Pennsylvania Academic Standards for Mathematics Grade 11

Transcription

1 correlated to the Pennsylvania Academic Standards for Mathematics Grade 11 1/

2 Algebra 1: Concepts and Skills 2001 correlated to the Pennsylvania Academic Standards for Mathematics Grade Numbers, Number Systems and Number Relationships Pennsylvania s public schools shall teach, challenge and support every A. Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms). PE: 9-14, 71-97, , , 265, , 629 TE: 8-14, 62F, 66, 71-97, , , 265, 438E, , 629, 630E, 688E 2.2 Computation and Estimation Pennsylvania s public schools shall teach, challenge and support every A. Develop and use computation concepts, operations and procedures with real numbers in problem-solving situations. PE: 9-15, 17-28, 32, 37, 70-99, 102, 104, , , , 265, , 629 TE: 9-15, 17-28, 32, 37, 70-99, 102, 104, , , 159, , 265, , 629, 630D, 630E, 630F B. Use estimation to solve problems for which an exact answer is not needed. PE: 5, 83, 244, 299, , 776 TE: 5, 83, 244, 299, , 776 1

3 C. Construct and apply mathematical models, including lines and curves of best fit, to estimate values of related quantities. PE: , , , , , 545, , , , TE: , , , , , 545, , , , D. Describe and explain the amount of error that may exist in a computation using estimates. Algebra 1: Concepts and Skills assumes that measurement has been covered in earlier course work. E. Recognize that the degree of precision needed in calculating a number depends on how the results will be used and the instruments used to generate the measure. Algebra 1:Concepts and Skills assumes that measurement has been covered in earlier course work. F. Demonstrate skills for using computer spreadsheets and scientific and graphing calculators. PE: 170, , 374, 395, 461, 522, , 528, 530, 544, 597, 611, 645 TE: 13, 17, 170, , 374, 395, 451, 456, 461, 471, 522, , 528, 530, 532, 544, 597, 611, 645 2

4 2.3 Measurement and Estimation Pennsylvania s public schools shall teach, challenge and support every A. Select and use appropriate units and tools to measure to the degree of accuracy required in particular measurement situations. Algebra 1: Concepts and Skills assumes that measurement has been covered in earlier course work. B. Measure and compare angles in degrees and radians. See McDougal Littell Geometry and McDougal Littell Algebra 2. C. Demonstrate the ability to produce measures with specified levels of precision. Algebra 1: Concepts and Skills assumes that measurement has been covered in earlier course work. 3

5 2.4 Mathematical Reasoning and Connections Pennsylvania s public schools shall teach, challenge and support every A. Use direct proofs, indirect proofs or proof by contradiction to validate conjectures. PE: , TE: , 299F, 320D, 688F, B. Construct valid arguments from stated facts. C. Determine the validity of an argument. PE: 84-85, 120, 142, 147, 155, 161, 296, 328, 334, 340, 400, 405, 467, 509, 591, 620, 650, 655, 661, 667, 702, 707, 726, , 750 TE: 84-85, 87, 120, 142, 147, 155, 161, 296, 328, 334, 340, 400, 405, 467, 509, 591, 620, 648, 650, 655, 661, 667, 702, 707, 726, D. Use truth tables to reveal the logic of mathematical statements. E. Demonstrate mathematical solutions to problems (e.g., in the physical sciences). PE: 28, 95, 97, 142, 175, 240, 274, 282, 365, 372, 406, 528, 535, 538, 545, 592, 612, 621, 645, 702, 706 TE: 28, 95, 97, 142, 175, 240, 274, 282, 365, 372, 406, 438F, 528, 535, 538, 545, 564E, 592, 612, 621, 645, 702, 706 4

6 2.5 Mathematical Problem Solving and Communication Pennsylvania s public schools shall teach, challenge and support every A. Select and use appropriate mathematical concepts and techniques from different areas of mathematics and apply them to solving non-routine and multi-step problems. TE: 266D, 266F, 496D, 564D, 688D Also see McDougal Littell Algebra 2. B. Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas and results. PE: 9-13, 30-31, 33-35, 45-53, 71-75, , 199, , 385, , , , 563, 757 TE: 1E, 8-14, 16-17, 21, 30-31, 33-35, 37, 41, 45-53, 62F, 71-75, 77, 83, 88, 95, 109, 115, 173, , 199, 249, , 271, 320E, 385, , , 496E, , 549, 563, 757 C. Present mathematical procedures and results clearly, systematically, succinctly and correctly. PE: 13, 23, 38, 155, 168, 334, 385, 487, 563 TE: 1E, 11, 13, 23, 38, 41, 62F, 155, 159, 168, 320E, 334, 385, 487, 496E, 563 D. Conclude a solution process with a summary of results and evaluate the degree to which the results obtained represent an acceptable response to the initial problem and why the reasoning is valid. PE: 13, 23, 38, 155, 164, 168, 334, 338, 371, 385, 487, 507, 530, 535, 563, 598, 605, 607, 612, 725, 756 TE: 13, 23, 38, 155, 164, 168, 334, 338, 371, , 487, 507, 530, 535, 563, 598, 605, 607, 612, 725, 756 5

7 2.6 Statistics and Data Analysis Pennsylvania s public schools shall teach, challenge and support every A. Design and conduct an experiment using random sampling. Describe the data as an example of a distribution using statistical measures of center and spread. Organize and represent the results with graphs. (Use standard deviation, variance and t-tests.) PE: 199, , 635, 757 TE: , , 635, 757 B. Use appropriate technology to organize and analyze data taken from the local community. PE: 645 TE: 645 C. Determine the regression equation of best fit (e.g., linear, quadratic, exponential). D. Make predictions using interpolation, extrapolation, regression and estimation using technology to verify them. PE: 248, 299, 302, , 544 TE: 210, 248, 299, 302, , 544 E. Determine the validity of the sampling method described in a given study. See McDougal Littell Algebra 1. F. Determine the degree of dependence of two quantities specified by a two-way table. G. Describe questions of experimental design, control groups, treatment groups, cluster sampling and reliability. This standard is left for a statistics course. H. Use sampling techniques to draw inferences about large populations. PE: TE: I. Describe the normal curve and use its properties to answer questions about sets of data that are assumed to be normally distributed. 6

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9 2.7 Probability and Predictions Pennsylvania s public schools shall teach, challenge and support every A. Compare odds and probability. B. Apply probability and statistics to perform an experiment involving a sample and generalize its results to the entire population. PE: 635 TE: 635 C. Draw and justify a conclusion regarding the validity of a probability or statistical argument. D. Use experimental and theoretical probability distributions to make judgments about the likelihood of various outcomes in uncertain situations. E. Solve problems involving independent simple and compound events. 8

10 2.8 Algebra and Functions Pennsylvania s public schools shall teach, challenge and support every A. Analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically. PE: 22-23, 209, , 237, , , , , , , , , , , , , , , , TE: 22-23, 205, 209, , , , , , , , , , , , , , , , , , B. Give examples of patterns that occur in data from other disciplines. PE: 205, 207, 238, 240, 267, 483, 645 TE: 205, 207, 238, , 267, 438E, 438F, , 481, 483, 487, 507, 525, 535, 538, 545, 564E, 645 C. Use patterns, sequences and series to solve routine and non-routine problems. PE: 52, 214, 240, 249, 300, 305, 461, 467, , , , 645 TE: 49, 52, 214, , 249, 283, 299, 300, 305, 461, 467, , , , 645, 688D D. Formulate expressions, equations, inequalities, systems of equations, systems of inequalities and matrices to model routine and non-routine problem situations. PE: 42-53, 67, 69, , 140, 159, 165, , 205, 207, 214, 238, 240, 249, 257, 270, 274, 298, 300, 303, 338, , , , 535, 552, , TE: 42-53, 67, 69, 128E, , 140, , 159, 165, , 205, 207, 214, 238, 240, 249, 257, 266D, 270, 274, 298, 300, 303, 338, 386D, 386E, , , , 535, 552, , , 644, 666, E. Use equations to represent curves (e.g., lines, circles, ellipses, parabolas, hyperbolas). PE: 226, 247, , TE: 200E, 226, 247, , 279, 283,

11 F. Identify whether systems of equations and inequalities are consistent or inconsistent. PE: TE: 200F, G. Analyze and explain systems of equations, systems of inequalities and matrices. PE: TE: 128E, 266D, 386D, 386E,

12 H. Select and use an appropriate strategy to solve systems of equations and inequalities using graphing calculators, symbol manipulators, spreadsheets and other software. PE: TE: 166D, , 428 I. Use matrices to organize and manipulate data, including matrix addition, subtraction, multiplication and scalar multiplication. J. Demonstrate the connection between algebraic equations and inequalities and the geometry of relations in the coordinate plane. PE: , , , , , TE: 200D, , 266D, 266E, , , , , 422, , K. Select, justify and apply an appropriate technique to graph a linear function in two variables, including slope-intercept, x- and y-intercepts, graphing by transformations and the use of a graphing calculator. PE: , , , TE: , , , 266E L. Write the equation of a line when given the graph of the line, two points on the line, or the slope of the line and a point on the line. PE: , , , TE: , M. Given a set of data points, write an equation for a line of best fit. N. Solve linear, quadratic and exponential equations both symbolically and graphically. PE: , , , , TE: 128E, , , 438E, 438F, 496F, , , O. Determine the domain and range of a relation, given a graph or set of ordered pairs. PE: 49, , 218, , TE: 1F, 49, , 218, 220, , P. Analyze a relation to determine whether a direct or inverse variation exists and represent it algebraically and graphically. PE: , 261, ,

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14 Q. Represent functional relationships in tables, charts and graphs. PE: 48-53, 58, 195, 220, , 262, , 461, , 490, , 554 TE: 1F, 48-53, 58, 195, 220, , 262, , 461, , 484, 490, R. Create and interpret functional models. PE: , 245, , 271, , 316, 459, , , , , 545 TE: , 238, 245, , 271, , 316, 457, 459, 476, , , , , 545 S. Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). PE: , , , , 459, 461, , , , 534, TE: , 230, , , , 457, 459, 461, , 519, , 534, , 640 T. Analyze and categorize functions by their characteristics. PE: 232, 234, , 249, 475, 484, 520, , TE: 232, 234, , 245, 249, 475, 484, 487, 520, ,

15 2.9 Geometry Pennsylvania s public schools shall teach, challenge and support every A. Construct geometric figures using dynamic geometry tools (e.g., Geometer s Sketchpad, Cabri Geometre). B. Prove that two triangles or two polygons are congruent or similar using algebraic, coordinate and deductive proofs. C. Identify and prove the properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles and diagonals using deductive proofs. D. Identify corresponding parts in congruent triangles to solve problems. PE: 248, 354, 445, 696, TE: 248, 354, 445, 696, E. Solve problems involving inscribed and circumscribed polygons. F. Use the properties of angles, arcs, chords, tangents and secants to solve problems involving circles. G. Solve problems using analytic geometry. PE: , , , 751 TE: , 266D, , 743, , 751 H. Construct a geometric figure and its image using various transformations. PE: 518, 520, 523, 529, 542, 544, 546, TE: 518, 520, 523, 529, 542, 544, 546,

16 I. Model situations geometrically to formulate and solve problems. J. Analyze figures in terms of the kinds of symmetries they have. 15

17 2.10 Trigonometry Pennsylvania s public schools shall teach, challenge and support every A. Use graphing calculators to display periodic and circular functions; describe properties of the graphs. B. Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem. 16

18 2.11 Concepts of Calculus Pennsylvania s public schools shall teach, challenge and support every A. Determine maximum and minimum values of a function over a specified interval. B. Interpret maximum and minimum values in problem situations. C. Graph and interpret rates of growth/decay. D. Determine sums of finite sequences of numbers and infinite geometric series. E. Estimate areas under curves using sequences of areas. This standard is left for an introductory calculus course. 17