# AGS Math Algebra 2 Correlated to Kentucky Academic Expectations for Mathematics Grades 6 High School

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1 AGS Math Algebra 2 Correlated to Kentucky Academic Expectations for Mathematics Grades 6 High School Copyright 2008 Pearson Education, Inc. or its affiliate(s). All rights reserved

2 AGS Math Algebra 2 Grade 6 Number Properties and Operations Middle grades students understand fractions, decimals, percents and integers, compare them and locate their relative positions on a number line. They develop and use proportional reasoning to solve problems. They work with large numbers and small numbers. They use factors, multiples and prime factorizations. They perform arithmetic operations with fractions, decimals and integers, use properties in computation, develop fluency and develop strategies to estimate the result of operations on rational numbers. Number Sense Kentucky Academic Expectations for Mathematics PAGE(S) WHERE TAUGHT MA MA MA MA MA MA MA MA Students will provide examples of and identify fractions, decimals and percents. DOK 1 Students will describe and provide examples of representations of numbers (whole numbers, fractions in simplest form, mixed numbers, decimals, percents) and operations in a variety of equivalent forms using models, diagrams, and symbols (e.g., number lines, 10 by 10 grids, rectangular arrays, number sentences), based on real-world and mathematical problems. Students will convert between any two of the following numbers: fractions, decimals, and percents (less than or equal to 100%); and will compare and order these numbers. DOK 2 Estimation Students will estimate to solve real-world and mathematical problems with whole numbers, fractions, decimals and percents, checking for reasonable and appropriate computational results. DOK 2 Number Operations Students will add, subtract, multiply and divide whole numbers, fractions and decimals to solve real-world problems and apply order of operations to simplify numerical expressions. DOK 2 Students will explain how operations (addition and subtraction; multiplication and division) are inversely related. Ratios and Proportional Reasoning Students will describe and apply ratios to solve realworld problems. DOK 2 Properties of Numbers and Operations Students will identify and apply prime numbers, composite numbers, prime factorization, factors, multiples and divisibility to solve real-world and mathematical problems (e.g., prime factorization to determine a least common multiple [LCM] or greatest common factor [GCF]). DOK 2 TE/SE: 2-3, 50, 104, , 177, 183, 191, , 223, 242, 373, 456, 458, 462, 466 TE/SE: 2-3, 6, 8-9, 11-12, 22-23, 48-51, 59-60, , 191, , 223, 242, 373, 456, 462 TE/SE: 2-3, 15-18, 19-21, 22-23, 50, 104, , 191, , 223, , 242, 373, 456, 462 TE/SE: 115, 170, 192, 225, 236, 247 (TE), 277, 453, 456 TE/SE: 2-3, 6, 8-9, 11-12, 40-41, 48-51, 59-60, 84-85, 96, , , 191, , 373, 462 TE/SE: 6-7, 8-10, 11-14, 17, 26-27, 30, 75-78, 89-90, 102, , 224, 226, , , 534 TE/SE: 49, 51, 58, 66, 171, , TE/SE: 75, 77, 79, 82, 170, Grade 6 2 of 23

3 MA AGS Math Algebra 2 Grade 6 Students will identify the use of properties (commutative properties of addition and multiplication, the associative properties of addition and multiplication and the identity properties for addition and multiplication) to simplify numerical expressions. DOK 1 TE/SE: 4-5, 6-7, 8-10, 11-14, 15-16, 19, 24-25, 72-74, 75-78, 81, , 224, , , Measurement Students continue to measure and estimate measurements including fractions and decimals. They use formulas to find perimeter, area, circumference and volume. They use rulers and protractors. They use US Customary and metric units of measurement. MA MA MA MA Measuring Physical Attributes Students will measure lengths (to the nearest eighth of an inch or the nearest centimeter) and will determine and use in real-world and mathematical problems: area and perimeter of triangles; area and perimeter of quadrilaterals (rectangles, squares); (using the Pythagorean theorem will not be required as a strategy) and area and perimeter of compound figures composed of triangles and quadrilaterals. DOK 2 Students will estimate measurements in standard units including fractions and decimals. Students will explain how measurements and measurement formulas are related or different (perimeter and area of rectangles). Systems of Measurement Students will convert units within the same measurement system and use these units to solve real-world problems. TE/SE: 42, 78, , 144, , 209, 226, 479 TE/SE: 253, , 453, 456, , TE/SE: , , 157, , 174, 226 TE/SE: , , , , , , , Geometry Middle grades students expand analysis of two-dimensional shapes and three-dimensional shapes. They translate shapes in a coordinate plane. They extend work with congruent and similar figures, including proportionality. They use the Pythagorean theorem. MA MA MA Shapes and Relationships Students will describe and provide examples of the basic geometric elements (points, rays, lines, segments, angles [acute, right, obtuse], planes, radius, diameter, circumference). DOK 2 Students will describe, and provide examples of the elements (e.g., sides, vertices, angles, congruent parts) of two-dimensional figures (circles, triangles, quadrilaterals, regular polygons), and will apply these elements and figures to solve real-world and mathematical problems. DOK 2 Students will describe, provide examples of, and identify elements (e.g., vertices, angles, faces, edges, congruent parts) of common three-dimensional figures (spheres, cones, cylinders, prisms, and pyramids). TE/SE: 28-29, 64-65, , , , 174, , , , , , , , , TE/SE: , , , 174, , 204, , 226, 254, 257, , , 538 TE/SE: , 209, 226, , , , 485 Grade 6 3 of 23

4 MA MA MA MA AGS Math Algebra 2 Grade 6 Students will identify and describe congruent figures, and will apply congruent figures to solve real-world and mathematical problems. DOK 2 Students will identify similar figures and apply similar figures to solve real-world and mathematical problems. Transformations of Shapes Students will describe, provide examples of, and apply line symmetry to real-world and mathematical problems Students will: reflect figures across a horizontal or vertical line in the first quadrant; translate figures in a plane in the first quadrant and determine the coordinates of the image after transformation in the first quadrant. DOK 2 MA Students will identify rotations of figures in the plane (90 and 180 ). MA Coordinate Geometry Students will identify and graph ordered pairs on a positive coordinate system (Quadrant I), correctly identifying the origin, axes and ordered pairs; and will apply graphing in the coordinate system to solve realworld and mathematical problems. DOK 2 Students explore the relationships between congruent chords, arcs, and central angles in a circle and congruent angles associated with parallel lines and a transversal. TE/SE: 64-65, TE/SE: , 317 TE/SE: , TE/SE: 45, 48-49, 54, 115, , , TE/SE: 48, TE/SE: 36-37, 45-47, 48-50, 52-53, 54-57, 61-63, 64-65, 66, , , , , , , Data Analysis and Probability Middle grades students extend the early development of data representations and examine the appropriateness of graphs and representations of data. They examine central tendencies and dispersion. They develop organized approaches to counting and use experimental and theoretical probabilities MA MA MA MA MA Grade 6 4 of 23 Representations of Data Sets Students will analyze and make inferences from data displays (drawings, tables/charts, pictographs, bar graphs, circle graphs, line plots, Venn diagrams, line graphs, stem-and-leaf plots). DOK 3 Students will explain how different representations of data (e.g., tables, graphs, diagrams, plots) are related. Students will determine and construct appropriate data displays (bar graphs, line plots, Venn diagrams, tables, line graphs), and will explain why the type of display is appropriate for the data. DOK 2 Characteristics of Data Sets Students will determine and apply the mean, median, mode and range of a set of data. DOK 2 Probability Students will describe or determine (e.g., tables, tree diagrams) the sample space of an event for a realworld or mathematical situation. DOK 2 TE/SE: 126, , 466, 468, 495 TE/SE: , 466, 468, 495 TE/SE: , 466, 468, 495 TE/SE: , 469, 495 TE/SE: , , , , , 398, ,

5 MA AGS Math Algebra 2 Grade 6 Students will determine single event probabilities TE/SE: 378 (TE), 462 (TE) based on the results of an experiment and will make inferences based on the data. DOK 3 MA Students will explore the theoretical probability of simple events. TE/SE: , 401, 491 Algebraic Thinking Middle grades students extend pattern work to include arithmetic sequences. They use linear functions and linear equations. They plot rational number pairs in the Cartesian plane. They simplify algebraic and numeric expressions. They explore the effects of change on related variables. They use and solve two-step single variable equations and inequalities. MA MA MA MA MA MA MA MA Patterns, Relations and Functions Students will extend, describe rules for patterns and find a missing term in a pattern from real-world and mathematical problems. DOK 3 Students will create tables for functions and will apply the tables to solve real-world problems. DOK 2 Students will describe, define, provide examples of, and apply to real-world and mathematical problems functions using tables, graphs and verbal rules. Students will explain how tables, graphs and patterns relate to each other. Students will explain how the change in one quantity affects change in another quantity (e.g., in tables or graphs, input/output tables). Variables, Expressions and Operations Students will substitute values for variables (up to two different variables) and evaluate algebraic expressions. DOK 2 Students will describe, define and provide examples of variables and expressions with a missing value based on real-world and mathematical problems Equations and Inequalities Students will model and solve real-world and mathematical problems with simple equations and inequalities (e.g., 8x = 4, x+2 > 5). DOK 2 TE/SE: , , , , 416, TE/SE: 45, 66, , , 242, 246, 252, 416, 421, 425 TE/SE: 36-38, 39-42, 45-47, 54-58, 67, , 236, , , 248, 258, , , 492 TE/SE: 36-38, 45-47, 54-58, 67, , 236, , , 248, , , 492 TE/SE: 39-42, 45-47, 54-58, 67, , 236, , , 248, 258, , , , , TE/SE: 40-41, 48-49, 59, 84-85, 89-91, 94, 96, , , , 192, 195, 200, 214, 242 TE/SE: 2-3, 6-14, 17-18, 24-27, 30-33, 40-41, 48-49, 59, 79-85, , , , 192, 195, 200 TE/SE: 2-3, 6-7, 8-10, 11-14, 17-18, 24-25, 26-27, 30, 31-33, 79-85, , , , , Grade 6 5 of 23

6 AGS Algebra 2 Grade 7 Number Properties and Operations Middle grades students understand fractions, decimals, percents and integers, compare them and locate their relative positions on a number line. They develop and use proportional reasoning to solve problems. They work with large numbers and small numbers. They use factors, multiples and prime factorizations. They perform arithmetic operations with fractions, decimals and integers, use properties in computation, develop fluency and develop strategies to estimate the result of operations on rational numbers. Number Sense Kentucky Academic Expectations for Mathematics PAGE(S) WHERE TAUGHT MA MA MA MA Students will provide examples of and identify integers, fractions, decimals, percents and π. DOK 1 Students will describe and provide examples of representations of numbers (whole numbers, fractions, decimals, percents, integers, square roots, and π) and operations in a variety of equivalent forms using models, diagrams, and symbols (e.g., number lines, 10 by 10 grids, rectangular arrays, number sentences), based on realworld and mathematical problems Students will convert among whole numbers, fractions, decimals, percents and π, and will compare and order these numbers. DOK 2 Estimation Students will estimate to solve real-world and mathematical problems with fractions, decimals and percents, checking for reasonable and appropriate computational results. DOK 2 TE/SE: TE/SE: 2-3, 24-25, 104, , 177, 183, , , 223, 242, 373, 456, 458, 462, 466 TE/SE: 2-3, 8-9, 11-12, 22-25, 48-51, 59-60, , , , , 223, 242, 373, 456, 462 TE/SE: 2-3, 15-18, 19-21, 22-23, 50, 104, , , , 223, , 242, 373, 456, 462 TE/SE: 115, 170, 192, 225, 236, 247 (TE), 277, 453, 456 MA Number Operations Students will add, subtract, multiply and divide whole numbers, fractions and decimals to solve real-world problems and apply order of operations (including positive whole number exponents) to simplify numerical expressions. DOK 2 TE/SE: 2-3, 6, 8-9, 11-12, 40-41, 48-51, 59-60, 84-85, 96, , , 191, , 373, 462 MA Students will explain how operations (addition and subtraction; multiplication and division) are inversely related. TE/SE: 6-7, 8-10, 11-14, 17, 26-27, 30, 75-78, 89-90, 102, , 224, 226, , , 534 MA Students will add and subtract integers. TE/SE: 5, 6-7, 11-13, 16-17, 24-25, 26-27, 43-44, 46, 48-50, 59-60, 66, 81-82, 84, 89, 98 MA Ratios and Proportional Reasoning Students will apply ratios and proportional reasoning to solve real-world problems (e.g., percents, sales tax, discounts, rate). DOK 3 TE/SE: 48-51, 58, 59-60, 66, 68, 171, , 242, 429, , Grade 7 6 of 23

7 MA MA AGS Algebra 2 Grade 7 Properties of Numbers and Operations Students will identify and apply prime numbers, composite numbers, prime factorization, factors, multiples and divisibility to solve real-world and mathematical problems (e.g., prime factorization to determine a least common multiple [LCM] or greatest common factor [GCF]). DOK 2 Students will identify the use of properties (commutative properties of addition and multiplication, the associative properties of addition and multiplication and the identity properties for addition and multiplication) to justify a given step in solving problems. DOK 1 TE/SE: 75, 77, 79, 82, 170, TE/SE: 4-5, 6-7, 8-10, 11-14, 15-16, 19, 24-25, 72-74, 75-78, 81, , 224, , , Measurement Students continue to measure and estimate measurements including fractions and decimals. They use formulas to find perimeter, area, circumference and volume. They use rulers and protractors. They use US Customary and metric units of measurement. MA MA MA MA MA Measuring Physical Attributes Students will measure lengths (to the nearest eighth of an inch or the nearest centimeter) and will determine and use in real-world and mathematical problems: area and perimeter of triangles; area and perimeter of quadrilaterals (rectangles, squares, trapezoids) (using the Pythagorean theorem will not be required as a strategy); area and circumference of circles and area and perimeter of compound figures composed of triangles, quadrilaterals and circles. DOK 2 Students will estimate measurements of regular and irregular polygons and circles in standard units. Students will explain how measurements and measurement formulas are related or different (e.g., perimeter and area of rectangles). Students will find the measures of angles by estimation and measurement with a protractor or angle ruler. Systems of Measurement Students will convert units within the same measurement system and use these units to solve real-world problems. TE/SE: , 144, , 226, 272 Students learn about precision and units of measurement; they estimate values of functions and a variety of measurements in problems with real-world applications. TE/SE: 253, , 453, 456, , TE/SE: 42, 78, , 144, , 157, , 174, 190, 209, 226, 272, 479 Students determine angle measures by applying geometric properties. TE/SE: 64-65, 189, , , , , 538 TE/SE: , , , , , , , Grade 7 7 of 23

8 AGS Algebra 2 Grade 7 Geometry Middle grades students expand analysis of two-dimensional shapes and three-dimensional shapes. They translate shapes in a coordinate plane. They extend work with congruent and similar figures, including proportionality. They use the Pythagorean theorem. MA MA MA MA MA MA MA Shapes and Relationships Students will describe, provide examples of and identify (using correct notation, label and name) the basic geometric elements (e.g., points, segments, rays, lines, angles and planes), in real-world and mathematical problems. Students will describe and provide examples of the elements (e.g., sides, vertices, angles, congruent parts) of two-dimensional figures (circles, triangles [acute, right, obtuse, scalene, isosceles, equilateral], quadrilaterals [square, rectangle, rhombus, parallelogram, trapezoid], regular polygons), and will apply these elements and figures to solve real-world and mathematical problems. DOK 2 Students will describe, provide examples of, and identify elements (e.g., vertices, angles, faces, edges, congruent parts) of common three-dimensional figures (spheres, cones, cylinders, prisms, and pyramids). Students will describe and provide examples of congruent and similar figures, and will apply congruent and similar figures to solve real-world and mathematical problems. DOK 2 Transformations of Shapes Students will translate (slide) and reflect (flip) figures in a coordinate plane. Students will identify rotations (clockwise or counterclockwise) of figures about the origin in the plane (90, 180, 270 ). Coordinate Geometry Students will identify and graph ordered pairs on a coordinate system, correctly identifying the origin, axes and ordered pairs; and will apply graphing in the coordinate system to solve real-world and mathematical problems. DOK 2 TE/SE: 28-29, 64-65, , , , 174, , , , , , , , , TE/SE: , , , 174, , 204, , 226, 254, 257, , , 538 TE/SE: , 209, 226, , , , 485 TE/SE: , 317 TE/SE: 45, 48-49, 54, 115, , , TE/SE: 48, TE/SE: 36-37, 45-47, 48-50, 52-53, 54-57, 61-63, 64-65, 66, , , , , , , Data Analysis and Probability Middle grades students extend the early development of data representations and examine the appropriateness of graphs and representations of data. They examine central tendencies and dispersion. They develop organized approaches to counting and use experimental and theoretical probabilities MA Representations of Data Sets Students will analyze and make inferences from data displays (drawings, tables/charts, pictographs, bar graphs, circle graphs, line plots, Venn diagrams, line graphs, stem-and-leaf plots, scatter plots). DOK 3 TE/SE: 126, , 466, 468, 495 Grade 7 8 of 23

9 MA MA MA MA MA MA MA MA AGS Algebra 2 Grade 7 Students will explain how different representations of data TE/SE: , 466, 468, 495 (e.g., tables, graphs, diagrams, plots) are related. Students will read/interpret, analyze and make inferences from box and whisker plots of data and make predictions and draw conclusions from the data. Students will determine and construct appropriate data displays (bar graphs, line plots, Venn diagrams, tables, line graphs, stem-and-leaf plots), and will explain why the type of display is appropriate for the data. DOK 2 Students will make decisions about how misleading representations affect interpretations and conclusions about data (e.g., changing the scale on a graph). Characteristics of Data Sets Students will determine the mean, median, mode and range of a set of data, and will identify clusters, gaps and outliers within the data. DOK 2 Probability Students will apply counting techniques to determine the size of a sample space for a real-world or mathematical situation. DOK 2 Students will: determine theoretical probabilities of simple events; determine probabilities based on the results of an experiment and make inferences from probability data. DOK 3 Students will tabulate experimental results from simulations and explain how theoretical and experimental probabilities are related. Students display data in frequency tables, stemand-leaf plots, histograms, line graphs, and circle graphs. TE/SE: 66, 126, , 466, 468, 495 TE/SE: , 466, 468, 495 Students analyze the impact of data displays and how data could be used by different people. TE/SE: 458 (TE) TE/SE: , 469, 495 TE/SE: , , , , , 398, , TE/SE: , 401, 462 (TE), 491 TE/SE: 378 (TE), 462 (TE) Algebraic Thinking Middle grades students extend pattern work to include arithmetic sequences. They use linear functions and linear equations. They plot rational number pairs in the Cartesian plane. They simplify algebraic and numeric expressions. They explore the effects of change on related variables. They use and solve two-step single variable equations and inequalities. MA MA MA MA Patterns, Relations and Functions Students will extend, describe rules for patterns and find a missing term in a pattern from real-world and mathematical problems. DOK 3 Students will represent, analyze, and generalize first degree relationships using tables, graphs and words, and will apply the relationships to solve real-world and mathematical problems. DOK 2 Students will explain how tables, graphs, patterns, verbal rules and equations relate to each other. Students will explain how the change in one quantity affects the change in another quantity (e.g., in tables or graphs). DOK 2 TE/SE: , , , , 416, TE/SE: 36-38, 39-42, 43-44, 45-47, 48-51, 52-53, 54-58, 59-60, 61-63, 67-69, TE/SE: 36-38, 45-47, 54-58, 67, , 236, , , 248, , , 492 TE/SE: 39-42, 45-47, 54-58, 67, , 236, , , 248, 258, , , , , Grade 7 9 of 23

10 MA MA MA AGS Algebra 2 Grade 7 Variables, Expressions and Operations Students will substitute values for variables (up to three different variables) and evaluate algebraic expressions. DOK 2 Students will describe, define and provide examples of variables and expressions with a missing value based on real-world and mathematical problems. Equations and Inequalities Students will model and solve real-world and mathematical problems with one- or two-step single variable, first-degree equations or inequalities (e.g., 2x+1 = 9, 3x+3 < 9). (Statements and solutions use only non-negative numbers.) DOK 2 TE/SE: 40-41, 48-49, 59, 84-85, 89-91, 94, 96, , , , 192, 195, 200, 214, 242 TE/SE: 2-3, 6-14, 17-18, 24-27, 30-33, 40-41, 48-49, 59, 79-85, , , , 192, 195, 200 TE/SE: 39-42, 43-44, 45-47, 48-51, 52-53, 54-58, 59-60, 61-63, 67-69, Grade 7 10 of 23

11 AGS Algebra 2 Grade 8 Number Properties and Operations Middle grades students understand fractions, decimals, percents and integers, compare them and locate their relative positions on a number line. They develop and use proportional reasoning to solve problems. They work with large numbers and small numbers. They use factors, multiples and prime factorizations. They perform arithmetic operations with fractions, decimals and integers, use properties in computation, develop fluency and develop strategies to estimate the result of operations on rational numbers. Number Sense Kentucky Academic Expectations for Mathematics PAGE(S) WHERE TAUGHT MA MA MA Students will provide examples of and identify rational numbers and irrational numbers (square roots and π only). DOK 1 Students will describe and provide examples of representations of numbers (rational, square roots, and π) and operations in a variety of equivalent forms using models, diagrams and symbols (e.g., number lines, 10 by 10 grids, rectangular arrays, number sentences) based on realworld and mathematical problems. Students will convert, compare and order multiple numerical representations (e.g., fractions, decimals, percentages) of rational numbers and irrational numbers (square roots and π only). DOK 2 TE/SE: TE/SE: 2-3, 24-25, 104, , 177, 183, , , , 242, 254, 456, 458, 462, 466 TE/SE: 2-3, 8-9, 11-12, 22-25, 48-51, 59-60, , , , , 223, 242, 254, 456, 462 TE/SE: 2-3, 15-18, 19-21, 22-23, 50, 104, , , , , , 242, 254, 456, 462 MA Estimation Students will estimate to solve real-world and mathematical problems with rational numbers, checking for reasonable and appropriate computational results. DOK 2 TE/SE: 115, 170, 192, 225, 236, 247 (TE), 277, 453, 456 MA Number Operations Students will add, subtract, multiply and divide rational numbers to solve real-world problems and apply order of operations (including positive whole number exponents) to simplify numerical expressions. DOK 2 TE/SE: 2-3, 6, 8-9, 11-12, 40-41, 48-51, 59-60, 84-85, 96, , , , , 373, 462 MA Students will explain how operations (additions and subtraction; multiplication and division; squaring and taking the square root of a number) are inversely related. TE/SE: 6-7, 8-10, 11-14, 17, 26-27, 30, 75-78, 89-90, 102, , 224, 226, , , 534 MA Ratios and Proportional Reasoning Students will apply ratios and proportional reasoning to solve real-world problems (e.g., percents, constant rate of change, unit pricing, percent of increase or decrease). DOK 3 TE/SE: 48-51, 58, 59-60, 66, 68, 171, , 242, 429, , Grade 8 11 of 23

12 MA AGS Algebra 2 Grade 8 Properties of Numbers and Operations Students will identify the use of properties (commutative properties of addition and multiplication, the associative properties of addition and multiplication, the identity properties for addition and multiplication, inverse properties and the distributive property of multiplication over addition and subtraction) to justify a given step in solving problems. DOK 1 TE/SE: 4-5, 6-7, 8-10, 11-14, 15-16, 19, 24-25, 72-74, 75-78, 81, , 224, , , Measurement Students continue to measure and estimate measurements including fractions and decimals. They use formulas to find perimeter, area, circumference and volume. They use rulers and protractors. They use US Customary and metric units of measurement. MA MA MA MA MA MA MA Measuring Physical Attributes Students will measure lengths (to the nearest sixteenth of an inch or the nearest millimeter) and will determine and use in real-world or mathematical problems: area and perimeter of triangles and quadrilaterals; area and circumference of circles; area and perimeter of compound figures composed of triangles, quadrilaterals and circles; area from circumference or perimeter and circumference or perimeter from area. DOK 3 Students will estimate measurements in standard units in real-world and mathematical problems. Students will evaluate the measures of angles by estimation, measurement with a protractor or angle ruler and determine angle measures in mathematical and/or real-world situations (e.g., supplementary, exterior, vertical). DOK 2 Students will apply formulas to determine the volume of right rectangular prisms in real-world problems. DOK 2 Students will use formulas to find surface area of right rectangular prisms in real-world and mathematical problems. Students will apply the Pythagorean theorem to determine the length of a hypotenuse. DOK 2 Systems of Measurement Students will convert units within the same measurement system and use these units to solve realworld problems. DOK 2 TE/SE: , 144, , 226, 272 TE/SE: 253, , 453, 456, , TE/SE: 64-65, 189, , , , , 538 TE/SE: , 209, 226, Students use formulas to find the surface area of circular solids, including spheres, cylinders, and cones. TE/SE: TE/SE: , 322, , 346, 352, 539 TE/SE: , , , , , , , Grade 8 12 of 23

13 AGS Algebra 2 Grade 8 Geometry Middle grades students expand analysis of two-dimensional shapes and three-dimensional shapes. They translate shapes in a coordinate plane. They extend work with congruent and similar figures, including proportionality. They use the Pythagorean theorem. MA MA MA MA MA MA MA MA Shapes and Relationships Students will describe and provide examples of basic geometric elements that include points, segments, rays, lines, angles, and planes and will use these elements in real-world and mathematical problems. Students will identify and compare properties of twodimensional figures (circles, triangles acute, right, obtuse, scalene, isosceles, equilateral], quadrilaterals [square, rectangle, rhombus, parallelogram, trapezoid], regular/irregular polygons), and will apply these properties and figures to solve real-world and mathematical problems. DOK 2 Students will compare properties of three-dimensional figures (spheres, cones, cylinders, prisms, pyramids), and will apply these properties and figures to solve realworld and mathematical problems. DOK 2 Students will: provide examples of congruent and similar figures; apply congruent and similar figures to solve realworld and mathematical problems and apply proportional reasoning to solve problems involving scale drawings and proportional figures. DOK 3 Transformations of Shapes Students will describe, provide examples of, and apply to real-world and mathematical problems rotational symmetry (90º, 180º, 360º). Students will transform (translations, reflections, and dilations with the center of dilation at the origin) figures in a coordinate plane and determine the new coordinates of the image after the transformation. DOK 2 Students will identify rotations (clockwise or counterclockwise) of figures about the origin in a coordinate plane. Coordinate Geometry Students will identify and graph ordered pairs on a coordinate system, correctly identifying the origin, axes and ordered pairs; and will apply graphing in the coordinate system to solve real-world and mathematical problems. DOK 2 TE/SE: 28-29, 64-65, , , , 174, , , , , , , , , TE/SE: , , , 174, , 204, , 226, 254, 257, , , 538 TE/SE: , 209, 226, , , , 485 TE/SE: , 317 Students explore line symmetry of parabolas and geometric shapes. TE/SE: , TE/SE: 45, 48-49, 54, 115, , , TE/SE: 48, TE/SE: 36-37, 45-47, 48-50, 52-53, 54-57, 61-63, 64-65, 66, , , , , , , Grade 8 13 of 23

14 AGS Algebra 2 Grade 8 Data Analysis and Probability Middle grades students extend the early development of data representations and examine the appropriateness of graphs and representations of data. They examine central tendencies and dispersion. They develop organized approaches to counting and use experimental and theoretical probabilities MA MA MA Representations of Data Sets Students will analyze and make inferences from data displays (drawings, tables/charts, pictographs, bar graphs, circle graphs, line plots, Venn diagrams, line graphs, stem-and-leaf plots, scatter plots, histograms, box-and-whiskers plots). DOK 3 Students will explain how different representations of data (e.g., tables, graphs, diagrams, plots) are related. Students will: construct data displays (Venn diagrams, tables, line graphs, stem-and-leaf plots, circle graphs, scatter plots); explain why the type of display is appropriate for the data and explain how misleading representations affect interpretations and conclusions about data (e.g., changing the scale on a graph). DOK 2 TE/SE: 126, , 466, 468, 495 TE/SE: , 466, 468, 495 TE/SE: , 466, 468, 495 MA Students will construct box-and-whiskers plots. Students display data in frequency tables, stemand-leaf plots, histograms, line graphs, and circle graphs. TE/SE: 66, 126, , 466, 468, 495 MA MA MA MA Students will make decisions about how misleading representations affect interpretations and conclusions about data (e.g., changing the scale on a graph). Characteristics of Data Sets Students will: determine the mean, median, mode, and range of a set of data; identify clusters, gaps, and outliers and apply these concepts to compare sets of data. DOK 2 Experiments and Samples Students will explain how data gathering, bias issues, and faulty data analysis can affect the results of data collection. Probability Students will apply counting techniques to determine the size of a sample space for a real-world or mathematical situation. DOK 2 Students analyze the impact of data displays and how data could be used by different people. TE/SE: 458 (TE) TE/SE: , 469, 495 Students analyze the impact of data displays and how data could be used by different people. TE/SE: 458 (TE) TE/SE: , , , , , 398, , Grade 8 14 of 23

15 MA MA AGS Algebra 2 Grade 8 Students will: determine theoretical probabilities of simple events; determine probabilities based on the results of an experiment and make inferences from probability data. DOK 3 Students will tabulate experimental results from simulations and explain how theoretical and experimental probabilities are related. TE/SE: , 401, 462 (TE), 491 TE/SE: 378 (TE), 462 (TE) MA Students will determine theoretical probabilities and represent them using area models. TE/SE: , 401, 491 Algebraic Thinking Middle grades students extend pattern work to include arithmetic sequences. They use linear functions and linear equations. They plot rational number pairs in the Cartesian plane. They simplify algebraic and numeric expressions. They explore the effects of change on related variables. They use and solve two-step single variable equations and inequalities. MA MA MA MA MA MA Patterns, Relations and Functions Students will use variables to describe numerical patterns TE/SE: , , 394, 400, 491 based on arithmetic sequences in real-world and mathematical problems (e.g., ƒ(ν) = 2Ν+3). Students will represent, analyze and generalize simple first and second degree relationships using tables, graphs, words and algebraic notations, and will apply the relationships to solve real-world and mathematical problems. DOK 2 Students will explain how the change in one variable affects the change in another variable (e.g., if rate remains constant, an increase in time results in an increase in distance). DOK 2 Variables, Expressions and Operations Students will evaluate and simplify algebraic expressions applying the order of operations. DOK 2 Students will describe, define and provide examples of variables and expressions with a missing value based on real-world and mathematical problems. Equations and Inequalities Students will model and solve single variable, firstdegree real-world and mathematical problems (e.g., 5x+2 = x+22, x-4 < -60). DOK 2 TE/SE: 2-3, 6-14, 17-18, 24-27, 30-33, 39-63, 67-69, 79-85, , , , , , , TE/SE: 39-42, 45-47, 54-58, 67, , 236, , , 248, 258, , , , , TE/SE: 40-41, 48-49, 59, 84-85, 89-91, 94, 96, , , , 192, 195, 200, 214, 242 TE/SE: 2-3, 6-14, 17-18, 24-27, 30-33, 40-41, 48-49, 59, 79-85, , , , 192, 195, 200 TE/SE: 39-42, 43-44, 45-47, 48-51, 52-53, 54-58, 59-60, 61-63, 67-69, Grade 8 15 of 23

16 AGS Algebra 2 Grade High School Number Properties and Operations High school students should enter high school with a strong background in rational numbers and numerical operations and expand this to real numbers. This becomes the foundation for algebra and working with algebraic symbols. They understand large and small numbers and their representations, powers and roots. They compare and contrast properties of numbers and number systems and develop strategies to estimate the results of operations on real numbers. Students will use, and understand the limitations of, graphing calculators and computer spreadsheets appropriately as learning tools. MA-HS MA-HS MA-HS MA-HS-1.2. Number Sense Students will compare real numbers using order relations (less than, greater than, equal to) and represent problems using real numbers. Students will demonstrate the relationships between different subsets of the real number system Students will use scientific notation to express very large or very small quantities. Estimation Students will estimate solutions to problems with real numbers (including very large and very small quantities) in both real-world and mathematical problems, and use the estimations to check for reasonable computational results. Number Operations 1 MA-HS Students will solve real-world and mathematical problems to specified accuracy levels by simplifying expressions with real numbers involving addition, subtraction, multiplication, division, absolute value, integer exponents, roots (square, cube) and factorials. DOK 2 MA-HS MA-HS Students will: describe and extend arithmetic and geometric sequences; determine a specific term of a sequence given an explicit formula; determine an explicit rule for the nth term of an arithmetic sequence and apply sequences to solve real-world problems. DOK 3 Students will write an explicit rule for the nth term of a geometric sequence. TE/SE: 15-18, 19-21, 22-23, 26-27, 29, 31, 33, 471 TE/SE: 15-18, , , , 223, , TE/SE: , 260 TE/SE: 115, 170, 192, 225, 236, 247 (TE), 277, 453, 456 TE/SE: 90-91, 94, 98-99, , 164, , 177, 180, 183, 191, 198, 201, 206, , TE/SE: , , , , , TE/SE: , , 399, 490 MA-HS Students will recognize and solve problems that can be modeled using a finite geometric series, such as home mortgage problems and other compound interest problems. TE/SE: 393 (TE), 395 (TE) Grade High School 16 of 23

17 MA-HS MA-HS AGS Algebra 2 Grade High School Ratios and Proportional Reasoning Students will apply ratios, percents and proportional reasoning to solve real-world problems (e.g., those involving slope and rate, percent of increase and decrease) and will explain how slope determines a rate of change in linear functions representing real-world problems. DOK 2 Properties of Numbers and Operations Students will identify real number properties (commutative properties of addition and multiplication, associative properties of addition and multiplication, distributive property of multiplication over addition and subtraction, identity properties of addition and multiplication and inverse properties of addition and multiplication) when used to justify a given step in simplifying an expression or solving an equation. TE/SE: 48-51, 58, 59-60, 66, 68, 171, , 242, 429, , TE/SE: 4-5, 6-7, 8-10, 11-14, 15-16, 19, 24-25, 72-74, 75-78, 81, , 224, , , MA-HS Students will use equivalence relations (reflexive, symmetric, transitive TE/SE: 4-5 Measurement High school students continue to measure and estimate measurements including fractions and decimals. They use formulas to find surface area and volume. They use US Customary and metric units of measurement. They use the Pythagorean theorem and other right triangle relationships to solve real-world problems MA-HS MA-HS MA-HS MA-HS MA-HS High School Measuring Physical Attributes Students will determine the surface area and volume of right rectangular prisms, pyramids, cylinders, cones and spheres in real-world and mathematical problems. DOK 2 Students will describe how a change in one or more dimensions of a geometric figure affects the perimeter, area and volume of the figure. DOK 3 Students will apply definitions and properties of right triangle relationships (right triangle trigonometry and the Pythagorean theorem) to determine length and angle measures to solve real-world and mathematical problems. DOK 3 Students will apply special right triangles and the converse of the Pythagorean theorem to solve realworld problems. Systems of Measurements Students will continue to apply to both real-world and mathematical problems U.S. customary and metric systems of measurement. TE/SE: , 209, 226, , , 485 TE/SE: , , 174, 209, 226, , 261, 485 TE/SE: 173, , , , , 332, 334, 337, , 346, 349, , , 539 TE/SE: 173, , , , 346, 539 TE/SE: , , , , , , , Grade High School 17 of 23

18 AGS Algebra 2 Grade High School Geometry High school students expand analysis of two-dimensional shapes and three-dimensional shapes. They translate shapes in a coordinate plane. They extend work with congruent and similar figures, including proportionality. MA-HS MA-HS MA-HS MA-HS High School Shapes and Relationships Students will analyze and apply spatial relationships (not using Cartesian coordinates) among points, lines and planes (e.g., betweenness of points, midpoint, segment length, collinear, coplanar, parallel, perpendicular, skew). DOK 2 Students will use spatial relationships to prove basic theorems. Students will analyze and apply angle relationships (e.g., linear pairs, vertical, complementary, supplementary, corresponding and alternate interior angles) in real-world and mathematical problems. DOK 2 Students will use angle relationships to prove basic theorems TE/SE: 28-29, 64-65, , , , 174, , , , , , , , , TE/SE: 64-65, , , , , , , , 430 TE/SE: 64-65, 189, , , , , 538 TE/SE: 64-65, 189, , , , 430 MA-HS MA-HS MA-HS MA-HS MA-HS Students will classify and apply properties of two-dimensional geometric figures (e.g., number of sides, vertices, length of sides, sum of interior and exterior angle measures). DOK 2 Students will know the definitions and basic properties of a circle and will use them to prove basic theorems and solve problems. Students will solve real-world and mathematical problems by applying properties of triangles (e.g., Triangle Sum theorem and Isosceles Triangle theorems). DOK 2 Students will use the properties of triangles to prove basic theorems. Students will classify and apply properties of three-dimensional geometric figures. DOK 2 MA-HS Students will describe the intersection of a plane with a three-dimensional figure. MA-HS Students will visualize solids and surfaces in threedimensional space when given two-dimensional representations (e.g., nets, multiple views) and create two-dimensional representations for the surfaces of three-dimensional objects. TE/SE: , , , 174, , 204, , 226, 254, 257, , , 538 TE/SE: 143, , 190, 254, 257, , , , , , , , TE/SE: , TE/SE: , , 349 TE/SE: , 209, 226, , , 465, 485 TE/SE: 264, 266, TE/SE: , 209, , , , 485 Grade High School 18 of 23

19 AGS Algebra 2 Grade High School MA-HS Students will apply the concepts of congruence and similarity to solve real-world and mathematical problems. DOK 3 TE/SE: , 317 MA-HS Students will prove triangles congruent and similar. TE/SE: , 317 MA-HS MA-HS MA-HS MA-HS MA-HS Transformations of Shapes Students will identify and describe properties of and apply geometric transformations within a plane to solve real-world and mathematical problems. DOK 3 Coordinate Geometry Students will apply algebraic concepts and graphing in the coordinate plane to analyze and solve problems (e.g., finding the final coordinates for a specified polygon, midpoints, betweenness of points, parallel and perpendicular lines, the distance between two points, the slope of a segment). DOK 2 Foundational Statements Students will identify definitions, axioms and theorems, explain the necessity for them and give examples of them. Students will recognize that there are geometries, other than Euclidean geometry, in which the parallel postulate is not true. Students will be able to perform constructions such as a line parallel to a given line through a point not on the line, the perpendicular bisector of a line segment and the bisector of an angle. TE/SE: 45, 48-49, 54, 115, , , TE/SE: 36-37, 45-47, 48-50, 52-53, 54-57, 61-63, 64-65, 66, , , , , , , TE/SE: 4-5, 19, 24, 97-99, 169, 180, 198, , , , , , , , Students explore relationships and properties of intersecting and parallel lines in a plane, as well as shapes in three-dimensional space. The geometry studied in this text is Euclidean. TE/SE: 49, 51, 64-65, 135, TE/SE: Data Analysis and Probability High school students extend data representations, interpretations and conclusions. They describe data distributions in multiple ways and connect data gathering issues with data interpretation issues. They relate curve of best fit with two-variable data and determine line of best fit for a given set of data. They distinguish between combinations and permutations and compare and contrast theoretical and experimental probability. MA-HS MA-HS MA-HS Data Representations Students will analyze and make inferences from a set of data with no more than two variables, and will analyze problems for the use and misuse of data representations. DOK 3 Students will construct data displays for data with no more than two variables. DOK 2 Students will represent real-world data using matrices and will use matrix addition, subtraction, multiplication (with matrices no larger than 2x2) and scalar multiplication to solve real-world problems TE/SE: 126, , 466, 468, 495 TE/SE: , 466, 468, 495 Students represent data in matrices in Algebra. In Algebra 2, students represent data in frequency tables, stem-and-leaf plots, histograms, and circle graphs. TE/SE: , 466, 468, 495 Grade High School 19 of 23

20 MA-HS MA-HS MA-HS MA-HS MA-HS MA-HS MA-HS MA-HS AGS Algebra 2 Grade High School Characteristics of Data Sets Students will describe and compare data distributions and make inferences from the data based on the shapes of graphs, measures of center (mean, median, mode) and measures of spread (range, standard deviation). DOK 2 Students will know the characteristics of the Gaussian normal distribution (bell-shaped curve). Students will: identify an appropriate curve of best fit (linear, quadratic, exponential) for a set of two-variable data; determine a line of best fit equation for a set of linear two-variable data and apply a line of best fit to make predictions within and beyond a given set of twovariable data. DOK 3 Students will recognize when arguments based on data confuse correlation and causation. Experiments and Samples Students will recognize potential for bias resulting from the misuse of sampling methods (e.g., non-random sampling, polling only a specific group of people, using limited or extremely small sample sizes) and explain why these samples can lead to inaccurate inferences DOK 2. Students will design simple experiments or investigations to collect data to answer questions of interest. Students will explain the differences between randomized experiments and observational studies. Probability Students will: determine theoretical and experimental (from given data) probabilities; make predictions and draw inferences from probabilities; compare theoretical and experimental probabilities and determine probabilities involving replacement and non-replacement. DOK 3 TE/SE: 66, 126, , 469, 495 Students display data in frequency tables, stem-and-leaf plots, histograms, line graphs, and circle graphs. TE/SE: 66, 126, , 466, 468, 495 Students display data in frequency tables, stem-and-leaf plots, histograms, and circle graphs. TE/SE: 66, 126, , 466, 468, 495 Students analyze the impact of data displays and how data could be used by different people. TE/SE: 458 (TE) Students analyze the impact of data displays and how data could be used by different people. TE/SE: 458 (TE) TE/SE: 378 (TE), 462 (TE) TE/SE: 378 (TE), 462 (TE) TE/SE: , 401, 491 Grade High School 20 of 23

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