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6.RP.1Ratios And Proportional RelationshipsUnderstand Ratio Concepts And Use Ratio Reasoning To Solve Problems.Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
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6.RP.2Ratios And Proportional RelationshipsUnderstand Ratio Concepts And Use Ratio Reasoning To Solve Problems.Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.
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6.RP.3Ratios And Proportional RelationshipsUnderstand Ratio Concepts And Use Ratio Reasoning To Solve Problems.Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
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6.RP.3.aRatios And Proportional RelationshipsUnderstand Ratio Concepts And Use Ratio Reasoning To Solve Problems.Make tables of equivalent ratios relating quantities with whole- number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
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6.RP.3.bRatios And Proportional RelationshipsUnderstand Ratio Concepts And Use Ratio Reasoning To Solve Problems.Solve unit rate problems including those involving unit pricing and constant speed.
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6.RP.3.cRatios And Proportional RelationshipsUnderstand Ratio Concepts And Use Ratio Reasoning To Solve Problems.Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
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6.RP.3.dRatios And Proportional RelationshipsUnderstand Ratio Concepts And Use Ratio Reasoning To Solve Problems.Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
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6.NS.1The Number SystemApply And Extend Previous Understandings Of Multiplication And Division To Divide Fractions By Fractions.Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
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6.NS.2The Number SystemCompute Fluently With Multi-Digit Numbers And Find Common Factors And Multiples.Fluently divide multi-digit numbers using the standard algorithm.
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6.NS.3The Number SystemCompute Fluently With Multi-Digit Numbers And Find Common Factors And Multiples.Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
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6.NS.4The Number SystemCompute Fluently With Multi-Digit Numbers And Find Common Factors And Multiples.Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
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6.NS.5The Number SystemApply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
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6.NS.6The Number SystemApply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
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6.NS.6.aThe Number SystemApply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
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6.NS.6.bThe Number SystemApply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
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6.NS.6.cThe Number SystemApply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
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6.NS.7The Number SystemApply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.Understand ordering and absolute value of rational numbers.
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6.NS.7.aThe Number SystemApply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.
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6.NS.7.bThe Number SystemApply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.Write, interpret, and explain statements of order for rational numbers in real-world contexts.
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6.NS.7.cThe Number SystemApply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
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6.NS.7.dThe Number SystemApply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.Distinguish comparisons of absolute value from statements about order.
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6.NS.8The Number SystemApply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
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6.EE.1Expressions And EquationsApply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.Write and evaluate numerical expressions involving whole-number exponents.
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6.EE.2Expressions And EquationsApply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.Write, read, and evaluate expressions in which letters stand for numbers.
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6.EE.2.aExpressions And EquationsApply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.Write expressions that record operations with numbers and with letters standing for numbers.
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6.EE.2.bExpressions And EquationsApply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.
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6.EE.2.cExpressions And EquationsApply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole- number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
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6.EE.3Expressions And EquationsApply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.Apply the properties of operations to generate equivalent expressions.
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6.EE.4Expressions And EquationsApply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).
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6.EE.5Expressions And EquationsReason About And Solve One-Variable Equations And Inequalities.Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
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6.EE.6Expressions And EquationsReason About And Solve One-Variable Equations And Inequalities.Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
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6.EE.7Expressions And EquationsReason About And Solve One-Variable Equations And Inequalities.Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
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6.EE.8Expressions And EquationsReason About And Solve One-Variable Equations And Inequalities.Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
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6.EE.9Expressions And EquationsRepresent And Analyze Quantitative Relationships Between Dependent And Independent Variables.Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
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6.G.1GeometrySolve Real-World And Mathematical Problems Involving Area, Surface Area, And Volume.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.
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6.G.2GeometrySolve Real-World And Mathematical Problems Involving Area, Surface Area, And Volume.Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
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6.G.3GeometrySolve Real-World And Mathematical Problems Involving Area, Surface Area, And Volume.Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
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6.G.4GeometrySolve Real-World And Mathematical Problems Involving Area, Surface Area, And Volume.Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
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6.SP.1Statistics And ProbabilityDevelop Understanding Of Statistical Variability.Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
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6.SP.2Statistics And ProbabilityDevelop Understanding Of Statistical Variability.Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
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6.SP.3Statistics And ProbabilityDevelop Understanding Of Statistical Variability.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.
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6.SP.4Statistics And ProbabilitySummarize And Describe Distributions.Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
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6.SP.5Statistics And ProbabilitySummarize And Describe Distributions.Summarize numerical data sets in relation to their context, such as by:
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6.SP.5.aStatistics And ProbabilitySummarize And Describe Distributions.Reporting the number of observations.
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6.SP.5.bStatistics And ProbabilitySummarize And Describe Distributions.Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
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6.SP.5.cStatistics And ProbabilitySummarize And Describe Distributions.Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
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6.SP.5.dStatistics And ProbabilitySummarize And Describe Distributions.Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
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