# Grade 6. Prentice Hall. Connected Mathematics 6th Grade Units Alaska Standards and Grade Level Expectations. Grade 6

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1 Prentice Hall Connected Mathematics 6th Grade Units 2004 Grade 6 C O R R E L A T E D T O Expectations Grade 6

2 Content Standard A: Mathematical facts, concepts, principles, and theories Numeration: Understand and use numeration Measurement: Select and use systems, units, and tools of measurement Numeration Performance Standards that apply to grades 4-6: [6] N-1 reading, writing, ordering, or [counting L] (M1.2.1) [6] N-2 [identifying place value positions from thousandths to millions L] (M1.2.2) [6] N-3 converting between whole numbers written in expanded notation and standard form (M1.2.4) of fractions, mixed numbers, or percents by [modeling L], identifying, describing, or illustrating M1.2.1 Read, write, model, order, and count with positive whole numbers to 1,000,000 and negative whole numbers. M1.2.2 Use, model, and identify place value positions from to 1,000,000. M1.2.3 Model and explain the processes of multiplication and division. Describe the relationships among the four basic operations. M1.2.4 Identify and describe different uses for the same numerical representation. M1.2.5 Model and explain the process of adding and subtracting fractions with common denominators and decimals that represent money. M1.2.6 Identify and describe factors and multiples including those factors and multiples common to a pair or set of numbers. M1.2.7 Demonstrate the commutative and identity properties of multiplication. Understanding Numbers The student demonstrates conceptual understanding of fractions (proper or mixed numbers), decimals, percents (whole number), or integers by SE: Bits and Pieces I (20-24, 31-33, 38, 41-44, 55, 57, 67-68, 73-76); How Likely Is It? (18, 21, 31); Bits and Pieces II (6-7) TG: Bits and Pieces I (30a-i, 38a-d, 52a-h, 66a-g, 83a-g, 86-87, 88-89, 90-92, 94-95, 96-97, 98); How Likely Is It? (21a-c, 41a-d); Bits and Pieces II (17a-e) SE: Bits and Pieces I (43-45, 48-49, 51, 52, 55, 63-64) TG: Bits and Pieces I (52c-h, 92, 95) SE: Bits and Pieces I (39-44, 55, 57, 67-68, 73-76); Bits and Pieces II (18-22) [6] N-4 equal parts of a whole, a region, or a set (M1.2.4) TG: Bits and Pieces I (52a-h, 66a-g, 83a-g, 86-87, 88-89, 90-92, 94-95, 96-97, 98); Bits and Pieces II (30a-f) SE: Shapes and Designs (26); Bits and Pieces I (5-13, 19-25, 36, 39-40, 55-57) TG: Shapes and Designs (41b); Bits and Pieces I (18a-j, 30a-i) 1

3 [6] N-5 equivalent fractions or mixed numbers (M1.2.4 & M3.2.5) [6] N-6 [using models, explanations, number lines, or real-life situations L] describing or illustrating the relationships among the four basic operations (M1.2.3) [6] N-7 [using models, explanations, number lines, or real-life situations L] describing or illustrating the process of adding and subtracting fractions with different denominators (M1.2.5) SE: Bits and Pieces I (5-13, 18, 19-25, 30, 35); Bits and Pieces II (31-34, 45, 48) TG: Bits and Pieces I (18a-j, 30a-i); Bits and Pieces II (42a-c, 53a-g) Understanding Meaning of Operations The student demonstrates conceptual understanding of mathematical operations by SE: Data About Us (54-55); Covering and Surrounding (46, 49-50, 59, 60); How Likely Is It? (36); Bits and Pieces II (48, 55-56, 58-59, 66-67, 69-71) TG: Data About Us (67j); Covering and Surrounding (45b, 45c, 55e, 55f, 68d, 68e, 68f); How Likely Is It? (71, 75-77); Bits and Pieces II (53a-g, 63a-g, 76a-f) SE: How Likely Is It? (37); Bits and Pieces II (43-48, 49-52, 53) [6] N-8 describing or illustrating commutative, [associative, inverse L] or identity properties of addition or multiplication using models or explanations (M1.2.7) TG: Bits and Pieces II (53a-g) Number Theory The student demonstrates conceptual understanding of number theory by SE: Bits and Pieces II (6-11, 12-13, 17) TG: Bits and Pieces II (17a-e, 79, 87) [6] N-9 identifying or describing factors and multiples common to a pair or set of numbers (e.g., Least Common Multiple, L.C.M., or Greatest Common Factor, G.C.F.) (M1.2.6) SE: Prime Time (26-29, 36-39, 40, 50-51, 58-64, 66-67) TG: Prime Time (35a-d, 45a-c) [6] N-10 [modeling (base 10 blocks) distributive property L] (M1.3.6) SE: Bits and Pieces II (6-11, 12-13, 17) TG: Bits and Pieces II (17a-e, 79, 87) 2

4 Measurement Performance Standards that apply to grades 4-6: M2.2.1 Estimate and measure weights, lengths, and temperatures to the nearest unit using the metric and standard systems. M2.2.2 Identify and use equivalent measurements (e.g., 60 minutes = 1 hour, 7 days = 1 week). M2.2.3 Use a variety of measuring tools; describe the attribute(s) they measure. M2.2.4 Estimate and measure the dimensions of geometric figures. M2.2.5 Tell time using analog and digital clocks identifying AM and PM; find elapsed time. M2.2.6 Read, write, and use money notation, determining possible combinations of coins and bills to equal given amounts; count back change for any given situation. Measurable Attributes The student demonstrates understanding of measurable attributes by [6] MEA-1 [estimating length to the nearest eighth-seinch or millimeter L] (M2.2.1) Covering and Surrounding (20, 21-26, 30-31, 47- Bits and Pieces I (16, 37, 58, 61-62); 48); Bits and Pieces II (35-36, 38-39, 62) [6] MEA-2 identifying equivalent measures within systems English length (inches, feet, yards, miles) weight (ounces, pounds, [tons L]) volume (fluid ounces, cups, pints, quarts, gallons) Metric length (millimeters, centimeters, meters, kilometers) volume (milliliters, liters) (M2.2.2) Measurement Techniques The student uses measurement techniques by [6] MEA-3 using a scaled ruler to an eighth of an inch or millimeter on a map or drawing (M2.2.1 & M2.2.3) [6] MEA-4 calculating elapsed time (minutes, hours) (M2.2.5) [6] MEA-5 solving real-world problems involving elapsed time between U.S. time zones (including Alaska Standard time) (M2.2.5) TG: Covering and Surrounding (28a-b, 34d); Bits and Pieces II (42a) SE: Prime Time (24, 55); Data About Us (66); Bits and Pieces I (15-16, 61-62); Bits and Pieces II (36, 62) TG: Bits and Pieces II (82) SE: Shapes and Designs (32-34); Covering and Surrounding (22-23, 25-27, 38-39); Bits and Pieces II (38-39, 62) TG: Shapes and Designs (41h-i) SE: How Likely Is It? (10, 22-23); Shapes and Designs (37); Bits and Pieces I (51) RELATED MATERIAL: SE: Bits and Pieces II (43-48, 49-52, 53) TG: How Likely Is It? (28a-b) RELATED MATERIAL: SE: How Likely Is It? (10, 22-23); Shapes and Designs (32-34, 37); Bits and Pieces I (51); Covering and Surrounding (25-27) TG: How Likely Is It? (28a-b) 3

5 [6] MEA-6 converting and using equivalent measurements within the same system (M2.2.2) [6] MEA-7 measuring length to the nearest 1/8 of an inch or nearest millimeter (M2.2.1) [6] E&C-1 identifying or using [a variety of L] strategies (e.g., truncating, rounding to compatible numbers) to estimate the results of addition, subtraction or multiplication from thousandths to millions or simple division (M3.2.1) [6] E&C-2 [recalling basic addition, subtraction, multiplication, and division facts efficiently L] (M3.2.2) SE: Prime Time (24, 55); Data About Us (66); Bits and Pieces I (15-16, 61-62); Bits and Pieces II (36, 62) TG: Bits and Pieces II (82) SE: Covering and Surrounding (20, 21-26, 30-31, 38-39, 40-44, 47-48); Bits and Pieces II (35-36, 38-39, 62) TG: Covering and Surrounding (28a-b, 34d); Bits and Pieces II (42a) Estimation and Computation Performance Standards that apply to grades 4-6: M3.2.1 Describe and use a variety of estimation strategies including rounding to the appropriate place value, multiplying by powers of 10, and using front-end estimation to check the reasonableness of solutions. M3.2.2 Recall and use basic multiplication and division facts orally, with paper and pencil without a calculator. M3.2.3 Add and subtract whole numbers and fractions with common denominators to 12 and decimals, including money amounts, using models and algorithms. M3.2.4 Multiply and divide multi-digit whole numbers by 2-digit numbers, limiting the 2-digit divisors to those that end in 0; multiply and divide decimals that represent money by whole numbers. M3.2.5 Find equivalent fractions. Convert between fractions and mixed numbers. M3.2.6 Develop and interpret scales and scale models. Estimation The student determines reasonable answers to real-life situations, paper/pencil computations, or calculator results by SE: Shapes and Designs(47); Bits and Pieces I (65); Covering and Surrounding (19-20, 21-26, 27, 28, 30-31); Bits and Pieces II (31-34, 35-40, 41, 64-66, 72-73) TG: Covering and Surrounding (28a-28b); Bits and Pieces II (42a-42b, 76a-76b) Computation The student accurately solves problems (including real-world situations) involving SE: Bits and Pieces II (48, 50, 52, 56-59, 60-62, 63); Prime Time (6-9, 17-19); How Likely Is It? (36-37) TG: Bits and Pieces II (53c, 53e, 53h, 63a-g); Prime Time (16a-e, 25a-e); How Likely Is It? (71, 75-77) 4

6 [6] E&C-3 adding or subtracting whole numbers, fractions with unlike denominators to 12, or decimals to the hundredths place (M3.2.3) SE: How Likely Is It? (36-37); Bits and Pieces II (43-48, 49-52, 53) [6] E&C-4 multiplying whole numbers by two- or three-digit numbers, dividing three-digit numbers by one or two-digit numbers, or multiplying or dividing decimals that represent money by whole numbers, or multiplying or dividing proper fractions (M3.2.4) TG: How Likely Is It? (71, 75-77); Bits and Pieces II (53a-g) SE: Prime Time (32-34, 36-39, 46-50); How Likely Is It? (26-27, 28); Bits and Pieces II (5-6, 8-11, 67, 69-71) TG: Prime Time (35a-b, 45a-c, 57a-f); How Likely Is It?; (13b); Bits and Pieces II (17a-f, 76a-f) [6] E&C-5 [developing or interpreting scale models (scale factors such as 1 in. = 1 ft.) L] (M3.2.6) [6] F&R-1 extending patterns (found in the number system, formed by multiples, factors, perfect squares up to 100, powers of ten), up to 10 terms, represented in tables, sequences, or in problem situations (M4.2.1) [6] F&R-2 using rules to express the generalization of a pattern using words, lists, or tables, with or without variables (M4.2.4) SE: Shapes and Designs (32-34); Covering and Surrounding (22-23, 25-27, 38-39); Bits and Pieces II (38-39, 62) TG: Shapes and Designs (41h-i) Functions and Relationships Performance Standards that apply to grades 4-6: M4.2.1 Use patterns and their extensions to make predictions and solve problems; describe patterns found in the number system including those formed by multiples, factors, perfect squares, and powers of 10. M4.2.2 Generate and solve simple functions by identifying and applying multiplication and division patterns. M4.2.3 Use a calculator to find a missing item in a number sequence. M4.2.4 Use words, lists, and tables to represent and analyze patterns. M4.2.5 Explain the purpose of variables and use them in open sentences to express relationships and describe simple functions. Describing Patterns and Functions The student demonstrates conceptual understanding of functions, patterns, or sequences by SE: Prime Time (36-39, 58-60, 64); Shapes and Designs (42-45, 47-49, 50); Covering and Surrounding (70-75); How Likely Is It? (43-45) TG: Prime Time (36-39, 58-60, 64); Shapes and Designs (50a-d); Covering and Surrounding (81ai); How Likely Is It? (43-45) SE: Prime Time (58-60, 64); Shapes and Designs (42-45, 47-49, 50); Covering and Surrounding (70-75) 5

7 [6] F&R-3 identifying or applying multiplication or division patterns to find missing values in a function (M4.2.2) TG: Prime Time (64a-b); Shapes and Designs (50ad); Covering and Surrounding (81a-i) SE: Shapes and Designs (42-45, 47, 50); Covering and Surrounding (70-71, 74-75) [6] F&R-4 [using manipulatives, including a calculator, as tools when describing, extending, or representing a number sequence L] (M4.2.1 & M 4.2.3) Modeling and Solving Equations and Inequalities The student demonstrates algebraic thinking by TG: Shapes and Designs (50a-d); Covering and Surrounding (81a-i) SE: Prime Time (33-34, 58-60, 64); Data About Us (42-45, 48-49); Shapes and Designs (47, 49, 50); Covering and Surrounding (72-75) TG: Prime Time (64a, 64b); Data About Us (52a, 52d, 77, 78); Shapes and Designs (50a-d); Covering and Surrounding (81a-i) [6] F&R-5 solving for an unknown represented by a letter, (addition, subtraction, multiplication, or division) (e.g., 3 n = 15, n 5 = 12) (M4.2.5) SE: Shapes and Designs (47, 49, 50); Bits and Pieces II (14-16, 19, 24-26, 28-29) Geometry: Construct, transform, and analyze geometric figures. Geometry Performance Standards that apply to grades 4-6: Geometric Relationships The student demonstrates an understanding of geometric relationships by [6] G-1 using the attributes and properties (sides and angles) of regular polygons to identify, classify, or compare regular or irregular polygons (M5.2.1) TG: Shapes and Designs (50a-d); Bits and Pieces II (30b) M5.2.1 Identify and compare various triangles and quadrilaterals according to their sides and/or angles. M5.2.2 Compare and contrast plane and solid figures (e.g., circle/sphere, square/cube, triangle/pyramid) using relevant attributes, including the number of vertices, edges, and the number and shape of faces. M5.2.3 Identify and model geometric figures that are congruent, similar, and/or symmetrical. M5.2.4 Distinguish between area and perimeter; find both using a variety of methods including rulers, grid paper, and tiles. M5.2.5 Identify and model transformations of geometric figures, describing the motions as slides, flips, or rotations. M5.2.6 Locate and describe objects in terms of their position with and without compass directions; identify coordinates for a given point or locate points of given coordinates on a grid. M5.2.7 Sketch and identify line segments, midpoints, intersections, parallel, and perpendicular lines. SE: Shapes and Designs (8-10, 15-18, 22, 27, 32, 39, 46, 52-54); Covering and Surrounding (30, 47, 49-50, 57-59) 6

8 [6] G-2 identifying, comparing or describing attributes and properties of circles (radius, and diameter) (M5.2.2) [6] G-3 using the attributes and properties of prisms (vertices, length and alignment of edges, shape and number of bases, shape of faces) to [model L], identify, compare, or describe triangular or rectangular prisms (M5.2.2) TG: Shapes and Designs (14a-b, 21a-g, 41a-i, 50ag, 63a-d); Covering and Surrounding (34b-c, 45bc, 55e-f, 68d-f, 81c, 81g) SE: Covering and Surrounding (69-75, 76-80, 81) TG: Covering and Surrounding (81a-h) SE: Ruins of Montarek (10-11, 13-17, 27-30, 41-43, 53-54, 56-57, 63-64, 70, 73-76) [6] G-4 identifying a 3-dimensional shape from the 2-dimensional drawing of the shape (M5.2.2) TG: Ruins of Montarek (25a-h, 39a-d, 51a-d, 61ai, 71a-c, 81a-e) SE: Ruins of Montarek (8, 10-11, 13-17, 27-30, 41-43, 53-54, 56-57, 63-64, 73-76) [6] G-5 identifying, creating, or drawing geometric figures that are congruent, similar, or symmetrical (M5.2.3) TG: Ruins of Montarek (25a-h, 39a-d, 51a-d, 61ai, 71a-c, 81a-e) Similarity, Congruence, Symmetry, and Transformation of Shapes The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes by [6] G-6 [drawing or describing the results of transformations of polygons such as slides, turns, or flips L] (M5.2.5) Perimeter, Area, Volume, and Surface Area [6] G-7 estimating or determining area or perimeter of polygons (parallelograms, trapezoids, triangles) using a key, ruler, or given measures (M5.2.4) SE: Shapes and Designs (43-44, 52-56, 58, 59-62, 63); Ruins of Montarek (10-12, 23-24) TG: Shapes and Designs (50a, 63a-d); Ruins of Montarek (25b-d, 93) SE: Shapes and Designs (52-56, 59-62, 63); Ruins of Montarek (9-12, 14-18, 23-24) TG: Shapes and Designs (63a, 63b, 63c, 63d); Ruins of Montarek (25a-h) The student solves problems (including real-world situations) by using perimeter, area, or volume by SE: Bits and Pieces II (37, 39-40, 43-45, 54-58); Covering and Surrounding (6-12, 47-48, 56-57) TG: Bits and Pieces II (42a-b, 63a-f); Covering and Surrounding (18a-g, 55a-f, 68a-f) 7

9 [6] G-8 [estimating the area and circumference of a circle using a grid or manipulatives and comparing the relationship of the diameter to the circumference (π) L] (M5.2.4 & M5.3.4) SE: Covering and Surrounding (69-75, 76-80, 81) TG: Covering and Surrounding (81a-h) [6] G-9 [estimating or determining the volume of a right rectangular prism using manipulatives and formulas (e.g., cereal box, sand box, planter) L] (M5.3.4) SE: Ruins of Montarek (70) The topics of volume and surface area are covered more deeply in the 7th grade texts. Introductory topics include: SE: Covering and Surrounding (6-12); Bits and Pieces II (73); Ruins of Montarek (13-17, 27-30, 41-43, 53-54, 56-57, 63-64, 73-76) Position and Direction The student demonstrates understanding of position and direction by [6] G-10 graphing a vertical or horizontal line segment (given whole number coordinates for its end points) on a coordinate grid or identifying its length or midpoint (e.g., using a map to trace a route and calculate distance) (M5.2.6 & M5.2.7) TG: Ruins of Montarek (25a-h, 39a-d, 51a-d, 61ai, 71a-c, 81a-e) SE: Data About Us (42-52); Shapes and Designs (29); Bits and Pieces I (22-24, 27-28, 63-64, 82); Bits and Pieces II (46-47) TG: Shapes and Designs (41e); Bits and Pieces I (30d, 92); Bits and Pieces II (53e-f) Construction The student demonstrates a conceptual understanding of geometric drawings or constructions by [6] G-11 [drawing or measuring quadrilaterals with given dimensions or angles L] (M5.3.7) SE: Data About Us (52c, 52d, 52e, 73, 77); Shapes and Designs (11, 17-18, 19, 21, 43, 51, 54-56, 57-62, 64-65, 68); Covering and Surrounding (48-49) TG: Shapes and Designs (21c-g, 63c-e, 75a-c); Covering and Surrounding (55b-c) 8

10 [6] S&P-1 [designing an investigation and collecting L], organizing, or displaying, using appropriate scale for data displays (tables, bar graphs, line graphs, or circle graphs), data in realworld problems (e.g., social studies, friends, or school), with whole numbers up to 100 (M6.2.1 & M6.2.2) Statistics and Probability: Formulate questions, gather and interpret data, and make predictions Statistics and Probability Performance Standards that apply to grades 4-6: M6.2.1 Collect, organize, and display data creating a variety of visual displays including tables, charts, and line graphs. M6.2.2 Present the data using a variety of appropriate representations and explain the meaning of the data. M6.2.3 Describe and interpret a data set using mean, median, mode, and range. M6.2.4 Estimate whether a game is mathematically fair or unfair; analyze and present probability data using simple fractions. M6.2.5 Conduct simple probability experiments using concrete materials and represent the results using fractions and probability. Data Display The student demonstrates an ability to classify and organize data by SE: Data About Us (7-13, 22-24, 30-36, 42-46, 58-61); How Likely Is It? (57) TG: Data About Us (21a-i, 29a-d, 41a-f, 52a-e, 67a-l, 70, 71, 72-73, 74-75, 76-77, 78); Shapes and Designs (41h, 41i); How Likely Is It? (64a) Analysis and Central Tendency The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating; or drawing or justifying conclusions) by [6] S&P-2 using information from a variety of displays (tables, bar graphs, line graphs, circle graphs, or Venn diagrams) (M6.2.2) [6] S&P-3 using mean, median, mode, or range (M6.2.3) Probability SE: Data About Us (7-8, 11, 24, 30-36, 42-46, 60-61, 68-70) TG: Data About Us (21a-i, 29a-d, 41a-f, 52a-e, 67a-l) SE: Data About Us (9-14, 21, 24-27, 29, 38-39, 53-61, 69-70) TG: Data About Us (21c-i, 29b-c, 41d, 67a-l, 71, 72-73, 74-75, 76, 78) The student demonstrates a conceptual understanding of probability and counting techniques by [6] S&P-4 [analyzing whether a game is mathematically fair or unfair by explaining the probability of all possible outcomes L] (M6.2.4) SE: Prime Time (10, 12-15, 19, 22); How Likely Is It? (7-8, 16, 20, 24, 34, 42-43, 46, 49-50, 51-52, 56, 67) 9

11 TG: Prime Time (16b-d, 25a-d); How Likely Is It? (13c-d, 21b-c, 41a-b, 41d, 48d-e, 56a-b) [6] S&P-5 solving or identifying solutions to SE: How Likely Is It? (12, 33, 39-40, 43, 44-45, problems involving possible combinations (e.g., if 47, 48, 49, 59-60, 61-63, 64) ice cream sundaes come in 3 flavors with 2 possible toppings, how many different sundaes can be made using only one flavor of ice cream with one topping?) (M6.2.5) TG: How Likely Is It? (21c, 41b-c, 48a--c, 56a-b) Content Standards B, C, D, and E: Process skills and abilities Applying conceptual knowledge and skills as designated in all strands of Content Standard A by problem solving, communicating, reasoning, and making connections Problem-Solving Performance Standards that apply to grades 4-6: M7.2.1 Read and summarize a problem, using mathematical terms and symbols. M7.2.2 Select and apply a variety of strategies including making a table, chart or list, drawing pictures, making a model, and comparing with previous experience to solve problems. M7.2.3 Explain and verify results of the original problem and apply what was learned to new situations. Problem Solving: Understand and be able to select and use a variety of problem-solving strategies The student demonstrates an ability to problem solve by [6] PS-1 selecting, modifying, and applying appropriate problem solving strategies (e.g., graphing, Venn diagrams, tables, lists, working backwards, guess and check, or extend a pattern) and verifying results (M7.3.2) SE: Prime Time (20-21, 23, 32); Data About Us (42-45, 48-49); Shapes and Designs (32-34); Covering and Surrounding (19-20); How Likely Is It? (42-43); Bits and Pieces II (48, 59); Ruins of Montarek (40-44) TG: Data About Us (52a, 52d, 77, 78); Shapes and Designs (41h, 41i); Covering and Surrounding (28a-b); How Likely Is It? (48a-c); Bits and Pieces II (53f, 53g, 63f, 63g); Ruins of Montarek (51a-d) [6] PS-2 evaluating and interpreting solutions to problems (M7.3.3) SE: Data About Us (42-45, 48-49); Shapes and Designs (32-34); Covering and Surrounding (19-20); How Likely Is It? (14-16); Bits and Pieces II (46-47); Ruins of Montarek (40-44) TG: Data About Us (52a, 52d, 77, 78); Shapes and Designs (41h, 41i); Covering and Surrounding (28a-b); How Likely Is It? (48a-c); Bits and Pieces II (53f, 53g, 63f, 63g); Ruins of Montarek (51a-d) 10

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