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1 Academic Content Standards Grades Nine, Ten, Eleven, Twelve Ohio COURSES 1, 2, 3, 4 Core -Plus Mathematics Contemporary Mathematics in Context STANDARDS PAGE REFERENCES Grade Nine Number, Number Sense and Operations Standard Number and Number Systems 1. Identify and justify whether properties (closure, identity, inverse, commutative and associative) hold for a given set and operations; e.g., even integers and multiplication. 2. Compare, order, and determine equivalent forms for rational and irrational numbers. Course 1: , 226, 229, 336, 490, , 505 Course 1: p. 263 #31, 550 #29, 583 #23 Meaning of Operations 3. Explain the effects of operations such as multiplication or division, and of computing powers and roots on the magnitude of quantities. Opportunity to address throughout: See for examples: 83-89, 94 #10, p143 #30, 33, 38, p285 #24, p299 #1, 316 #29, 319 #36 Computation and Estimation 4. Demonstrate fluency in computations using real numbers. Course 1: 25, 46, 101, 143, 211, 284, 319, , 396, 490, 549 Student Study Guide 1-38 Codes used for Teacher s Guide pages are the initial caps of headings on that page.

2 5. Estimate the solutions for problem situations involving square and cube roots. Course 1: , 344, , 397 #38, 455 #35, 509 #29, 520 #10, #11, 521 #20, 523 #27 Measurement Standard Measurement Units 1. Convert rates within the same measurement system; e.g., miles per hour to feet per second; kilometers per hour to meters per second. Opportunity to address: Course 1: 111 #6, , 128, 134, , 397 #40, Use Measurement Techniques and Tools 2. Use unit analysis to check computations involving measurement. 3. Use the ratio of lengths in similar twodimensional figures or three-dimensional objects to calculate the ratio of their areas or volumes respectively. 4. Use scale drawings and right triangle trigonometry to solve problems that include unknown distances and angle measures. Not addressed Course 1: 12, 62, 63, 68, 285, 452 #22, 490 #35 Course 2: Course 2: , 464, , , , Solve problems involving unit conversion for situations involving distances, areas, volumes and rates within the same measurement system. Course 1: 397, 452 #24 Opportunity to address: 68, 285 #25, 472, 474 Course 2: Review and 39 #13 Geometry and Spatial Sense Standard Characteristics and Properties 1. Define the basic trigonometric ratios in right triangles: sine, cosine and tangent. 2. Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle measures in similar figures. Course 2: , Course 2: 459, 460, 464, , , , Visualization and Geometric Models 3. Analyze two-dimensional figures in a coordinate plane; e.g., use slope and distance formulas to show that a quadrilateral is a parallelogram. Course 2: , , 189 #25, 191 #29, 253 #2 Academic Content Standards 2 Core-Plus Mathematics

3 Patterns, Functions and Algebra Standard Use Patterns, Relations and Functions 1. Define function with ordered pairs in which each domain element is assigned exactly one range element. 2. Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations. 3. Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations. 4. Demonstrate the relationship among zeros of a function, roots of equations, and solutions of equations graphically and in words. 5. Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum. Use Algebraic Representations 6. Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slopeintercept form. 7. Use formulas to solve problems involving exponential growth and decay. 8. Find linear equations that represent lines that pass through a given set of ordered pairs, and find linear equations that represent lines parallel or perpendicular to a given line through a specific point. 9. Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology. 10. Solve quadratic equations with real roots by factoring, graphing, using the quadratic formula and with technology. Course 2: , 345 #2&#3, 349 #16, 354 #35 Course 1: U1, U3, U5, U7 Throughout see for examples: 4-8, 22, 28-44, 53, 56-58, , , Course 1: U1, U3, U5, U7 Throughout see for examples:59-68, 70, , , , Course 1: See also Course 2: , , 347, 348 And Course 3: , , 365 Course 1: U3, U5, U7 303, , 316, 323, 325, 331, 345, 483 #12, 487, 488 #24, 524 #30 Course 1: , 264 #35, 284 #21, 423 #35, 454 #29, 489 #26, 508 #26, 585 #32 Course 1: , Course 2: Course 1: , , 321 #44, 395 #31, 489 #28 Course 2: 61-63, 187 #16, 191 #29, 193 #35 Course 1: , , 208 Course 2: 49-67, 70-72, , 146, 149 Course 1: CPMP-Tools Algebra software Course 2: , 348 Course 3: , Academic Content Standards 3 Core-Plus Mathematics

4 11. Add, subtract, multiply and divide monomials and polynomials (division of polynomials by monomials only). 12. Simplify rational expressions by eliminating common factors and applying properties of integer exponents. Analyze Change 13. Model and solve problems involving direct and inverse variation using proportional reasoning. 14. Describe the relationship between slope and the graph of a direct variation and inverse variation. 15. Describe how a change in the value of a constant in a linear or quadratic equation affects the related graphs. Data Analysis and Probability Standard Course 1: , , , 490, 508, 585 Course 2: , 340, 348 Course 3: , Course 1: , , , , , 348, , 423 #32, 585 Course 3: , Course 1: Student Study Guide Course 2: 25-29, Course 2: Opportunity to address 30-33, 42 #20 Course 1: 158 #1, 178 #24, #25, , , 482, 485 #18, 488 #25 CPMP-Tools CAS Parameter slider Course 2: 232, 333, 335, 352 #28 Data Collection 1. Classify data as univariate (single variable) or bivariate (two variables) and as quantitative (measurement) or qualitative (categorical) data. Course 1: Opportunity to address: Units 1, 2, 3, 5, 7, 8 (p137 #19) 2. Create a scatterplot for a set of bivariate data, sketch the line of best fit, and interpret the slope of the line of best fit. Course 1: Course 2: , 298, , CPMP-Tools Statistics software Statistical Methods 3. Analyze and interpret frequency distributions based on spread, symmetry, skewness, clusters and outliers. 4. Describe and compare various types of studies (survey, observation, experiment), and identify possible misuses of statistical data. Course 1: Course 1: 98 #20 p99 #21 Course 2: , Course 3: 89-91, 95 Academic Content Standards 4 Core-Plus Mathematics

5 5. Describe characteristics and limitations of sampling methods, and analyze the effects of random versus biased sampling; e.g., determine and justify whether the sample is likely to be representative of the population. 6. Make inferences about relationships in bivariant data, and recognize the difference between evidence of relationship (correlation) and causation. Probability 7. Use counting techniques and the Fundamental Counting principle to determine the total number of possible outcomes for mathematical situations. 8. Describe, create and analyze a sample space and use it to calculate probability. 9. Identify situations involving independent and dependent events, and explain differences between, and common misconceptions about, probabilities associated with those events. 10. Use theoretical and experimental probability, including simulations or random numbers, to estimate probabilities and to solve problems dealing with uncertainty; e.g., compound events, independent events, simple dependent events. Course 3: 74-80, 89-91, 92 #1-2, 95 #5-6, 97 #10-11, 98 #14-15, 104 #4, 256 #21, 257 #23, #5 & #6, 270 STM, 279 #17-18, 280 #20, , 313 #24, b., and Course 4 Course 2: , Course 1: 291, 509 #30, 581 #22, and 584 #29 Course 2: 539 #9 Course 1: , , 545 #10, 547 #18, 553 #1, 586 Course 2: Course 2: 522, 535, Course 1: , CPMP-Tools Statistics Simulation software See also: Course 2: , , Course 3: 74-88, Academic Content Standards 5 Core-Plus Mathematics

6 Grade Ten STANDARDS PAGE REFERENCES Number, Number Sense and Operations Standard Number and Number Systems 1. Connect physical, verbal and symbolic representations of irrational numbers; e.g., construct 2 as a hypotenuse or on a number line. Meaning of Operations Course 2: 13, 40 #17, 41 #18, 48 #36, 343, 356, 478, 479, 585 #30 Previously addressed: Course 1: 347 #25, 351 #36, 392 #20, #21, 446 #24, 451 #21, 454 #35 2. Explain the meaning of the nth root. Previously addressed: Course 1: 335, 351 #35 Computation and Estimation 3. Use factorial notation and computations to represent and solve problem situations involving arrangements. 4. Approximate the nth root of a given number greater than zero between consecutive integers when n is an integer; e.g., the 4th root of 50 is between 2 and 3. Measurement Standard Opportunity to address: Course 2, Unit 8 Lesson 1 Previously addressed: Course 1: 335, 351#35 Use Measurement Techniques and Tools 1. Explain how a small error in measurement may lead to a large error in calculated results. Course 2: Opportunity to address Calculate relative error. Not addressed 3. Explain the difference between absolute error and relative error in measurement. Not addressed 4. Give examples of how the same absolute error can be problematic in one situation but not in another; e.g., compare accurate to the nearest foot when measuring the height of a person versus when measuring the height of a mountain. 5. Determine the measures of central and inscribed angles and their associated major and minor arcs. Opportunity to address: Course 2: Previously addressed: Course 1: , #6d, 573, #3f, and #17 Opportunity to address: Course 2: Course 3: , , Academic Content Standards 6 Core-Plus Mathematics

7 Geometry and Spatial Sense Standard Characteristics and Properties 1. Formally define and explain key aspects of geometric figures, including: a. interior and exterior angles of polygons; b. segments related to triangles (median, altitude, midsegment); c. points of concurrency related to triangles (centroid, incenter, orthocenter, circumcenter); d. circles (radius, diameter, chord, circumference, major arc, minor arc, sector, segment, inscribed angle). 2. Recognize and explain the necessity for certain terms to remain undefined, such as point, line and plane. 3. Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including: a. prove the Pythagorean Theorem; b. prove theorems involving triangle similarity and congruence; c. prove theorems involving properties of lines, angles, triangles and quadrilaterals; d. test a conjecture using basic constructions made with a compass and straightedge or technology. Spatial Relationships 4. Construct right triangles, equilateral triangles, parallelograms, trapezoids, rectangles, rhombuses, squares and kites, using compass and straightedge or dynamic geometry software. 5. Construct congruent figures and similar figures using tools, such as compass, straightedge, and protractor or dynamic geometry software. Transformations and Symmetry 6. Identify the reflection and rotation symmetries of two- and three-dimensional figures. Course 2: 184 #9 CPMP-Tools Geometry software Course 3: 42 #7, 46 #15, 47 #21, , , , , , Previously addressed: Course 1: 46, 51, 62, 95 #13, 175, 205, 306, 315, 365, 389, 428, 550 #28, 590, 597 Course 2: Opportunity to address Unit 3 Course 3: Opportunity to address Unit 3 p. 31 Course 2: , , 510 #22&#23, 512 #25 CPMP-Tools Geometry software Course 3: 28-39, 40-51, , , , , , 402, 416 Previously addressed: Course 1: 257, , , , Course 2: , 171, 176, 178 #7, 253, 354 #36 CPMP-Tools Geometry software Previously addressed: Course 1: 367, 381, 420 CPMP-Tools Geometry software Course 2: , 177, , , 252 Course 3: 28, 190 Previously addressed: Course 1: 386 Course 2: 101 #26, 193 #34 Previously addressed: Course 1: , , , 454 Academic Content Standards 7 Core-Plus Mathematics

8 7. Perform reflections and rotations using compass and straightedge constructions and dynamic geometry software. 8. Derive coordinate rules for translations, reflections and rotations of geometric figures in the coordinate plane. 9. Show and describe the results of combinations of translations, reflections and rotations (compositions); e.g., perform compositions and specify the result of a composition as the outcome of a single motion, when applicable. Visualization and Geometric Models Course 2: , , CPMP-Tools Geometry Software Course 2: , , 225 #21 Course 2: , , , Course 3: Solve problems involving chords, radii and arcs within the same circle. Patterns, Functions and Algebra Standard Use Patterns, Relations and Functions Course 2: 178, 356 #42 Course 3: , , Define function formally and with f(x) notation. Course 2: , , 349 #17, 583 #24 2. Describe and compare characteristics of the following families of functions: square root, cubic, absolute value and basic trigonometric functions; e.g., general shape, possible number of roots, domain and range. Use Algebraic Representations Course 2: 10-15, 17 #4, 18-23, , 478 #9 & #10, 520 Course 3: 100, 116, 117, 120, 418, , , 599 (and Course 4) Previously addressed: Course 1: 346 #24, 487 #23, 522 #23 3. Solve equations and formulas for a specified variable; e.g., express the base of a triangle in terms of the area and height. 4. Use algebraic representations and functions to describe and generalize geometric properties and relationships. 5. Solve simple linear and nonlinear equations and inequalities having square roots as coefficients and solutions. 6. Solve equations and inequalities having rational expressions as coefficients and solutions. Course 2: 25-46, 69-72, 68 #27, 229 #38, 391 #29 Course 2: 6 # 5e, 7 #7, 11-12, 16 #1h, 18 #5&#6, 39 #13&#14, 40-41, 93 #9, , 124 #11, 125 #14, , 194 #41, , Course 2: , 374 #23, 375 #24, 485 #32 Course 3: , Previously addressed: Course 1: , 528 Course 2: , , 193 #37, , 348 #13&#14, 353 #32, 357 #47, , 385 #20, 391 #29 Academic Content Standards 8 Core-Plus Mathematics

9 7. Solve systems of linear inequalities. Course 2: 49-68, 70-72, 130 #27, , , 514 #29, 584 #26 Course 3: , Graph the quadratic relationship that defines circles. Course 2: , 184 #11, 187 #17, 356 #42 9. Recognize and explain that the slopes of parallel lines are equal and the slopes of perpendicular lines are negative reciprocals. 10. Solve real-world problems that can be modeled using linear,quadratic, exponential or square root functions. 11. Solve real-world problems that can be modeled, using systems of linear equations and inequalities. Analyze Change 12. Describe the relationship between slope of a line through the origin and the tangent function of the angle created by the line and the positive x-axis. Course 2: , 183 #7&#8, 184 #9&#10, 187 #16, 189 #25, 191 #29, 193 #36, 251 #23 Course 2: Units 1 and 5 Previously addressed: Course 1: Throughout see: Units 1, 3, 5, 7 Course 2: 49-67, 69-72, , 357 #47 Course 3: , , Course 2: 478 #10, 480 #16, 482 #26 CPMP-Tools Geometry software Data Analysis and Probability Standard Data Collection 1. Describe measures of center and the range verbally, graphically and algebraically. 2. Represent and analyze bivariate data using appropriate graphical displays (scatterplots, parallel box-and-whisker plots, histograms with more than one set of data, tables, charts, spreadsheets) with and without technology. 3. Display bivariate data where at least one variable is categorical. 4. Identify outliers on a data display; e.g., use interquartile range to identify outliers on a boxand-whisker plot. Course 2: 155 #26, 230 #43, 278 #18 Previously addressed: Course 1: , Course 2: 48 #34, , , CPMP-Tools Statistics software Previously addressed: Course 1: , , Previously addressed: Course 1: 75 TATS, 76 #1, 78 #3, 80 #7, 91 #4, 93 #8, 110 #4, 112 CYU, 115 # 5bii, 135 #12, Course 2: 77 #4c, 155 #26, , 272 #4, 278 #18 Previously addressed: Course 1: , 127, 128, , Academic Content Standards 9 Core-Plus Mathematics

10 Statistical Methods 5. Provide examples and explain how a statistic may or may not be an attribute of the entire population; e.g., intentional or unintentional bias may be present. 6. Interpret the relationship between two variables using multiple graphical displays and statistical measures; e.g., scatterplots, parallel box-andwhisker plots, and measures of center and spread. Probability 7. Model problems dealing with uncertainty with area models (geometric probability). 8. Differentiate and explain the relationship between the probability of an event and the odds of an event, and compute one given the other. Opportunity to address in Course 2: , 312, 313 Course 4: Unit 9 Lesson 2 Course 2: , 278 #18, , Previously addressed: Course 1: 74-78, 91 #4, 93 #8, 95 #12, 98 #20, 106 #6, 110 #4, 111 #6, 115 #5, 131 #5, 132 #6, 133 #9, 135 #12, 137, 138 Course 2: , 540 #12&#13, 554 #8, 582 #22 Previously addressed: Course 1: , 578 #13 & 14, 583 #24, 588 #5 Course 2: Opportunity to address: , Course 3: 278 Academic Content Standards 10 Core-Plus Mathematics

11 Grade Eleven STANDARDS PAGE REFERENCES Number, Number Sense and Operations Standard Number and Number Systems 1. Determine what properties hold for matrix addition and matrix multiplication; e.g., use examples to show addition is commutative and when multiplication is not commutative. 2. Determine what properties hold for vector addition and multiplication, and for scalar multiplication. 3. Represent complex numbers on the complex plane. Meaning of Operations 4. Use matrices to represent given information in a problem situation. Previously addressed: Course 2: , 148 #8, 150 #12 Course 4: Unit 2 Course 3: 360 #14 Course 4: Unit 3 Previously addressed: Course 2: , , , , , Model, using the coordinate plane, vector addition and scalar multiplication. Course 4: Unit 2 Computation and Estimation 6. Compute sums, differences and products of matrices using paper and pencil calculations for simple cases, and technology for more complicated cases. CPMP-Tools Algebra software Previously addressed: Course 2: , , , 154 #20, 229 #37, 351 #21, 356 #44, 514 #30 7. Compute sums, differences, products and quotients of complex numbers. Course 4: Unit 3 8. Use fractional and negative exponents as optional ways of representing and finding solutions for problem situations; e.g., 27 2/3 = (27 1/3 ) 2 = 9. Course 3: Unit 5 Review 51 #31, 72 #32, 557 #30 Previously addressed: Course 1: , 351, Course 2: 24 #22&#25, 559 #21, Unit 2 Unit Resource Master URM 54 Academic Content Standards 11 Core-Plus Mathematics

12 9. Use vector addition and scalar multiplication to solve problems. Course 4: Unit 2 Measurement Standard Measurement Units 1. Determine the number of significant digits in a measurement. 2. Use radian and degree angle measures to solve problems and perform conversions as needed. Course 3: Opportunity to address: 237 Previously addressed: Course 2: Course 3: , , Previously addressed: Course 2: , Use Measurement Techniques and Tools 3. Derive a formula for the surface area of a cone as a function of its slant height and the circumference of its base. 4. Calculate distances, areas, surface areas and volumes of composite three-dimensional objects to a specified number of significant digits. 5. Solve real-world problems involving area, surface area, volume and density to a specified degree of precision. Geometry and Spatial Sense Standard Opportunity to address Course 1: 448 #13 Course 3: Review 50 #27 Previously addressed: Course 1: 447 #12, 448, #13, #14, 451 #24, 458 # Course 3: Review 7-8, 26 #25, 50 #27, 156 #36, 257 #25, 281 #26, 314 #31, 380 #1, 383 #12, 418 #32 Previously addressed: Course 1: 25, 62, 64, 70, 205, 320, 321, 394, 415, 423, 447, 448, 452, 453, Course 2: 506 #9 and review tasks Spatial Relationships 1. Use polar coordinates to specify locations on a plane. Course 4: Unit 2, Unit 8 Transformations and Symmetry 2. Represent translations using vectors. Course 4: Unit 2 3. Describe multiplication of a vector and a scalar graphically and algebraically, and apply to problem situations. Course 4: Unit 2 Academic Content Standards 12 Core-Plus Mathematics

13 4. Use trigonometric relationships to determine lengths and angle measures; i.e., Law of Sines and Law of Cosines. Visualization and Geometric Models Course 3: 125 #30, , , 593 #15, 594 #18 Previously addressed: Course 2: , Identify, sketch and classify the cross sections of three-dimensional objects. Patterns, Functions and Algebra Standard Use Patterns, Relations and Functions Course 4: Unit 6 Previously addressed: Course 1: , 438, 445, 446, 453, Identify and describe problem situations involving an iterative process that can be represented as a recursive function; e.g., compound interest. Course 3: , , , Previously addressed: Course 1: , , , Translate a recursive function into a closed form expression or formula for the nth term to solve a problem situation involving an iterative process; e.g., find the value of an annuity after 7 years. 3. Describe and compare the characteristics of the following families of functions: quadratics with complex roots, polynomials of any degree, logarithms, and rational functions; e.g., general shape, number of roots, domain and range, asymptotic behavior. 4. Identify the maximum and minimum points of polynomial, rational and trigonometric functions graphically and with technology. 5. Identify families of functions with graphs that have rotation symmetry or reflection symmetry about the y-axis, x-axis or y = x. Use Algebraic Representations 6. Represent the inverse of a function symbolically and graphically as a reflection about y = x. Course 3: , , Course 3: 28 #33, 282 #28, , , , , , , , , 595 #21 Course 4: Unit 1 Course 3: 28 #33, 282 #28, , , , , , , , , 595 #21 CPMP-Tools Algebra software Course 4: Unit 1 Previously addressed: Course 1: Course 3: 597 #29 Course 4: Unit 1 Previously addressed: Course 1: 478 Course 2: 21 Course 3: 547 #8, 552 #14, 573 #25, , 595 #24 Academic Content Standards 13 Core-Plus Mathematics

14 7. Model and solve problems with matrices and vectors. 8. Solve equations involving radical expressions and complex roots. 9. Solve 3 by 3 systems of linear equations by elimination and using technology, and interpret graphically what the solution means (a point, line, plane, or no solution). 10. Describe the characteristics of the graphs of conic sections. Course 4: Unit 2 Previously addressed: Course 2: Course 3: , 358 Course 4: Unit 3 Course 3: , 506 #19 Course 4: Unit 3 and 6 Previously addressed: Course 2: 152 #17 CPMP-Tools Algebra software Course 4: Unit 3 and 6 Analyze Change 11. Describe how a change in the value of a constant in an exponential, logarithmic or radical equation affects the graph of the equation. Data Analysis and Probability Standard Course 3: Opportunity to address: 28 #33, 125 #28, 552 #14, 564, 573 #25 & #26 Course 4: Unit 1, Unit 3, and Unit 4 Previously addressed: Course 1: , , 345 #20 & #21, 351 #34 Data Collection 1. Design a statistical experiment, survey or study for a problem; collect data for the problem; and interpret the data with appropriate graphical displays, descriptive statistics, concepts of variability, causation, correlation and standard deviation. 2. Describe the role of randomization in a welldesigned study, especially as compared to a convenience sample, and the generalization of results from each. Statistical Methods 3. Describe how a linear transformation of univariate data affects range, mean, mode and median. Course 3: 74-88, CPMP-Tools Statistics software Course 4: Unit 9 L2 Previously addressed: Course 2: U4 Projects Course 3: 74-91, CPMP-Tools Custom Tool: Randomization Distributions Course 4: Unit 9 L2 Previously addressed: Course 2: Unit 4 Assessments, Projects Course 3: Previously addressed: Course 1: , 134, 136 #15, 139 #21 Course 2: Review tasks Academic Content Standards 14 Core-Plus Mathematics

15 4. Create a scatterplot of bivariate data, identify trends, and find a function to model the data. Course 3: Review 51 #34 Previously addressed: Course 1: 156, , 169, , 178, , , 302, 310, 311, 467 CPMP-Tools Statistics software Course 2: 3-5, 8 #11, 13-14, 19 #8, 20 #10, 21 #12, 23 #19, 100 #23, , Use technology to find the Least Squares Regression Line, the regression coefficient, and the correlation coefficient for bivariate data with a linear trend, and interpret each of these statistics in the context of the problem situation. Course 3: Review tasks 126 #32 CPMP-Tools Statistics software Previously addressed: Course 2: , , 357 #46, 551 #5 6. Use technology to compute the standard deviation for a set of data, and interpret standard deviation in relation to the context or problem situation. Course 3: , , , , , , CPMP-Tools Statistics Custom Tools: Estimation Center and Estimate Center and Spread Previously addressed: Course 1: , , , 136, 139, 141, , 250 #22, 279 #22 Course 2: 250 #22, 279#22 7. Describe the standard normal curve and its general properties, and answer questions dealing with data assumed to be normal. Course 3: , , , , CPMP-Tools Statistics software Previously addressed: Course 1: , 120, 139 #22, 141 #27 8. Analyze and interpret univariate and bivariate data to identify patterns, note trends, draw conclusions, and make predictions. Course 3: 74-91, 92-99, , , , , , , CPMP-Tools Statistics software Previously addressed: Examples Throughout in Course 1: 18, 44, 98, 137, 139 #25, 172 #11, 348 #31 Course 2: Evaluate validity of results of a study based on characteristics of the study design, including sampling method, summary statistics and data analysis techniques. Course 3: 74-91, Course 4: Unit 9 Academic Content Standards 15 Core-Plus Mathematics

16 Probability 10. Understand and use the concept of random variable, and compute and interpret the expected value for a random variable in simple cases. 11. Examine statements and decisions involving risk; e.g., insurance rates and medical decisions. Course 3: 260 #2 Previously addressed: Course 1: , , , Course 2: , Course 3: 269 #7 Previously addressed: Course 2: 542 #19, 547 #4, p548, STMC, 556 #14, 587 #1 Academic Content Standards 16 Core-Plus Mathematics

17 Grade Twelve STANDARDS PAGE REFERENCES Number, Number Sense and Operations Standard Number and Number Systems 1. Determine what properties (closure, identity, inverse, commutative and associative) hold for operations with complex numbers. Course 4: Unit 3 Computation and Estimation 2. Apply combinations as a method to create coefficients for the Binomial Theorem, and make connections to everyday and workplace problem situations. Course 4: Unit 9 Measurement Standard Use Measurement Techniques and Tools 1. Solve problems involving derived measurements; e.g., acceleration and pressure. Course 4: Unit 7 2. Use radian measures in the solution of problems involving angular velocity and acceleration. 3. Apply informal concepts of successive approximation, upper and lower bounds, and limits in measurement situations; e.g., measurement of some quantities, such as volume of a cone, can be determined by sequences of increasingly accurate approximations. Geometry and Spatial Sense Standard Previously addressed: Course 3: Course 4: Unit 7 Transformations and Symmetry 1. Use matrices to represent translations, reflections, rotations, dilations and their compositions. Previously addressed: Course 2: CPMP-Tools Algebra software 2. Derive and apply the basic trigonometric identities; i.e., angle addition, angle subtraction and double angle. Course 4: Unit 4 Academic Content Standards 17 Core-Plus Mathematics

18 Visualization and Geometric Models 3. Relate graphical and algebraic representations of lines, simple curves and conic sections. Course 4: Units 1, 3, 4, 5, 6 4. Recognize and compare specific shapes and properties in multiple geometries; e.g., plane, spherical and hyperbolic. Previously addressed: Course 2: Unit 3 Project Course 3: 48 Patterns, Functions and Algebra Standard Use Patterns, Relations and Functions 1. Analyze the behavior of arithmetic and geometric sequences and series as the number of terms increases. Previously addressed: Course 3: , , , Translate between the numeric and symbolic form of a sequence or series. 3. Describe and compare the characteristics of transcendental and periodic functions; e.g., general shape, number of roots, domain and range, asymptotic behavior, extrema, local and global behavior. 4. Represent the inverse of a transcendental function symbolically. Use Algebraic Representations 5. Set up and solve systems of equations using matrices and graphs, with and without technology. 6. Make arguments about mathematical properties using mathematical induction. 7. Make mathematical arguments using the concepts of limit. Previously addressed: Course 3: , , , Course 4: Units 1, 3, 4 Previously addressed: Course 3: 125 #28, , 570 #17, 573 #25, 26, 28, 29, , , Previously addressed: Course 3: , 570 #17, , , 604 STM part c Previously addressed: Course 2: 50-67, Course 3: Course 4: Unit 8 Course 4: Unit 7 8. Compare estimates of the area under a curve over a bounded interval by partitioning the region with rectangles; e.g., make successive estimates using progressively smaller rectangles. 9. Translate freely between polar and Cartesian coordinate systems. Course 4: Unit 7 Course 4: Unit 2 and 4 Academic Content Standards 18 Core-Plus Mathematics

19 Analyze Change 10. Use the concept of limit to find instantaneous rate of change for a point on a graph as the slope of a tangent at a point. Course 4: Unit 7 Data Analysis and Probability Standard Data Collection 1. Identify and use various sampling methods (voluntary response, convenience sample, random sample, stratified random sample, census) in a study. Course 4: Unit 9 Statistical Methods 2. Transform bivariate data so it can be modeled by a function; e.g., use logarithms to allow nonlinear relationship to be modeled by linear function. Course 4: Unit 5 3. Describe the shape and find all summary statistics for a set of univariate data, and describe how a linear transformation affects shape, center and spread. 4. Apply the concept of a random variable to generate and interpret probability distributions, including binomial, normal and uniform. 5. Use sampling distributions as the basis for informal inference. Previously addressed: Course 1: , 134, 136, 137, 139 #21 CPMP-Tools Statistics software Course 2: 278 #18 Course 4: Unit 9 CPMP-Tools Statistics software Previously addressed: Course 1: , , , Course 2: , Course 3: , , , Course 4: Unit 9 L1, L13 Previously addressed: Course 2: 574 #3, 575 #6 Course 3: 74-91, , , Probability 6. Use theoretical or experimental probability, including simulations, to determine probabilities in real-world problem situations involving uncertainty, such as mutually exclusive events, complementary events, and conditional probability. Course 4: Unit 9 L1 CPMP-Tools Statistics Simulation software Previously addressed: Course 1: , Course 2: Course 3: Academic Content Standards 19 Core-Plus Mathematics

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Core-Plus Mathematics, CCSS Edition

Core-Plus Mathematics is a high school mathematics program consisting of a four-year series of print and digital student textbooks and supporting materials for teachers, developed by the Core-Plus Mathematics Project (CPMP) at Western Michigan University, with funding from the National Science Foundation. Development of the program started in 1992. The first edition, entitled Contemporary Mathematics in Context: A Unified Approach, was completed in 1995. The third edition, entitled Core-Plus Mathematics: Contemporary Mathematics in Context, was published by McGraw-Hill Education in 2015.

  • 1Key Features
  • 2Evaluations, Research, and Reviews
    • 2.1Positive reviews
    • 2.2Negative reviews

Key Features[edit]

The first edition of Core-Plus Mathematics was designed to meet the curriculum, teaching, and assessment standards from the National Council of Teachers of Mathematics[1][2][3][4] and the broad goals outlined in the National Research Council report, Everybody Counts: A Report to the Nation on the Future of Mathematics Education.[5] Later editions were designed to also meet the American Statistical AssociationGuidelines for Assessment and Instruction in Statistics Education (GAISE)[6] and most recently the standards for mathematical content and practice in the Common Core State Standards for Mathematics (CCSSM).[7]

The program puts an emphasis on teaching and learning mathematics through mathematical modeling and mathematical inquiry. Each year, students learn mathematics in four interconnected strands: algebra and functions, geometry and trigonometry, statistics and probability, and discrete mathematical modeling.[8][9]

First Edition (1994-2003)[edit]

The program originally comprised three courses, intended to be taught in grades 9 through 11. Later, authors added a fourth course intended for college-bound students.[10]

Unit No.Course 1Course 2Course 3
1Patterns in DataMatrix ModelsMultiple-Variable Models
2Patterns of ChangePatterns of Location, Shape and SizeModeling Public Opinion
3Linear ModelsPatterns of AssociationSymbol Sense and Algebraic Reasoning
4Graph ModelsPower ModelsShapes and Geometric Reasoning
5Patterns in Space and VisualizationNetwork OptimizationPatterns in Variation
6Exponential ModelsGeometric Form and Its FunctionFamilies of Functions
7Simulation ModelsPatterns in ChanceDiscrete Models of Change
CapstonePlanning a Benefits CarnivalForest, the Environment, and MathematicsMaking the Best of It: Optimal Forms and Strategies
Course 4 Units
Core UnitsAdditional Units for Students Intending to Pursue Programs in:
Mathematical, Physical and Biological Sciences or EngineeringSocial, Management, and Health Sciences or Humanities
1. Rates of Change6. Polynomial and Rational Functions5. Binomial Distributions and Statistical Inference
2. Modeling Motion7. Functions and Symbolic Reasoning9. Informatics
3. Logarithmic Functions and Data Models8. Space Geometry10. Problem Solving, Algorithms, and Spreadsheets
4. Counting Models

Second Edition (2008-2011)[edit]

The course was re-organized around interwoven strands of algebra and functions, geometry and trigonometry, statistics and probability, and discrete mathematics. Lesson structure was updated, and technology tools, including CPMP-Tools software was introduced.[11][12]

Unit No.Course 1Course 2Course 3Course 4: Preparation for Calculus
1Patterns of ChangeFunctions, Equations, and SystemsReasoning and ProofFamilies of Functions
2Patterns in DataMatrix MethodsInequalities and Linear ProgrammingVectors and Motion
3Linear FunctionsCoordinate MethodsSimilarity and CongruenceAlgebraic Functions and Equations
4Vertex-Edge GraphsRegression and CorrelationSamples and VariationTrigonometric Functions and Equations
5Exponential FunctionsNonlinear Functions and EquationsPolynomial and Rational FunctionsExponential Functions, Logarithms, and Data Modeling
6Patterns in ShapeNetwork OptimizationCircles and Circular FunctionsSurfaces and Cross Sections
7Quadratic FunctionsTrigonometric MethodsRecursion and IterationConcepts of Calculus
8Patterns in ChanceProbability DistributionsInverse FunctionsCounting Methods and Induction
Core plus mathematics teacher edition

Holt Mathematics Course 1

CCSS Edition (2015)[edit]

The course was aligned with the Common Core State Standards (CCSS) mathematical practices and content expectations. Expanded and enhanced Teacher's Guides include a CCSS pathway and a CPMP pathway through each unit. Course 4 was split into two versions: one called Preparation for Calculus, for STEM-oriented students, and an alternative course, Transition to College Mathematics and Statistics (TCMS), for college-bound students whose intended program of study does not require calculus.[13][14][15]

Unit No.Course 1Course 2Course 3Course 4: Preparation for CalculusTCMS
1Patterns of ChangeFunctions, Equations, and SystemsReasoning and ProofFamilies of FunctionsInterpreting Categorical Data
2Patterns in DataMatrix MethodsInequalities and Linear ProgrammingVectors and MotionFunctions Modeling Change
3Linear FunctionsCoordinate MethodsSimilarity and CongruenceAlgebraic Functions and EquationsCounting Methods
4Discrete Mathematical ModelingRegression and CorrelationSamples and VariationTrigonometric Functions and EquationsMathematics of Financial Decision-Making
5Exponential FunctionsNonlinear Functions and EquationsPolynomial and Rational FunctionsExponential Functions, Logarithms, and Data ModelingBinomial Distributions and Statistical Inference
6Patterns in ShapeModeling and OptimizationCircles and Circular FunctionsSurfaces and Cross SectionsInformatics
7Quadratic FunctionsTrigonometric MethodsRecursion and IterationConcepts of CalculusSpatial Visualization and Representations
8Patterns in ChanceProbability DistributionsInverse FunctionsCounting Methods and InductionMathematics of Democratic Decision-Making

Evaluations, Research, and Reviews[edit]

Project and independent evaluations and many research studies have been conducted on Core-Plus Mathematics, including content analyses, case studies, surveys, small- and large-scale comparison studies, research reviews, and a longitudinal study.

Positive reviews[edit]

There are multiple research studies and evaluations in which students using Core-Plus Mathematics performed significantly better than comparison students on assessments of conceptual understanding, problem solving, and applications, and results were mixed for performance on assessments of by-hand calculation skills.[16][17][18][19][20][21][22][23][24][25][26] Some of these studies were funded by the National Science Foundation, the same organization that funded the development of Core-Plus Mathematics program.

Large-scale comparison studies[edit]

A three-part study of Core-Plus Mathematics and more conventional curricula were reported by researchers at the University of Missouri.[16][17][18] The research was conducted as part of the Comparing Options in Secondary Mathematics: Investigating Curricula project, supported by the National Science Foundation under REC-0532214. The research was reported in the March and July 2013 issues of the Journal for Research in Mathematics Education and in the December 2013 issue of the International Journal of Science and Mathematics Education. The three studies examined student achievement in schools in 5 geographically dispersed states. The first study involved 2,161 students in 10 schools in first-year high school mathematics courses, the second study involved 3,258 students in 11 schools in second-year mathematics courses, and the third study involved 2,242 students in 10 schools in third-year mathematics courses. Results in the first study showed that Core-Plus Mathematics students scored significantly higher on all three end-of-year outcome measures: a test of common objectives, a problem solving and reasoning test, and a standardized achievement test. Results in the second study showed that Core-Plus Mathematics students scored significantly higher on a standardized achievement test, with no differences on the other measures. Results in the third study showed that Core-Plus Mathematics students scored significantly higher on a test of common objectives, with no differences on the other measure.

Other comparison studies[edit]

A study conducted by Schoen and Hirsch, two authors of Core-Plus Mathematics, reported that students using early versions of Core-Plus Mathematics did as well as or better than those in traditional single-subject curricula on all measures except paper-and-pencil algebra skills.[19]

A study on field-test versions of Core-Plus Mathematics, supported by a grant from the National Science Foundation (Award MDR 9255257) and published in 2000 in the Journal for Research in Mathematics Education, reported that students using the first field-test versions of Core-Plus Mathematics scored significantly better on tests of conceptual understanding and problem solving, while Algebra II students in conventional programs scored significantly better on a test of paper-and-pencil procedures.[24]

Other studies reported that Core-Plus Mathematics students displayed qualities such as engagement, eagerness, communication, flexibility, and curiosity to a much higher degree than did students who studied from more conventional programs.[22] A review of research in 2008 concluded that there were modest effects for Core-Plus Mathematics on mostly standardized tests of mathematics.[25]

With regard to achievement of students in minority groups, an early peer-reviewed paper documenting the performance of students from under-represented groups using Core-Plus Mathematics reported that at the end of each of Course 1, Course 2, and Course 3, the posttest means on standardized mathematics achievement tests of Core-Plus Mathematics students in all minority groups (African Americans, Asian Americans, Hispanics, and Native/Alaskan Americans) were greater than those of the national norm group at the same pretest levels. Hispanics made the greatest pretest to posttest gains at the end of each course.[26] A later comparative study reported that Hispanic high school students using Core-Plus Mathematics made modest gains compared to the performance of students with other demographic backgrounds.[20]

Regarding preparation for college, studies of SAT and ACT test results reported that Core-Plus Mathematics students performed significantly better than comparison students on the SAT and performed as well on the ACT.[27] Several studies examined the subsequent college mathematics performance of students who used different high school textbook series. These studies did not detect any differential effect of high school curriculum on placement in college mathematics courses, in subsequent performance, or in course-taking patterns.[28][29][30][31][32][33][34]

Reviews of instructional materials and programs[edit]

EdReports, an independent nonprofit, recently completed evidenced-based reviews of K-12 instructional materials. In their analysis of Core-Plus Mathematics Courses 1-3, the three-year core program was found to meet expectations for alignment to the high school Common Core State Standards for Mathematics in terms of content, focus, and coherence, and in terms of rigor and mathematical practices. The Core-Plus Mathematics instructional materials also met EdReports criteria that the materials are well designed and reflect effective lesson structure and pacing.[35]

In an in-depth analysis by The Center for Research on Reform in Education at Johns Hopkins University, Core-Plus Mathematics was given a 'moderate' evidence rating, and is the only comprehensive three-year high school mathematics program to be rated at any level (strong, moderate, or promising) for meeting federal ESSA Standards for Evidence in terms of promoting student achievement.[36]

Other research studies[edit]

In terms of core content development, a study comparing the development of quadratic equations in the Korean national curriculum and Core-Plus Mathematics found that some quadratic equation topics are developed earlier in Korean textbooks, while Core-Plus Mathematics includes more problems requiring explanations, various representations, and higher cognitive demand.[37]

Several studies have analyzed the teacher’s role in Core-Plus Mathematics.[23][38][39]

Negative reviews[edit]

In November 1999, David Klein, professor of mathematics at California State University, Northridge, sent an open letter to the U.S. Department of Education, in response to the U.S. Department of Education Expert Panel in Mathematics and Science designation of Core-Plus Mathematics as 'exemplary.' Klein's open letter urged the Department of Education to withdraw its recommendations of the several reform mathematics programs including Core-Plus Mathematics. The letter was co-signed by more than 200 American scientists and mathematicians.[40] Other mathematicians were critical of the letter and were concerned that the letter gives the false impression that the mathematical community agrees with the letter’s conclusions. “In fact, there is no such clear-cut consensus on the issues the letter raises.”[41]

Prof. Klein asserts that the mathematics programs criticized by the open letter had common features: they overemphasized data analysis and statistics, while de-emphasizing far more important areas of arithmetic and algebra. Many of the 'higher-order thinking projects' turned out to be just aimless activities. The programs were obsessed with electronic calculators, and basic skills were disparaged.[42]

Specifically, Core-Plus Mathematics was criticized for exhibiting 'too shallow a coverage of traditional algebra, and a focus on highly contextualized work'.

R. James Milgram, Professor of Mathematics at Stanford University, analyzed the program's effect on students in a top-performing high school. According to Milgram, '...there was no measure represented in the survey, such as ACT scores, SAT Math scores, grades in college math courses, level of college math courses attempted, where the students even met, let alone surpassed the comparison group [which used a more traditional program].'[42]

Andover High School Survey[edit]

Core Plus Mathematics Course 1 Answers Download Pdf

One of the first schools to pilot Core-Plus was Andover High School in Bloomfield Hills, Michigan, which was ranked one of America's '100 best' high schools. Andover stopped traditional mathematics in 1994 and began using Core-Plus Mathematics.

A survey conducted in 1997 of Andover graduates found that 96 percent of students who returned the survey said they were placed into “remedial math” in college. In a neighboring school, 62 percent of the students who returned the survey took remedial math in college.[43] Activism by a group of parents caused Andover to return to offering a traditional math option. By 2000, half of students at Andover were taking Core-Plus and the other half were taking traditional math.

Students commented on the survey that Core Plus was one of the worst math programs and a waste of their time. They lamented never being taught 'any of the basics and most are suffering in college math courses'. They found themselves 'completely unprepared' for understanding college math.[44]

The survey study has been criticized for involving a self-selected sample, self-reported data, and biased survey methods.[45] Data provided by the University of Michigan registrar at this same time indicated that in collegiate mathematics courses at the University of Michigan graduates of Core-Plus did as well as or better than graduates of a traditional mathematics curriculum.[46] A later study (see below) found that graduates of the Core-Plus curriculum entering Michigan State University have placed into increasingly lower level mathematics courses as the implementation of the curriculum has progressed.[47] This study and the published report have been criticized for design flaws and for drawing conclusions that are not supported by the data.[48]

A study of Core-Plus students attending Michigan State University[edit]

In 2006, Richard O. Hill and Thomas H. Parker from Michigan State University (MSU) evaluated the effectiveness of the Core-Plus Mathematics Project in preparing the students for subsequent university mathematics. R. Hill and T. Parker analyzed the college mathematics records of students arriving at MSU from four high schools that implemented the Core-Plus Mathematics program between 1996 and 1999. They found a 'disconnect' between the mathematics expectations that students encounter in K-12 education and those that they encounter in college. The effectiveness of Core-Plus and the other NSF-funded high school curricula programs became a significant issue for college mathematics faculty.[47]

Core-Plus students placed into, and enrolled in, increasingly lower level courses. The percentages of students who eventually passed a technical calculus course showed a statistically significant decline averaging 27 percent a year; this trend was accompanied by an obvious and statistically significant increase in percentages of students who placed into low-level and remedial algebra courses. Except for some top students, graduates of Core-Plus mathematics were struggling in college mathematics, earning below average grades. They were less well prepared than either graduates in the Control group (who came from a broad mix of curricula) or graduates of their own high schools before the implementation of Core-Plus mathematics.[47]

Core Plus Mathematics Teacher Edition

Review by Prof. Harel[edit]

In 2009 professor of mathematics at the University of California in San Diego, Guershon Harel reviewed four high-school mathematics programs. The examined programs included Core-Plus Courses 1, 2, and 3. The examination focused on two topics in algebra and one topic in geometry, deemed by Prof. Harel central to the high school curriculum. The examination was intended 'to ensure these topics are coherently developed, completely covered, mathematically correct, and provide students a solid foundation for further study in mathematics'.[49]

From the outset, Prof. Harel noted that the content presentation in Core-Plus program is unusual in that its instructional units, from the start to the end, are made of word problems involving 'real-life' situations. This structure is reflected in the subtitle of the Core-Plus series: Contemporary Mathematics in Context. To review the program, it was necessary to go through all the problems in the core units and their corresponding materials in the Teacher’s Edition. Despite the unconventional textbook structure, the language used by the Core-Plus program was found mathematically sound.

Core Plus Mathematics Course 1 Answers Download Pdf

In the algebra section, fundamental theorems on linear functions and quadratic functions were found not justified, except for the quadratic formula. Theorems are often presented without proof.

Like in the algebra texts, the geometry text does not lead to a clear logical structure of the material taught. Because theoretical material is concealed within the text of the problems, 'a teacher must identify all the critical problems and know in advance the intended structure to establish the essential mathematical progression. This task is further complicated by the fact that many critical problems appear in the homework sections. Important theorems in geometry are not justified. Moreover, with the way the material is sequenced, some of these theorems cannot be justified'.[49]

According to Prof. Harel, the Core-Plus program 'excels in providing ample experience in solving application problems and in ensuring that students understand the meanings of the different parts of the modeling functions. The program also excels in its mission to contextualize the mathematics taught'. However, it fails 'to convey critical mathematical concepts and ideas that should and can be within reach for high school students'.[49]

Review by Prof. Wilson[edit]

Professor W. Stephen Wilson from Johns Hopkins University evaluated the mathematical development and coherence of the Core-Plus program in 2009. In particular, he examined 'the algebraic concepts and skills associated with linear functions because they are a critical foundation for the further study of algebra', and evaluated how the program presents the theorem that the sum of the angles of a triangle is 180 degrees, 'which is a fundamental theorem of Euclidean geometry and it connects many of the basics in geometry to each other'.[50]

Prof. Wilson noted that the major theme of the algebra portion of the program seems to involve creating a table from data, graphing the points from the table; given the table students are asked to find a corresponding function. In case of linear function, 'at no point is there an attempt to show that the equation's graph really is a line. Likewise, there is never an attempt to show that a line graph comes from the usual form of a linear equation'. Prof. Wilson considered this approach to be 'a significant flaw in the mathematical foundation'.[50]

Quoting the textbook, 'Linear functions relating two variables x and y can be represented using tables, graphs, symbolic rules, or verbal descriptions', Prof. Wilson laments that although this statement is true, 'the essence of algebra involves abstraction using symbols'.[50]

Prof. Wilson says that the Core-Plus program 'has a multitude of good problems, but never develops the core of the mathematics of linear functions. The problems are set in contexts and mathematics itself is rarely considered as a legitimate enterprise to investigate'. The program lacks attention to algebraic manipulation' to the point that 'symbolic algebra is minimized'.[50]

In regards to geometry portion, Prof. Wilson concludes that the program fails to build geometry up from foundations in a mathematically sound and coherent way'. He stresses out that 'one significant goal of a geometry course is to teach logic, and this program fails on that account'.[50]

Overall, the 'unacceptable nature of geometry' and the fashion in which the program downplays 'algebraic structure and skills' make the Core-Plus program unacceptable.

Historical Controversy[edit]

Mathematics programs initially developed in the 1990s that were based on the NCTM’s Curriculum and Evaluation Standards for School Mathematics, like Core-Plus Mathematics, have been the subject of controversy due to their differences from more conventional mathematics programs. In the case of Core-Plus Mathematics, there has been debate about (a) the international-like integrated nature of the curriculum, whereby each year students learn algebra, geometry, statistics, probability, and discrete mathematical modeling, as opposed to conventional U.S. curricula in which just a single subject is studied each year, (b) a concern that students may not adequately develop conventional algebraic skills, (c) a concern that students may not be adequately prepared for college, and (d) a mode of instruction that relies less on teacher lecture and demonstration and more on inquiry, problem solving in contextualized settings, and collaborative work by students.

For example, this debate led to some schools in Minnesota abandoning Core-Plus Mathematics in the early 2000s and returning to traditional mathematics curricula. In a master's degree research paper at the time, interviews with teachers at four schools that had dropped Core-Plus Mathematics suggested that many teachers 'did not feel that Core-Plus emphasized mastering skills enough', while parents 'felt that it did not prepare students for college' and some parents commented that the text was difficult to read. The author of the paper made suggestions for successful adoption of any new materials, including 'don't rush the adoption process,' have 'continued professional development for all,' and 'school districts need to be proactive regarding parent questions.' [51]

References[edit]

Core Plus Mathematics Textbook

  1. ^National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  2. ^National Council of Teachers of Mathematics. (1991). Mathematics professional standards for teaching mathematics. Reston, VA: National Council of Teachers of Mathematics.
  3. ^National Council of Teachers of Mathematics. (1995). Assessment standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  4. ^National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
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  7. ^Common Core State Standards Initiative (CCSSI). (2010). Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.
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  9. ^Maurer, S.; McCallum, W. (2006). 'Advising a precollege curriculum project'. Notices of the AMS. 53 (9): 1018–1020.
  10. ^Schoen, Harold L.; Hirsch, Christian R. (2003). 'The Core-Plus Mathematics Project: Perspectives and Student Achievement'(PDF).
  11. ^'Core-Plus Mathematics 2nd Edition: Redesigned and Enhanced Features'.
  12. ^'Core-Plus Mathematics 2nd Edition: Unit descriptions and topics'(PDF).
  13. ^'Core-Plus Mathematics CCSS Edition: Key Features'.
  14. ^'Core-Plus Mathematics CCSS Edition: Unit descriptions and topics'(PDF).
  15. ^'Transition to College Mathematics and Statistics'.
  16. ^ abGrouws, D. A.; Tarr, J. E.; Chávez, Ó.; Sears, R.; Soria, V. M.; Taylan, R. D. (2013). 'Curriculum and implementation effects on high school students' mathematics learning from curricula representing subject-specific and integrated content organizations'. Journal for Research in Mathematics Education. 44 (2): 416–463. doi:10.5951/jresematheduc.44.2.0416.
  17. ^ abTarr, J. E.; Grouws, D. A.; Chávez, Ó.; Soria, V. M. (2013). 'The effects of content organization and curriculum implementation on students' mathematics learning in second-year high school courses'. Journal for Research in Mathematics Education. 44 (4): 683–729. doi:10.5951/jresematheduc.44.4.0683.
  18. ^ abChávez, Ó.; Tarr, J. E.; Grouws, D. A.; Soria, V. M. (2013). 'Third-year high school mathematics curriculum: Effects of content organization and curriculum implementation'. International Journal of Science and Mathematics Education. 13: 97–120. doi:10.1007/s10763-013-9443-7.
  19. ^ abSchoen, H. L., & Hirsch, C. R. (2003). The Core-Plus Mathematics Project: Perspectives and student achievement. In S. Senk & D. Thompson (Eds.), Standards-based school mathematics curricula: What are they? What do students learn? (pp. 311–344). Hillsdale, NJ: Lawrence Erlbaum Associates.
  20. ^ abCapraro, M. M.; Capraro, R. M.; Yetkiner, Z. E.; Rangel-Chavez, A. F.; Lewis, C. W. (2010). 'Examining Hispanic student mathematics performance on high-stakes tests: An examination of one urban school district in Colorado'. Urban Review: Issues and Ideas in Public Education. 42 (3): 193–209. doi:10.1007/s11256-009-0127-0.
  21. ^Harwell, M.; Post, T. R.; Maeda, Y.; Davis, J.; Cutler, A.; Anderson, E.; Kahan, J. A. (2007). 'Standards-based mathematics curricula and secondary students' performance on standardized achievement tests'. Journal for Research in Mathematics Education. 38 (1): 71–101.
  22. ^ abLatterell, C. M. (2003). 'Testing the problem-solving skills of students in an NCTM-oriented curriculum'. The Mathematics Educator. 13 (1): 5–14.
  23. ^ abSchoen, H. L.; Finn, K. F.; Cebulla, K. J.; Fi, C. (2003). 'Teacher variables that relate to student achievement when using a standards-based curriculum'. Journal for Research in Mathematics Education. 34 (3): 228–259. doi:10.2307/30034779. JSTOR30034779.
  24. ^ abHuntley, M. A.; Rasmussen, C. L.; Villarubi, R. S.; Sangtong, J.; Fey, J. T. (2000). 'Effects of Standards-based mathematics education: A study of the Core-Plus Mathematics Project algebra and functions strand'. Journal for Research in Mathematics Education. 31 (3): 328–361. doi:10.2307/749810. JSTOR749810.
  25. ^ abSlavin, R.; Lake, C.; Groff, C. (2007). 'Effective programs in middle and high school mathematics: A best-evidence synthesis'. Review of Educational Research. 79 (2): 839–911. doi:10.3102/0034654308330968.
  26. ^ abSchoen, H. L., Hirsch, C. R., & Ziebarth, S. W. (1998). An emerging profile of the mathematical achievement of students in the Core-Plus Mathematics Project. Paper presented at the 1998 Annual Meeting of the American Educational Research Association. San Diego, CA.
  27. ^Schoen, H. L., Ziebarth, S. W., Hirsch, C. R., & BrckaLorenz, A. (2010). A five-year study of the first edition of the Core-Plus Mathematics curriculum. Charlotte, NC: Information Age Publishing, Inc.
  28. ^Schoen, H. L., & Hirsch, C. R. (2003, February). Responding to calls for change in high school mathematics: Implications for collegiate mathematics. American Mathematical Monthly, pp. 109–123.
  29. ^Norman, K. W.; Medhanie, A. G.; Harwell, M. R.; Anderson, E.; Post, T. R. (2011). 'High school mathematics curricula, university mathematics placement recommendations, and student university mathematics performance'. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies. 21 (5): 434–455. doi:10.1080/10511970903261902.
  30. ^Dupuis, D. N.; Medhanie, A. G.; Harwell, M. R.; Lebeau, B.; Monson, D. (2012). 'A multi-institutional study of the relationship between high school mathematics achievement and performance in introductory college statistics'. Statistics Education Research Journal. 11 (1): 4–20.
  31. ^Harwell, M. R.; Medhanie, A. G.; Post, T. R.; Norman, K. W.; Dupuis, D. N. (2012). 'Preparation of students completing a Core-Plus or commercially developed high school mathematics curriculum for intense college mathematics coursework'. Journal of Experimental Education. 80 (1): 96–112. doi:10.1080/00220973.2011.567311.
  32. ^Post, T. R.; Monson, D. S.; Anderson, E.; Harwell, M. R. (2012). 'Integrated curricula and preparation for college mathematics'. The Mathematics Teacher. 106 (2): 138–143. doi:10.5951/mathteacher.106.2.0138.
  33. ^Post, T. R.; Medhanie, A.; Harwell, M.; Norman, K. W.; Dupuis, D. N.; Muchlinski, T.; Anderson, E.; Monson, D. (2010). 'The impact of prior mathematics achievement on the relationship between high school mathematics curricula and post-secondary mathematics performance, course-taking, and persistence'. Journal for Research in Mathematics Education. 41 (3): 274–308.
  34. ^Teuscher, D.; Reys, R. E. (2012). 'Rate of change: AP calculus students' understandings and misconceptions after completing different curricular paths'. School Science and Mathematics. 112 (6): 359–376. doi:10.1111/j.1949-8594.2012.00150.x.
  35. ^'Educator-led, evidence-based reviews of K-12 instructional materials.' EdReports.org
  36. ^'Evidence for ESSA - Math Programs.' evidenceforessa.org.
  37. ^Hong, D. S.; Choi, K. M. (2014). 'A comparison of Korean and American secondary school textbooks: The case of quadratic equations'. Educational Studies in Mathematics. 85 (2): 241–263. doi:10.1007/s10649-013-9512-4.
  38. ^Herbel-Eisenmann, B.; Lubienski, S.; Id-Deen, L. (2006). 'Reconsidering the study of mathematics instructional practices: The importance of curricular context in understanding local and global teacher change'. Journal of Mathematics Teacher Education. 9 (4): 313–345. doi:10.1007/s10857-006-9012-x.
  39. ^Ziebarth, S. W., Hart, E., Marcus, R., Ritsema B., Schoen, H. L., & Walker, R. (2008). High school teachers as negotiators between curriculum intentions and enactment. In J. Remillard, G. Lloyd, & B. Herbel-Eisenmann (Eds.), Mathematics teachers at work. (pp. 171–189). New York: Routledge Falmer.
  40. ^Klein, David (1999). 'An open letter to United States secretary of Education, Richard Riley'.
  41. ^'Open Letter on Mathematics Curricula Ignites Debate.' For Your Information, Notices of the AMS, Volume 47, Number 2, page 248.
  42. ^ abKlein, David (2000). 'Math problems: Why the U.S. Department of Education's recommended math programs don't add up'.
  43. ^'Christian Science Monitor'. Archived from the original on 2003-02-19. Retrieved 20 February 2015.
  44. ^'Preliminary Report on a Survey of the Graduating Classes of 1997 of Andover High School and Lahser High School, Bloomfield Hills, Michigan, Gregory F. Bachelis, Ph.D. Professor of Mathematics, Wayne State University'. Math.wayne.edu. Retrieved 20 February 2015.
  45. ^'Frequently Asked Questions About the Core-Plus Mathematics Project'. Wmich.edu. Retrieved 20 February 2015.
  46. ^'Archived copy'. Archived from the original on 2007-06-08. Retrieved 2007-05-06.CS1 maint: Archived copy as title (link)
  47. ^ abcHill, Richard O.; Parker, Thomas H. (2006). 'A study of Core-Plus students attending Michigan State University'(PDF).
  48. ^'Frequently Asked Questions About the Core-Plus Mathematics Project'. Wmich.edu. Retrieved 20 February 2015.
  49. ^ abcHarel, Guershon (2009). 'A Review of Four High-School Mathematics Programs'(PDF).
  50. ^ abcdeWilson, W. Stephen (2009). 'Washington State high school math text review'(PDF).
  51. ^Richgels, Amber R. (2005). 'Why are school districts abandoning the Core-Plus Mathematics curriculum?'(PDF).

Core Plus Mathematics Answers

External links[edit]

Core Plus Mathematics Textbook Answers

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