Prentice Hall Mathematics: Course Correlated to: Alaska State Content Standards: Math (Grade 7)

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1 Alaska State Content Standards: Math (Grade 7) A. A student should understand mathematical facts, concepts, principles, and theories. 1. understand and use numeration, including numbers, number systems, counting numbers, whole numbers, integers, fractions, decimals, and percents; and SE/TE: 1-6: Comparing and Ordering Integers, 34-38; 3-1: Exponents and Order of Operations, ; 3-2: Scientific Notation, ; 3-3: Divisibility Tests, ; 3-4: Prime Factorization, ; 3-5: Simplifying Fractions, ; 3-6: Comparing and Ordering Fractions, ; 3-8: Mixed Numbers and Improper Fractions, ; 3-9: Fractions and Decimals, ; 6-1: Understanding Percents, ; 6-2: Percents, Fractions, and Decimals, ; 6-3: Percents Greater Than 100 or Less Than 1, irrationals and complex numbers SE/TE: 8-5: Square Roots and Irrational Numbers, select and use appropriate systems, units, and tools of measurement, including estimation 3. perform basic arithmetic functions, make reasoned estimates, and select and use appropriate methods or tools for computation or estimation including mental arithmetic, paper and pencil, a calculator, and a computer SE/TE: 1-4: Measuring in Metric Units, 23-28; 4-8: Measurement: Changing Units in the Customary System, ; 8-1: Estimating Length and Area, ; 8-2: Areas of Parallelograms and Triangles, ; 8-3: Areas of Other Figures, ; 8-4: Circumferences and Areas of Circles, ; 8-8: Surface Areas of Prisms and Cylinders, ; 8-9: Volumes of Rectangular Prisms and Cylinders, SE/TE: 1-2: Adding and Subtracting Decimals, 11-15; 1-3: Multiplying and Dividing Decimals, 17-22; 1-7: Adding and Subtracting Integers, 39-44; 1-8: Multiplying and Dividing Integers, 45-48; 4-2: Adding and Subtracting Fractions, ; 4-3: Adding and Subtracting Mixed Numbers, ; 4-4: Multiplying Fractions and Mixed Numbers, ; 4-5: Dividing Fractions and Mixed Numbers, ; 6-4: Finding a Percent of a Number, ; 6-5: Solving Percent Problems Using Proportions,

2 3. perform basic arithmetic functions, make reasoned estimates, and select and use appropriate methods or tools for computation or estimation including mental arithmetic, paper and pencil, a calculator, and a computer 4. represent, analyze, and use mathematical patterns, relations, and functions using methods such as tables, equations, and graphs 5. construct, draw, measure, transform, compare, visualize, classify, and analyze the relationships among geometric figures; and 6. collect, organize, analyze, interpret, represent, and formulate questions about data and make reasonable and useful predictions about the certainty, uncertainty, or impossibility of an event. SE/TE: 6-6: Solving Percent Problems Using Equations, ; 6-7: Applications of Percent, SE/TE: 9-1: Patterns and Graphs, ; 9-2: Number Sequences, ; 9-3: Patterns and Tables, ; 9-4: Functions and Rules, ; 9-5: Using Tables, Rules, and Graphs, SE/TE: 7-1: Lines and Planes, ; 7-2: Measuring and Classifying Angles, ; 7-3: Constructing Bisectors, ; 7-4: Triangles, ; 7-5: Quadrilaterals and Other Polygons, ; 7-7: Congruent Figures, ; 7-8: Circles, ; 10-6: Translations, ; 10-7: Symmetry and Reflections, ; 10-8: Rotations, SE/TE: 11-1: Reporting Frequency, ; 11-2: Spreadsheets and Data Displays, ; 11-3: Other Displays, ; 11-5: Random Samples and Surveys, ; 11-6: Estimating Population Size, ; 11-7: Using Data to Persuade, ; 11-8: Exploring Scatter Plots, ; 12-1: Probability, ; 12-2: Experimental Probability, B. A student should understand and be able to form and use appropriate methods to define and explain mathematical relationships. 1. use computational methods and appropriate technology as problem-solving tools SE/TE: 1-2: Adding and Subtracting Decimals, 11-15; 1-3: Multiplying and Dividing Decimals, 17-22; 1-7: Adding and Subtracting Integers, 39-44; 1-8: Multiplying and Dividing Integers, 45-48; 4-2: Adding and Subtracting Fractions, ; 4-3: Adding and Subtracting Mixed Numbers, ; 4-4: Multiplying Fractions and Mixed Numbers, ; 4-5: Dividing Fractions and Mixed Numbers, ; 6-4: Finding a Percent of a Number, ; 6-5: Solving Percent Problems Using Proportions,

3 1. use computational methods and appropriate technology as problem-solving tools 2. use problem solving to investigate and understand mathematical content 3. formulate mathematical problems that arise from everyday situations 4. develop and apply strategies to solve a variety of problems SE/TE: 6-6: Solving Percent Problems Using Equations, ; 6-7: Applications of Percent, ; Technology: 55, 76, 134, 212, 273, 339, 355, 422, 493, 525, 539, 642 SE/TE: 1-5: Using a Problem-Solving Plan, 30-33; 2-7: Write an Equations, ; 3-7: Solve a Simpler Problem and Look for a Pattern, ; 4-7: Try, Check, and Revise and Work Backward, ; 5-3: Draw a Diagram and Solve a Simpler Problem, ; 6-9: Write an Equation, ; 7-6: Draw a Diagram and Look for a Pattern, ; 8-10: Try, Check, and Revise and Write an Equation, ; 9-8: Write an Equation, ; 548; 11-4: Make a Table and Use Logical Reasoning, ; 12-3: Make an Organized List and Simulate a Problem, SE/TE: Real-World Snapshots: 66-67, , ; Real-World Problem Solving: 5, 14, 28, 47, 73, 75, 109, 113, 138, 157, 163, 166, 193, SE/TE: 1-5: Using a Problem-Solving Plan, 30-33; 2-7: Write an Equations, ; 3-7: Solve a Simpler Problem and Look for a Pattern, ; 4-7: Try, Check, and Revise and Work Backward, ; 5-3: Draw a Diagram and Solve a Simpler Problem, ; 6-9: Write an Equation, ; 7-6: Draw a Diagram and Look for a Pattern, ; 8-10: Try, Check, and Revise and Write an Equation, ; 9-8: Write an Equation, ; 548; 11-4: Make a Table and Use Logical Reasoning, ; 12-3: Make an Organized List and Simulate a Problem,

4 5. check the results against mathematical rules SE/TE: estimation: 7-9, 15, 19, 26, 33, 49, 64, 74, 91, 135, 136, 171, , 192, 235, 263, 290, 373, , 469, 472, 498, 582, 583, 673, use common sense to help interpret results SE/TE: Real-World Problem Solving: 5, 14, 28, 47, 73, 75, 109, 113, 138, 157, 163, 166, 193, 7. apply what was learned to new situations; and SE/TE: 1-5: Using a Problem-Solving Plan, 30-33; 2-7: Write an Equations, ; 3-7: Solve a Simpler Problem and Look for a Pattern, ; 4-7: Try, Check, and Revise and Work Backward, ; 5-3: Draw a Diagram and Solve a Simpler Problem, ; 6-9: Write an Equation, ; 7-6: Draw a Diagram and Look for a Pattern, ; 8-10: Try, Check, and Revise and Write an Equation, ; 9-8: Write an Equation, ; 548; 11-4: Make a Table and Use Logical Reasoning, ; 12-3: Make an Organized List and Simulate a Problem, use mathematics with confidence. SE/TE: Real-World Snapshots: 66-67, , ; Writing in Math: 8, 14, 21, 27, 37, 43, 48, 54, 59, 62, 64, 74, 76, 79, 86, 91, 96, 100, 104, 110, 115, 119, 124, 134, 139, 143, 148, 153, 158, 172, 179, 180, 190, 195, 199, 205, 210, 216, 221, 224, 229, 234, 244, 249, 258, 263, 266, 270, 273, 277, 284, 294, 300, 303, 309, 315, 321, 325, 339, 340, 349, 355, 360, 366, 368, 372, 376, 381, 385, 391, 396, 405, 411, 417, 420, 423, 429, 431, 435, 441, 445, 448, 452, 458, 462, 472, 477, 482, 487, 491, 497, 502, 505, 509, 514, 524, 530, 536, 543, 546, 552, 556, 561, 566, 577, 582, 583, 588, 594, 598, 599, 604, 609, 610, 617, 622, 633, 639, 642, 645, 650, 657, 663, 667, 672 4

5 C. A student should understand and be able to form and use appropriate methods to define and explain mathematical relationships. 1. express and represent mathematical ideas using oral and written presentations, physical materials, pictures, graphs, charts, and algebraic expressions 2. relate mathematical terms to everyday language 3. develop, test, and defend mathematical hypotheses; and 4. clarify mathematical ideas through discussion with others. SE/TE: 2-1: Evaluating and Writing Algebraic Expressions, 71-75; 2-8: Graphing and Writing Inequalities, ; 5-3: Draw a Diagram and Solve a Simpler Problem, ; 5-7: Maps and Scale Drawings, ; 7-6: Draw a Diagram and Look for a Pattern, ; 9-1: Patterns and Graphs, ; 9-6: Interpreting Graphs, ; 10-1: Graphing Points in Four Quadrants, ; 10-2: Graphing Linear Equations, ; 10-3: Finding the Slope of a Line, ; 548; 11-1: Reporting Frequency, ; 11-2: Spreadsheets and Data Displays, ; 11-3: Other Displays, ; 11-4: Make a Table and Use Logical Reasoning, ; 11-8: Exploring Scatter Plots, SE/TE: Writing in Math: 8, 14, 21, 27, 37, 43, 48, 54, 59, 62, 64, 74, 76, 79, 86, 91, 96, 100, 104, 110, 115, 119, 124, 134, 139, 143, 148, 153, 158, 172, 179, 180, 190, 195, 199, 205, 210, 216, 221, 224, 229, 234, 244, 249, 258, 263, 266, 270, 273, 277, 284, 294, 300, 303, 309, 315, 321, 325, 339, 340, 349, 355, 360, 366, 368, 372, 376, 381, 385, 391, 396, 405, 411, 417, 420, 423, 429, 431, 435, 441, 445, 448, 452, 458, 462, 472, 477, 482, 487, 491, 497, 502, 505, 509, 514, 524, 530, 536, 543, 546, 552, 556, 561, 566, 577, 582, 583, 588, 594, 598, 599, 604, 609, 610, 617, 622, 633, 639, 642, 645, 650, 657, 663, 667, 672 SE/TE: Open-Ended: 14, 16, 37, 53, 59, 86, 91, 124, 270, 273, 294, 315, 385, 386, 429, 446, 491, 525, 532, 557, 562, 577, 599, 611, 618, 632, 634, 635, 666; Real-World Snapshots: 66-67, , , , , , , , , , , SE/TE: Practice Game: 75, 163, 304, 430, 547, 634 5

6 D. A student should be able to use logic and reason to solve mathematical problems. 1. analyze situations SE/TE: Real-World Snapshots: 66-67, , ; Real-World Problem Solving: 5, 14, 28, 47, 73, 75, 109, 113, 138, 157, 163, 166, 193, 2. draw logical conclusions SE/TE: 11-4: Make a Table and Use Logical Reasoning, ; Real-World Problem Solving: 5, 14, 28, 47, 73, 75, 109, 113, 138, 157, 163, 166, 193, 196, 205, 223, 242, 247, 265, 276, 292, 304, 318, 323, 350, 355, 363, 384, 410, 430, 433, 455, 480, 490, 504, 506, 529, 534, 547, 551, 573, 600, 604, 614, 631, 648, use models, known facts, and relationships to explain the student s reasoning 4. use deductive reasoning to verify conclusions, judge the validity of arguments, and construct valid arguments; and SE/TE: reasoning: 7, 15, 22, 25, 27, 38, 40, 44, 48, 57, 59, 74, 76, 85, 87, 89, 92, 95, 99, 107, 113, 115, 119, 132, 133, 135, 137, 141, 145, 146, 148, 152, 157, 159, 165, 168, 169, 172, 174, 187, 190, 193, 198, 208, 213, 214, 215, 222, 227, 243, 244, 245, 247, 249, 257, 259, 261, 263, 264, 268, 270, 278, 286, 292, 300, 306, 309, 312, 313, 323, 328, 332, 348, 360, 367, 371, 381, 384, 385, 390, 392, 407, 411, 412, 421, 423, 426, 431, 435, 436, 448, 451, 452, 457, 469, 471, 484, 487, 490, 494, 495, 499, 402, 507, 523, 524, 528, 530, 535, 539, 543, 549, 559, 574, 577, 580, 581, 582, 583, 586, 587, 588, 591, 596, 598, 599, 603, 604, 606, 607, 608, 609, 610, 613, 614, 616, 617, 630, 633, 635, 637, 640, 642, 650, 651, 652, 654, 655, 658, 661, 666 SE/TE: reasoning: 25, 27, 38, 40, 44, 48, 57, 59, 74, 76, 85, 87, 89, 92, 95, 99, 107, 113, 115, 119, 132, 133, 135, 137, 141, 145, 146, 148, 152, 157, 159, 165, 168, 169, 172, 174, 187, 190, 193, 198, 208, 213, 214, 215, 222, 227, 243, 244, 245, 247, 249, 257, 259, 261, 263, 264, 268, 270, 278, 286, 292, 300, 306, 309, 312, 313, 323, 328, 332, 348, 360, 367, 381, 384, 385, 390, 392, 407, 411, 412, 421, 423, 426 6

7 4. use deductive reasoning to verify conclusions, judge the validity of arguments, and construct valid arguments; and 5. use inductive reasoning to recognize patterns and form mathematical propositions. SE/TE: reasoning: 431, 435, 436, 448, 451, 452, 457, 469, 471, 484, 487, 490, 495, 499, 402, 507, 523, 524, 528, 530, 535, 539, 543, 549, 559, 574, 577, 580, 581, 582, 583, 586, 587, 588, 596, 598, 599, 603, 604, 606, 607, 608, 609, 610, 613, 614, 616, 617, 630, 633, 635, 637, 640, 642, 650, 651, 654, 655 SE/TE: 9-1: Patterns and Graphs, ; 9-2: Number Sequences, ; 9-3: Patterns and Tables, ; 9-4: Functions and Rules, ; 9-5: Using Tables, Rules, and Graphs, E. A student should be able to apply mathematical concepts and processes to situations within and outside of school. 1. explore problems and describe results using graphical, numerical, physical, algebraic, and verbal mathematical models or representations SE/TE: Real-World Problem Solving: 5, 14, 28, 47, 73, 75, 109, 113, 138, 157, 163, 166, 193, 2. use mathematics in daily life; and SE/TE: Real-World Snapshots: 66-67, , ; Real-World Problem Solving: 5, 14, 28, 47, 73, 75, 109, 113, 138, 157, 163, 166, 193, 3. use mathematics in other curriculum areas. SE/TE: Interdisciplinary Connections: 7, 11, 26, 36, 48, 86, 97, 132, 139, 171, 189, 203, 206, 210, 216, 220, 224, 225, 242, 243, 249, 276, 284, 293, 297, 312, 320, 331, 366, 388, 404, 414, 417, 418, 446, 477, 482, 591, 594, , 617, 621, 667, 672 7

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