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6th Grade Topic Alignment Standards / Topics Code Indicators Number & Number Sense & Operations Greatest common factor Least common multiple Prime numbers and prime factorization 6N2 6N2b 6N2c 6N2 6N2a 6N2c 6N2 Squared and cubed numbers 6N1 Exponents 6N1 6N6 Order of operations 6N6 6N11 Estimating Sums and Differences 6N13 Find and use the prime factorization of composite numbers. For example: Use the prime factorization to recognize the least common multiple (LCM). Apply the prime factorization to solve problems and explain solutions. Find and use the prime factorization of composite numbers. For example: Use the prime factorization to recognize the greatest common factor (GCF). Apply the prime factorization to solve problems and explain solutions. Find and use the prime factorization of composite numbers. For example: Decompose and recompose whole numbers using factors and exponents (e.g., 32 = 2 x 2 x 2 x 2 x 2 = 25 ), and explain why “squared” means “second power” and “cubed” means “third power ” Decompose and recompose whole numbers using factors and exponents (e.g., 32 = 2 x 2 x 2 x 2 x 2 = 25 ), and explain why “squared” means “second power” and “cubed” means “third power ” Use the order of operations, including the use of exponents, decimals and rational numbers, to simplify numerical expressions. Use the order of operations, including the use of exponents, decimals and rational numbers, to simplify numerical expressions. Perform fraction and decimal computations and justify their solutions; e.g., using manipulatives, diagrams, mathematical reasoning. Estimate reasonable solutions to problem situations involving fractions and decimals; e.g., 7/8 + 12/13 is about equal to 2 and 4.23 x 5.8 is about equal to 25. Decimals Comparing and ordering decimals Review Estimating with decimals Adding and subtracting decimals 6N13 6N11 6N12 6N13 Multiplying & dividing decimals 6N8 6N11 6N12 6N13 Estimate reasonable solutions to problem situations involving fractions and decimals; e.g., 7/8 + 12/13 is about equal to 2 and 4.23 x 5.8 is about equal to 25. Perform fraction and decimal computations and justify their solutions; e.g., using manipulatives, diagrams, mathematical reasoning. Develop and analyze algorithms for computing with fractions and decimals, and demonstrate fluency in their use. Estimate reasonable solutions to problem situations involving fractions and decimals; e.g., 7/8 + 12/13 is about equal to 2 and 4.23 x 5.8 is about equal to 25. Represent multiplication and division situations involving fractions and decimals with models and visual representations; e.g., show with pattern blocks what it means to take 2 2/3 ÷ 1/6. Perform fraction and decimal computations and justify their solutions; e.g., using manipulatives, diagrams, mathematical reasoning. Develop and analyze algorithms for computing with fractions and decimals, and demonstrate fluency in their use. Estimate reasonable solutions to problem situations involving fractions and decimals; e.g., 7/8 + 12/13 is about equal to 2 and 4.23 x 5.8 is about equal to 25. Fractions Equivalent fractions Adapted from Prentice Hall Courses Review Trumbull County Educational Service Center Page 1 6th Grade Topic Alignment Standards / Topics Code Mixed numbers and improper fractions Comparing and ordering fractions Review Review Fractions with like & unlike denominators 6N11 6N12 Adding & subtracting mixed numbers 6N11 6N12 6N13 Percents, Fractions and decimals Multiplying & dividing fractions and/or mixed numbers 6N5 6N8 6N10 6N11 6N12 The customary system Changing units in the customary system 6N13 Review Review Indicators Perform fraction and decimal computations and justify their solutions; e.g., using manipulatives, diagrams, mathematical reasoning. Develop and analyze algorithms for computing with fractions and decimals, and demonstrate fluency in their use. Perform fraction and decimal computations and justify their solutions; e.g., using manipulatives, diagrams, mathematical reasoning. Develop and analyze algorithms for computing with fractions and decimals, and demonstrate fluency in their use. Estimate reasonable solutions to problem situations involving fractions and decimals; e.g., 7/8 + 12/13 is about equal to 2 and 4.23 x 5.8 is about equal to 25. Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100. Represent multiplication and division situations involving fractions and decimals with models and visual representations; e.g., show with pattern blocks what it means to take 2 2/3 ÷ 1/6. Recognize that a quotient may be larger than the dividend when the divisor is a fraction; e.g., 6 ÷ 1/2 = 12. Perform fraction and decimal computations and justify their solutions; e.g., using manipulatives, diagrams, mathematical reasoning. Develop and analyze algorithms for computing with fractions and decimals, and demonstrate fluency in their use. Estimate reasonable solutions to problem situations involving fractions and decimals; e.g., 7/8 + 12/13 is about equal to 2 and 4.23 x 5.8 is about equal to 25. Ratios, Proportions, and Percents Ratios 6N9 6N3 Unit rates 6N5 6N6 6N14 Understanding proportions 6N14 Using cross products 6N14 Scale drawings 6N14 Percents, fractions, and decimals Finding a percent of a number 6N5 6N4 Adapted from Prentice Hall Courses Give examples of how ratios are used to represent comparisons; e.g., part-to-part, part-towhole, whole-to-part. Explain why a number is referred to as being “rational,” and recognize that the expression a/b can mean ‘a’ parts of size 1/b each, a divided by b, or the ratio of a to b. Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100. Use the order of operations, including the use of exponents, decimals and rational numbers, to simplify numerical expressions. Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions. Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions. Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions. Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions. Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100. Describe what it means to find a specific percent of a number, using real-life examples. Trumbull County Educational Service Center Page 2 6th Grade Topic Alignment Standards / Topics Code 6N5 6N14 Estimating with percents 6N15 6N4 6N14 6N15 Indicators Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100. Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions. Determine the percent of a number and solve related problems; e.g., find the percent markdown if the original price was $140, and the sale price is $100. Describe what it means to find a specific percent of a number, using real-life examples. Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions. Determine the percent of a number and solve related problems; e.g., find the percent markdown if the original price was $140, and the sale price is $100. Integers Using a number line 6N7 Adding and subtracting integers 6N7 Multiplying and Dividing integers Graphing in the Coordinate Plane 6N7 Enrichment Use simple expressions involving integers to represent and solve problems; e.g., if a running back loses 15 yards on the first carry but gains 8 yards on the second carry, what is the net gain/loss? Use simple expressions involving integers to represent and solve problems; e.g., if a running back loses 15 yards on the first carry but gains 8 yards on the second carry, what is the net gain/loss? Use simple expressions involving integers to represent and solve problems; e.g., if a running back loses 15 yards on the first carry but gains 8 yards on the second carry, what is the net gain/loss? Measurement Metric System Perimeter and Area of quadrilaterals Review 6M3 6M3a 6M4 6M5 Perimeter and Area of triangles 6M3 6M3b 6M6 Circumference of a Circle 6M2 6M3 6M3b Adapted from Prentice Hall Courses Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by: estimating lengths using string or links, areas using tiles or grid, and volumes using cubes; Determine which measure (perimeter, area, surface area, volume) matches the context for a problem situation; e.g., perimeter is the context for fencing a garden, surface area is the context for painting a room. Understand the difference between perimeter and area, and demonstrate that two shapes may have the same perimeter, but different areas or may have the same area, but different perimeters. Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by: measuring attributes (diameter, side lengths, or heights) and using established formulas for circles, triangles, rectangles, parallelograms and rectangular prisms. Describe what happens to the perimeter and area of a two-dimensional shape when the measurements of the shape are changed; e.g. length of sides are doubled. Use strategies to develop formulas for finding circumference and area of circles, and to determine the area of sectors; e.g., 1/2 circle, 2/3 circle, 1/3 circle, 1/4 circle. Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by: measuring attributes (diameter, side lengths, or heights) and using established formulas for circles, triangles, rectangles, parallelograms and rectangular prisms. Trumbull County Educational Service Center Page 3 6th Grade Topic Alignment Standards / Topics Code Indicators Surface Area of Prisms and Pyramids 6M4 6M1 Use strategies to develop formulas for finding circumference and area of circles, and to determine the area of sectors; e.g., 1/2 circle, 2/3 circle, 1/3 circle, 1/4 circle. Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by: measuring attributes (diameter, side lengths, or heights) and using established formulas for circles, triangles, rectangles, parallelograms and rectangular prisms. Determine which measure (perimeter, area, surface area, volume) matches the context for a problem situation; e.g., perimeter is the context for fencing a garden, surface area is the context for painting a room. Understand and describe the difference between surface area and volume. Surface area of Cylinders 6M3 6M1 Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by: Understand and describe the difference between surface area and volume. Volume of Rectangular Prisms 6M3 6M1 Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by: Understand and describe the difference between surface area and volume. Area of a Circle 6M2 6M3 6M3 b 6M3 Volume of Cylinders 6M3a 6M1 6M3 6M3b Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by: estimating lengths using string or links, areas using tiles or grid, and volumes using cubes; Understand and describe the difference between surface area and volume. Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by: measuring attributes (diameter, side lengths, or heights) and using established formulas for circles, triangles, rectangles, parallelograms and rectangular prisms. Geometry and Spatial Sense Points, Lines, Segments, and Rays 6G2 6G4 Angles 6G2 Triangles 6G1 6G2 6G3 Polygons 6G1 6G2 Congruent and Similar Figures Adapted from Prentice Hall Courses 6G6 Use standard language to define geometric vocabulary: vertex, face, altitude, diagonal, isosceles, equilateral, acute, obtuse and other vocabulary as appropriate. Identify and define relationships between planes; i.e., parallel, perpendicular and intersecting. Use standard language to define geometric vocabulary: vertex, face, altitude, diagonal, isosceles, equilateral, acute, obtuse and other vocabulary as appropriate. Classify and describe two-dimensional and three-dimensional geometric figures and objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides, congruent angles/sides. Use standard language to define geometric vocabulary: vertex, face, altitude, diagonal, isosceles, equilateral, acute, obtuse and other vocabulary as appropriate. Use multiple classification criteria to classify triangles; e.g., right scalene triangle. Classify and describe two-dimensional and three-dimensional geometric figures and objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides, congruent angles/sides. Use standard language to define geometric vocabulary: vertex, face, altitude, diagonal, isosceles, equilateral, acute, obtuse and other vocabulary as appropriate. Draw similar figures that model proportional relationships; e.g., model similar figures with a 1 to 2 relationship by sketching two of the same figure, one with corresponding sides twice the length of the other. Trumbull County Educational Service Center Page 4 6th Grade Topic Alignment Standards / Topics Code Symmetry 6G6 Transformation 6G5 Scale drawings 6G6 3 dimensional figures and spatial relations 6G1 6G2 6G7 Indicators Draw similar figures that model proportional relationships; e.g., model similar figures with a 1 to 2 relationship by sketching two of the same figure, one with corresponding sides twice the length of the other. Predict and describe sizes, positions and orientations of two-dimensional shapes after transformations such as reflections, rotations, translations and dilations. Draw similar figures that model proportional relationships; e.g., model similar figures with a 1 to 2 relationship by sketching two of the same figure, one with corresponding sides twice the length of the other. Classify and describe two-dimensional and three-dimensional geometric figures and objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides, congruent angles/sides. Use standard language to define geometric vocabulary: vertex, face, altitude, diagonal, isosceles, equilateral, acute, obtuse and other vocabulary as appropriate. Build three-dimensional objects with cubes, and sketch the two-dimensional representations of each side; i.e., projection sets. Patterns, Functions & Algebra Graphing functions 6P1 6P2 6P4 6P5 6P7 Describing a pattern 6P1 6P2 Variables and expressions 6P6 Writing algebraic expressions 6P2 Make a table and look for a pattern 6P1 Using number sense to solve one-step equations 6P3 The distributive property 6P3 Using Spreadsheets to Organize Data Graphing in the Coordinate Plane 6P8 6P5 Graphing functions 6P1 6P2 Adapted from Prentice Hall Courses Represent and analyze patterns, rules and functions, using physical materials, tables and graphs. Use words and symbols to describe numerical and geometric patterns, rules and functions. Solve simple linear equations and inequalities using physical models, paper and pencil, tables and graphs. Produce and interpret graphs that represent the relationship between two variables. Identify and describe situations with constant or varying rates of change, and compare them. Represent and analyze patterns, rules and functions, using physical materials, tables and graphs. Use words and symbols to describe numerical and geometric patterns, rules and functions. Evaluate simple expressions by replacing variables with given values, and use formulas in problem-solving situations. Use words and symbols to describe numerical and geometric patterns, rules and functions. Represent and analyze patterns, rules and functions, using physical materials, tables and graphs. Recognize and generate equivalent forms of algebraic expressions, and explain how the commutative, associative and distributive properties can be used to generate equivalent forms; e.g., perimeter as 2(l + w) or 2l + 2w. Recognize and generate equivalent forms of algebraic expressions, and explain how the commutative, associative and distributive properties can be used to generate equivalent forms; e.g., perimeter as 2(l + w) or 2l + 2w. Use technology to analyze change; e.g., use computer applications or graphing calculators to display and interpret rate of change. Produce and interpret graphs that represent the relationship between two variables. Represent and analyze patterns, rules and functions, using physical materials, tables and graphs. Use words and symbols to describe numerical and geometric patterns, rules and functions. Trumbull County Educational Service Center Page 5 6th Grade Topic Alignment Standards / Topics Code Indicators 6P4 6P5 Solve simple linear equations and inequalities using physical models, paper and pencil, tables and graphs. Produce and interpret graphs that represent the relationship between two variables. 6P7 Identify and describe situations with constant or varying rates of change, and compare them. Data Analysis and Probability Mean, Median, and Mode 6D4 Organizing and Displaying Data 6D2 6D4 Bar Graphs, Line Graphs, Circle Graphs 6D5 6D1 Understand the different information provided by measures of center (mean, mode and median) and measures of spread (range). Select, create and use graphical representations that are appropriate for the type of data collected. Understand the different information provided by measures of center (mean, mode and median) and measures of spread (range). Describe the frequency distribution of a set of data, as shown in a histogram or frequency table, by general appearance or shape; e.g., number of modes, middle of data, level of symmetry, outliers. Read, construct and interpret line graphs, circle graphs and histograms. 6D5 6D6 Select, create and use graphical representations that are appropriate for the type of data collected. Compare representations of the same data in different types of graphs, such as a bar graph and circle graph. Describe the frequency distribution of a set of data, as shown in a histogram or frequency table, by general appearance or shape; e.g., number of modes, middle of data, level of symmetry, outliers. Make logical inferences from statistical data. Stem-and Leaf Plots 6D2 6D6 Select, create and use graphical representations that are appropriate for the type of data collected. Make logical inferences from statistical data. Misleading Graphs and Statistics 6D3 Design and simulate an experiment 6D4 6D6 6D7 6D2 6D3 Adapted from Prentice Hall Courses Compare representations of the same data in different types of graphs, such as a bar graph and circle graph. Understand the different information provided by measures of center (mean, mode and median) and measures of spread (range). Make logical inferences from statistical data. Design an experiment to test a theoretical probability and explain how the results may vary. Trumbull County Educational Service Center Page 6