-169, 178-193, 214-225, 246-249, 312-333, 420-421 Applications (Home, Career, Community): pages 63, 67, 111, 123, 130, 180, 185, 191, 193, 223, 315, 326; Mental Math: pages 119, 132, 185, 187, 189, 218, 249; Manipulatives: pages 101, 103, 111, 113, 117, 121, 125, 127, 184, 215, 217, 221, 225, 321, 323, 331; Group Problem Solving: pages 67, 101, 105, 111, 115, 125, 131, 185, 215, 219, 225, 321, 323 TRL: Estimation Exercise 5, 7, 11; Community Connection 5, 7, 11; Application Activity 5; Everyday Math 5; Activities: 24-26, 34-43, 53, 58-63, 69-73, 80-81, 98-104; Workbook Activities: 25-27, 35-45, 55, 60-66, 72-77, 84-85, 103-110

3. Use scientific notation with positive and negative powers of 10, with appropriate treatment of significant digits, to solve real-world and mathematical problems.

SE: pages 4-5, 54-55, 58-59, 74-75, 92-93, 233-235 TE: pages 4-5, 54-55, 58-59, 74-75, 92-93, 233-235 Applications (Home, Career, Community): page 93 Mental Math: page 55; Manipulatives: pages 5, 235 Group Problem Solving: page 58; Chapter 4 Project: page 75 TRL: Estimation Exercise 4; Community Connection 4; Activities: 2, 20, 22, 33. 75; Workbook Activities: 3, 20, 22, 34, 79

4. Classify numbers as rational or irrational. SE: pages 62-67, 98-132, 166-169, 178-193, 214-225, 246-249, 312-333, 420-421 TE: pages 62-67, 98-132, 166-169, 178-193, 214-225, 246-249, 312-333, 420-421 Applications (Home, Career, Community): pages 63, 67, 111, 123, 130, 180, 185, 191, 193, 223, 315, 326 Mental Math: pages 119, 132, 185, 187, 189, 218, 249 Manipulatives: pages 101, 103, 111, 113, 117, 121, 125, 127, 184, 215, 217, 221, 225, 321, 323, 331 Group Problem Solving: pages 67, 101, 105, 111, 115, 125, 131, 185, 215, 219, 225, 321, 323 TRL: Estimation Exercise 5, 7, 11; Community Connection 5, 7, 11; Application Activity 5; Everyday Math 5; Activities: 24-26, 34-43, 53, 58-63, 69-73, 80-81, 98-104; Workbook Activities: 25-27, 35-45, 55, 60-66, 72-77, 84-85, 103-110

22


GRADE 8 MATHEMATICS PATHWAYS B. Computation and Operation Standard: Compute fluently and make reasonable estimates with rational and irrational numbers in real-world and mathematical problems. Understand the meanings of the basic operations, including the use of integer exponents and nth roots, and how the operations relate to one another. Appropriately use calculators and other technologies to solve problems. The student will: 1. Use calculator approximations of irrational and rational numbers in multi-step real-

world and mathematical problems.

SE: pages 61, 127, 189, 193, 213, 248-249, 333 TE: pages 61, 127, 189, 193, 213, 248-249, 333 Additional TE Calculator Exercises: pages 65, 109, 127, 189, 213, 215, 332

2. Find integer approximations of square roots of positive integers without a calculator. SE: pages 242-260 TE: pages 242-260 Applications (Home, Career, Community): pages 252, 253, 257, 261; Mental Math: page 241; Manipulatives: page 261; Group Problem Solving: pages 247, 251, 255 TRL: Application Activity 9; Everyday Math 9; Activities: 79-84; Workbook Activities: 83-88

3. Multiply and divide expressions involving exponents with a common base. SE: pages 230-237 TE: pages 230-237 Manipulatives: pages 235, 237 TRL: Estimation Exercise 9; Community Connection 9; Activities: 74-76; Workbook Activities: 78-80

4. Use the inverse relationship between nth roots and nth powers of rational numbers to solve real-world and mathematical problems.

The opportunity to explore this concept can be found in the SE and TE on page 249. Mental Math: page 249


SE: pages 9, 25, 57, 127, 140, 248-249, 492-493 TE: pages 9, 25, 57, 127, 140, 248-249, 492-493 Mental Math: page 249; Manipulatives: pages 25, 127 Group Problem Solving: pages 9, 57 TRL: Activities: 81; Workbook Activities: 85

23


GRADE 8 MATHEMATICS PATHWAYS 6. Know, use and translate calculator notational conventions to mathematical notation. This concept can be specifically found in the SE and TE on pages 492-493.

The opportunity to use this concept can be found in the SE and TE on pages 9, 16, 41, 53, 57, 61, 90, 109, 127, 140, 155, 189, 193, 213, 215, 233, 241, 244, 256, 280, 291, 301, 305, 333, 343, 346, 379, 411. Additional TE calculator: pages 5, 16, 41, 43, 53, 57, 61, 65, 67, 71, 78, 90, 109, 127, 141, 155, 189, 197, 199, 213, 215, 233, 241, 244, 255, 280, 291, 301,. 305, 332, 343, 346, 364, 379, 411, 427

7. Understand that use of a calculator requires appropriate mathematical reasoning and does not replace the need for mental computation.

The opportunity to explore this concept can be found in the SE and TE on pages 9, 16, 41, 53, 57, 61, 90, 109, 127, 140, 155, 189, 193, 213, 215, 233, 241, 244, 256, 280, 291, 301, 305, 333, 343, 346, 379, 411. Additional TE activities: Mental Math: pages 7, 8, 11, 31, 37, 42, 55, 69, 90, 95, 119, 132, 144, 161, 171, 185, 187, 189, 196, 211, 218, 244, 249, 272, 333, 387, 405, 417, 424; Calculator activities: pages 5, 16, 41, 43, 53, 57, 61, 65, 67, 71, 78, 90, 109, 127, 141, 155, 189, 197, 199, 213, 215, 233, 241, 244, 255, 280, 291, 301,. 305, 332, 343, 346, 364, 379, 411, 427

III. PATTERNS, FUNCTIONS AND ALGEBRA A. Patterns and Functions Standard: Understand and describe progressions. Use graphs and tables to solve real-world and mathematical problems. The student will: 1. Recognize when a list of numbers forms an arithmetic or geometric progressions and

be able to determine subsequent terms in the progression.

SE: pages 42, 230-231, 330-333, 351, 377, 393-394, 399, 428 TE: pages 42, 230-231, 330-333, 351, 377, 393-394, 399, 428 Applications (Home, Career, Community): page 43 Mental Math: pages 42, 333, 393; Manipulatives: pages 331 Group Problem Solving: pages 377 TRL: Estimation Exercise 9; Community Connection 9; Application Activity 2, 13; Everyday Math 2, 13; Activities: 104; Workbook Activities: 109-110

2. Represent quantitative relationships graphically and use the graphs to solve real-world and mathematical problems.

SE: pages 177, 312-351, 398-409, 412-419 TE: pages 177, 312-351, 398-409, 412-419 Applications (Home, Career, Community): pages 315, 326, 343, 353, 401, 409, 419; Mental Math: pages 333, 405, 417 Manipulatives: pages 331, 341, 421 Group Problem Solving: pages 321, 323, 331, 347, 403, 413, 415, 417 TRL: Estimation Exercise 11, 13; Community Connection 11, 13; Activities: 98-110, 125-129, 131-134; Workbook Activities: 103-116, 132-136, 138-142

24


GRADE 8 MATHEMATICS PATHWAYS 3. Generate a table of values from a formula and graph the resulting ordered pairs on a

grid. SE: pages 330-351 TE: pages 330-351 Applications (Home, Career, Community): pages 343, 353 Mental Math: pages 333; Manipulatives: pages 331, 341 Group Problem Solving: pages 347 TRL: Activities: 104-110; Workbook Activities: 109-116

B. Algebra (Algebraic Thinking) Standard: Use algebraic operations to generate equivalent expressions, and use proportional reasoning to solve real-world and mathematical problems. Demonstrate the ability to manipulate an equation by applying arithmetic operations to both sides to maintain equivalence. The student will: 1. Multiply and divide expressions of the form axn.

SE: pages 142-147 TE: pages 142-147 Applications (Home, Career, Community): page 147; Mental Math: page 144; Group Problem Solving: page 145 TRL: Activities: 45-46; Workbook Activities: 46-48

2. Use simple formulas with more than one variable to solve real-world and mathematical problems.

SE: pages 52, 238-246, 248-260, 264-291, 294-307, 344-347 TE: pages 52, 238-246, 248-260, 264-291, 294-307, 344-347 Applications (Home, Career, Community): pages 239, 245, 271, 287, 296, 303; Mental Math: pages 244, 272; Manipulatives: pages 239, 241, 243, 275; Group Problem Solving: pages 239, 241, 247, 269, 273, 281, 283, 300, 305, 347 TRL: Estimation Exercise 9, 10; Community Connection 9, 10; Activities: 19, 76-92, 94-97, 109; Workbook Activities: 19, 80-97, 99-102, 115

3. Use proportions and percents with one unknown quantity to solve real-world and mathematical problems.

SE: pages 66-67, 170-175, 178-193 TE: pages 66-67, 170-175, 178-193 Applications (Home, Career, Community): pages 67, 173, 180, 185, 191, 193; Mental Math: pages 171, 185, 187, 189; Manipulatives: pages 173, 184 Group Problem Solving: pages 67, 173, 175, 176, 181, 185, 189, 191, 193 TRL: Activities: 26, 54-56, 58-63; Workbook Activities: 27, 55-58, 60-66

25


GRADE 8 MATHEMATICS PATHWAYS 4. Apply the correct order of operations including addition, subtraction, multiplication,

division, grouping symbols and powers, to simplify and evaluate algebraic expressions.

SE: pages 6-9, 24-25, 40-41, 54-65, 68-69, 82, 84-87, 110-115, 119-123, 126-131, 136-151, 156-162, 230-245 TE: pages 6-9, 24-25, 40-41, 54-65, 68-69, 82, 84-87, 110-115, 119-123, 126-131, 136-151, 156-162, 230-245 Applications (Home, Career, Community): pages 41, 59, 63, 67, 111, 123, 131, 147, 151, 159, 239, 245 Mental Math: pages 7, 8, 69, 119, 144, 161, 244 Manipulatives: pages 25, 41, 85, 111, 113, 121, 127, 149, 151, 235, 237, 239, 241, 243; Group Problem Solving: pages 9, 57, 61, 87, 111, 115, 131, 145, 151, 159, 163, 239, 241 TRL: Estimation Exercise 6, 9; Community Connection 6, 9; Application Activity 6; Everyday Math 6; Activities: 4-5, 8, 16, 20-25, 27, 30-31, 37-38, 40, 42-48, 50-52, 52-54, 74-79; Workbook Activities: 3-4, 7, 16, 20-26, 28, 31-32, 41, 43-50, 78-83

IV. DATA ANALYSIS, STATISTICS, AND PROBABILITY A. Data and Statistics Standard: Represent data and use various measures associated with data to draw conclusions and identify trends. The student will: 1. Construct and analyze histograms, circle graphs, stem-and-leaf plots and box-and-

whisker plots.

SE: pages 398-399, 404-407, 418-419 TE: pages 398-399, 404-407, 418-419 Applications (Home, Career, Community): page 419 Mental Math: page 405 TRL: Estimation Exercise 13; Community Connection 13; Activities: 127-128, 134; Workbook Activities: 134-135, 142

2. Compute the quartiles of a data set. This concept falls outside the scope of AGS Mathematics Pathways. B. Probability Standard: Calculate and express probabilities numerically and apply probability concepts to solve real-world and mathematical problems. The student will: 1. Understand that if p is the probability of an event occurring, then 1 – p is the

probability of the event not occurring.

This concept falls outside the scope of AGS Mathematics Pathways.

2. Convert between odds and probabilities. This concept falls outside the scope of AGS Mathematics Pathways. 3. Use a variety of experiments to explore the relationship between experimental and

theoretical probabilities and the effect of sample size on this relationship. This concept falls outside the scope of AGS Mathematics Pathways.

26


GRADE 8 MATHEMATICS PATHWAYS V. SPATIAL SENSE, GEOMETRY AND MEASUREMENT A. Spatial Sense Standard: Recognize the relationship between different representations of two- and three-dimensional shapes. Understand the effect of various transformations. The student will: 1. Use models and visualization to understand and create various two-dimensional

diagrams of three-dimensional shapes.

SE: pages 281, 292-308 TE: pages 281, 292-308 Applications (Home, Career, Community): pages 293, 296, 303 Group Problem Solving: pages 300, 305 TRL: Application Activity 10, Everyday Math 10; Activities: 93-97; Workbook Activities: 98-102

2. Predict the position and orientation of simple three-dimensional geometric shapes under transformations such as reflections, rotations and translations.

SE: pages 382-394 TE: pages 382-394 Applications (Home, Career, Community): pages 384, 387, 391, 395 Mental Math: pages 393; Group Problem Solving: pages 392 TRL: Application Activity 12, Everyday Math 12; Activities: 127-131; Workbook Activities: 121-124

B. Geometry Standard: Use basic geometric principles and proportional reasoning to solve real-world and mathematical problems. The student will: 1. Apply the relationship between changes in one or more linear distances in a planar

figure and the change in area.

Volume: SE/TE: page 308; TRL: Application Activity 10, Everyday Math 10

2. Use the concept of similarity in simple two-dimensional figures to solve real-world and mathematical problems involving proportionality.

SE: pages 174-175, 374-375 TE: pages 174-175, 374-375 Applications (Home, Career, Community): page 375 TRL: Activities: 56, 117; Workbook Activities: 58, 123

3. Know how to find the volumes of cubes, prisms, spheres and cylinders. SE: pages 240-241, 253, 302-307 TE: pages 240-241, 253, 302-307 Applications (Home, Career, Community): pages 253, 303 Manipulatives: page 241; Group Problem Solving: pages 241, 305 TRL: Activities: 78, 96-97; Workbook Activities: 82, 101-102

4. Know how to find the surface areas of cubes, prisms and cylinders. SE: pages 294-301 TE: pages 294-301 Applications (Home, Career, Community): page 296 Group Problem Solving: page 300 TRL: Activities: 94-95; Workbook Activities: 99-100

27


GRADE 8 MATHEMATICS PATHWAYS 5. Calculate perimeter and area of two-dimensional figures obtained by putting together

triangles, parallelograms, and sectors of circles to solve real-world and mathematical problems.

SE: pages 282-287 TE: pages 282-287 Applications (Home, Career, Community): page 287 Group Problem Solving: page 283 TRL: Activities: 89-91; Workbook Activities: 93-96

C. Measurement Standard: Make calculations of time, length, area and volume within and between standard measuring systems using good judgment in choice of units. The student will: 1. Find approximate equivalent measures of length, temperature and weight for common

units in U.S. customary and metric measuring systems.

SE: pages 70, 162, 238-241, 266-289, 294-307 TE: pages 70, 162, 238-241, 266-289, 294-307 Applications (Home, Career, Community): pages 239, 271, 287, , 296, 303; Mental Math: pages 272; Manipulatives: pages 239, 241, 2785; Group Problem Solving: pages 71, 163, 239, 241, 269, 273, 281, 283, 301, 305 TRL: Estimation Exercise 10; Community Connection 10; Application Activity 3, 6, Everyday Math 3, 6; Activities: 77-78, 85-92, 94-97; Workbook Activities: 81-82, 89-97, 99-102

2. Use arithmetic to solve simple real-world and mathematical problems involving mixed units such as minutes and hours in elapsed time, degrees and minutes in latitude and longitude and feet and inches in distance.

SE: pages 162, 176-177 TE: pages 162, 176-177 Applications (Home, Career, Community): page 177 Group Problem Solving: pages 163, 176 TRL: Application Activity 6, Everyday Math 6; Activities: 57; Workbook Activities: 59

28


MINNESOTA MATHEMATICS AGS PUBLISHING GRADES 9, 10, 11 ALGEBRA LIFE SKILLS

MATH CONSUMER

MATHEMATICS GEOMETRY

I. MATHEMATICAL REASONING Standard: Apply skills of mathematical representation, communication and reasoning throughout the remaining three content strands. The student will: 1. Assess the reasonableness of a solution by comparing

the solution to appropriate graphical or numerical estimates or by recognizing the feasibility of solutions in a given context and rejecting extraneous solutions.

Pages xvi-xvii; 17, 52, 83, 106, 147, 176, 194, 233, 275, 301, 345, 367, 387; please also refer to Mental Math and Manipulatives activities in the Teacher’s Edition.

Pages xv, 10-11, 17, 26-27, 44-45, 49, 156-157, 161, 293; please also refer to Mental Math activities in the Teacher’s Edition.

Pages xv, 3, 6, 7, 13, 18, 20, 21, 35, 50-51, 60-61, 72, 82, 85, 86, 127, 193, 212-215, 249, 252-253, 286-291, 292-293; please also refer to Mental Math activities in the Teacher’s Edition.

SE/TE: pages xvi, xvii, 35-60, 72-80, 85-88; Estimation: pages 26, 54, 76, 119, 176, 201, 245, 279, 328, 351-353, 375, 391, 415 TE: Applications: pages 37, 39, 45, 48, 50, 74, 79, 88; Learning Styles: pages 38-40, 43, 44, 47, 49, 53, 54, 56, 57, 73, 74, 76, 78-80, 86-88; Mental Math: pages 9, 19, 23, 38, 43, 78, 90, 93, 107, 114, 124, 133, 165, 183, 201, 207, 209, 233, 227, 238, 262, 297, 327, 350, 361, 390, 420 Teacher’s Resource Library: Estimation Exercises 1-12; Application Activity 2; Geometry on the Job 2; Community Connection 2; Activities: 8-13, 16-17, 19; Workbook Activities: 9-19, 24-26, 28

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GRADES 9, 10, 11 ALGEBRA LIFE SKILLS MATH

CONSUMER MATHEMATICS

GEOMETRY


Pages 74-75, 98-103, 174-178, 188-189; explain results: refer to Learning Styles: Auditory/ Visual; Interpersonal/Group Learning, and Group Problem Solving in the Teacher’s Edition.

The opportunity to explore this concept can be found throughout the student textbook; explain results: refer to Learning Styles: Auditory/ Visual; Interpersonal/Group Learning, and Group Problem Solving in the Teacher’s Edition.

The opportunity to explore this concept can be found throughout the student textbook; explain results: refer to Learning Styles: Auditory/ Visual; Interpersonal/Group Learning, and Group Problem Solving in the Teacher’s Edition.

SE/TE pages 34-60, 72-80, 85-88 TE: Applications: pages 37, 39, 45, 48, 50, 74, 79, 88; Learning Styles: pages 38-40, 43, 44, 47, 49, 53, 54, 56, 57, 73, 74, 76, 78-80, 86-88; Mental Math: pages 38, 43; Manipulatives: pages 52, 59; TRL: Estimation Exercise 2; Application Activity 2; Geometry on the Job 2; Community Connection 2; Activities 8-13, 16-17, 19; Workbook 9-19, 24-26, 28

3. Translate a problem described verbally or by tables, diagrams, or graphs, into suitable mathematical language, solve the problem mathematically and interpret the result in the original context.

Transl. written PS into math lang.: 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, 417; Alg. in Your Life: pp. 15, 41, 77, 107, 128, 157, 187, 242, 262, 296, 331, 375, 394; Apps.: pp. 26, 58, 90, 118, 150, 178, 214, 244, 282, 322, 350, 380, 402

Translating written problem-solving into suitable mathematical language: 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; Apps.: pages 14, 28, 46, 66, 82, 98, 114, 126, 148, 170, 186, 206, 222, 240, 266, 286, 306

Translating written problem-solving into suitable mathematical language: pages 11, 12, 49, 70, 100, 101, 120, 121, 141, 146, 149, 154, 181, 185, 209, 211, 217, 253, 255, 261, 295, 305, 309, 339; Applications: pages 26, 52, 76, 106, 134, 164, 202, 242, 262, 298, 324, 348

SE/TE: Geometry In Your Life: pages 23, 27, 45, 50, 95, 111, 159, 179, 217, 227, 252, 289, 291, 322, 349, 3372, 388, 412; Problem Solving: pages 6, 14, 19, 27, 45, 57, 76, 95, 97, 108, 111, 114, 126, 137, 171, 197, 207, 213, 246, 257, 261, 285, 316, 325, 350, 387, 399, 412; Applications: pages 30, 60, 98, 138, 186, 230, 264, 304, 338, 378, 404, 422 TE: Applications: All Applications-Home, Career, Community; Learning Styles: All Learning Styles Activities; Teacher’s Resource Library: Activities: 1-92; Workbook Activities: 1-126

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GEOMETRY


The opportunity to explore this concept can be found on pages 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, 391and 417; Algebra in Your life: pp. 15, 41, 77, 107, 128, 157, 187, 242, 262, 296, 331, 375, and 394; and Applications: pages 26, 58, 90, 118, 150, 178, 214, 244, 282, 322, 350, 380, 402

The opportunity to explore this concept can be found 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, 306

The opportunity to explore this concept can be found on pages 11, 12, 49, 70, 100, 101, 120, 121, 141, 146, 149, 154, 181, 185, 209, 211, 217, 253, 255, 261, 295, 305, 309, 339; Applications: pages 26, 52, 76, 106, 134, 164, 202, 242, 262, 298, 324, 348

The opportunity to explore this concept can be found in the SE/TE on the following pages Geometry In Your Life: pages 23, 27, 45, 50, 95, 111, 159, 179, 217, 227, 252, 289, 291, 322, 349, 3372, 388, 412; Problem Solving: pages 6, 14, 19, 27, 45, 57, 76, 95, 97, 108, 111, 114, 126, 137, 171, 197, 207, 213, 246, 257, 261, 285, 316, 325, 350, 387, 399, 412; Applications: pages 30, 60, 98, 138, 186, 230, 264, 304, 338, 378, 404, 422 TE: Applications: All Applications-Home, Career, Community; Learning Styles: All Learning Styles Activities; Teacher’s Resource Library: Activities: 1-92; Workbook Activities: 1-126

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GEOMETRY

5. Determine whether or not relevant information is missing from a problem and if so, decide how to best express the results that can be obtained without that information.

Pages xvi-xvii; and exploring this concept: pages 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 417; Algebra in Your life: pp. 15, 41, 77, 107, 128, 157, 187, 242, 262, 296, 331, 375, and 394; and Applications: pages 26, 58, 90, 118, 150, 178, 214, 244, 282, 322, 350, 380, 402

Page xv; and exploring this concept: 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, 306

Page xv; and exploring this concept: pages 11, 12, 49, 70, 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, 348

SE/TE: Problem Solving: pages 6, 14, 19, 27, 45, 57, 76, 95, 97, 108, 111, 114, 126, 137, 171, 197, 207, 213, 246, 257, 261, 285, 316, 325, 350, 387, 399, 412; Applications: pages 30, 60, 98, 138, 186, 230, 264, 304, 338, 378, 404, 422; Estimation: pages 26, 54, 76, 119, 176, 201, 245, 279, 328, 351-353, 375, 391, 415; TE: Mental Math: pages 9, 19, 23, 38, 43, 78, 90, 93, 107, 114, 124, 133, 165, 183, 201, 207, 209, 233, 227, 238, 262, 297, 327, 350, 361, 390, 420; Manipulatives: pages 8, 18, 25, 52, 59, 82, 96, 132, 150, 159, 163, 167, 215, 219, 224, 239, 278, 284, 327, 331, 359, 390, 412

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GEOMETRY

6. Know and use the relationship that exists among a logical implication of the form “if A, then B,” its converse “if B, then A,” its inverse “if not A, then not B,” and its contrapositive “if not B, then not A.”

Logical/Mathematical vocabulary is used throughout the AGS Algebra textbook. New vocabulary appears in bold type in the text and they are defined in the text left column and in the glossary. Common logical vocabulary is also reinforced through the Teacher’s Resource Library activities as an integral portion of the entire program.

Logical/Mathematical vocabulary is used throughout the AGS Life Skills Math textbook. New vocabulary appears in bold type in the text and they are defined in the text left column and in the glossary. Common logical vocabulary is also reinforced through the Teacher’s Resource Library activities as an integral portion of the entire program.

Logical/Mathematical vocabulary is used throughout the AGS Consumer Mathematics textbook. New vocabulary appears in bold type in the text and they are defined in the text left column and in the glossary. Common logical vocabulary is also reinforced through the Teacher’s Resource Library activities as an integral portion of the entire program.

SE/TE: pages 34-60, 69-80, 89-97, 299-301 TE: Applications: pages 37, 39, 45, 48, 50, 70, 74, 79, 90, 91; Learning Styles: pages 38-40, 43, 44, 47, 49, 53, 54, 56, 57, 70, 71, 73, 74, 76, 78-80, 90, 93, 94, 97, 99, 300, 301; Mental Math: pages 38, 43, 78, 90, 93; Manipulatives: pages 52, 59, 96 TRL: Estimation Activity 2; Application Activity 2; Geometry on the Job 2; Community Connection 2; Activities 8-13, 15-17, 20-22, 63; Workbook 9-19, 22-26, 29-31, 96

II. NUMBER SENSE, COMPUTATION AND OPERATIONS A. Number Sense Standard: Use rational and irrational numbers, represented in a variety of ways, to quantify information and to solve real-world and mathematical problems.

Pages 218-244, 326-335

Terms ‘Rational/irrational’ are not specifically defined. However; these numbers are found throughout the student textbook and they are used throughout problem-solving and application activities.

Terms ‘Rational/irrational’ are not specifically defined. However; these numbers are found throughout the student textbook and they are used throughout problem-solving and application activities.

SE/TE pp. xvi-xvii; 58-59, 302, 314; App.: pp. 30, 60, 98, 138, 186, 230, 264, 304, 338, 378, 404, 422; PS: pp. 6, 14, 19, 27, 45, 57, 76, 95, 97, 108, 111, 114, 126, 137, 171, 197, 207, 213, 246, 257, 285, 316, 350, 387, 399, 412; Geo. in your Life: pp. 23, 27, 45, 50, 95, 111, 159, 179, 217, 227, 252, 289, 291, 322, 349, 372, 388, 412; Writing About Math: pp. 17, 21, 23, 24, 37, 50, 67, 71, 93, 125, 130, 134, 145, 157, 168, 201, 213, 223, 227, 244, 248, 298, 301, 316, 324, 350, 353, 363, 375, 399, 411; TE: All Apps.; All Group PS; TRL: 4-5; Est. Ex. 1-12; App. Act. 1-12; Com. Con. 1-12

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GEOMETRY

B. Computation and Operation Standard: Appropriately use calculators and other technologies to solve algebraic, geometric, probabilistic and statistical problems. The student will: 1. Apply the correct order of operations and grouping

symbols when using calculators and other technologies.

Pages xv; defined with examples: pages 30-61, 138-139, 142, 160-161, 390-391; specific calculator activities: pages 9, 21, 53, 55, 82, 110, 130, 159, 191, 240, 261, 301, 330, 378, 401

Pages 352-353; defined with examples: pages 352-353; specific calculator activities: pages 13, 27, 44, 65, 81, 97, 113, 122, 143, 147, 154, 185, 204, 221, 239, 255, 285, 297

Pages 394-395; defined with examples: pages 394-395; specific calculator activities: pages 23, 47, 61, 92, 119, 151, 182, 215, 256, 274, 318, 339, 394-395

SE/TE: pages 58-59, 314; Calculator Practice: pages 22, 54, 76, 119, 130, 134, 183, 213, 240, 250, 273, 280, 298, 333, 358, 369, 398 TE: Calculator: pages 22, 26, 54, 57, 76, 119, 129, 134, 183, 215, 219, 224, 239, 273, 208, 298, 303

2. Know, use and translate calculator notational conventions to mathematical notation.

This particular concept can be found on page xv. The opportunity to explore this concept can be found on pages 9, 21, 53, 55, 82, 110, 130, 159, 191, 240, 261, 301, 330, 378, 401.

This particular concept can be found on page 352-353. The opportunity to explore this concept can be found on pages 13, 27, 44, 65, 81, 97, 113, 122, 143, 147, 154, 185, 204, 221, 239, 255, 285, 297.

This particular concept can be found on page 394-395. The opportunity to explore this concept can be found on pages 23, 47, 61, 92, 119, 151, 182, 215, 256, 274, 318, 339, 394-395

SE/TE: The opportunity to explore this concept can be found on pages 22, 54, 76, 119, 130, 134, 183, 213, 240, 250, 273, 280, 298, 333, 358, 369, 398 TE: Calculator: pages 22, 26, 54, 57, 76, 119, 129, 134, 183, 215, 219, 224, 239, 273, 208, 298, 303

3. Recognize the impact of units such as degrees and radians on calculations.

Refer to AGS Algebra 2.

Page 219 Refer to AGS Algebra 2.

The opportunity to explore this concept can be found in the SE/TE pages 15-27, 36-40, 360-369. TE Applications: pages 18, 37, 38; Learning Styles: pages 17, 19, 22, 23, 38-40, 362, 363, 366, 367, 369; Mental Math: page 361; TRL: Estimation Exercise 2; Community Connection 2; Activities 4-6, 8, 77-79; Workbook 5-7, 9-10

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GEOMETRY

4. Recognize that applying an inverse function with a calculator may lead to extraneous or incomplete solutions.

This concept falls outside the scope of AGS Algebra.

This concept falls outside the scope of AGS Life Skills Math.

This concept falls outside the scope of AGS Consumer Mathematics.

This concept falls outside the scope of AGS Geometry.

5. Understand the limitations of calculators such as missing or additional features on graphs due to viewing parameters or misleading representations of zero or very large numbers.





6. Understand that use of a calculator requires appropriate mathematical reasoning and does not replace the need for mental computation.

The opportunity to explore this concept can be found through Mental Math and calculator activities in the Teacher’s Edition. Additional calculator activities are found in the student edition on pages 9, 21, 53, 55, 82, 110, 130, 159, 191, 240, 261, 301, 330, 378, 401.

The opportunity to explore this concept can be found through Mental Math and calculator activities in the Teacher’s Edition. Additional calculator activities are found in the student edition on pages 13, 27, 44, 65, 81, 97, 113, 122, 143, 147, 154, 185, 204, 221, 239, 255, 285, 297.

The opportunity to explore this concept can be found through Mental Math and calculator activities in the Teacher’s Edition. Additional calculator activities are found in the student edition on pages 23, 47, 61, 92, 119, 151, 182, 215, 256, 274, 318, 339, 394-395.

The opportunity to explore this concept can be found in the TE: Mental Math: pages 9, 19, 23, 38, 43, 78, 90, 93, 107, 114, 124, 133, 165, 183, 201, 207, 209, 233, 227, 238, 262, 297, 327, 350, 361, 390, 420; and calculator activities: pages 22, 26, 54, 57, 76, 119, 129, 134, 183, 215, 219, 224, 239, 273, 208, 298, 303 SE: Additional calculator activities are found in the student edition on pages 22, 54, 76, 119, 130, 134, 183, 213, 240, 250, 273, 280, 298, 333, 358, 369, 398

III. PATTERNS, FUNCTIONS, AND ALGEBRA A. Patterns and Functions Standard: Represent and analyze real-world and mathematical problems using numeric, graphic and symbolic methods for a variety of functions. The student will: 1. Know the numeric, graphic and

symbolic properties of linear, step, absolute value and quadratic functions. Graphic properties may include rates of change, intercepts, maxima and minima.

Pages 72-73, 78-81, 118, 248-282, 286-322, 384-402



SE/TE pages 96-97, 122-130, 228-229, 336-337, 420-421 TE: Applications: page 421; Learning Styles: pages 97, 123, 125, 126, 128, 129, 130, 229, 337, 421; Mental Math: pages 124, 420; Manip.: p.96; TRL: Act. 22, 27, 49, 71, 92; Wkbk 31, 42, 43, 73, 104, 126

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GEOMETRY

2. Model exponential growth and decay, numerically, graphically and symbolically, using exponential functions with integer inputs.

The opportunity to explore this concept can be found on pages 122-150 and 346-347.




3. Analyze the effects of coefficient changes on linear and quadratic functions and their graphs.




The opportunity to explore this concept can be found in the SE/TE: pages 336-337, 420-421 TE: Learning Styles: pages 337, 421; Applications: pages 421; TRL: Activities 71, 92; Workbook: 104, 126

4. Apply basic concepts of linear, quadratic and exponential expressions or equations in real-world problems such as loans, investments and the path of a projectile.

Pages 94-118, 137, 139, 141, 150, 163, 167, 171, 177, 178, 253, 262, 291, 313, 321, 322, 389, 391, 402

Pages 320, 344 Pages 362, 386 SE/TE: pages 97, 111, 115, 126, 137 TE: Learning Styles: pages 97, 111, 126, 137; Applications: page 137; TRL: Activities 22; Workbook: 38, 39

5. Distinguish functions from other relations using graphic and symbolic methods.

Pages 265-271 This concept falls outside the scope of AGS Life Skills Math.


SE/TE: pages 122-130 TE: Learning Styles: pages 123, 125, 126, 129, 130; Mental Math: page 124; TRL: Activities 27, 28; Workbook 42, 43

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GEOMETRY

B. Algebra (Algebraic Thinking) Standard: Solve simple equations and inequalities numerically, graphically, and symbolically. Use recursion to model and solve real-world and mathematical problems. The student will: 1. Translate among equivalent forms of expressions, such

as, simplify algebraic expressions involving nested pairs of parentheses and brackets, simplify rational expressions, factor a common term from an expression and apply associative, commutative and distributive laws.

Pages 16-21, 30-45, 56-57, 94-115, 131-133, 136-150, 166-178, 222-223, 346-347, 390-391

Pages 70-98, 107-114, 120-126, 130-148, 210-223, 228-240, 276-286, 303-305, 321

Pages 66-72, 130-131, 138-164, 171-173, 176-202, 248-262, 266-298, 319-320, 363

Algebra Review: SE/TE: pages 8, 24, 41, 69, 133, 201, 272, 277, 296, 314, 318, 351, 354, 394, 401, 410, 413; Algebraic Skills: pages 24-29, 51-54, 58-59, 96-97, 103-137, 184-185, 228-229, 262-263, 302-303, 336-337, 376-377, 402-403, 420-421 TE: Learning Styles: pages 24, 27, 52-54, 97, 105-107, 110-114, 117, 119, 120, 123, 125, 126, 128-131, 134-136, 138, 139, 185, 201, 229, 263, 272, 296, 303, 337, 401; Applications: pages 108, 116, 118, 137, 263, 394, 401; Mental Math: pages 133, 201, 262; Manipulative: pages 8, 25, 59, 96, ; TRL: Activities 2, 6, 7, 11, 13, 22-30, 40, 49, 55, 58, 64, 71, 74, 75, 90; Workbook 7, 8, 11, 12, 15-17, 19, 22, 23, 31-46, 63, 73, 85, 89, 97, 104, 107, 108, 124

2. Understand the relationship between absolute value and distance on the number line and graph simple expressions involving absolute value such as, |x - 3| = 6 or |x + 2| < 5.




3. Find equations of a line given two points on the line, a point and the slope of the line or the slope and the y-intercept of the line.



SE/TE pages 127-130 TE Learning Styles: pages 129, 130; TRL: Activities 28; Workbook 42, 43

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GEOMETRY

4. Translate among equivalent forms of linear equations and inequalities.




SE/TE: pages 96-97 TE: Learning Styles: page 97 Manipulatives: page 96 ; TRL: Activities 22; Workbook 31

5. Use a variety of models such as equations, inequalities, algebraic formulas, written statements, tables and graphs or spreadsheets to represent functions and patterns in real-world and mathematical problems.

Pages 5, 138-141, 156-159, 265-271, 341

Pages 10, 11, 17, 46, 53, 55, 59, 82, 85, 88, 90-97, 100, 114, 121, 122, 125, 126, 128-129, 154, 159, 164-169, 178-179, 182, 186, 202-206, 209, 219-221, 228, 237-239, 242-243, 247-250, 253-254, 258-260, 263-266, 268-273, 276-286, 294, 298-300, 303-305

Pages 62, 68-71, 170-179, 186-193, 200-201, 225-228, 268-276, 336-338

The opportunity to explore patterns can be found in the SE/TE pages 6, 110-130, 138, 169, 184-185, 230, 270, 274-281, 338; TE: Applications: pages 116, 118, 169, 281; Learning Styles: pages 6, 110-114, 117, 119, 120, 123, 125, 126, 128-130, 185, 275, 276, 281; Mental Math: pages 114, 124; Manipulatives page 278; TRL: Application: pages 6, 9; Geometry on the Job 6, 9; Activities 24-28, 40, 56-58; Workbook 34-43, 63, 86, 87-89

6. Apply the laws of exponents to perform operations on expressions with integer exponents.

Pages 56-58, 122-150, 154-178

Pages 320, 344 Pages 362, 386 SE/TE: pages 28-29 TRL: Activities 7; Workbook 8

7. Solve linear equations and inequalities in one variable with numeric, graphic and symbolic methods.



SE/TE: pages 96-97, 336-337 TE: Learning Styles: pages 97, 337; Manipulatives: page 96; TRL: Activities 22, 71; Workbook 31, 104

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GEOMETRY

8. Find real solutions to quadratic equations in one variable with numeric, graphic and symbolic methods.



SE/TE: pages 228-229, 420-421 TE: Learning Styles: pages 229, 421; Applications: page 421; Mental Math: pages ; Manipulatives: page 420; TRL: Activities 49, 92; Workbook 73, 126

9. Use appropriate terminology and mathematical notation to define and represent recursion.

Pages 22-25, 78-83, 104-115, 196-199, 259

Pages 53, 60, 90-97, 178-179, 270-273, 276-286, 303-305

Pp. 62, 68-71, 170-179, 186-193, 200-01, 225-28, 268-76, 336-38


10. Create and use recursive formulas to model and solve real-world and mathematical problems.

The opportunity to explore this concept can be found on pages 5, 7, 11, 13, 26, 35, 45, 49, 57, 58, 67, 69, 73, 75, 83, 89, 90, 99, 103, 105, 107, 109, 113, 115, 117, 118, 137, 139, 141, 150, 163, 167, 171, 177, 178, 203, 212, 213, 214, 229, 236, 241, 253, 262, 282, 291, 313, 321, 322, 331, 335, 344, 350, 369, 379, 380, 389, 391, 402.

Recursive patterns can be specifically found on pages 96-97. The opportunity to explore this concept can be found on pages 2, 3, 4, 13, 14, 21, 24, 28, 41, 43, 46, 52, 57, 59, 66, 77, 80, 82, 91, 96, 98, 105, 107, 110, 112, 114, 125, 126, 133, 136, 139, 141, 148, 155, 159, 161, 163, 165, 167, 169, 170, 178, 180, 181, 183, 185, 186, 196, 198, 201, 206, 216, 218, 222, 229, 238, 240, 249, 251, 261, 266, 279, 281, 286, 296, 306.

The opportunity to explore this concept can be found on pages 11, 12, 26, 49, 52, 70, 76, 100, 101, 106, 120, 121, 134, 141, 146, 149, 154, 164, 181, 185, 202, 209, 211, 217, 242, 253, 255, 261, 262, 295, 298. 305, 309, 324, 339, 348.


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GEOMETRY

11. Solve systems of two linear equations and inequalities with two variables using numeric, graphic and symbolic methods.



SE/TE: pages 376-377 TE: Learning Styles: page 377; TRL: Activities 82; Workbook 116

12. Understand how slopes can be used to determine whether lines are parallel or perpendicular. Given a line and a point not on the line, find the equations for the lines passing through that point and parallel or perpendicular to the given line.

Pages 286-296, 304-305



SE/TE: pages 115-130, 413-416 TE: Learning Styles: pages 117, 119, 120, 123, 125, 126, 128-130; Applications: pages 116, 118; Mental Math: page 124; TRL: Activities 26-28; Workbook 38-43

IV. DATA ANALYSIS, STATISTICS, AND PROBABILITY A. Data and Statistics Standard: Represent data and use various measures associated with data to draw conclusions and identify trends. Understand the effects of display distortion and measurement error on the interpretation of data. The student will: 1. Construct and analyze circle graphs, bar graphs,

histograms, box-and-whisker plots, scatter plots and tables, and demonstrate the strengths and weaknesses of each format by choosing appropriately among them for a given situation.

Pages 101-103, 182-195, 204-205

Pages 10-11, 17, 46, 55, 59, 82, 85, 88, 100, 114, 121, 122, 125, 128-129, 154, 159, 164-169, 180, 182, 186, 202-206, 209, 219-221, 228, 237-239, 242-243, 247-250, 253-254, 258-260, 263-266, 268, 269, 285, 294, 298-300

Pages 4, 6-11, 13-14, 18-19, 21-22, 25, 43, 46, 49, 51, 52, 55, 59-60, 62, 69, 72, 74-76, 88, 90, 102, 104, 120, 126-127, 140, 145, 148, 152-157, 161, 185, 198, 212, 214, 216, 218, 220-223, 226, 229-234, 238, 240, 250-252, 254-256, 258-259, 265, 272, 284-285, 297, 306-308, 311-312, 314, 317, 331, 339, 347

SE/TE: page 378 TE: Applications: page 379; TRL: Application Activity 10; Geometry on the Job 10

2. Use measures of central tendency and variability, such as, mean, median, maximum, minimum, range, standard deviation, quartile and percentile, to describe, compare and draw conclusions about sets of data.

Pages 188-195 Pages 190-206, 212-213


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GEOMETRY

3. Determine an approximate best-fit line from a given scatter plot and use the line to draw conclusions.





4. Know the influence of outliers on various measures and representations of data about real-world and mathematical problems.





5. Understand the relationship between correlation and causation.

The opportunity to explore this concept can be found on pages 182-214

The opportunity to explore this concept can be found on pages 190-206, 212-213.



6. Interpret data credibility in the context of measurement error and display distortion.





7. Compare outcomes of voting methods such as majority, plurality, ranked by preference, run-off and pair-wise comparison.





B. Probability Standard: Use appropriate counting procedures, calculate probabilities in various ways and apply theoretical probability concepts to solve real-world and mathematical problems. The student will: 1. Select and apply appropriate counting procedures to

solve real-world and mathematical problems, including probability problems.

Pages 196-214

Pages 50-66


SE/TE: pages 262-263 TE: Learning Styles: page 263; Applications: page 263; Mental Math: page 262; TRL: Activities 55; Workbook 85

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GEOMETRY

2. Use area, trees, unions and intersections to calculate probabilities and relate the results to mutual exclusiveness, independence and conditional probabilities, in real-world and mathematical problems.

Pages 196-214 Pages 50-66 This concept falls outside the scope of AGS Consumer Mathematics.


3. Use probability models, including area and binomial models, in real-world and mathematical problems.

Pages 196-214 The opportunity to explore this concept can be found on pages 50-66.



4. For simple probability models, determine the expected values of random variables.



5. Know the effect of sample size on experimental and simulation probabilities.



6. Use a variety of experimental, simulation and theoretical methods to calculate probabilities.



V. SPATIAL SENSE, GEOMETRY AND MEASUREMENT

A. Spatial Sense Standard: Use models to represent and understand two- and three-dimensional objects and their cross sections from different perspectives.

Pages 22-25, 78-83, 137, 139, 141, 219, 345, 367, 368-380

Pages 18-28, 98, 105, 108-110, 114, 250-252, 278-286, 289

Pages 176-202, 254-257, 342-345

SE/TE: pages 142-186, 236-257, 347-350 TE: Applications: pages 146, 152, 163, 169, 244, 249, 349; Learning Styles: pages 145, 146, 148, 151-154, 157, 159, 160, 163-165, 168-171, 173, 174, 177, 178, 181, 182, 185, 186, 240, 241, 245, 246, 249, 251, 350; TRL: App. Activity 5; Geometry on the Job 5; Estimation Activity 5; Com. Con. 5; Act. 31-40, 50-53, 73; Wkbk 47-63, 74-82, 106

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GEOMETRY

B. Geometry Standard: Apply basic theorems of plane geometry, right triangle trigonometry, coordinate geometry and a variety of visualization tools to solve real-world and mathematical problems. The student will: 1. Know and use theorems about triangles and parallel

lines in elementary geometry to justify facts about various geometrical figures and solve real-world and mathematical problems. These theorems include criteria for two triangles to be congruent or similar and facts about parallel lines cut by a transversal.

Pages 354-375, 399 Pages 276-277 Pages 212, 344-347 SE/TE: pages 72-80, 190-213, 268-304, 317-320 TE: Applications: pages 74, 79, 196, 212, 281, 285, 304; Learning Styles: pages 73-76, 78-80, 194, 195, 197, 199-201, 205, 206, 210-213, 272, 273, 275, 276, 281,283, 287, 291-293, 295, 296, 300, 301, 303; Mental Math: page 78; TRL: Application Activity 8; Geometry on the Job 8; Estimation Activity 8; Community Connection 8; Activities 16-17, 41-44, 56-64; Workbook 24-26, 64-67, 86-97

2. Know and use theorems about circles to justify geometrical facts and solve real-world and mathematical problems. These theorems include the relationships involving tangent lines and radii, the relationship between inscribed and central angles and the relationship between the measure of a central angle and arc length.

Pages 101-103, 343-345

Pages 219-221 Pages 250-251, 254-256, 306-308

SE/TE: pages 42, 342-378 TE: Applications: pages 349, 374, 379; Learning Styles: pages 345, 346, 350, 352, 353, 355, 358, 362, 366, 367, 369, 37, 373, 375, 377 TRL: Application Activity 10; Geometry on the Job 10; Activities 9, 72-82; Workbook Activities 105-116

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GEOMETRY

3. Know and use properties of two- and three-dimensional figures to solve real-world and mathematical problems such as: finding area, perimeter, volume and surface area; applying direct or indirect methods of measurement; the Pythagorean theorem and its converse; and properties of 45°-45°-90° and 30°-60°-90° triangles.

Pages 22-25, 78-83, 139, 141, 163, 166-167, 171, 177-178, 219, 331, 343-345, 364-367

Pages 18-28, 98, 105, 108-110, 114, 250-252, 278-286, 289

Pages 176-202, 254-257, 342-345

SE/TE: pages 268-304, 308-338, 372-375, 384-399 TE: Applications: pages 281, 285, 304, 323, 329, 374, 391, 394; Learning Styles: pages 272, 273, 275, 276, 281, 283, 287, 291-293, 295, 296, 300, 301, 303, 311, 312, 315, 316, 319, 320, 324, 328, 332-334, 337, 373, 375, 385-387, 389-390, 393, 395; Mental Math: pages 327, 390; Manipulatives: pages 327, 331, 390; TRL: Application Activity 8, 9; Geometry on the Job 8, 9; Estimation Activity 8, 9; Community Connection 8, 9; Activities 56-71, 81, 83-86; Workbook Activities 86-104, 115, 117-120

4. Apply the basic concepts of right triangle trigonometry including sine, cosine and tangent to solve real-world and mathematical problems.



SE/TE: pages 368-369 TE: Learning Styles: pages 369, 371 TRL: Activities 79, 80; Workbook Activities 113, 114

5. Use coordinate geometry to represent and examine geometric concepts such as the distance between two points, the midpoint of a line segment, the slope of a line and the slopes of parallel and perpendicular lines.

Pages 258-264, 268-271, 286-297



SE/TE: pp. 115-120, 131-135, 138, 294-298, 413-414 TE: Apps: pp. 116, 118; Learning Styles: pp. 117, 119, 120, 131, 134, 135, 138, 139, 295, 296; Mental Math: pages 133, 297; Manips: p. 132; TRL: App. Act. 4; Geo. on the Job 4; Act. 26, 29, 62; Wkbk. 38-39, 44, 45, 94-5

44




GEOMETRY

6. Use numeric, graphic and symbolic representations of transformations such as reflections, translations and change of scale in one, two and three dimensions to solve real-world and mathematical problems.

Pages 234-237, 242, 387

Pages 276-277 Pages 212-215, 344-347

SE/TE: pages 214-227, 234-264 TE: Applications: pages 217, 220, 225, 244, 249, 260, 263, 265; Learning Styles: pages 216-218, 220, 221, 223, 225, 226, 240, 241, 245, 246, 249, 251, 255, 256, 259, 263; Mental Math: pages 238, 262; Manipulatives: page 239 TRL: Activities 45-48, 50-55; Workbook Activities 68-72, 74-85

7. Perform basic constructions with a straightedge and compass.



Construction using compass/straightedge/ protractor: SE/TE pages 12-14, 16, 18, 19, 45, 49, 50, 71, 80, 83, 86-87, 89, 91-94, 125, 127-129, 131, 134, 145-148, 151-154, 172-178, 186, 193, 198-199, 202-204, 207, 217, 249, 250, 256-257, 322, 365-367, 404; TE: Learning Styles: pages 13, 14, 19, 49, 50, 80, 83, 94, 131, 134, 151, 153; Manipulatives: page 18; TRL: Workbook 42, 43

45




GEOMETRY

8. Draw accurate representations of planar figures using a variety of tools.



Construction using compass/straightedge/ protractor: SE/TE pages 12-14, 16, 18, 19, 45, 49, 50, 71, 80, 83, 86-87, 89, 91-94, 125, 127-129, 131, 134, 145-148, 151-154, 172-178, 186, 193, 198-199, 202-204, 207, 217, 249, 250, 256-257, 322, 365-367, 404; TE: Learning Styles: pages 13, 14, 19, 49, 50, 80, 83, 94, 131, 134, 151, 153; Manipulatives: page 18; TRL: Workbook 42, 43

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GEOMETRY

C. Measurement Standard: Use the interconnectedness of geometry, algebra and measurement to explore real-world and mathematical problems.

Problem-Solving: pages 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; App.: pages 26, 58, 90, 118, 150, 178, 214, 244, 282, 322, 350, 380, 402; Writing About Math: pages 15, 33, 47, 65, 104, 125, 127, 130, 161, 167, 171, 194, 209, 221, 223, 225, 229, 231, 241, 243, 252, 257, 261, 264, 267, 291, 293, 303, 308, 309, 312, 339, 359, 389; Est. Act.: pages 17, 52, 83, 106, 147, 176, 194, 233, 275, 301, 345, 367, 387; Algebra In Your Life: pages 15, 41, 77, 107, 128, 157, 187, 242, 262, 296, 331, 375, 394

Pages 20, 23-27, 70-82, 93-98, 102-14, 271-86; and Problem Solving: pp. 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; App: pp. 14, 28, 46, 66, 82, 98, 114, 126, 148, 170, 186, 206, 222, 240, 266, 286, 306; Writing About Math: pp. 5, 12, 26, 41, 54, 72, 79, 91, 96, 109, 121, 135, 138, 147, 158, 166, 176, 182, 184, 195, 205, 213, 215, 217, 233, 252, 256, 257, 262, 276, 278, 295, 298; Est. Act.: pp 10-11, 17, 26-27, 44-45, 49, 156-157, 161, 293

Pages 44-45, 176-202, 340-345; and Problem-Solving Exercises: pages 11, 12, 49, 70, 100, 101, 120, 121, 141, 146, 149, 154, 181, 185, 209, 211, 217, 253, 255, 261, 295, 305, 309, 339; Applications: pages 26, 52, 76, 106, 134, 164, 202, 242, 262, 298, 324, 348; Writing About Mathematics: pages 3, 15, 17, 33, 42, 51, 61, 73, 83, 86, 90, 127, 127, 130, 140, 155, 176, 197, 218, 229, 252, 257, 274, 297, 319, 320, 337; Estimation Activities: pages 3, 6, 7, 13, 18, 20, 21, 35, 50-51, 60-61, 72, 82, 86, 127, 193, 212-215, 249, 252-253, 286-291, 292-293

SE/TE: pages 161-165, 179-183, 197-230, 270-338, 343-378, 383-404 TE: Applications: pages 163, 196, 212, 217, 220, 225, 230, 281, 285, 304, 323, 329, 349, 374, 379, 391, 394, 401; Learning Styles: pages 163-165, 181, 182, 194, 195, 197, 199-201, 205, 206, 210-213, 216-218, 220, 221, 223, 225, 226, 229, 272, 273, 275, 276, 281, 283, 287, 291-293, 295, 296, 300, 301, 303, 311, 312, 315, 316, 319, 320, 324, 328, 332-334, 337, 345, 346, 352, 353, 355, 358, 362, 363, 366, 367, 369, 371, 373, 375, 377, 385-387, 389, 390, 393, 395, 397, 401, 403, 404; Mental Math: pages 165, 183, 201, 207, 209, 223, 227, 297, 327, 350, 361, 390; Manipulatives: pages 163, 215, 219, 224, 278, 284, 327, 331, 359, 390; TRL: Estimation Exercises 6, 8-11; Community Connection 6, 8-11; Application Activities 6, 8-11; Geometry on the Job 6, 8-11; Activities 35, 39, 41-49, 56-88; Workbook 53, 54, 61, 62, 64-73, 86-122

47


GRADES 11, 12 ALGEBRA 2 STATISTICS Standard: Use tables of the normal distribution and properties of that distribution to make judgments about populations based on random samples from these populations. The student will: 1. Use the concept of normal distribution and its properties to answer questions about

sets of data.

The opportunity to explore this concept can be found on pages 457-466.

2. Describe and use sampling distributions and the central limit theorem. Calculate confidence intervals when appropriate.

This concept falls outside the scope of AGS Algebra2.

3. Understand the importance of appropriate sampling methods. For instance, the time of day of a survey could lead to inaccuracies in the outcome.


ALGEBRA Standard: Demonstrate facility with a wide range of algebraic operations and use the relationship between coordinate geometry an algebraic equations to solve real-world and mathematical problems. The student will: 1. Solve systems of two, three or more simultaneous linear equations or inequalities,

in particular, deciding whether a given system of equations has one solution, no solution or infinitely many solutions and, in this latter case, describing them parametrically.

Pages 135-144

2. Solve problems with quadratic functions and equations, where some of the coefficients may be expressed in terms of parameters.

Pages 70-104. 108-144. 295-303

3. Perform the four arithmetic operations with polynomials, except that division is restricted to division by monomials and linear binomials.

Pages 148-174

4. Simplify a wide variety of algebraic expressions, including those in which numerator or denominator needs to be rationalized.

Specific rational expressions: pages 178-192; other algebraic expressions: pages 1-30, 34-66, 70-104, 108-144, 148-174, 196-223, 230-258, 262-310, 314-354, 368-398, 402-434, 454-455, 463-465

5. Apply the laws of exponents to perform operations on expressions with fractional exponents.

Pages 212-214

6. Know the numeric, graphic and symbolic properties of power, logarithmic and exponential functions.

Pages 72, 150, 196-226, 230-258

7. Solve a wide variety of mathematical and real-world problems involving power, exponential and logarithmic functions and equations, discard extraneous solutions and present results graphically.

The opportunity to explore this concept can be found on pages 72, 150, 196-226, and 230-258.

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GRADES 11, 12 ALGEBRA 2 8. Know the numeric, graphic and symbolic properties of rational function. Pages 48-51, 59-66 9. Solve a wide variety of mathematical and real-world problems involving rational

functions, discard extraneous solutions and present results graphically. Pages 48-51, 59-66

10. Factor polynomials representing the difference of squares, perfect square trinomials and quadratics with rational factors.

Pages 70-104, 157-159

11. Make sketches including axes, centers, asymptotes, vertices of parabo0la, ellipses (including circles0 and hyperbolas with axes parallel to the coordinate axes, given their equations, and completing the square if necessary.

Pages 113-134, 273-303, 308-310

12. Find equations of parabolas, ellipses and hyperbolas when presented with their graphs having axes parallel to the coordinate axes.


13. Add, subtract, multiply and divide complex numbers, interpret sums geometrically, and find complex solutions of quadratic equations.

Pages 408-412, 430-433

14. Know and use the Factor and Remainder Theorems. This concept falls outside the scope of AGS Algebra2. 15. Find the inverse of a function and the composition of functions by numeric and

symbolic methods. Know the relationship between the graphs of a function and its inverse.

Pages 243-245, 336-339, 426-429

16. Know and use formal notation for sequences and series to solve related problems. Pages 384-395 TRIGONOMETRY & GEOMETRY Standard: Understand the properties of the standard trigonometric functions and apply them to real-world and mathematical problems, especially geometrical problems. Develop increased mastery of geometric proof methodology. The student will: 1. Know the six trigonometric functions defined for an angle in a right triangle.

Pages 314-318, 322-326, 337-356

2. Given the coordinates of a point on the terminal side of an angle in standard position in the xy-plane, find the values of the trigonometric functions.

The opportunity to explore this concept can be found on pages 319-321.

3. Convert between degrees and radian measures. Pages 319-321 4. Solve applied problems about triangles using the law of sines including the

ambiguous case. Pages 342-345, 340-356

5. Solve applied problems about triangles using the law of cosines. Pages 346-355 6. Graph the functions of the form Asin(Bt + C), (Bt + C), and Atan(Bt + C) and know

the meaning of the terms frequency, amplitude, phase shift and period. Pages 332-337, 342-345, 349, 356

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GRADES 11, 12 ALGEBRA 2 7. Simplify trigonometric expressions using identities and verify simple trigonometric

identities including sin2x + cos2x = 1, sum, difference, double angle and half-angle formulas for sine and cosine.

Pages 327-331

8. Find all the solutions of a trigonometric equation on various intervals. Pages 342-355 9. Know and be able to use the definitions of the inverse trigonometric functions and

related methods to solve problems such as find cos(x) and tan(x) given the value of sin x and the quadrant containing the terminal side.

Pages 314-356

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