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 6th Grade Math Pacing/Curriculum MapSouth Carolina Math StandardsSouth Carolina Support Document6th Grade Math Unpacked Standards DocumentiReady Year-Long PacingiReady ToolboxMDC Formative Assessment Lessons and Tasks6th Grade Essential StandardsFeedback for 21-22 RevisionsiReady Lesson NumberStandards“I Can” StatementsVocabularyStandards Mastery Assessment(30 minutes)Unit 1: Ratios and Proportional Relationships (25 days)Unit 1 ResourcesLesson 1: Ratios(4 days)6.RP.1 Interpret the concept of a ratio as the relationship between two quantities, including part to part and part to whole.Understand the concept of a ratio as a way of expressing relationships between quantities.Write a ratio to describe the relationship between two quantities.Write a ratio using three different formats: a to b, a/b, a:b.Use ratio language, e.g. for every, for each.Ratio 6.RP.A.1: RatiosLesson 2: Understand Unit Rate(3 days)**6.RP.2 Investigate relationships between ratios and rates.**6.RP.2a Translate between multiple representations of ratios (i.e., a/b, a:b, a to b, visual models).**6.RP.2b Recognize that a rate is a type of ratio involving two different units.**6.RP.2c Convert from rates to unit rates.Understand the concept of a unit rate.Use rate and unit rate language.Find rates and unit rate.RatioRateUnit rate6.RP.A.2: Unit RateLesson 3: Equivalent Ratios(5 days)6.RP.3 Apply the concepts of ratios and rates to solve real-world and mathematical problems.6.RP.3a Create a table consisting of equivalent ratios and plot the results on the coordinate plane.6.RP.3b Use multiple representations, including tape diagrams, tables, double number lines, and equations, to find missing values of equivalent ratios.6.RP.3c Use two tables to compare related ratios.Use a table to find equivalent ratios.Find missing values in equivalent ratio tables.Plot the pairs of values in a table on a coordinate plane.Use a table and graph to reason about equivalent ratios.Use a table and graph to compare ratios.Equivalent ratios6.RP.A.3a: Equivalent RatiosUnit 1: Mid-Unit AssessmentLesson 4: Solve Problems with Unit Rate(6 days)6.RP.3d Apply concepts of unit rate to solve problems, including unit pricing and constant speed.6.RP.3f Solve one-step problems involving ratios and unit rates (e.g., dimensional analysis).Solve unit rate problems about unit pricing.Solve unit rate problems involving constant speed.Use ratio reasoning to convert measurement units within the same system.Unit price6.RP.A.3b, 6.RP.A.3d: Solve Problems with Unit RatesLesson 5: Solve Problems with Percent(5 days)6.RP.3e Understand that a percentage is a rate per 100 and use this to solve problems involving wholes, parts, and percentages.Understand percent as a rate per hundred.Find a percent of a quantity as a rate per hundred. Solve percent problems involving finding the whole.Percent6.RP.A.3c: Solve Problems with PercentUnit 1: End-of-Unit AssessmentiReady Lesson NumberStandards“I Can” StatementsVocabularyStandards Mastery Assessment(30 minutes)Unit 2: The Number System (45 days)Unit 2 ResourcesLesson 6: Understand Division with Fractions(3 days)6.NS.1 Compute and represent quotients of positive fractions using a variety of procedures (e.g., visual models, equations, and real-world situations).Understand the meanings of division.Use a model to show division of fractions.Use an understanding of multiplication of fractions to explain division of fractions. 6.NS.A.1-1: Understand Division with FractionsLesson 7: Divide with Fractions(6 days)6.NS.1 Compute and represent quotients of positive fractions using a variety of procedures (e.g., visual models, equations, and real-world situations).Solve word problems using division of fractions.Write an equation to solve a problem using division of fractions.Write a story problem that will use division of fractions. Multiplicative inverseReciprocal6.NS.A.1-2: Divide with FractionsLesson 8: Divide Multi-Digit Numbers(4 days)6.NS.2 Fluently divide multi-digit whole numbers using a standard algorithmic approachFluently divide multi-digit numbers using the standard algorithm (4-digit by 2-digit)Understand how to set up a problem based on the context of the problem.Interpret what the quotient represents.Recognize that what is known or not known is based on the type of division needed.6.NS.B.2: Divide Multi-Digit NumbersUnit 2: Mid-Unit AssessmentLesson 9: Add and Subtract Decimals(4 days)6.NS.3 Fluently add, subtract, multiply and divide multi-digit decimal numbers using a standard algorithmic approach.Understand the role of place value in the operations of addition and subtraction.Identify when it is appropriate to use the standard algorithm.Estimate sums and difference before using the standard algorithm, and use these sums and differences to check reasonableness of answers.Add and subtract multi-digit decimals.Model the operations of addition and subtraction with manipulatives, diagrams, and story contexts for multi-digit decimals.6.NS.B.3-1: Add and Subtract Multi-Digit DecimalsLesson 10: Multiply and Divide Decimals(4 days)6.NS.3 Fluently add, subtract, multiply and divide multi-digit decimal numbers using a standard algorithmic approach.Fluently multiply and divide multi-digit decimals using the standard algorithm for each operation.Understand the role of place value in the operations of multiplication and division.Identify when it is appropriate to use the standard algorithm.Use estimation to approximate products and quotients to check for reasonableness of answers.Model the operations of multiplication and division with manipulatives, diagrams, and story contexts for multi-digit decimals.6.NS.B.3-2: Multiply and Divide DecimalsLesson 11: Common Factors and Multiples(4 days)6.NS.4 Find common factors and multiples using two whole numbers. 6.NS.4a Compute the greatest common factor (GCF) of two numbers both less than or equal to 100.6.NS.4b Compute the least common multiple (LCM) of two numbers both less than or equal to 12.6.NS.4c Express sums of two whole numbers, each less than or equal to 100, using the distributive property to factor out a common factor of the original addends.Understand that greatest common factor (GCF) and least common multiple (LCM) are ways to discuss number relationships in multiplication and division.Use the distributive property to express a sum of two numbers with a common factor as a multiple of a sum of two whole numbers with no common factor.Find the GCF of two whole numbers less than or equal to 100 and the LCM of two whole numbers less than or equal to 12.Model factorization of whole numbers 1-100.Greatest common factor (GCF)Least common multiple (LCM).NS.B.4: Common Factors and Multiples6Lesson 12: Understand Positive and Negative Numbers(3 days)**6.NS.5 Understand that the positive and negative representations of a number are opposites in direction and value. Use integers to represent quantities in real-world situations and explain the meaning of zero in each situation.**6.NS.6a Understand the concept of opposite numbers, including zero, and their relative locations on the number line.Relate positive and negative numbers to the real world.Understand integers and other rational numbers as points on a number line.Understand the sign of a number indicates its direction on the number line from zero.Recognize that the opposite of a number is the number itself; 0 is its own opposite.Positive numbersNegative numbersSigned numbersOpposite numbersIntegers6.NS.C.5, 6.NS.C.6a, 6.NS.C.6c-1: Positive and Negative NumbersLesson 13: Absolute Value and Ordering Numbers(5 days)**6.NS.5 Understand that the positive and negative representations of a number are opposites in direction and value. Use integers to represent quantities in real-world situations and explain the meaning of zero in each situation.6.NS.7 Understand and apply the concepts of comparing, ordering, and finding absolute value to rational numbers.6.NS.7a Interpret statements using equal to (=) and not equal to (≠).6.NS.7b Interpret statements using less than (<), greater than (>), and equal to (=) as relative locations on the number line6.NS.7c Use concepts of equality and inequality to write and to explain real-world andmathematical situations6.NS.7d Understand that absolute value represents a number’s distance from zero on the number line and use the absolute value of a rational number to represent real world situations.6.NS.7e Recognize the difference between comparing absolute values and ordering rational numbers. For negative rational numbers, understand that as the absolute value increases, the value of the negative number decreases.Write, interpret, and explain statements of order for rational numbers. Understand absolute value of a rational number as the distance from 0 on the number line. Interpret absolute value as the magnitude of the number from 0 in a real-world situation.Distinguish comparisons of absolute value from statements about order.Absolute value6.NS.C.7: Absolute Value and Ordering NumbersLesson 14: The Coordinate Plane(6 days)**6.NS.6b Understand that the signs of the coordinates in ordered pairs indicate their location on an axis or in a quadrant on the coordinate plane.**6.NS.6c Recognize when ordered pairs are reflections of each other on the coordinate plane across one axis, both axes, or the origin. **6.NS.6d Plot rational numbers on number lines and ordered pairs on coordinate planes6.NS.8 Extend knowledge of the coordinate plane to solve real-world and mathematical problems involving rational numbers6.NS.8a Plot points in all four quadrants to represent the problem6.NS.8b Find the distance between two points when ordered pairs have the same x-coordinates or same y-coordinates6.NS.8c Relate finding the distance between two points in a coordinate plane to absolute value using a number line. Identify the origin and four quadrants of the coordinate plane. Plot ordered pairs in all quadrants.Use the signs of coordinates to locate points in quadrants. Recognize that if the coordinates only differ by the signs, the points are reflections across one or both axes.Use the coordinates and absolute values to find distances between points.Solve real-world problems by graphing points in all quadrants.Quadrants6.NS.C.6b, 6.NS.C.6c-2: Ordered Pairs6.NS.C.8: Solve Problems Using the Coordinate PlaneTranslating Between Fractions, Decimals and PercentsNOT IN IREADY- new to SCCCR(4 days)**6.NS.9 Investigate and translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Fractions should be limited to those with denominators of 2, 3, 4, 5, 8, 10, and 100.Translate between fractions, decimals, and percents.N/AUnit 2: End-of-Unit AssessmentADD QUESTIONS ON TRANSLATING BETWEEN FRACTIONS, DECIMALS, AND PERCENTS TO THE IREADY ASSESSMENTS, AS IREADY DOES NOT INCLUDE TRANSLATING BETWEEN FRACTIONS, DECIMALS, AND PERCENTS IN THIS UNIT.iReady Lesson NumberStandards“I Can” StatementsVocabularyStandards Mastery Assessment(30 minutes)Unit 3: Expressions and Equations (38 days)Unit 3 ResourcesLesson 15: Numerical Expressions with Exponents(5 days)6.EEI.1 Write and evaluate numerical expressions involving whole-number exponents and positive rational number bases using the Order of Operations.Write numerical expressions involving whole-number exponents.Evaluate numerical expressions involving whole-number exponents.BaseExponentExponential Expression6.EE.A.1: Numerical Expressions With ExponentsLesson 16: Algebraic Expressions(6 days)6.EEI.2 Extend the concepts of numerical expressions to algebraic expressions involving positive rational numbers. 6.EEI.2a Translate between algebraic expressions and verbal phrases that include variables.6.EEI.2b Investigate and identify parts of algebraic expressions using mathematical terminology, including term, coefficient, constant, and factor6.EEI.2c Evaluate real-world and algebraic expressions for specific values using the Order of Operations. Grouping symbols should be limited to parentheses, braces, and brackets. Exponents should be limited to whole-numbers.Write, read, and evaluate variable expressions.Apply the order of operations on expressions with variables, including those with exponents.Translate an expression from its word form to an algebraic expression and vice versa.Identify parts of expressions using appropriate mathematical vocabulary.CoefficientConstantVariableTermVariable term6.EE.A.2a, 6.EE.A.2b: Write Expressions6.EE.A.2c: Evaluate ExpressionsLesson 17: Equivalent Expressions(6 days)6.EEI.3 Apply mathematical properties (e.g., commutative, associative, distributive) to generate equivalent expressions. 6.EEI.4 Apply mathematical properties (e.g., commutative, associative, distributive) to justify that two expressions are equivalent. Understand that the properties used with numbers also apply to expressions with variables.Recognize and generate equivalent expressions.Substitute values into expressions to prove mutative Property of AdditionAssociative Property of AdditionDistributive PropertyLike terms6.EE.A.3, 6.EE.A.4: Equivalent ExpressionsUnit 3: Mid-Unit AssessmentLesson 18: Understand Solutions to Equations(3 days)6.EEI.5 Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use models to write and solve equations.Use substitution to determine whether a given number in a specified set makes an equation true.EquationLesson 19: Solve Equations(6 days)6.EEI.6 Write expressions using variables to represent quantities in real-world and mathematical situations. Understand the meaning of the variable in the context of the situation**6.EEI.7 Write and solve one-step linear equations in one variable involving non-negative rational numbers for real-world and mathematical situations. Recognize that real-world mathematical problems can be expressed using a variable to represent an unknown.Recognize that both sides of an equation are equal, and whatever operation is performed on one side of the equation must be done to on the other side to maintain the equality.Write and solve equations that represent real-world mathematical problems that use variables and involve non-negative rational numbers.6.EE.B.5-1, 6.EE.B.6, 6.EE.B.7: Solve EquationsLesson 20: Solving Inequalities(5 days)**6.EEI.8 Extend knowledge of inequalities used to compare numerical expressions to include algebraic expressions in real-world and mathematical situations. **6.EEI.8a Write an inequality of the form ? > ? or ? < ? and graph the solution set on a number line.**6.EEI.8b Recognize that inequalities have infinitely many solutionsWrite an inequality that represents real-world mathematical problems containing a constraint or a condition (<,>)Recognize that a variable can stand for an infinite number of solutions when used in inequalities.Represent inequalities on a number line.Inequality6.EE.B.5-2: Solve InequalitiesLesson 21: Dependent and Independent Variables(5 days)6.EEI.9 Investigate multiple representations of relationships in real-world and mathematical situations.6.EEI.9a Write an equation that models a relationship between independent and dependent variables. 6.EEI.9b Analyze the relationship between independent and dependent variables using graphs and tables6.EEI.9c Translate among graphs, tables, and equationsRecognize that a change in the independent variable creates a change in the dependent variable.Make a table, graph, or equation to represent a problem’s context.Identify relationships between tables, graphs, and equations.Recognize when quantitative relationships between dependent and independent relationships are linear.Dependent variableIndependent variable6.EE.C.9: Dependent and Independent VariablesUnit 3: End-of-Unit AssessmentiReady Lesson NumberStandards“I Can” StatementsVocabularyStandards Mastery Assessment(30 minutes)Unit 4: Geometry (17 days)Unit 4 ResourcesLesson 22: Area of Polygons(4 days)**6.GM.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.Identify special quadrilaterals (squares, rhombi, trapezoids, parallelograms, rectangles, and kites).Relate the area of triangles and the area of rectangles.Identify the relationship between bases and heights in polygons.Decompose and compose polygons into rectangles and triangles to find the area. 6.G.A.1: Area of PolygonsLesson 23: Polygons in the Coordinate Plane(4 days)6.GM.3 Apply the concepts of polygons and the coordinate plane to real-world and mathematical situations. 6.GM.3a Given coordinates of the vertices, draw a polygon in the coordinate plane6.GM.3b Find the length of an edge if the vertices have the same x-coordinates or same y-coordinates.Understand that a line segment from one coordinate pair to another represents a distance.Understand that if two points have the same x- or y-coordinates they are on the same vertical or horizontal line.Find the vertical or horizontal distance between two points on the coordinate plane.Plot points in all four quadrants of the Cartesian coordinate plane.Plot a polygon in the Cartesian coordinate plane with given coordinates.Polygon6.G.A.3: Polygons in the Coordinate PlaneLesson 24: Nets and Surface Area(4 days)6.GM.4 Unfold three-dimensional figures into two-dimensional rectangles and triangles (nets) to find the surface area and to solve real-world and mathematical problemsRecognize that surfaces of some three-dimensional shapes are composed of two-dimensional faces (polygons).Use a net to represent a 3D figure (polyhedron).Use a net to find the surface area of polyhedron made up of rectangles and triangles.BaseNetSurface areaTriangular prismPyramid6.G.A.4: Nets and Surface AreaLesson 25: Volume(4 days)6.GM.2 Use visual models (e.g., model by packing) to discover that the formulas for the volume of a right rectangular prism (? = ???, ? = ??) are the same for whole or fractional edge lengths. Apply these formulas to solve real-world and mathematical problems. Measuring with fractional units requires relating volume to multiplication with fractions.Use the formulas: V=lwh and V=BhProve that the volume formula works by creating diagrams of prisms with unit fraction edge lengths and showing how unit fraction cubes pack them.6.G.A.2: VolumeUnit 4: End-of-Unit AssessmentiReady Lesson NumberStandards“I Can” StatementsVocabularyStandards Mastery Assessment(30 minutes)Unit 5: Statistics and Probability (16 days)Unit 5 ResourcesLesson 26: Understand Statistical Questions(3 days)6.DS.1 Differentiate between statistical and non-statistical questions. Understand that data generated from statistical questions will varyRecognize that responses to statistical questions have variations that can be used to draw conclusions about the data set.Identify the difference between a statistical and non-statistical question.Write a simple statistical question.Create models that represent the data from statistical questions such as charts and tables.Statistical questions6.SP.A.1, 6.SP.A.2: Statistical QuestionsLesson 27: Measures of Center and Variability(4 days)**6.DS.2 Use center (mean, median, mode), spread (range, interquartile range, mean absolute value), and shape (symmetrical, skewed left, skewed right) to describe the distribution of a set of data collected to answer a statistical question. 6.DS.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. Understand that a data distribution can be viewed by its center (mean, median, and model), spread (range), and overall shape, and it can be analyzed by its distribution.Understand that the mean, median, and mode of a set of numerical data are measures of center of that set of data.Understand that the range of a set of numerical data is a measure of how the data varies.ClusterSkewed leftSkewed rightSymmetrical graphsPeakOutlierMedianModeRangeMean Absolute Deviation (MAD)6.SP.A.3: Measures of Center and VariabilityLesson 28: Display Data on Dot Plots, Histograms, and Box Plots(4 days)6.DS.4 Select and create an appropriate display for numerical data, including dot plots, histograms, and box plots. Create dot plots, histograms, and box plots, including labeling and scaling axes appropriately.Know when data are best represented on dot plots, histograms, or box plots.Describe the overall pattern of data, determine variability, and identify striking deviations from the overall pattern. Lower quartileUpper quartileBox plotInterquartile range (IQR)6.SP.B.4: Display DataLesson 29: Analyze Numerical Data(4 days)6.DS.5 Describe numerical data sets in relation to their real-world context. 6.DS.5a State the sample size6.DS.5b Describe the qualitative aspects of the data (e.g., how it was measured, units of measurement)6.DS.5c Give measures of center (median, mean).6.DS.5d Find measures of variability (interquartile range, mean absolute deviation) using a number line.6.DS.5e Describe the overall pattern (shape) of the distribution.6.DS.5f Justify the choices for measure of center and measure of variability based on the shape of the distribution5.DS.5g Describe the impact that inserting or deleting a data point has on the measures of center (median, mean) for a data set.Interpret a set of numerical data by noticing and describing patterns and deviations.Understand mean absolute deviation (MAD).Determine variability (IQR, MAD).6.SP.B.5: Analyze Numerical DataUnit 5: End-of-Unit Assessment**These standards were identified as essential learning for the next grade level. 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