Prentice Hall Connected Mathematics 2, 6th Grade Units 2009

Transcription

1 Prentice Hall Connected Mathematics 2, 6th Grade Units 2009 Grade 6 C O R R E L A T E D T O Grade 6

2 Introduction The Correlation of Connected Mathematics 2 (CMP2), 6 h Grade Units 2009 to the Kentucky Core Content for Mathematics Assessment, Grade 6, demonstrates the alignment of content between CMP2 and the Core Content. This document contains references from the Teacher Guides (TG) and Student Editions (SE) to the relevant standards in Grade 6. Additional Topics that will be available on Pearson SuccessNet were added to this correlation to further enhance the alignment of CMP2 to the Kentucky Core Content. As part of the CMP2 program, teachers also have these resources to draw from for professional development, support for parents and students, assessment, and practice. Additional CMP2 Teacher Resources include: Implementing and Teaching Guide, Strategies for English Language Learners, Parent Guide, Special Needs Handbook, Teaching Transparencies, Grade 6 Additional Practice and Skills Workbook, Grade 6 Assessment Resources, Additional CMP2 Technology Resources include: StudentEXPRESS CD-ROM, ExamView 6.0 Test Bank CD-ROM, TeacherSTATION (includes Teacher Express, MindPoint QuizShow and Presentation Resources), Teaching Middle Grades with TI Technology, Success Tracker, and pearsonschool.com The National Science Foundation funded Connected Mathematics Project between 1991 and 1997 to develop a middle school mathematics program. That program, Connected Mathematics, was a complete mathematics curriculum to help students develop understanding of important concepts, skills, procedures, and ways of thinking and reasoning in number, geometry, measurement, algebra, probability, and statistics. The National Science Foundation funded a revision of Connected Mathematics in This revision, CMP2 took advantage of lessons learned in the six years that the first edition was used in classrooms. With the introduction of CMP2, it is important to note that for more than five years, the authors worked to build on the solid foundation already established by the first CMP and the research supporting the program. Research has been the central, guiding force in the product development process. Authors and product developers relied on the efficacy data for making improvements in design and content, resulting in an even more effective program. Fifteen sites, with varying characteristics that are representative of schools across the nation, participated in three rounds of revisions for each grade level. Input from more than 15,000 students and 300 teachers was integrated into CMP2. CMP2 has already proven to support student learning, helps students to develop and maintain their skills, and enhances their mathematical thinking and reasoning. Connected Mathematics 2 provides 24 Student Units (8 per grade level). Every unit develops a big mathematical idea, important clusters of related concepts, skills, procedures, and ways of thinking. Students develop understanding of algorithms and strategies for computing and estimating in a variety of ways. They learn to recognize when an algorithm or strategy applies to a new context and when they can build on the skills and strategies they know in order to develop new strategies. In these processes, students practice skills as an ongoing activity throughout the curriculum. In addition, Connected Mathematics 2 helps students develop algebraic reasoning. The program aims to expand student views of algebra beyond symbolic manipulation and offers opportunities for students to apply algebraic reasoning to problems in many different contexts throughout the course of the curriculum. 1

3 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. 6 th Grade Number Sense MA Students will provide examples of and identify fractions, decimals and percents. DOK 1 MA 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. SE: Bits and Pieces I Investigation 1: Fundraising Fractions (5 11), Investigation 3: Moving Between Fractions and Decimals (36 40), Investigation 4: Working With Percent (56 60) TG: Bits and Pieces I Investigation 1: Fundraising Fractions (11 40), Investigation 3: Moving Between Fractions and Decimals (79 90), Investigation 4: Working With Percent ( ) SE: Bits and Pieces I Investigation 1: Fundraising Fractions (5 11), Investigation 2: Sharing and Comparing with Fractions (19 23), Investigation 3: Moving Between Fractions and Decimals (36 40, 45 46), Investigation 4: Working With Percent (56, 60); Bits and Pieces II Investigation 1: Estimating With Fractions (12), Investigation 2: Adding and Subtracting Fractions (30), Investigation 3: Multiplying With Fractions (32 37); Investigation 4: Dividing With Fractions (49 53); Bits and Pieces III Investigation 1: Decimals More or Less! (19), Investigation 3: The Decimal Divide (36 37) TG: Bits and Pieces I Investigation 1: Fundraising Fractions (11 40), Investigation 2: Sharing and Comparing with Fractions (46 56), Investigation 3: Moving Between Fractions and Decimals (79 90, ), Investigation 4: Working With Percent ( , ); Bits and Pieces II Investigation 1: Estimating With Fractions (32), Investigation 2: Adding and Subtracting Fractions (57), Investigation 3: Multiplying With Fractions (60 74), Investigation 4: Dividing With Fractions (92 108); Bits and Pieces III Investigation 1: Decimals More or Less! (35), Investigation 3: The Decimal Divide (62 64) 2

4 MA 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. Estimation MA Students will estimate to solve real-world and mathematical problems with whole numbers, fractions, decimals and percents, checking for reasonable and appropriate computational results. SE: Bits and Pieces I Investigation 2: Sharing and Comparing with Fractions (23 25), Investigation 3: Moving Between Fractions and Decimals (36 42, 44 46, 51), Investigation 4: Working With Percent (56 57, 60); Bits and Pieces III Investigation 1: Decimals More or Less! (10 12), Investigation 2: Decimal Times (21 23, 26 27), Investigation 3: The Decimal Divide (38 39, 41); How Likely Is it? Investigation 1: A First Look at Chance (6 10) TG: Bits and Pieces I Investigation 2: Sharing and Comparing with Fractions (57 66), Investigation 3: Moving Between Fractions and Decimals (79 106, 110), Investigation 4: Working With Percents ( , ); Bits and Pieces III Investigation 1: Decimals More or Less! (25 32), Investigation 2: Decimal Times (37 42, 51 56), Investigation 3: The Decimal Divide (65 70, 75 78); How Likely Is it? Investigation 1: A First Look at Chance (14 28) SE: Bits and Pieces I Investigation 4: Working With Percents (56 57); Bits and Pieces II Investigation 1: Estimating With Fractions (5 9), Investigation 3: Multiplying With Fractions Situations (36 38); Covering and Surrounding Investigation 5: Measuring Irregular Shapes and Circles (70 71); Bits and Pieces III Investigation 1: Decimals More or Less! (6 7, 10 11), Investigation 2: Relating Fractions and Decimal Multiplication (21 23, 24 25, 33) TG: Bits and Pieces I Investigation 4: Working With Percents ( ); Bits and Pieces II Investigation 1: Estimating With Fractions (20 30), Investigation 3: Multiplying With Fractions (71 80); Covering and Surrounding Investigation 5: Measuring Irregular Shapes and Circles ( ); Bits and Pieces III Investigation 1: Decimals More or Less! (16 20, 25 28), Investigation 2: Decimal Times (37 42, 47 50, 59) 3

5 Number Operations MA 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. MA Students will explain how operations (addition and subtraction; multiplication and division) are inversely related. SE: Prime Time Investigation 2: Whole-Number Patterns and Relationships (24 26); Bits and Pieces I Investigation 2: Sharing and Comparing with Fractions (25 27), Investigation 3: Moving From Fractions to Decimals (44, 51); Bits and Pieces II Investigation 2: Adding and Subtracting Fractions (18 23), Investigation 3 Multiplying With Fractions (32 39), Investigation 4: Dividing With Fractions (49 54); Bits and Pieces III Investigation 1: Decimals More or Less! (8 12), Investigation 2: Decimal Times (21 27), Investigation 3: The Decimal Divide (36 41), Investigation 4: Using Percents (50 54), Investigation 5: More About Percents 62 64); KY Additional Lesson Grade 6 Topic 10: Number Properties (23-24) TG: Prime Time Investigation 2: Whole- Number Patterns and Relationships (41 44); Bits and Pieces I Investigation 2: Sharing and Comparing with Fractions (67 72), Investigation 3: Moving From Fractions to Decimals (97 100, 110); Bits and Pieces II Investigation 2: Adding and Subtracting Fractions (35 54), Investigation 3: Multiplying With Fractions (60 84), Investigation 4: Dividing With Fractions (92 114); Bits and Pieces III Investigation 1: Decimals More or Less! (21 32), Investigation 2: Decimal Times (37 56), Investigation 3: The Decimal Divide (62 74), Investigation 4: Using Percents (81 96), Investigation 5: More About Percents ( ); KY Additional Lesson Grade 6 Topic 10: Number Properties (19-20) SE: Prime Time Investigation 1: Factors and Products (11 13, 44), Investigation 2: Whole- Number Patterns and Relationships (33); Bits and Pieces II Investigation 2: Adding and Subtracting Fractions (21 22), Investigation 3 Multiplying With Fractions (45), Investigation 4: Dividing With Fractions (53 54); KY Additional Lesson Grade 6 Topic 10: Number Properties (23-24) TG: Prime Time Investigation 1: Factors and Products (25 30, 72), Investigation 2: Whole- Number Patterns and Relationships (51); Bits and Pieces II Investigation 2: Adding and Subtracting Fractions (47 50), Investigation 3 Multiplying With Fractions (87), Investigation 4: Dividing With Fractions ( ); KY Additional Lesson Grade 6 Topic 10: Number Properties (19-20) 4

6 Ratios and Proportional Reasoning MA Students will describe and apply ratios to solve real-world problems. Properties of Numbers and Operations MA 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]). MA 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 SE: Prime Time Investigation 3: Common Multiples and Common Factors (44); Bits and Pieces I Investigation 4: Working With Percents (61 63); Bits and Pieces II Investigation 2: Adding and Subtracting Fractions (28 29), Investigation 3: Multiplying With Fractions (44); KY Additional Lesson Grade 6 Topic 5: Unit Rates (9-10) TG: Prime Time Investigation 3: Common Multiples and Common Factors (72); Bits and Pieces I Investigation 4: Working With Percents (133, 134); Bits and Pieces II Investigation 2: Adding and Subtracting Fractions (57), Investigation 3: Multiplying With Fractions (87); KY Additional Lesson Grade 6 Topic 5: Unit Rates (9-10) SE: Prime Time Investigation 1: Factors and Products (7 13,15 16), Investigation 2: Whole- Number Patterns and Relationships (22 24, 26 29, 31), Investigation 3: Choosing Common Multiples or Common Factors (37 38, 39 40, 40 41, 41), Investigation 4: Factorizations: Searching for Factor Strings (50 55), Investigation 5: Putting It All Together (61 64); KY Additional Lesson Grade 6 Topic 10: Number Properties (23-24) TG: Prime Time Investigation 1: Factors and Products (17 32), Investigation 2: Whole- Number Patterns and Relationships (36 40, 45 48, 50), Investigation 3: Common Multiples and Common Factors (54 58, 59 62, 63 66, 67 70), Investigation 4: Factorizations: Searching for Factor Strings (75 92), Investigation 5: Putting It All Together (96 100); KY Additional Lesson Grade 6 Topic 10: Number Properties (19-20) SE: Prime Time Investigation 3: Common Multiples and Common Factors (45, 46); Bits and Pieces II Investigation 4: Dividing With Fractions (59); Covering and Surrounding Investigation 1: Designing Bumper Cars (15); KY Additional Lesson Grade 6 Topic 10: Number Properties (23-24) 5

7 Measurement TG: Prime Time Investigation 3: Common Multiples and Common Factors (72); Bits and Pieces II Investigation 4: Dividing With Fractions (117); Covering and Surrounding Investigation 1: Designing Bumper Cars (35); KY Additional Lesson Grade 6 Topic 10: Number Properties (19-20) 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. Measuring Physical Attributes MA 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. MA Students will estimate measurements in standard units including fractions and decimals. SE: Covering and Surrounding Investigation 1: Designing Bumper Cars (5 9), Investigation 2: Changing Area, Changing Perimeter (31, 34), Investigation 3: Measuring Triangles (38 43), Investigation 4: Measuring Parallelograms (57 62); Bits and Pieces III Investigation 1: Decimals More or Less! (16) TG: Covering and Surrounding Investigation 1: Designing Bumper Cars (18 32), Investigation 2: Changing Area, Changing Perimeter (58, 59), Investigation 3: Measuring Triangles (61 82), Investigation 4: Measuring Parallelograms ( , 106); Bits and Pieces III Investigation 1: Decimals More or Less! (34) SE: Bits and Pieces I Investigation 2: Sharing and Comparing with Fractions (31); Shapes and Designs Investigation 2: Measuring Angles (32 35); Covering and Surrounding Investigation 2: Changing Area, Changing Perimeter (22 23); KY Additional Lesson Grade 6 Topic 6: Accurate and Precise Measurement (11-12) 6

8 MA Students will explain how measurements and measurement formulas are related or different (perimeter and area of rectangles). Systems of Measurement MA Students will convert units within the same measurement system and use these units to solve real-world problems. TG: Bits and Pieces I Investigation 2: Sharing and Comparing with Fractions (31); Shapes and Designs Investigation 2: Measuring Angles (45 48); Covering and Surrounding Investigation 2: Changing Area, Changing Perimeter (43 46); KY Additional Lesson Grade 6 Topic 6: Accurate and Precise Measurement (11-12) SE: Covering and Surrounding Investigation 1: Designing Bumper Cars (5 9), Investigation 2: Changing Area, Changing Perimeter (20 23), Investigation 4: Measuring Parallelograms (57); Bits and Pieces III Investigation 1: Decimals More or Less! (17) TG: Covering and Surrounding Investigation 1: Designing Bumper Cars (18 32), Investigation 2: Changing Area, Changing Perimeter (38 42, 45 48), Investigation 4: Measuring Parallelograms (97 100); Bits and Pieces III Investigation 1: Decimals More or Less! (34) SE: Bits and Pieces I Investigation 3: Moving From Fractions to Decimals (44, 51); Bits and Pieces II Investigation 4: Dividing With Fractions (55, 61); Covering and Surrounding Investigation 1: Designing Bumper Cars (15), Bits and Pieces III Investigation 1: Decimals More or Less! (18) TG: Bits and Pieces I Investigation 3: Moving From Fractions to Decimals (97 100, 110); Bits and Pieces II Investigation 4: Dividing With Fractions (115, 118); Covering and Surrounding Investigation 1: Designing Bumper Cars (35); Bits and Pieces III Investigation 1: Decimals More or Less! (35) 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. Shapes and Relationships MA SE: Shapes and Designs Investigation 2: Students will describe and provide Polygons and Angles (24 39, 40 46, 51); Bits examples of the basic geometric elements and Pieces III Investigation 5: More About (points, rays, lines, segments, angles Percents (66) [acute, right, obtuse], planes, radius, diameter, circumference). 7

9 MA Students will describe, and provide examples of the elements (e.g., sides, vertices, angles, congruent parts) of twodimensional figures (circles, triangles, quadrilaterals, regular polygons), and will apply these elements and figures to solve real-world and mathematical problems. MA 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). MA Students will identify and describe congruent figures, and will apply congruent figures to solve real-world and mathematical problems. TG: Shapes and Designs Investigation 2: Polygons and Angles (36 40, 43 48, 53 60); Bits and Pieces III Investigation 5: More About Percents ( ) SE: Shapes and Designs Investigation 1: Bees and Polygons (8 11, 14 15), Investigation 2: Polygons and Angles (32 35, 38-39), Investigation 3: Polygon Properties and Tiling (54-71, 68), Investigation 4: Building Polygons (70 72, 74 75); Covering and Surrounding Investigation 3: Measuring Triangles (40 41), Investigation 4: Measuring Parallelograms (56 59), Investigation 5: Measuring Irregular Shapes and Circles (72 77, 81); KY Additional Lesson Grade 6 Topic 7: Congruent Figures (13-14) TG: Shapes and Designs Investigation 1: Bees and Polygons (18 22, 27 30), Investigation 2: Polygons and Angles (45 48, 53 56), Investigation 3: Polygon Properties and Tiling (63 78, 80), Investigation 4: Building Polygons (83 90, 91 94); Covering and Surrounding Investigation 3: Measuring Triangles (69 74), Investigation 4: Measuring Parallelograms (93 96, ), Investigation 5: Measuring Irregular Shapes and Circles ( , 130); KY Additional Lesson Grade 6 Topic 7: Congruent Figures (13-14) SE: Covering and Surrounding Investigation 3: Measuring Triangles (50); Investigation 4: Finding areas and Perimeters (58 59); How Likely Is it? Investigation 4: Probability, Genetics, and Games (66, 68); KY Additional Lesson Grade 6 Topic 9: 3-D Figures (21-22) TG: Covering and Surrounding Investigation 3: Measuring Triangles (85), Investigation 4: Measuring Parallelograms ( ); How Likely Is it? Investigation 4: Probability, Genetics, and Games (88, 89); KY Additional Lesson Grade 6 Topic 9: 3-D Figures (17-18) SE: Covering and Surrounding Investigation 3: ACE Exercises (47), Investigation 4: Measuring Parallelograms (66); How Likely Is it? Investigation 4: Probability, Genetics, and Games (66); KY Additional Lesson Grade 6 Topic 7: Congruent Figures (13-14) 8

10 MA Students will identify similar figures and apply similar figures to solve real-world and mathematical problems. Transformations of Shapes MA Students will describe, provide examples of, and apply line symmetry to real-world and mathematical problems. MA 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. TG: Covering and Surrounding Investigation 3: Measuring Triangles (84 85), Investigation 4: Measuring Parallelograms (107); How Likely Is it? Investigation 4: Probability, Genetics, and Games (88); KY Additional Lesson Grade 6 Topic 7: Congruent Figures (13-14) SE: KY Additional Lesson Grade 6 Topic 8: Similar Figures and Scale Drawings (15-19) This standard is also addressed in the Grade 7 unit: SE: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (10-20), Investigation 2: Similar Figures (22-37), Investigation 3: Similar Polygons (42-43, 47-50, 52-53, 57), Investigation 4: Similarity and Ratios (61-71, 76), Investigation 5: Using Similar Triangles and Rectangles (78-93) TG: KY Additional Lesson Grade 6 Topic 8: Similar Figures and Scale Drawings (15-16) This standard is also addressed in the Grade 7 unit: TG: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (25-31), Investigation 2: Similar Figures (32-53), Investigation 3: Similar Polygons (65-68, 70-71, 73), Investigation 4: Similarity and Ratios (75-89), Investigation 5: Using Similar Triangles and Rectangles (91-104) SE: Shapes and Designs Investigation 1: Bees and Polygons (12 13, 18 19, 21), Investigation 2: Polygons and Angles (49), Investigation 4: Building Polygons (74 75) TG: Shapes and Designs Investigation 1: Bees and Polygons (23 26), Investigation 2: Polygons and Angles (60), Investigation 4: Building Polygons (91 94) SE: Shapes and Designs Investigation 2: Polygons and Angles (49); KY Additional Lesson Grade 6 Topic 2: Translations in the Coordinate Plane (3-4), Topic 3: Reflections in the Coordinate Plane (5-6) 9

11 MA Students will identify rotations of figures in the plane (90 and 180 ). TG: Shapes and Designs Investigation 2: Polygons and Angles (60); KY Additional Lesson Grade 6 Topic 2: Translations in the Coordinate Plane (3-4), Topic 3: Reflections in the Coordinate Plane (5-6) SE: Shapes and Designs Investigation 3: Polygon Properties and Tiling (47); KY Additional Lesson Grade 6 Topic 4: Rotations in the Coordinate Plane (7-8) TG: Shapes and Designs Investigation 3: Polygon Properties and Tiling (59); KY Additional Lesson Grade 6 Topic 4: Rotations in the Coordinate Plane (7-8) Coordinate Geometry MA SE: Covering and Surrounding Investigation Students will identify and graph ordered 2: Changing Area, Changing Perimeter (20 21, pairs on a positive coordinate system 24, 27, 29), Investigation 5: Measuring Irregular (Quadrant I), correctly identifying the Shapes and Circles (86); Data About Us origin, axes and ordered pairs; and will Investigation 2: Using Graphs to Explore Data apply graphing in the coordinate system to (36 39) solve real-world and mathematical problems. TG: Covering and Surrounding Investigation 2: Changing Area, Changing Perimeter (38 42, 47 50, 57), Investigation 5: Measuring Irregular Shapes and Circles (131); Data About Us Investigation 2: Using Graphs to Explore Data (57 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. Representations of Data Sets MA SE: Prime Time Investigation 2 Whole-Number Students will analyze and make inferences Patterns and Relationships (26 29, 31, 34), from data displays (drawings, Investigation 4: Factorizations: Searching for tables/charts, pictographs, bar graphs, Factor Strings (51 55); Bits and Pieces I circle graphs, line plots, Venn diagrams, Investigation 1: Fundraising Fractions (16); line graphs, stem-and-leaf plots). Bits and Pieces III Investigation 5: More About Percents (66); How Likely Is it? DOK 3 Investigation 1: A First Look at Chance (17, 18); Data About Us Investigation 1: Looking at Data (7 9, 14 17), Investigation 2: Using Graphs to Explore Data (30 38), Investigation 3: What Do We Mean by Mean? (52 53) 10

12 MA Students will explain how different representations of data (e.g., tables, graphs, diagrams, plots) are related. MA 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. Characteristics of Data Sets MA Students will determine and apply the mean, median, mode and range of a set of data. TG: Prime Time Investigation 2: Whole- Number Patterns and Relationships (45 48, 50, 51), Investigation 4: Factorizations: Searching for Factor Strings (87 92); Bits and Pieces I Investigation 1: Fundraising Fractions (42); Bits and Pieces III Investigation 5: More About Percents ( ); How Likely Is it? Investigation 1: A First Look at Chance (34, 35); Data About Us Investigation 1: Looking at Data (16 20, 31 36), Investigation 2: Using Graphs to Explore Data (47 62), Investigation 3: What Do We Mean by Mean? (81 86) SE: Covering and Surrounding Investigation 2: Changing Area, Changing Perimeter (20 21, 24); KY Additional Lesson Grade 6 Topic 12: Tables and Functions (27-28) TG: Covering and Surrounding Investigation 2: Changing Area, Changing Perimeter (38 42, 47 50); KY Additional Lesson Grade 6 Topic 12: Tables and Functions (23-24) SE: Prime Time Investigation 2: Whole-Number Patterns and Relationships (26 29); Data About Us Investigation 1: Looking at Data (7 11, 18 20) TG: Prime Time Investigation 2: Whole- Number Patterns and Relationships (45 48); Data About Us Investigation 1: Looking at Data (16 26, 37 40) SE: Bits and Pieces III Investigation 3: The Decimal Divide (40); Data About Us Investigation 1: Looking at Data (9 17), Investigation 3: What Do We Mean by Mean? (50 55) TG: Bits and Pieces III Investigation 3: The Decimal Divide (71 74); Data About Us Investigation 1: Looking at Data (21 36), Investigation 3: What Do We Mean by Mean? (74 90) 11

13 Experiments and Samples Probability MA Students will describe or determine (e.g., tables, tree diagrams) the sample space of an event for a real-world or mathematical situation. MA Students will determine single event probabilities 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. SE: How Likely Is it? Investigation 2: Experimental and Theoretical Probability (24 27), Investigation 4: Probability, Genetics, and Games (57 61) TG: How Likely Is it? Investigation 2: Experimental and Theoretical Probability (45 52), Investigation 4: Probability, Genetics, and Games (79 86) SE: How Likely Is it? Investigation 1: A First Look at Chance (6 12, 16), Investigation 2: Experimental and Theoretical Probability (22, 24 26), Investigation 3: Making Decisions With Probability (39 40, 43), Investigation 4: Probability, Genetics, and Games (55 56, 60 61) TG: How Likely Is it? Investigation 1: A First Look at Chance (15 32, 34), Investigation 2: Experimental and Theoretical Probability (37 40, 45 48), Investigation 3: Making Decisions With Probability (59 62, 67 70), Investigation 4: Probability, Genetics, and Games (77 80, 83 86) SE: How Likely Is it? Investigation 1: A First Look at Chance (8 10), Investigation 2: Experimental and Theoretical Probability (22 27), Investigation 3: Making Decisions With Probability (39 43), Investigation 4: Probability, Genetics, and Games (57 61) TG: How Likely Is it? Investigation 1: A First Look at Chance (25 28), Investigation 2: Experimental and Theoretical Probability (37 52), Investigation 3: Making Decisions With Probability (59 70), Investigation 4: Probability, Genetics, and Games (79 86) 12

14 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. Patterns, Relations and Functions MA Students will extend, describe rules for patterns and find a missing term in a pattern from real-world and mathematical problems. DOK 3 MA Students will create tables for functions and will apply the tables to solve real-world problems. MA Students will describe, define, provide examples of, and apply to real-world and mathematical problems functions using tables, graphs and verbal rules. SE: Prime Time Investigation 2: Whole-Number Patterns and Relationships (33), Investigation 3: Common Multiples and Common Factors (46, 47); Bits and Pieces I Investigation 3: Moving Between Fractions and Decimals (39 40, 49); Shapes and Designs Investigation 3: Polygon Properties and Tiling (67); KY Additional Lesson Grade 6 Topic 1: Patterns and Sequences (1-2) TG: Prime Time Investigation 2: Whole- Number Patterns and Relationships (51), Investigation 3: Common Multiples and Common Factors (72); Bits and Pieces I Investigation 3: Moving Between Fractions and Decimals (85 90, 109); Shapes and Designs Investigation 3: Polygon Properties and Tiling (80); KY Additional Lesson Grade 6 Topic 1: Patterns and Sequences (1-2) SE: Shapes and Designs Investigation 3 Polygon Properties and Tiling (54-55, 68); KY Additional Lesson Grade 6 Topic 12: Tables and Functions (27-28) TG: Shapes and Designs Investigation 3: Polygon Properties and Tiling (63 66, 81); KY Additional Lesson Grade 6 Topic 12: Tables and Functions (23-24) SE: Shapes and Designs Investigation 3: Polygon Properties and Tiling (54-55, 68); KY Additional Lesson Grade 6 Topic 11: Algebraic Expressions (25-26), Topic 12: Tables and Functions (27-28) TG: Shapes and Designs Investigation 3: Polygon Properties and Tiling (63 66, 81); KY Additional Lesson Grade 6 Topic 11: Algebraic Expressions (21-22), Topic 12: Tables and Functions (23-24) 13

15 MA Students will explain how tables, graphs and patterns relate to each other. MA 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 MA Students will substitute values for variables (up to two different variables) and evaluate algebraic expressions. MA Students will describe, define and provide examples of variables and expressions with a missing value based on real-world and mathematical problems. SE: Covering and Surrounding Investigation 2: Changing Area, Changing Perimeter (20 21); Bits and Pieces III Investigation 5: More About Percents (66); Data About Us Investigation 2: Using Graphs to Explore Data (36 39); KY Additional Lesson Grade 6 Topic 12: Tables and Functions (27-28) TG: Covering and Surrounding Investigation 2: Changing Area, Changing Perimeter (38 42); ); Bits and Pieces III Investigation 5: More About Percents ( ); Data About Us Investigation 2: Using Graphs to Explore Data (57 66); KY Additional Lesson Grade 6 Topic 12: Tables and Functions (23-24) SE: Covering and Surrounding Investigation 2: Changing Area, Changing Perimeter (26 29), Investigation 5: Measuring Irregular Shapes and Circles (86) TG: Covering and Surrounding Investigation 2: Changing Area, Changing Perimeter (55 57), Investigation 5: Measuring Irregular Shapes and Circles (131) SE: Bits and Pieces II Investigation 2: Adding and Subtracting Fractions (21 22); KY Additional Lesson Grade 6 Topic 11: Algebraic Expressions (25-26) TG: Bits and Pieces II Investigation 2: Adding and Subtracting Fractions (47 50); KY Additional Lesson Grade 6 Topic 11: Algebraic Expressions (21-22) SE: Bits and Pieces II Investigation 2: Adding and Subtracting Fractions (20 22), Investigation 3: Multiplying With Fractions (37 38); Bits and Pieces III Investigation 1: Decimals More or Less! (12), Investigation 2: Decimal Times (24 25), Investigation 3: The Decimal Divide (40); KY Additional Lesson Grade 6 Topic 11: Algebraic Expressions (25-26) TG: Bits and Pieces II Investigation 2: Adding and Subtracting Fractions (41 50), Investigation 3: Multiplying With Fractions (75 80); Bits and Pieces III Investigation 1: Decimals More or Less! (29 32), Investigation 2: Decimal Times (47 50), Investigation 3: The Decimal Divide (71 74); KY Additional Lesson Grade 6 Topic 11: Algebraic Expressions (21-22) 14

16 Equations and Inequalities MA Students will model and solve real-world and mathematical problems with simple equations and inequalities (e.g., 8x = 4, x+2 > 5). SE: Bits and Pieces II Investigation 2: Adding and Subtracting Fractions (20 22); Bits and Pieces III Investigation 3: The Decimal Divide (40) TG: Bits and Pieces II Investigation 2: Using Addition and Subtraction (41 50); Bits and Pieces III Investigation 3: The Decimal Divide (71 74) 15