The Common Core in Wyoming

RP Ratios and Proportional Relationships

• RP.A Understand ratio concepts and use ratio reasoning to solve problems.

  • RP.A.B.1 Basic students write a ratio relationship between two quantities;

    • Write a ratio (6-R.1)
    • Write an equivalent ratio (6-R.6)

  • RP.A.P.1 Proficient students describe a ratio relationship between two quantities, including comparing one of the quantities to the total;

    • Write a ratio: word problems (6-R.3)

  • RP.A.B.2 Basic students write a unit rate to describe two quantities using whole numbers;

    • Unit rates (6-R.9)

  • RP.A.P.2 Proficient students write a unit rate to describe two quantities using rational numbers and use unit rate language to describe two quantities;

    • Unit rates (6-R.9)

  • RP.A.A.1 Advanced students explain the concept of a unit rate using unit rate language;

    • Unit rates (6-R.9)
    • Ratios and rates: word problems (6-R.15)

  • RP.A.B.3 Basic students make tables of equivalent ratios relating quantities with whole number measurements and plot the pairs of values on the coordinate plane;

    • Ratio tables (6-R.7)

  • RP.A.P.3 Proficient students determine missing values in tables of equivalent ratios relating quantities with whole number measurements;

    • Write an equivalent ratio (6-R.6)
    • Ratio tables (6-R.7)

  • RP.A.A.2 Advanced students compare ratios using tables of equivalent ratios relating quantities with whole number measurements;

  • RP.A.B.4 Basic students solve unit rate problems given the unit rate;

    • Unit prices with fractions and decimals (6-V.3)

  • RP.A.P.4 Proficient students solve unit rate problems that require determining a unit rate;

    • Unit rates (6-R.9)
    • Ratios and rates: word problems (6-R.15)

  • RP.A.A.3 Advanced students solve unit rate problems that require determining two unit rates;

    • Unit prices (6-V.2)
    • Unit prices with customary unit conversions (6-V.4)

  • RP.A.B.5 Basic students solve for a percent of a quantity given the whole of 10 or 100;

  • RP.A.P.5 Proficient students solve, in a mathematical context, for a percent of a quantity as a rate per 100 and to solve problems that involve finding the whole, given the part and the percent;

    • Percents of numbers and money amounts (6-S.11)
    • Percents of numbers: fractional and decimal percents (6-S.13)
    • Find what percent one number is of another (6-S.14)

  • RP.A.A.4 Advanced students solve, in a real-world context, for a percent of a quantity as a rate per 100 and to solve problems that involve finding the whole, given the part and the percent;

    • Percents of numbers and money amounts (6-S.11)
    • Percents of numbers: word problems (6-S.12)
    • Find what percent one number is of another: word problems (6-S.15)
    • Find the total given a part and a percent (6-S.16)
    • Which is the better coupon? (6-V.1)
    • Sale prices (6-V.5)
    • Sale prices: find the original price (6-V.6)
    • Percents - calculate tax, tip, mark-up, and more (6-V.7)

  • RP.A.B.6 Basic students use ratio reasoning to convert measurement units within the same system.

    • Convert and compare customary units (6-T.3)
    • Customary unit conversions involving fractions and mixed numbers (6-T.6)
    • Convert and compare metric units (6-T.7)

  • RP.A.P.6 Proficient students use ratio reasoning to convert measurement units and to transform units appropriately when multiplying or dividing quantities.

    • Convert and compare customary units (6-T.3)
    • Multiply and divide mixed customary units (6-T.5)
    • Customary unit conversions involving fractions and mixed numbers (6-T.6)
    • Convert and compare metric units (6-T.7)
    • Convert between customary and metric systems (6-T.9)

  • RP.A.A.5 Advanced students use ratio reasoning to convert measurement units and transform units appropriately when multiplying and dividing in a real-world context.

    • Convert and compare customary units (6-T.3)
    • Multiply and divide mixed customary units (6-T.5)
    • Customary unit conversions involving fractions and mixed numbers (6-T.6)
    • Convert and compare metric units (6-T.7)
    • Convert between customary and metric systems (6-T.9)
    • Unit prices with customary unit conversions (6-V.4)

NS The Number System

• NS.B Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

  • NS.B.B.1 Basic students compute quotients of a fraction by a unit fraction;

  • NS.B.P.1 Proficient students compute quotients of any two fractions including a mixed number;

    • Divide fractions (6-L.6)
    • Divide fractions and mixed numbers (6-L.9)

  • NS.B.B.2 Basic students solve problems in mathematical contexts involving division of a fraction by a unit fraction.

  • NS.B.P.2 Proficient students solve problems in mathematical contexts involving division of fractions by fractions.

    • Divide fractions (6-L.6)

  • NS.B.A.1 Advanced students interpret quotients of fractions by identifying real-world contexts.

    • Divide fractions by whole numbers in recipes (6-L.4)
    • Divide fractions and mixed numbers: word problems (6-L.10)

• NS.C Compute fluently with multi-digit numbers and find common factors and multiples.

  • NS.C.B.1 Basic students divide three-digit or four-digit dividends by two-digit divisors using the standard algorithm;

    • Divide 4-digit numbers by 2-digit numbers (5-D.16)

  • NS.C.P.1 Proficient students divide multi-digit numbers with fractional remainders using the standard algorithm;

    • Divide whole numbers - 2-digit divisors (6-C.5)
    • Divide whole numbers - 3-digit divisors (6-C.6)

  • NS.C.B.2 Basic students add, subtract, multiply, or divide decimals to tenths using the standard algorithms;

    • Maps with decimal distances (6-G.5)
    • Multiply decimals (6-H.3)
    • Division with decimal divisors (6-H.9)

  • NS.C.P.2 Proficient students add, subtract, multiply, or divide decimals to hundredths using the standard algorithms;

    • Add and subtract decimal numbers (6-G.1)
    • Add and subtract decimals: word problems (6-G.2)
    • Multiply decimals (6-H.3)
    • Divide decimals by whole numbers (6-H.5)
    • Divide decimals by whole numbers: word problems (6-H.6)
    • Multiply and divide decimals by powers of ten (6-H.7)
    • Division with decimal divisors (6-H.9)
    • Add, subtract, multiply, or divide two decimals (6-O.6)
    • Add, subtract, multiply, or divide two decimals: word problems (6-O.7)
    • Evaluate numerical expressions involving decimals (6-O.8)

  • NS.C.A.1 Advanced students add, subtract, multiply, or divide decimals to thousandths using the standard algorithms for each operation;

    • Add and subtract decimal numbers (6-G.1)
    • Add and subtract decimals: word problems (6-G.2)
    • Multiply decimals (6-H.3)
    • Divide decimals by whole numbers (6-H.5)
    • Divide decimals by whole numbers: word problems (6-H.6)
    • Multiply and divide decimals by powers of ten (6-H.7)
    • Division with decimal divisors (6-H.9)
    • Add, subtract, multiply, or divide two decimals (6-O.6)
    • Add, subtract, multiply, or divide two decimals: word problems (6-O.7)
    • Evaluate numerical expressions involving decimals (6-O.8)

  • NS.C.B.3 Basic students determine the greatest common factor of two whole numbers less than or equal to 20 and the least common multiple of two prime numbers less than or equal to 12.

    • Greatest common factor (5-F.8)

  • NS.C.P.3 Proficient students determine 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.

    • Least common multiple (5-F.10)
    • Greatest common factor (6-E.8)

  • NS.C.A.2 Advanced students use the distributive property to express a sum of two whole numbers between 1 and 100 with a common factor times the sum of two whole numbers with no common factor.

• NS.D Apply and extend previous understandings of numbers to the system of rational numbers.

  • NS.D.P.1 Proficient students represent quantities in real-world contexts using rational numbers; do simple applications involving positive and negative numbers;

    • Understanding integers (6-M.1)
    • Compare temperatures above and below zero (6-T.10)

  • NS.D.B.1 Basic students represent one integer on a horizontal number line;

    • Integers on number lines (6-M.2)
    • Graph integers on horizontal and vertical number lines (6-M.3)

  • NS.D.P.2 Proficient students represent two or more rational numbers on a horizontal number line;

    • Decimal number lines (6-F.8)
    • Integers on number lines (6-M.2)
    • Graph integers on horizontal and vertical number lines (6-M.3)
    • Rational numbers: find the sign (6-P.11)

  • NS.D.B.2 Basic students graph ordered pairs of integers in the first quadrant of a coordinate plane;

    • Objects on a coordinate plane (5-T.2)
    • Graph points on a coordinate plane (5-T.3)

  • NS.D.P.3 Proficient students graph ordered pairs of integers in all four quadrants of a coordinate plane;

    • Objects on a coordinate plane (6-X.2)
    • Graph points on a coordinate plane (6-X.3)

  • NS.D.A.1 Advanced students identify the quadrant a point lies in given descriptions of its coordinates with real-world context;

    • Quadrants (6-X.4)
    • Quadrants and axes (7-P.2)

  • NS.D.B.3 Basic students compare a positive and a negative number;

  • NS.D.P.4 Proficient students compare two or more rational numbers;

    • Compare integers (6-M.7)
    • Compare rational numbers (6-P.4)
    • Put rational numbers in order (6-P.5)

  • NS.D.A.2 Advanced students explain statements of order for rational numbers in real-world contexts;

    • Compare temperatures above and below zero (6-T.10)

  • NS.D.P.5 Proficient students determine the absolute value of a rational number and explain the absolute value of any rational number as its distance from 0 on the number line;

    • Absolute value (6-M.6)
    • Absolute value of rational numbers (6-P.8)

  • NS.D.A.3 Advanced students explain statements of order of absolute values;

  • NS.D.P.6 Proficient students solve problems in both mathematical and real-world contexts by graphing points in all four quadrants of the coordinate plane;

    • Objects on a coordinate plane (6-X.2)
    • Graph points on a coordinate plane (6-X.3)
    • Coordinate planes as maps (6-X.6)
    • Follow directions on a coordinate plane (6-X.8)

  • NS.D.B.4 Basic students use coordinates to find distances between points with the same first coordinate or the same second coordinate in the first quadrant.

  • NS.D.P.7 Proficient students use coordinates to find distances between points with the same first coordinate or the same second coordinate in all four quadrants.

    • Distance between two points (6-X.7)

  • NS.D.A.4 Advanced students use coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate in all four quadrants.

    • Distance between two points (6-X.7)

EE Expressions and Equations

• EE.E Apply and extend previous understandings of arithmetic to algebraic expressions.

  • EE.E.B.1 Basic students write and evaluate one-step numerical expressions involving one whole number exponent;

    • Write multiplication expressions using exponents (6-D.1)
    • Evaluate exponents (6-D.2)
    • Find the missing exponent or base (6-D.4)
    • Exponents with decimal bases (6-D.5)
    • Exponents with fractional bases (6-D.6)

  • EE.E.P.1 Proficient students write and evaluate multi-step numerical expressions involving whole number exponents;

    • Evaluate numerical expressions involving whole numbers (6-O.4)

  • EE.E.A.1 Advanced students write and evaluate numerical multi-step expressions involving the distributive property and whole number exponents;

    • Evaluate numerical expressions involving whole numbers (6-O.4)

  • EE.E.B.2 Basic students write and read one-step expressions with rational numbers with variables;

    • Write variable expressions (5-U.1)
    • Write variable expressions: word problems (6-Y.3)

  • EE.E.P.2 Proficient students write and read two-step expressions with rational numbers with variables;

    • Write variable expressions: two operations (6-Y.2)

  • EE.E.A.2 Advanced students write and read three-step or four-step expressions with rational numbers with variables;

    • Write variable expressions: two operations (6-Y.2)

  • EE.E.B.3 Basic students evaluate one-step or two-step expressions with whole numbers given the value of the variable, using the order of operations;

    • Evaluate variable expressions with whole numbers (6-Y.4)

  • EE.E.P.3 Proficient students evaluate expressions with up to three steps given the values of up to two variables, using the order of operations;

    • Evaluate variable expressions with whole numbers (6-Y.4)
    • Evaluate multi-variable expressions (6-Y.5)
    • Evaluate variable expressions with decimals, fractions, and mixed numbers (6-Y.6)

  • EE.E.A.3 Advanced students evaluate expressions with more than three steps given the values of up to two variables, using the conventional order of operations;

    • Evaluate variable expressions with whole numbers (6-Y.4)
    • Evaluate multi-variable expressions (6-Y.5)
    • Evaluate variable expressions with decimals, fractions, and mixed numbers (6-Y.6)

  • EE.E.P.4 Proficient students identify parts of an expression using mathematical language;

    • Identify terms and coefficients (6-Y.8)
    • Sort factors of variable expressions (6-Y.9)

  • EE.E.B.4 Basic students apply the properties of operations to identify equivalent expressions based on the commutative property.

  • EE.E.P.5 Proficient students apply the properties of operations to identify and generate equivalent expressions.

    • Properties of addition (6-Y.11)
    • Properties of multiplication (6-Y.12)
    • Multiply using the distributive property (6-Y.14)
    • Write equivalent expressions using properties (6-Y.19)
    • Add and subtract like terms (6-Y.20)
    • Identify equivalent expressions II (6-Y.22)

  • EE.E.A.4 Advanced students explain why two expressions are equivalent.

    • Properties of addition (6-Y.11)
    • Properties of multiplication (6-Y.12)

• EE.F Reason about and solve one-variable equations and inequalities.

  • EE.F.P.1 Proficient students understand solving a one-variable equation or one-variable inequality as a process of answering the question "which values from a specified set, if any, make the equation or inequality true?";

    • Does x satisfy an equation? (6-Z.1)
    • Solutions to inequalities (6-AA.1)

  • EE.F.B.1 Basic students use substitution to determine whether a given whole number in a specified set makes a one-step equation or a one-step inequality true;

    • Does x satisfy an equation? (6-Z.1)
    • Which x satisfies an equation? (6-Z.2)
    • Solutions to inequalities (6-AA.1)

  • EE.F.P.2 Proficient students use substitution to determine whether a given non-negative rational number in a specified set makes a one-step equation or a one-step inequality true;

    • Does x satisfy an equation? (6-Z.1)
    • Which x satisfies an equation? (6-Z.2)
    • Solutions to inequalities (6-AA.1)

  • EE.F.A.1 Advanced students use substitution to determine whether a given rational number in a specified set makes a two-step equation or a two-step inequality true;

    • Does x satisfy an equation? (6-Z.1)
    • Which x satisfies an equation? (6-Z.2)
    • Solutions to inequalities (6-AA.1)

  • EE.F.B.2 Basic students understand that a variable represents an unknown number;

    • Write variable expressions: word problems (6-Y.3)

  • EE.F.P.3 Proficient students understand and use variables to represent numbers and write expressions with only one operation and only one variable when solving problems in both mathematical and real-world contexts;

    • Write variable expressions: two operations (6-Y.2)
    • Write variable expressions: word problems (6-Y.3)

  • EE.F.A.2 Advanced students understand and use variables to represent numbers and write expressions with two or more operations and only one variable when solving problems in both mathematical and real-world contexts;

    • Write variable expressions: two operations (6-Y.2)
    • Write variable expressions: word problems (6-Y.3)

  • EE.F.B.3 Basic students solve both mathematical and real-world contexts by solving equations of the form x + p = q or x - p = q for cases in which p, q and x are all whole numbers;

    • Model and solve equations using algebra tiles (6-Z.5)
    • Solve one-step equations with whole numbers (6-Z.10)

  • EE.F.P.4 Proficient students solve problems in both mathematical and real-world contexts by writing and solving equations of the form x + p = q, x - p = q, px = q, and x/p = q for cases in which p, q, and x are all whole numbers or positive rational numbers;

    • Write an equation from words (6-Z.3)
    • Model and solve equations using algebra tiles (6-Z.5)
    • Write and solve equations that represent diagrams (6-Z.7)
    • Solve one-step equations with whole numbers (6-Z.10)
    • Solve one-step equations: word problems (6-Z.16)

  • EE.F.A.3 Advanced students solve both mathematical and real-world contexts by writing and solving equations of the form x + p = q, x - p = q, px = q, and x/p = q for cases in which p, q, and x are all non-negative rational numbers;

    • Write an equation from words (6-Z.3)
    • Model and solve equations using algebra tiles (6-Z.5)
    • Write and solve equations that represent diagrams (6-Z.7)
    • Solve one-step equations with whole numbers (6-Z.10)
    • Solve one-step multiplication and division equations with decimals and fractions (6-Z.12)
    • Solve one-step equations: word problems (6-Z.16)

  • EE.F.B.4 Basic students write an inequality of the form x > c or x < c to represent a mathematical context.

    • Write inequalities from number lines (6-AA.3)

  • EE.F.P.5 Proficient students write an inequality of the form x > c or x < c to represent real world contexts and recognize that inequalities of the form x > c or x < c have infinitely many solutions and represent and interpret solutions of inequalities on number line diagrams.

    • Graph inequalities on number lines (6-AA.2)
    • Write inequalities from number lines (6-AA.3)

  • EE.F.A.4 Advanced students write an inequality of the form x ≥ c or x ≤ c to represent real world contexts, recognize that inequalities of the form x ≥ c or x ≤ c have infinitely many solutions, and represent and interpret solutions of inequalities of the form x ≥ c or x ≤ c on number line diagrams.

    • Graph inequalities on number lines (6-AA.2)
    • Write inequalities from number lines (6-AA.3)

• EE.G Represent and analyze quantitative relationships between dependent and independent variables.

  • EE.G.B.1 Basic students describe in words the apparent relationship between the values of two variables given in a table.

  • EE.G.P.1 Proficient students write equations to represent the apparent relationship between the values of two variables given in a table or a graph.

    • Write an equation from a graph using a table (6-BB.3)
    • Write a two-variable equation (6-BB.10)

  • EE.G.A.1 Advanced students analyze the relationship between the dependent and independent variables using graphs and tables and relate these to the equation.

    • Write an equation from a graph using a table (6-BB.3)
    • Complete a table for a two-variable relationship (6-BB.8)
    • Write a two-variable equation (6-BB.10)
    • Identify the graph of an equation (6-BB.11)
    • Graph a two-variable equation (6-BB.13)
    • Interpret a graph: word problems (6-BB.14)

G Geometry

• G.H Solve real-world and mathematical problems involving area, surface area, and volume.

  • G.H.B.1 Basic students determine the area of right triangles by composing into rectangles in both mathematical and real-world contexts;

    • Area of triangles (5-DD.7)

  • G.H.P.1 Proficient students determine the area of triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes in both mathematical and real-world contexts;

    • Area of squares and rectangles (5-DD.5)
    • Area of triangles (5-DD.7)
    • Area of parallelograms and trapezoids (5-DD.8)
    • Area of rectangles and squares (6-FF.2)
    • Area of triangles (6-FF.6)
    • Area of trapezoids (6-FF.8)
    • Area of quadrilaterals (6-FF.10)
    • Area of compound figures (6-FF.11)

  • G.H.A.1 Advanced students find a missing dimension given the area of a triangle or a special quadrilateral and all but one dimension;

    • Area of quadrilaterals (6-FF.10)

  • G.H.B.2 Basic students apply the formulas V= lwh to find volumes of right rectangular prisms with two whole-number edge lengths and one fractional edge length in both mathematical and real-world contexts;

  • G.H.P.2 Proficient students apply the formulas V= lwh and V= bh to find volumes of right rectangular prisms with fractional edge lengths in both mathematical and real-world contexts;

  • G.H.A.2 Advanced students apply the formulas V= lwh and V= bh to find volumes of right rectangular prisms with fractional edge lengths and perform additional operations with the volume to solve real-world problems;

  • G.H.B.3 Basic students solve for the area of a rectangle given the coordinates of three points, one being the origin, on the coordinate plane in both mathematical and real-world contexts;

  • G.H.P.3 Proficient students solve for the area of a rectangle given the coordinates of three vertex points, excluding the origin, on the coordinate plane in both mathematical and real-world contexts;

  • G.H.A.3 Advanced students solve for the area of a right triangle or a rectangle given coordinates for two points on the coordinate plane to solve problems in both mathematical and real-world contexts;

  • G.H.B.4 Basic students identify the net of a right prism.

  • G.H.P.4 Proficient students represent three-dimensional figures using nets made up of rectangles and triangles and use nets to find the surface area of three-dimensional figures.

    • Nets of three-dimensional figures (6-EE.3)

  • G.H.A.4 Advanced students use nets to find the surface area of three-dimensional figures in both mathematical and real-world contexts.

    • Nets of three-dimensional figures (6-EE.3)

SP Statistics and Probability

• SP.I Develop understanding of statistical variability.

  • SP.I.P.1 Proficient students recognize a statistical question as one that anticipates variability;

    • Identify representative, random, and biased samples (6-HH.12)

  • SP.I.A.1 Advanced students create a statistical question as one that anticipates variability;

  • SP.I.P.2 Proficient students understand that a set of data can be described by its center, spread, and overall shape;

    • Create line plots (6-GG.4)
    • Interpret stem-and-leaf plots (6-GG.21)

  • SP.I.A.2 Advanced students make generalizations about the center, the spread, and the overall shape of the distribution of a numerical data set presented in a graph;

    • Interpret line plots (6-GG.3)
    • Box plots (6-GG.23)

  • SP.I.B.1 Basic students understand that the mean and the median are measures of center.

    • Calculate mean, median, mode, and range (6-HH.2)

  • SP.I.P.3 Proficient students understand that the mean and the median are measures of center, and the mean absolute deviation and the interquartile range are measures of variation for a numerical data set.

    • Calculate mean, median, mode, and range (6-HH.2)
    • Interpret charts and graphs to find mean, median, mode, and range (6-HH.3)
    • Mean, median, mode, and range: find the missing number (6-HH.4)

  • SP.I.A.3 Advanced students make generalizations about the mean absolute deviation and the interquartile range as measures of variation for a numerical data set.

• SP.J Summarize and describe distributions.

  • SP.J.P.1 Proficient students display numerical data in plots on a number line, including dot plots, histograms, and box plots;

    • Interpret line plots (6-GG.3)
    • Create line plots (6-GG.4)
    • Interpret bar graphs (6-GG.9)
    • Create bar graphs (6-GG.10)
    • Interpret double bar graphs (6-GG.12)
    • Create double bar graphs (6-GG.13)
    • Interpret histograms (6-GG.14)
    • Create histograms (6-GG.15)
    • Interpret line graphs (6-GG.17)
    • Create line graphs (6-GG.18)
    • Interpret double line graphs (6-GG.19)
    • Create double line graphs (6-GG.20)
    • Box plots (6-GG.23)

  • SP.J.B.1 Basic students report the number of observations found in a numerical data set.

    • Create frequency charts (6-GG.6)
    • Create histograms (6-GG.15)

  • SP.J.P.2 Proficient students use data to describe the nature of an attribute under investigation, including how it was measured and its units of measurement;

    • Identify representative, random, and biased samples (6-HH.12)

  • SP.J.A.1 Advanced students use measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation) for a numerical data set to describe the distribution of the data without calculating the measures;

  • SP.J.P.3 Proficient students calculate measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation) for a numerical data set.

    • Calculate mean, median, mode, and range (6-HH.2)
    • Interpret charts and graphs to find mean, median, mode, and range (6-HH.3)
    • Mean, median, mode, and range: find the missing number (6-HH.4)
    • Calculate mean absolute deviation (6-HH.6)

  • SP.J.A.2 Advanced students demonstrate and describe the relationship between the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.