A Correlation of Pearson Integrated High School Mathematics Mathematics II Common Core, 2014 to the California Common Core State s for Mathematics s Map Mathematics II Copyright 2017 Pearson Education, Inc. or its affiliate(s). All rights reserved
California Common Core State s for Mathematics s Map Mathematics II 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 REAL NUMBER SYSTEM. Extend the properties of exponents to rational exponents. N RN 1. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5 1/3 to be the cube root of 5 because we want (5 1/3 ) 3 = 5 (1/3)3 to hold, so (5 1/3 ) 3 must equal 5. N RN 2. Rewrite expressions involving radicals and rational exponents using the properties of exponents. SE: 595 603, 606 612, 615 619, 624 628 TG: 585 590, 593 597, 600 603, 608 611 SE: 624 628 TG: 608 611 1 For some standards that appear in multiple courses (e.g., Mathematics I and Mathematics II), 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 II Page 2
N RN 3. Language 1 Y N Reviewer Notes Use properties of rational and irrational numbers. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. SE: 631 633 TG: 614 Domain THE COMPLEX NUMBER SYSTEM N CN 1. Perform arithmetic operations with complex numbers. [i 2 as highest power of i] Know there is a complex number i such that i 2 = 1, and every complex number has the form a + bi with a and b real. SE: 778 787 TG: 749 754 N CN 2. N CN 7. Use the relation i 2 = 1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Use complex numbers in polynomial identities and equations. [Quadratics with real coefficients] Solve quadratic equations with real coefficients that have complex solutions. SE: 778 787 TG: 749 754 SE: 778 787 TG: 749 754 California Common Core State s Map: Mathematics II Page 3
N CN 8. Language 1 Y N Reviewer Notes (+) Extend polynomial identities to the complex numbers. For example, rewrite x 2 + 4 as (x + 2i)(x 2i). Please see Pearson Integrated Mathematics, Mathematics III Common Core: SE: 282 288, 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. Please see Pearson Integrated Mathematics, Mathematics III Common Core: SE: 295 300 TG: 292 297 ALGEBRA I Domain SEEING STRUCTURE IN EXPRESSIONS A SSE 1a. A SSE 1b. Interpret the structure of expressions. [Quadratic and exponential] Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, and coefficients. 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. For example, interpret P(1 + r) n as the product of P and a factor not depending on P. SE: 791 795 TG: 759 763 SE: 454 457, 671 674, 678 681, 685 690, 694 697, 791 795 TG: 452 455, 651 654, 658 660, 664 668, 672 674, 759 763 California Common Core State s Map: Mathematics II Page 4
A SSE 2. Language 1 Y N Reviewer Notes Use the structure of an expression to identify ways to rewrite it. For example, see x 4 y 4 as (x 2 ) 2 (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 y 2 )(x 2 + y 2 ). SE: 671 674, 678 681, 685 690, 694 697 TG: 651 654, 658 660, 664 668, 672 674 A SSE 3a. Write expressions in equivalent forms to solve problems. [Quadratic and exponential] Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Factor a quadratic expression to reveal the zeros of the function it defines. SE: 750 756, 760 764 TG: 725 729, 733 736 A SSE 3b. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. SE: 750 756, 760 764 TG: 725 729, 733 736 California Common Core State s Map: Mathematics II Page 5
A SSE 3c. Domain A APR 1. Language 1 Y N Reviewer Notes Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15 t can be rewritten as (1.15 1/12 ) 12t 1.012 12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. ARITHMETIC WITH POLYNOMIALS AND RATIONAL EXPRESSIONS Perform arithmetic operations on polynomials. [Polynomials that simplify to quadratics] 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. Domain CREATING EQUATIONS A CDE 1. Create equations that describe numbers or relationships. 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: 760 764 TG: 733 736 SE: 639 643, 646 649, 653 658, 662 667 TG: 623 627, 630 633, 636 640, 643 647 SE: 740 743, 750 756, 768 774, 809 811, 915 918 TG: 717 720, 725 729, 741 745, 776 777, 882 883 California Common Core State s Map: Mathematics II Page 6
A CDE 2. Language 1 Y N Reviewer Notes Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. SE: 707 712 TG: 687 691 A CDE 4. Domain A REI 4a. A REI 4b. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [Include formulas involving quadratic terms.] REASONING WITH EQUATIONS AND INEQUALITIES Solve equations and inequalities in one variable. [Quadratics with real coefficients] Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p) 2 = q that has the same solutions. Derive the quadratic formula from this form. Solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. SE: 748 749 TG: 724 SE: 760 764, 768 774 TG: 733 736, 741 745 SE: 740 743, 750 756, 760 764, 768 774, 778 787 TG: 717 720, 725 729, 733 736, 741 745, 749 754 California Common Core State s Map: Mathematics II Page 7
A REI 7. Language 1 Y N Reviewer Notes Solve systems of equations. [Linearquadratic systems] Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = 3x and the circle x 2 + y 2 = 3. FUNCTIONS Domain INTERPRETING FUNCTIONS Interpret functions that arise in applications in terms of the context. [Quadratic] F IF 4. 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. F IF 5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. SE: 802 805 TG: 769 772 SE: 707 712, 732 735, 905 911, 919 926, 930 934 TG: 687 691, 710 713, 873 878, 884 889, 893 898 SE: 707 712, 732 735 TG: 687 691, 710 713 California Common Core State s Map: Mathematics II Page 8
F IF 6. Language 1 Y N Reviewer Notes 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: 727 730 TG: 707 708 F IF 7a. Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewisedefined] Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph linear and quadratic functions and show intercepts, maxima, and minima. SE: 707 712, 716 719, 720 722, 740 743 TG: 687 691, 697 698, 699 702, 717 720 F IF 7b. 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. SE: 716 719, 919 928, 930 934 TG: 697 698, 884 889, 893 898 California Common Core State s Map: Mathematics II Page 9
F IF 8a. 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. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. SE: 750 756, 760 764, 919 926 TG: 725 729, 733 736, 884 889 F IF 8b. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02) t, y = (0.97) t, y = (1.01) 12t, and y = (1.2) t/10, and classify them as representing exponential growth or decay. SE: 760 764, 905 911, 919 926 TG: 733 736, 873 878, 884 889 F IF 9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. SE: 720 722 TG: 699 702 California Common Core State s Map: Mathematics II Page 10
Language 1 Y N Reviewer Notes Domain BUILDING FUNCTIONS F BF 1a. Build a function that models a relationship between two quantities. [Quadratic and exponential] Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context. SE: 720 722, 955 959, 964 967, 971 975, 979 984 TG: 699 702, 921 925, 929 932, 936 939, 943 947 F BF 1b. Write a function that describes a relationship between two quantities. Combine standard function types using arithmetic operations. SE: 720 722, 791 795, 938 941 TG: 699 702, 759 763, 902 905 F BF 3. Build new functions from existing functions. [Quadratic, absolute value] 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. SE: 716 719, 905 911, 919 926, 930 934 TG: 697 698, 873 878, 884 889, 893 898 California Common Core State s Map: Mathematics II Page 11
F BF 4a. Language 1 Y N Reviewer Notes 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) =2x 3. Please see Pearson Integrated Mathematics, Mathematics III Common Core: SE: 477 487, 525 534 TG: 457 465, 505 514 Domain F LE 3. F LE 6. LINEAR, QUADRATIC, AND EXPONENTIAL MODELS Construct and compare linear, quadratic, and exponential models and solve problems. [Include quadratic] Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Interpret expressions for functions in terms of the situation they model. Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity. CA Please see Pearson Integrated Mathematics, Mathematics I Common Core: SE: 301 308 TG: 290 297 SE: 734, 738 739, 746 747, 759, 770 771, 798 799, 819, 822 823, 833, 835 TG: 712, 715, 722, 731, 743, 765, 783, 787, 799, 800 California Common Core State s Map: Mathematics II Page 12
Language 1 Y N Reviewer Notes Domain TRIGONOMETRIC FUNCTIONS Prove and apply trigonometric identities. F TF 8. Prove the Pythagorean identity sin 2 (θ) + cos 2 (θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. Please see Pearson Integrated Mathematics, Mathematics III Common Core: SE: 651 659 TG: 622 631 GEOMETRY Domain CONGRUENCE G CO 9. Prove geometric theorems. [Focus on validity of underlying reasoning while using variety of ways of writing proofs.] Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints, Please see Pearson Integrated Mathematics, Mathematics I Common Core: SE: 636 645, 660 669, 670 678, 679 685, 665 694, 795 802, 851 857, 894 903 TG: 616 623, 640 648, 649 657, 658 664, 665 672, 776 784, 837 843, 878 887 California Common Core State s Map: Mathematics II Page 13
G CO 10. Language 1 Y N Reviewer Notes Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 ; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Please see Pearson Integrated Mathematics, Mathematics I Common Core: SE: 686 694, 744 752, 753 760, 761 768, 787 794, 803 810, 811 819, 820 826, 827 836, 837 844, 904 911, 912 917 TG: 665 672, 724 732, 733 740, 741 748, 769 775, 785 793, 794 801, 802 809, 810 818, 819 827, 888 895, 896 903 G CO 11. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. Please see Pearson Integrated Mathematics, Mathematics I Common Core: SE: 858 867, 868 876, 877 885, 886 893, 904 911, 912 917 TG: 844 852, 853 860, 861 869, 870 877, 888 895, 896 903 California Common Core State s Map: Mathematics II Page 14
Domain G SRT 1a. Language 1 Y N Reviewer Notes SIMILARITY, RIGHT TRIANGLES, AND TRIGONOMETRY Understand similarity in terms of similarity transformations. Verify experimentally the properties of dilations given by a center and a scale factor: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. For related content, please see: SE: 390 392, 393 397 TG: 392 393, 394 397 G SRT 1b. G SRT 2. G SRT 3. Verify experimentally the properties of dilations given by a center and a scale factor: The dilation of a line segment is longer or shorter in the ratio given by the scale factor. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. Use the properties of similarity transformations to establish the Angle Angle (AA) criterion for two triangles to be similar. For related content, please see: SE: 390 392, 393 397 TG: 392 393, 394 397 SE: 401 406 TG: 402 406 SE: 401 406 TG: 402 406 California Common Core State s Map: Mathematics II Page 15
G SRT 4. Language 1 Y N Reviewer Notes Prove theorems involving similarity. [Focus on validity of underlying reasoning while using variety of formats.] Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. SE: 378 380, 381 385, 415 421 TG: 383, 384 387, 419 423 G SRT 5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. SE: 121 125, 129 133, 138 144, 148 150, 156 160, 165 170, 173 179, 199 203, 207 211, 223 227, 263 266, 270 277, 289 293, 298 301, 306 312,337 343, 348 353, 358 364, 369 373 TG: 127 131, 135 139, 144 148, 152 154, 160 164, 169 173, 177 181, 205 208, 212 216, 230 233, 273 276, 280 285, 297 301, 306 309, 314 318, 349 353, 357 361, 366 371, 375 379 G SRT 6. Define trigonometric ratios and solve problems involving right triangles. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. SE: 435 437 TG: 436 California Common Core State s Map: Mathematics II Page 16
G SRT 7. Language 1 Y N Reviewer Notes Explain and use the relationship between the sine and cosine of complementary angles. SE: 438 442 TG: 437 440 G SRT8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. SE: 415 421, 426 432, 438 442, 447 450 TG: 419 423, 428 432, 437 440, 445 448 G SRT 8.1 Derive and use the trigonometric ratios for special right triangles (30, 60, 90 and 45, 45, 90 ). CA Students explore properties of special right triangles, and apply these properties to find the area of a regular hexagon and to discover the relationships between the lengths of an apothem, a radius, and a side in an equilateral triangle. Students explore the trigonometric ratios and apply them to solve problems involving angles of elevation and angles of depression. SE:426 434, 435 437, 438 446, 447 453, 458 459, 462 TG: 428 435, 436, 437 444, 445 451, 455 456, 460 California Common Core State s Map: Mathematics II Page 17
Domain CIRCLES Language 1 Y N Reviewer Notes Understand and apply theorems about circles. G C 1. Prove that all circles are similar. Please see Pearson Integrated Mathematics, Mathematics III Common Core: SE: 855 864 TG: 815 823 G C 2. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. Please see Pearson Integrated Mathematics, Mathematics III Common Core: SE: 855 864, 876 885, 886 896, 897 905, 906 914 TG: 815 823, 834 842, 843 852, 853 861, 862 870 G C 3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Please see Pearson Integrated Mathematics, Mathematics III Common Core: SE: 737 746, 897 905 TG: 707 716, 853 861 California Common Core State s Map: Mathematics II Page 18
G C 4. Language 1 Y N Reviewer Notes (+) Construct a tangent line from a point outside a given circle to the circle. Please see Pearson Integrated Mathematics, Mathematics I Common Core: SE: 495 504, 507 514, 515 522 TG: 478 486, 488 495, 496 502 G C 5. Domain G CPE 1. Find arc lengths and areas of sectors of circles. [Radian introduced only as unit of measure] Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians. CA EXPRESSING GEOMETRIC PROPERTIES WITH EQUATIONS Translate between the geometric description and the equation for a conic section. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. Please see Pearson Integrated Mathematics, Mathematics III Common Core: SE: 855 864, 865 872, 873 875 TG: 815 823, 824 831, 832 833 SE: 720 726 TG: 699 706 California Common Core State s Map: Mathematics II Page 19
G CPE 2. Language 1 Y N Reviewer Notes Derive the equation of a parabola given a focus and directrix. Please see Pearson Integrated Mathematics, Mathematics III Common Core: SE: 212 221 G CPE 4. G CPE 6. Domain G GMD 1. Use coordinates to prove simple geometric theorems algebraically. Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2). [Include simple circle theorems.] Find the point on a directed line segment between two given points that partitions the segment in a given ratio. GEOMETRIC MEASUREMENT AND DIMENSION Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri s principle, and informal limit arguments. TG: 210 220 SE: 814 823, 824 832 TG: 779 789, 790 797 SE: 369 377 TG: 375 382 SE: 533 536, 559 565, 569 571, 572 576 TG: 533 534, 554 558, 562, 563 566 California Common Core State s Map: Mathematics II Page 20
G GMD 3. Language 1 Y N Reviewer Notes Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. SE: 559 565, 572 576, 581 586 TG: 554 558, 563 566, 570 574 G GMD 5. Know that the effect of a scale factor k greater than zero on length, area, and volume is to multiply each by k, k², and k³, respectively; determine length, area and volume measures using scale factors. CA Students explore scale factors in the form of the magnitudes of dilations. Areas and volumes of similar solids are explored in Integrated Mathematics III (Lesson 10 6). SE: 393 400, 401 408, 409 411, 561 562(Problem 2), 566 567(#22), 579 580(#22), 587(#13) TG: 394 401, 402 409, 411 413, 556 (Problem 2), 559 (#22), 568 (#22), 574 (#13) G GMD 6. Verify experimentally that in a triangle, angles opposite longer sides are larger, sides opposite larger angles are longer, and the sum of any two side lengths is greater than the remaining side length; apply these relationships to solve real world and mathematical problems. CA SE: 239 248, 249 256, 259 TG: 246 254, 255 263, 267 California Common Core State s Map: Mathematics II Page 21
Domain S CP 1. Language 1 Y N Reviewer Notes STATISTICS AND PROBABILITY CONDITIONAL PROBABILITY AND THE RULES OF PROBABILITY Understand independence and conditional probability and use them to interpret data. [Link to data from simulations or experiments.] Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ( or, and, not ). SE: 841 844, 865 870 TG: 809 812, 832 836 S CP 2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. SE: 865 870 TG: 832 836 S CP 3. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. SE: 880 886 TG: 848 852 California Common Core State s Map: Mathematics II Page 22
S CP 4. Language 1 Y N Reviewer Notes Construct and interpret two way frequency tables of data when two categories are associated with each object being classified. Use the two way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. SE: 848 851, 873 876, 880 886 TG: 816 819, 840 843, 848 852 S CP 5. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. SE: 848 851, 865 870, 880 886 TG: 816 819, 832 836, 848 852 S CP 6. Use the rules of probability to compute probabilities of compound events in a uniform probability model. Find the conditional probability of A given B as the fraction of B s outcomes that also belong to A, and interpret the answer in terms of the model. SE: 865 870 TG: 832 836 California Common Core State s Map: Mathematics II Page 23
S CP 7. Apply the Addition Rule, P(A or B) = P(A) + P(B) P(A and B), and interpret the answer in terms of the model. Language 1 Y N Reviewer Notes For related content, please see: SE: 880 884 TG: 848 852 S CP 8. S CP 9. (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B A) = P(B)P(A B), and interpret the answer in terms of the model. (+) Use permutations and combinations to compute probabilities of compound events and solve problems. SE: 864 872 TG: 832 839 SE: 855 864 TG: 824 831 Domain USING PROBABILITY TO MAKE DECISIONS S MD 6. Use probability to evaluate outcomes of decisions. [Introductory; apply counting rules.] (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). For related content, please see Pearson Integrated Mathematics, Mathematics III Common Core: SE: 29 33 TG: 30 32 S MD 7. (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). For related content, please see Pearson Integrated Mathematics, Mathematics III Common Core: SE: 46 49 TG: 43 44 California Common Core State s Map: Mathematics II Page 24
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 II 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: 9 10, 16 17, 39, 46 47, 55, 62, 70 71, 80 81, 89 90, 96, 104 105, 113, 118, 127 128, 135, 145 147, 152 153, 162 163, 170 171, 179 180, 181 TG: 10, 18, 41, 49, 57, 64, 73 74, 82, 91, 98, 106, 114 115, 122, 132, 139 140, 149 150, 155 156, 165, 173 174, 177, 181 183, 185 California Common Core State s Map: Mathematics II Page 25
Language 1 Y N Reviewer Notes MP 2. Reason abstractly and quantitatively. Pearson s Integrated High School Mathematics, Mathematics II 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: 407, 462, 485, 604 605, 621 623, 651 652, 661, 668, 670, 683 684, 692 693, 699 700, 704, 715, 726, 745 746, 758 759, 766, 796 797, 847 TG: 36, 125, 204, 332, 247, 407, 418, 462, 484, 585, 590 591, 593, 604 606, 630, 633 634, 641, 647, 649, 661 662, 668 670, 675 676, 682, 695, 705, 720 721, 730 731, 738, 738, 763 764, 808, 814, 816, 848, 899 California Common Core State s Map: Mathematics II Page 26
MP 3. Language 1 Y N Reviewer Notes Construct viable arguments and critique the reasoning of others. Pearson s Integrated High School Mathematics, Mathematics II 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: 7 10, 15 18, 23 25, 30 32, 38, 45 47, 54 57, 62, 70 71, 80 81, 88 90, 96 97, 104 105, 113 114, 127 128, 135 137, 145 147, 152 153, 154 155, 161 164 TG: 9, 11, 17, 19, 25 26, 32 33, 40, 44, 48 50, 52, 57 58, 64, 72 74, 81 83, 85, 90 92, 94, 97, 99, 105 106, 115 116, 132 133, 139, 141 142, 149 150, 152, 155 156, 159, 164 167 California Common Core State s Map: Mathematics II Page 27
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 II 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: 17 18, 25, 32 33, 40, 55, 62, 70 71, 97, 118, 126, 136, 162 164, 179 180, 190 191, 196, 205 206, 222, 238, 260, 268 269 TG: 19, 27, 34, 42, 57, 64, 73, 99, 122, 132, 140, 165 166, 182, 192 193, 200, 209 210, 228, 243, 268, 277 278 California Common Core State s Map: Mathematics II Page 28
Language 1 Y N Reviewer Notes MP 5. Use appropriate tools strategically. Pearson s Integrated High School Mathematics, Mathematics II 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 10, 29, 107 114, 154 155, 163 164, 206, 213, 221, 230 231, 367, 378 380, 460, 534 536, 715 TG: 5, 9 11, 32, 109 116, 159, 166 167, 203, 210, 217 218, 227, 235 236, 373, 383, 457, 534, 694 California Common Core State s Map: Mathematics II Page 29
Language 1 Y N Reviewer Notes MP 6. Attend to precision. Pearson s Integrated High School Mathematics, Mathematics II 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: 54, 65 66, 72 73, 100 101, 118, 128, 263 264, 306 307, 339 340, 350, 438 439, 483, 557, 566, 587, 592, 645, 714, 725, 872 TG: 21, 29, 57, 67 68, 76, 101, 122, 133, 272, 314, 349, 357, 437, 445, 481, 552, 559, 575, 580, 628 California Common Core State s Map: Mathematics II Page 30
Language 1 Y N Reviewer Notes MP 7. Look for and make use of structure. Pearson s Integrated High School Mathematics, Mathematics II 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: 9, 16 17, 24 25, 33, 87 88, 334, 346 347, 558, 587, 605, 621, 623, 661, 669, 700, 725, 759, 777, 796, 799 TG: 9, 13, 18, 26, 34, 90, 126 127, 135, 144, 221, 230, 344, 355, 552, 575, 591, 604, 606, 641, 649 California Common Core State s Map: Mathematics II Page 31
MP 8. Language 1 Y N Reviewer Notes Look for and express regularity in repeated reasoning. Pearson s Integrated High School Mathematics, Mathematics II 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: 207, 220, 228, 424, 475, 483, 595, 606 613, 615 623, 624 630, 646 652, 653 661, 662 670, 768 777, 990 992 TG: 212, 226, 234, 418, 425, 473, 481, 583, 586, 593 597, 601 606, 609 612, 622, 631 634, 637 641, 644 649, 741 747, 953 California Common Core State s Map: Mathematics II Page 32