A Correlation of Pearson Integrated High School Mathematics Mathematics III Common Core, 2014 to the California Common Core State s for Mathematics s Map Mathematics III Copyright 2017 Pearson Education, Inc. or its affiliate(s). All rights reserved
California Common Core State s for Mathematics s Map Mathematics III Indicates a modeling standard linking mathematics to everyday life, work, and decision-making. (+) Indicates additional mathematics to prepare students for advanced courses. Language 1 Y N Reviewer Notes NUMBER AND QUANTITY Domain THE COMPLEX NUMBER SYSTEM Use complex numbers in polynomial identities and equations. [Polynomials with real coefficients; apply N.CN.9 to higher degree polynomials.] N CN 8. (+) Extend polynomial identities to the complex numbers. SE: 282 289, 290 294, 295 300 TG: 282 288, 289 291, 292 297 N CN 9. (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. SE: 295 300 TG: 292 297 1 For some standards that appear in multiple courses (e.g., Mathematics II and Mathematics III), some examples included in the language of the standard that did not apply to this standards map were removed. California Common Core State s Map: Mathematics III Page 2
ALGEBRA Language 1 Y N Reviewer Notes Domain SEEING STRUCTURE IN EXPRESSIONS Interpret the structure of expressions. [Polynomial and rational] A SSE 1a. Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, and coefficients. Please see Pearson Integrated Mathematics, Mathematics I Common Core: SE: 6 7, 12, 129 134, 146 157, 186 194, 195 202, 283 290, 309 318, 329 336, 344 353 TG: 5 11, 119 125, 134 141, 172 180, 181 188, 274 280, 298 306, 314 320, 327 334 A SSE 1b. A SSE 2. Interpret expressions that represent a quantity in terms of its context. Interpret complicated expressions by viewing one or more of their parts as a single entity. Use the structure of an expression to identify ways to rewrite it. SE: 193 202 TG: 194 201 SE: 169, 170 171, 172 173, 174 176, 177, 185 186, 187 188, 189 190, 191 192, 425 427, 428 431, 432 433, 434 435, 436, 437 438, 439 440, 441 442, 443, 444 445, 446 448, 449, 450 452, 453 454, 455, 456 458 TG: 170 178, 186 195, 413 418, 419 425, 426 433, 434 441 California Common Core State s Map: Mathematics III Page 3
A SSE 4. Domain A APR 1. A APR 2. A APR 3. Language 1 Y N Reviewer Notes Write expressions in equivalent forms to solve problems. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. ARITHMETIC WITH POLYNOMIALS AND RATIONAL EXPRESSIONS Perform arithmetic operations on polynomials. [Beyond quadratic] Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Understand the relationship between zeros and factors of polynomials. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x a is p(a), so p(a) = 0 if and only if (x a) is a factor of p(x). Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. SE: 720 721, 722 727 TG: 689, 690 693 SE: 250 255, 322 329 TG: 251 256, 318 325 SE: 256 262, 273 278 TG: 257 262, 274 278 SE: 178 181, 256 262, 282 286, 295 298, 301 TG: 179 182, 257 262, 282 286, 292 295, 299 California Common Core State s Map: Mathematics III Page 4
A APR 4. A APR 5. Language 1 Y N Reviewer Notes Use polynomial identities to solve problems. Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x 2 + y 2 ) 2 = (x 2 y 2 ) 2 + (2xy) 2 can be used to generate Pythagorean triples. (+) Know and apply the Binomial Theorem for the expansion of (x + y) n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal s Triangle. 2 SE: 290 293, 309 312 TG: 289 290, 307 308 SE: 303 308, 309 312 TG: 301 306, 307 308 A APR 6. A APR 7. Rewrite rational expressions. [Linear and quadratic denominators] Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. SE: 273 278, 339 343 TG: 274 278, 337 340 For related content, please see: SE: 339 346, 356 362 TG: 337 342, 344 348, 350 357 2. The Binomial Theorem may be proven by mathematical induction or by a combinatorial argument. California Common Core State s Map: Mathematics III Page 5
Language 1 Y N Reviewer Notes Domain CREATING EQUATIONS Create equations that describe numbers or relationships. [Equations using all available types of expressions, including simple root A CED 1. functions] Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. CA SE: 55 59, 63 69, 185 189, 193 198, 401 404, 413 415, 459 463, 562 566 TG: 53 57, 60 64, 186 190, 194 198, 392 395, 400 401, 442 446, 538 539 A CED 2. A CED 3. A CED 4. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. SE: 73 78, 110 114, 160 163, 363 368, 505 511 TG: 69 73, 107 111, 161 165, 358 363, 487 492 SE: 102 109, 119 125 TG: 98 106, 115 123 SE: 477 487, 660 667 TG: 457 465, 632 639 California Common Core State s Map: Mathematics III Page 6
Domain A REI 2. Language 1 Y N Reviewer Notes REASONING WITH EQUATIONS AND INEQUALITIES Understand solving equations as a process of reasoning and explain the reasoning. [Simple radical and rational] Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. SE: 401 404, 459 463 TG: 392 395, 442 446 A REI 11. Represent and solve equations and inequalities graphically. [Combine polynomial, rational, radical, absolute value, and exponential functions.] Explain why the x coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. SE: 203 207, 265 269, 401 404, 409 412, 459 463, 562 566 TG: 202 205, 266 270, 392 395, 399, 442 446, 538 539 FUNCTIONS Domain INTERPRETING FUNCTIONS Interpret functions that arise in applications in terms of the context. [Include rational, square root and cube root; emphasize selection of appropriate models.] California Common Core State s Map: Mathematics III Page 7
F IF 4. Language 1 Y N Reviewer Notes For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. SE: 73 78, 151 156, 239 244, 313 318, 376 381, 385 392, 488 494, 573 577 TG: 69 73, 151 156, 240 245, 309 313, 369 374, 379 385, 466 470, 549 553 F IF 5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Please see Pearson Integrated Mathematics, Mathematics I Common Core: SE: 135 143, 291 300 TG: 126 132, 281 289 Also see Pearson Integrated Mathematics, Mathematics II Common Core: SE: 707 715, 732 739 TG: 687 696, 710 716 F IF 6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. SE: 151 156, 160 163, 167 168, 313 318 TG: 151 156, 161 165, 169, 309 313 California Common Core State s Map: Mathematics III Page 8
F IF 7b. Language 1 Y N Reviewer Notes Analyze functions using different representations. [Include rational and radical; focus on using key features to guide selection of appropriate type of model function.] Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph square root, cube root, and piecewise defined functions, including step functions and absolute value functions. Please see Pearson Integrated Mathematics, Mathematics II Common Core: SE: 919 929, 930 937 TG: 884 892, 893 901 F IF 7c. F IF 7e. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. SE: 241 244, 256 264, 301 302, 313 321, 322 329 TG: 239 244, 257 265, 299 300, 309 317, 318 325 SE: 505 514, 515 524, 525 534, 542 550, 551 552, 597 606, 607 609, 610 618, 619 627, 628 637, 641 650 TG: 487 495, 496 504, 505 514, 522 529, 530, 574 583, 584 585, 586 593, 594 600, 601 609, 612 621 California Common Core State s Map: Mathematics III Page 9
F IF 8. Language 1 Y N Reviewer Notes Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Please see Pearson Integrated Mathematics, Mathematics II Common Core: SE: 750 759, 760 767 F IF 9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). TG: 725 732, 733 740 SE: 160 163, 322 326, 385 392, 488 494 TG: 161 165, 318 322, 379 385, 466 470 Domain BUILDING FUNCTIONS Build a function that models a relationship between two quantities. [Include all types of functions studied.] F BF 1b. Write a function that describes a relationship between two quantities. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Build new functions from existing functions. [Include simple, radical, rational, and exponential functions; emphasize common effect of each transformation across function types. Please see Pearson Integrated Mathematics, Mathematics II Common Core: SE: 791799, 938 944 TG: 759 766, 902 907 California Common Core State s Map: Mathematics III Page 10
F BF 3. F BF 4a. Domain F LE 4. Language 1 Y N Reviewer Notes Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = (x + 1)/(x 1) for x 1. LINEAR, QUADRATIC, AND EXPONENTIAL MODELS Construct and compare linear, quadratic, and exponential models and solve problems. For exponential models, express as a logarithm the solution to ab ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. [Logarithms as solutions for exponentials] SE: 81 87, 91 96, 151 156, 248 249, 322 326, 628 635 TG: 77 82, 87 91, 151 156, 250, 318 322, 601 606 SE: 477 487, 525 534 TG: 457 465, 505 514 SE: 542 547, 553 560 TG: 522 526, 531 534 F LE 4.1 Prove simple laws of logarithms. CA SE: 534 (#55 57), 535 537 TG: 513 (#55 57), 515 517 California Common Core State s Map: Mathematics III Page 11
F LE 4.2 Language 1 Y N Reviewer Notes Use the definition of logarithms to translate between logarithms in any base. CA Students use the definition of logarithms to evaluate expressions and to translate equations between logarithmic and exponential form. They use the Change of Base formula to rewrite logarithms using different bases. F LE 4.3 Understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. CA SE: 525 526, 533 534, 537 538, 540 541, 542 550, 553 561, 568 569 TG: 506, 512 513, 517 518, 520, 523 528, 532 536, 542 543 SE: 526 527, 531 533, 535 541, 542 550, 553 561, 568 569 TG: 507, 511, 515 521, 523 528, 532 536, 542 543 Domain TRIGONOMETRIC FUNCTIONS Extend the domain of trigonometric functions using the unit circle. F TF 1. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. SE: 581 586, 589 594 TG: 557 561, 566 570 California Common Core State s Map: Mathematics III Page 12
F TF 2. Language 1 Y N Reviewer Notes Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. SE: 581 586, 589 594, 597 603, 610 615, 619 623, 641 646 TG: 557 561, 566 570, 574 579, 586 590, 594 597, 612 617 F TF 2.1 F TF 5. Graph all 6 basic trigonometric functions. CA Model periodic phenomena with trigonometric functions. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. SE: 597 606, 607 609, 610 618, 619 6627, 628 637, 638 640, 644 645, 648 650, 651, 680 682 TG: 575 583, 584 585, 586 593, 594 600, 601 609, 610 611, 616, 618 621, 622 623, 650 652 SE: 597 603, 610 615, 619 623, 628 635, 641 646 TG: 574 579, 586 590, 594 597, 601 606, 612 617 GEOMETRY Domain SIMILARITY, RIGHT TRIANGLES, AND TRIGONOMETRY Apply trigonometry to general triangles. G SRT 9. (+) Derive the formula A = 1/2 ab sin(c) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. SE: 660 667 TG: 632 639 California Common Core State s Map: Mathematics III Page 13
G SRT 10. Language 1 Y N Reviewer Notes (+) Prove the Laws of Sines and Cosines and use them to solve problems. SE: 660 667, 670 678 TG: 632 639, 641 647 G SRT 11. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non right triangles (e.g., surveying problems, resultant forces). SE: 660 667, 668 669, 670 678 TG: 632 639, 640, 641 647 Domain G GPE 3.1 Domain EXPRESSING GEOMETRIC PROPERTIES WITH EQUATIONS Translate between the geometric description and the equation for a conic section. Given a quadratic equation of the form ax 2 + by 2 + cx + dy + e = 0, use the method for completing the square to put the equation into standard form; identify whether the graph of the equation is a circle, ellipse, parabola, or hyperbola and graph the equation. [In Mathematics III, this standard addresses only circles and parabolas.] CA GEOMETRIC MEASUREMENT AND DIMENSION Visualize relationships between twodimensional and three dimensional objects. For related content, please see: SE: 212 221 TE: 210 220 California Common Core State s Map: Mathematics III Page 14
G GMD 4. Language 1 Y N Reviewer Notes Identify the shapes of two dimensional crosssections of three dimensional objects, and identify three dimensional objects generated by rotations of two dimensional objects. SE: 774 780, 794 797 TG: 738 742, 754 756 Domain MODELING WITH GEOMETRY Apply geometric concepts in modeling situations. G MG 1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). SE: 755 760, 765 769, 785 789, 823 827, 832 835 TG: 724 727, 731 734, 746 749, 782 786, 790 792 G MG 2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). SE: 747 750, 755 760, 785 789 TG: 717 720, 724 727, 746 749 G MG 3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). SE: 747 750, 755 760, 785 789 TG: 717 720, 724 727, 746 749 California Common Core State s Map: Mathematics III Page 15
Domain S ID 4. Domain S IC 1. S IC 2. Language 1 Y N Reviewer Notes STATISTICS AND PROBABILITY INTERPRETING CATEGORICAL AND QUANTITATIVE DATA Summarize, represent, and interpret data on a single count or measurement variable. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. MAKING INFERENCES AND JUSTIFYING CONCLUSIONS Understand and evaluate random processes underlying statistical experiments. Understand statistics as a process for making inferences about population parameters based on a random sample from that population. Decide if a specified model is consistent with results from a given data generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? Make inferences and justify conclusions from sample surveys, experiments, and observational studies. SE: 13 14, 34 38 TG: 13, 33 37 SE: 22 25 TG: 22 25 SE: 29 33 TG: 30 31 California Common Core State s Map: Mathematics III Page 16
S IC 3. Language 1 Y N Reviewer Notes Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. SE: 22 25 TG: 22 25 S IC 4. S IC 5. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. SE: 42 45 TG: 41 42 SE: 46 49 TG: 43 44 S IC 6. Evaluate reports based on data. SE: 3 8, 15 18, 22 25 Domain S MD 6. S MD 7. USING PROBABILITY TO MAKE DECISIONS Use probability to evaluate outcomes of decisions. [Include more complex situations.] (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). TG: 5 9, 15 18, 22 25 For related content, please see: Mathematics III SE: 29 33 TG: 30 32 For related content, please see: Mathematics III SE: 46 49 TG: 43 44 California Common Core State s Map: Mathematics III Page 17
MP 1. Language 1 Y N Reviewer Notes MATHEMATICAL PRACTICES Make sense of problems and persevere in solving them. Pearson s Integrated High School Mathematics, Mathematics III Common Core five step lesson design raises student achievement. Every step in the lesson connects to the s for Mathematical Practice. Students make sense of problems and persevere in solving them by: Considering or attempting multiple entry points Analyzing information (givens, constraints, relationships, goals) Making conjectures and plan a solution pathway Using objects, drawings, and diagrams to solve problems Monitoring progress and change course as necessary Checking answers to problems and ask, Does this make sense? SE: 10, 20, 27, 29 33, 39, 42 45, 46 49, 52, 61, 71, 79 80, 89, 97, 108, 117, 124, 126 130, 133, 141, 148 TG: 11, 20, 27, 30 32, 38, 41 42, 43 44, 48, 58, 60, 66, 69, 74 75, 84, 87, 93, 104, 112, 120, 124 127 California Common Core State s Map: Mathematics III Page 18
Language 1 Y N Reviewer Notes MP 2. Reason abstractly and quantitatively. Pearson s Integrated High School Mathematics, Mathematics III Common Core five step lesson design raises student achievement. Every step in the lesson connects to the s for Mathematical Practice. Students reason abstractly and quantitatively through: Making sense of quantities and relationships in problem situations Representing abstract situations symbolically Creating a coherent representation of the problem Translating from contextualized to generalized or vice versa Flexibly use properties of operations SE: 12, 27, 28, 110 114, 124, 138 139, 141 142, 148, 158, 159, 184, 200 201, 211, 255, 272, 282 286, 289, 290 294, 299 300, 301 302 TG: 11, 26, 28, 52, 53, 107 111, 120, 132, 135, 137 138, 146, 156, 159, 183, 208, 255, 272, 282 286, 287, 289 291 California Common Core State s Map: Mathematics III Page 19
MP 3. Language 1 Y N Reviewer Notes Construct viable arguments and critique the reasoning of others. Pearson s Integrated High School Mathematics, Mathematics III Common Core five step lesson design raises student achievement. Every step in the lesson connects to the s for Mathematical Practice. Students construct viable arguments and critique the reasoning of others while: Using definitions and previously established causes/effects (results) in constructing arguments Making conjectures and use counterexamples to build a logical progression of statements to explore and support their ideas Listening to or read the arguments of others Asking probing questions to other students SE: 10 11, 20 21, 27, 39 40, 61 62, 70 72, 79 80, 89 90, 97 98, 108 109, 116 118, 124, 132 133, 141 142, 158, 164 166, 176 177, 183 184, 191, 200 TG: 10 11, 19 20, 22, 26, 28, 33, 37 39, 51, 58, 65 67, 73, 75, 83 85, 92 94, 103, 105, 112 113, 121, 129, 137 138 California Common Core State s Map: Mathematics III Page 20
MP 3.1 Language 1 Y N Reviewer Notes Students build proofs by induction and proofs by contradiction. CA [for higher mathematics only]. MP 4. Model with mathematics. Pearson s Integrated High School Mathematics, Mathematics III Common Core five step lesson design raises student achievement. Every step in the lesson connects to the s for Mathematical Practice. Students model with mathematics by: Determining equation that represents a situation Illustrating mathematical relationships using diagrams, twoway tables, graphs, flowcharts, and formulas Applying assumptions to make a problem simpler Checking to see if an answer makes sense within the context of a situation and change a model when necessary N/A SE: 11 12, 20, 28, 33, 39, 46 49, 52, 62, 72, 80, 89, 98, 109, 117 118, 124, 133 134, 141 142, 148, 158, 165 TG: 11, 20, 28, 32, 38, 43 44, 48, 58, 67, 75, 84, 94, 105, 113, 120, 130, 137 138, 146, 157, 166 California Common Core State s Map: Mathematics III Page 21
Language 1 Y N Reviewer Notes MP 5. Use appropriate tools strategically. Pearson s Integrated High School Mathematics, Mathematics III Common Core five step lesson design raises student achievement. Every step in the lesson connects to the s for Mathematical Practice. Students use appropriate tools strategically by: Choosing tools that are appropriate for the task. Examples: Manipulatives, Calculators, Rulers, and Digital Technology Using technological tools to visualize the results of assumptions, explore consequences, and compare predictions with data Identifying relevant external math resources (digital content on a website) and use them to pose or solve problems SE: 7, 17, 41, 90, 98, 99 101, 109, 139, 141 142, 160, 180, 184, 208, 248 249, 268, 297, 302, 372 375, 397 400, 413 417 TG: 9, 17, 39, 52, 85, 94, 96 97, 105, 138, 162, 179 181, 206, 250, 269, 294, 300, 368 369, 390 391, 400 402, 530 California Common Core State s Map: Mathematics III Page 22
Language 1 Y N Reviewer Notes MP 6. Attend to precision. Pearson s Integrated High School Mathematics, Mathematics III Common Core five step lesson design raises student achievement. Every step in the lesson connects to the s for Mathematical Practice. Students attend to precision while: Communicating precisely using appropriate terminology Specifying units of measure and provide accurate labels on graphs Expressing numerical answers with appropriate degree of precision Providing carefully formulated explanations SE: 29 33, 42 45, 52, 61, 183 184, 200 202, 212 213, 236, 250 252, 274 278, 325, 422, 425 427, 506 508, 576, 589 590, 696 699, 703 707, 794 796, 871 TG: 5, 30 32, 41 42, 48, 51, 57, 183, 199 200, 210 211, 236, 251 253, 274 278, 321, 408, 412, 414, 486, 548, 566 567, 667 California Common Core State s Map: Mathematics III Page 23
Language 1 Y N Reviewer Notes MP 7. Look for and make use of structure. Pearson s Integrated High School Mathematics, Mathematics III Common Core five step lesson design raises student achievement. Every step in the lesson connects to the s for Mathematical Practice. Students look for and make use of structure through: Looking for patterns or structure, recognizing that quantities can be represented in different ways Using knowledge of properties to efficiently solve problems Viewing complicated quantities both as single objects or compositions of several objects SE: 72, 81 82, 102, 119 121, 152 156, 159, 167 168, 222 224, 290 294, 309 312, 322 325, 354 355, 432 434, 440 441, 450 451, 515 517, 815 816, 821 822, 839 842, 855 TG: 52, 67, 77 78, 98, 115 117, 149, 152 156, 158, 169, 221 223, 289 291, 307, 318, 347 348, 420, 427, 435, 496, 771, 781 California Common Core State s Map: Mathematics III Page 24
MP 8. Language 1 Y N Reviewer Notes Look for and express regularity in repeated reasoning. Pearson s Integrated High School Mathematics, Mathematics III Common Core five step lesson design raises student achievement. Every step in the lesson connects to the s for Mathematical Practice. Students look for and express regularity in repeated reasoning when: Noticing repeated calculations and look for general methods and shortcuts Continually evaluating the reasonableness of intermediate results while attending to details and make generalizations based on findings SE: 15 17, 138 139, 184, 193 194, 274 278, 282 286, 290 294, 303 305, 336, 505, 510, 573 575, 755 760, 863, 871 TG: 15, 135, 183, 194 196, 274 278, 282 286, 289 291, 301, 332, 336, 486, 488, 548, 705, 821, 829 California Common Core State s Map: Mathematics III Page 25