anchor.diff:  5.G.2,Geometry,Graph Points On The Coordinate Plane To Solve Real-World And Mathematical Problems.,"Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation."
   5.G.3,Geometry,Classify Two-Dimensional Figures Into Categories Based On Their Properties.,"Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles."
   5.G.4,Geometry,Classify Two-Dimensional Figures Into Categories Based On Their Properties.,Classify two-dimensional figures in a hierarchy based on properties.
  -6.RP.1,Ratios And Proportional Relationships,Understand 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. For example, The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. For every vote candidate A received, candidate C received nearly three votes."
  -6.RP.2,Ratios And Proportional Relationships,Understand 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. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.1"
  +6.RP.1,Ratios And Proportional Relationships,Understand 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. For example, ÒThe ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.Ó ÒFor every vote candidate A received, candidate C received nearly three votes.Ó"
  +6.RP.2,Ratios And Proportional Relationships,Understand 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. For example, ÒThis recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.Ó ÒWe paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.Ó1"
   6.RP.3,Ratios And Proportional Relationships,Understand 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."
   6.RP.3.a,Ratios And Proportional Relationships,Understand 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."
   6.RP.3.b,Ratios And Proportional Relationships,Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems.,"Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?"
   6.RP.3.c,Ratios And Proportional Relationships,Understand 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."
   6.RP.3.d,Ratios And Proportional Relationships,Understand 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.
  -6.NS.1,The Number System,Apply 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. For example, create a story context for (2/3)  (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3)  (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b)  (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?"
  +6.NS.1,The Number System,Apply 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. For example, create a story context for (2/3) Ö (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) Ö (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) Ö (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?"
   6.NS.2,The Number System,Compute Fluently With Multi-Digit Numbers And Find Common Factors And Multiples.,Fluently divide multi-digit numbers using the standard algorithm.
   6.NS.3,The Number System,Compute 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."
  -6.NS.4,The Number System,Compute 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 1100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2)."
  +6.NS.4,The Number System,Compute 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 1Ð100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2)."
   6.NS.5,The Number System,Apply 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."
   6.NS.6,The Number System,Apply 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.
  -6.NS.6.a,The Number System,Apply 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."
  +6.NS.6.a,The Number System,Apply 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., Ð(Ð3) = 3, and that 0 is its own opposite."
   6.NS.6.b,The Number System,Apply 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."
   6.NS.6.c,The Number System,Apply 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.
   6.NS.7,The Number System,Apply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.,Understand ordering and absolute value of rational numbers.
  -6.NS.7.a,The Number System,Apply 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. For example, interpret 3 > 7 as a statement that 3 is located to the right of 7 on a number line oriented from left to right."
  -6.NS.7.b,The Number System,Apply 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. For example, write 3 oC > 7 oC to express the fact that 3 oC is warmer than 7 oC."
  -6.NS.7.c,The Number System,Apply 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. For example, for an account balance of 30 dollars, write |30| = 30 to describe the size of the debt in dollars."
  -6.NS.7.d,The Number System,Apply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.,"Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than 30 dollars represents a debt greater than 30 dollars."
  +6.NS.7.a,The Number System,Apply 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. For example, interpret Ð3 > Ð7 as a statement that Ð3 is located to the right of Ð7 on a number line oriented from left to right."
  +6.NS.7.b,The Number System,Apply 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. For example, write Ð3 oC > Ð7 oC to express the fact that Ð3 oC is warmer than Ð7 oC."
  +6.NS.7.c,The Number System,Apply 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. For example, for an account balance of Ð30 dollars, write |Ð30| = 30 to describe the size of the debt in dollars."
  +6.NS.7.d,The Number System,Apply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.,"Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than Ð30 dollars represents a debt greater than 30 dollars."
   6.NS.8,The Number System,Apply 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.
   6.EE.1,Expressions And Equations,Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.,Write and evaluate numerical expressions involving whole-number exponents.
   6.EE.2,Expressions And Equations,Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.,"Write, read, and evaluate expressions in which letters stand for numbers."
  -6.EE.2.a,Expressions And Equations,Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.,"Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5  y."
  +6.EE.2.a,Expressions And Equations,Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.,"Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation ÒSubtract y from 5Ó as 5 Ð y."
   6.EE.2.b,Expressions And Equations,Apply 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. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms."
   6.EE.2.c,Expressions And Equations,Apply 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). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2."
   6.EE.3,Expressions And Equations,Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.,Apply the properties of operations to generate equivalent expressions.
  
positive.code: S.MD.5.a,Using Probability To Make Decisions,Use Probability To Evaluate Outcomes Of Decisions,"Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast- food restaurant."
  S.MD.5.b,Using Probability To Make Decisions,Use Probability To Evaluate Outcomes Of Decisions,"Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident."
  S.MD.6,Using Probability To Make Decisions,Use Probability To Evaluate Outcomes Of Decisions,"(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator)."
  S.MD.7,Using Probability To Make Decisions,Use Probability To Evaluate Outcomes Of Decisions,"(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game)."
negative.code: A.REI.12,Reasoning With Equations And Inequalities,Represent And Solve Equations And Inequalities Graphically,"Graph the solutions to a linear inequality in two variables as a half- plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes."
  F.IF.1,Interpreting Functions,Understand The Concept Of A Function And Use Function Notation,"Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x)."
  F.IF.2,Interpreting Functions,Understand The Concept Of A Function And Use Function Notation,"Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context."
  F.IF.3,Interpreting Functions,Understand The Concept Of A Function And Use Function Notation,"Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ³ 1."
  F.IF.4,Interpreting Functions,Interpret Functions That Arise In Applications In Terms Of The Context,"For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity._"
  F.IF.5,Interpreting Functions,Interpret Functions That Arise In Applications In Terms Of The Context,"Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function._"
  F.IF.6,Interpreting Functions,Interpret Functions That Arise In Applications In Terms Of The Context,Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph._
  