anchor.diff:  2.MD.5,Measurement And Data,Relate Addition And Subtraction To Length.,"Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem."
   2.MD.6,Measurement And Data,Relate Addition And Subtraction To Length.,"Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram."
   2.MD.7,Measurement And Data,Work With Time And Money.,"Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m."
  -2.MD.8,Measurement And Data,Work With Time And Money.,"Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and  symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?"
  +2.MD.8,Measurement And Data,Work With Time And Money.,"Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?"
   2.MD.9,Measurement And Data,Represent And Interpret Data.,"Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units."
   2.MD.10,Measurement And Data,Represent And Interpret Data.,"Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put- together, take-apart, and compare problems4 using information presented in a bar graph."
   2.G.1,Geometry,Reason With Shapes And Their Attributes.,"Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.5 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes."
   2.G.2,Geometry,Reason With Shapes And Their Attributes.,Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
   2.G.3,Geometry,Reason With Shapes And Their Attributes.,"Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape."
   3.OA.1,Operations And Algebraic Thinking,Represent And Solve Problems Involving Multiplication And Division.,"Interpret products of whole numbers, e.g., interpret 5 _ 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 _ 7."
  -3.OA.2,Operations And Algebraic Thinking,Represent And Solve Problems Involving Multiplication And Division.,"Interpret whole-number quotients of whole numbers, e.g., interpret 56  8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56  8."
  +3.OA.2,Operations And Algebraic Thinking,Represent And Solve Problems Involving Multiplication And Division.,"Interpret whole-number quotients of whole numbers, e.g., interpret 56 Ö 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 Ö 8."
   3.OA.3,Operations And Algebraic Thinking,Represent And Solve Problems Involving Multiplication And Division.,"Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1"
  -3.OA.4,Operations And Algebraic Thinking,Represent And Solve Problems Involving Multiplication And Division.,"Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 _ ? = 48, 5 =   3, 6 _ 6 = ?."
  +3.OA.4,Operations And Algebraic Thinking,Represent And Solve Problems Involving Multiplication And Division.,"Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 _ ? = 48, 5 = ð Ö 3, 6 _ 6 = ?."
   3.OA.5,Operations And Algebraic Thinking,Understand Properties Of Multiplication And The Relationship Between Multiplication And Division.,"Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 _ 4 = 24 is known, then 4 _ 6 = 24 is also known. (Commutative property of multiplication.) 3 _ 5 _ 2 can be found by 3 _ 5 = 15, then 15 _ 2 = 30, or by 5 _ 2 = 10, then 3 _ 10 = 30. (Associative property of multiplication.) Knowing that 8 _ 5 = 40 and 8 _ 2 = 16, one can find 8 _ 7 as 8 _ (5 + 2) = (8 _ 5) + (8 _ 2) = 40 + 16 = 56. (Distributive property.)"
  -3.OA.6,Operations And Algebraic Thinking,Understand Properties Of Multiplication And The Relationship Between Multiplication And Division.,"Understand division as an unknown-factor problem. For example, find 32  8 by finding the number that makes 32 when multiplied by 8."
  -3.OA.7,Operations And Algebraic Thinking,Multiply And Divide Within 100.,"Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 _ 5 = 40, one knows 40  5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers."
  +3.OA.6,Operations And Algebraic Thinking,Understand Properties Of Multiplication And The Relationship Between Multiplication And Division.,"Understand division as an unknown-factor problem. For example, find 32 Ö 8 by finding the number that makes 32 when multiplied by 8."
  +3.OA.7,Operations And Algebraic Thinking,Multiply And Divide Within 100.,"Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 _ 5 = 40, one knows 40 Ö 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers."
   3.OA.8,Operations And Algebraic Thinking,"Solve Problems Involving The Four Operations, And Identify And Explain Patterns In Arithmetic.",Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3
   3.OA.9,Operations And Algebraic Thinking,"Solve Problems Involving The Four Operations, And Identify And Explain Patterns In Arithmetic.","Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends."
   3.NBT.1,Number And Operations In Base Ten,Use Place Value Understanding And Properties Of Operations To Perform Multi-Digit Arithmetic.4,Use place value understanding to round whole numbers to the nearest 10 or 100.
   3.NBT.2,Number And Operations In Base Ten,Use Place Value Understanding And Properties Of Operations To Perform Multi-Digit Arithmetic.4,"Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction."
  -3.NBT.3,Number And Operations In Base Ten,Use Place Value Understanding And Properties Of Operations To Perform Multi-Digit Arithmetic.4,"Multiply one-digit whole numbers by multiples of 10 in the range 1090 (e.g., 9 _ 80, 5 _ 60) using strategies based on place value and properties of operations."
  -3.NF.1,Number And OperationsFractions5,Develop Understanding Of Fractions As Numbers.,Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
  -3.NF.2,Number And OperationsFractions5,Develop Understanding Of Fractions As Numbers.,Understand a fraction as a number on the number line; represent fractions on a number line diagram.
  -3.NF.2.a,Number And OperationsFractions5,Develop Understanding Of Fractions As Numbers.,Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
  -3.NF.2.b,Number And OperationsFractions5,Develop Understanding Of Fractions As Numbers.,Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
  -3.NF.3,Number And OperationsFractions5,Develop Understanding Of Fractions As Numbers.,"Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size."
  -3.NF.3.a,Number And OperationsFractions5,Develop Understanding Of Fractions As Numbers.,"Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line."
  -3.NF.3.b,Number And OperationsFractions5,Develop Understanding Of Fractions As Numbers.,"Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model."
  -3.NF.3.c,Number And OperationsFractions5,Develop Understanding Of Fractions As Numbers.,"Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram."
  -3.NF.3.d,Number And OperationsFractions5,Develop Understanding Of Fractions As Numbers.,"Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model."
  +3.NBT.3,Number And Operations In Base Ten,Use Place Value Understanding And Properties Of Operations To Perform Multi-Digit Arithmetic.4,"Multiply one-digit whole numbers by multiples of 10 in the range 10Ð90 (e.g., 9 _ 80, 5 _ 60) using strategies based on place value and properties of operations."
  +3.NF.1,Number And OperationsÑFractions5,Develop Understanding Of Fractions As Numbers.,Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
  +3.NF.2,Number And OperationsÑFractions5,Develop Understanding Of Fractions As Numbers.,Understand a fraction as a number on the number line; represent fractions on a number line diagram.
  +3.NF.2.a,Number And OperationsÑFractions5,Develop Understanding Of Fractions As Numbers.,Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
  +3.NF.2.b,Number And OperationsÑFractions5,Develop Understanding Of Fractions As Numbers.,Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
  +3.NF.3,Number And OperationsÑFractions5,Develop Understanding Of Fractions As Numbers.,"Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size."
  +3.NF.3.a,Number And OperationsÑFractions5,Develop Understanding Of Fractions As Numbers.,"Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line."
  +3.NF.3.b,Number And OperationsÑFractions5,Develop Understanding Of Fractions As Numbers.,"Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model."
  +3.NF.3.c,Number And OperationsÑFractions5,Develop Understanding Of Fractions As Numbers.,"Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram."
  +3.NF.3.d,Number And OperationsÑFractions5,Develop Understanding Of Fractions As Numbers.,"Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model."
   3.MD.1,Measurement And Data,"Solve Problems Involving Measurement And Estimation Of Intervals Of Time, Liquid Volumes, And Masses Of Objects.","Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram."
   3.MD.2,Measurement And Data,"Solve Problems Involving Measurement And Estimation Of Intervals Of Time, Liquid Volumes, And Masses Of Objects.","Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.7"
  -3.MD.3,Measurement And Data,Represent And Interpret Data.,"Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets."
  -3.MD.4,Measurement And Data,Represent And Interpret Data.,"Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters."
  +3.MD.3,Measurement And Data,Represent And Interpret Data.,"Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step Òhow many moreÓ and Òhow many lessÓ problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets."
  +3.MD.4,Measurement And Data,Represent And Interpret Data.,"Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate unitsÑ whole numbers, halves, or quarters."
   3.MD.5,Measurement And Data,Geometric Measurement: Understand Concepts Of Area And Relate Area To Multiplication And To Addition.,Recognize area as an attribute of plane figures and understand concepts of area measurement.
  -3.MD.5.a,Measurement And Data,Geometric Measurement: Understand Concepts Of Area And Relate Area To Multiplication And To Addition.,"A square with side length 1 unit, called a unit square, is said to have one square unit of area, and can be used to measure area."
  +3.MD.5.a,Measurement And Data,Geometric Measurement: Understand Concepts Of Area And Relate Area To Multiplication And To Addition.,"A square with side length 1 unit, called Òa unit square,Ó is said to have Òone square unitÓ of area, and can be used to measure area."
   3.MD.5.b,Measurement And Data,Geometric Measurement: Understand Concepts Of Area And Relate Area To Multiplication And To Addition.,A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
   3.MD.6,Measurement And Data,Geometric Measurement: Understand Concepts Of Area And Relate Area To Multiplication And To Addition.,"Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units)."
   3.MD.7,Measurement And Data,Geometric Measurement: Understand Concepts Of Area And Relate Area To Multiplication And To Addition.,Relate area to the operations of multiplication and addition.
  
positive.code: F.BF.2,Building Functions,Build A Function That Models A Relationship Between Two Quantities,"Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms._"
  F.BF.3,Building Functions,Build New Functions From Existing Functions,"Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them."
  F.BF.4,Building Functions,Build New Functions From Existing Functions,Find inverse functions.
  F.BF.4.a,Building Functions,Build New Functions From Existing Functions,"Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x1) for x =_ 1."
  F.BF.4.b,Building Functions,Build New Functions From Existing Functions,(+) Verify by composition that one function is the inverse of another.
  F.BF.4.c,Building Functions,Build New Functions From Existing Functions,"(+) Read values of an inverse function from a graph or a table, given that the function has an inverse."
  F.BF.4.d,Building Functions,Build New Functions From Existing Functions,(+) Produce an invertible function from a non-invertible function by restricting the domain.
  
negative.code: G.GPE.1,Expressing Geometric Properties With Equations,Translate Between The Geometric Description And The Equation For A Conic Section,Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
  G.GPE.2,Expressing Geometric Properties With Equations,Translate Between The Geometric Description And The Equation For A Conic Section,Derive the equation of a parabola given a focus and directrix.
  G.GPE.3,Expressing Geometric Properties With Equations,Translate Between The Geometric Description And The Equation For A Conic Section,"(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant."
  G.GPE.4,Expressing Geometric Properties With Equations,Use Coordinates To Prove Simple Geometric Theorems Algebraically,"Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, Ã3) lies on the circle centered at the origin and containing the point (0, 2)."
  G.GPE.5,Expressing Geometric Properties With Equations,Use Coordinates To Prove Simple Geometric Theorems Algebraically,"Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point)."
  G.GPE.6,Expressing Geometric Properties With Equations,Use Coordinates To Prove Simple Geometric Theorems Algebraically,Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
  G.GPE.7,Expressing Geometric Properties With Equations,Use Coordinates To Prove Simple Geometric Theorems Algebraically,"Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula._"
  G.GMD.1,Geometric Measurement And Dimension,Explain Volume Formulas And Use Them To Solve Problems,"Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, CavalieriÕs principle, and informal limit arguments."
  G.GMD.2,Geometric Measurement And Dimension,Explain Volume Formulas And Use Them To Solve Problems,(+) Give an informal argument using CavalieriÕs principle for the formulas for the volume of a sphere and other solid figures.
  G.GMD.3,Geometric Measurement And Dimension,Explain Volume Formulas And Use Them To Solve Problems,"Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems._"
  G.GMD.4,Geometric Measurement And Dimension,Visualize Relationships Between Two-Dimensional And Three- Dimensional Objects,"Identify the shapes of two-dimensional cross-sections of three- dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects."
  G.MG.1,Modeling With Geometry,Apply Geometric Concepts In Modeling Situations,"Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder)._"
  