South Carolina Math Standards - SC CCR

794 standards, Kindergarten through AP.

South Carolina's College and Career Ready Standards use domain based organization, with K-5 domains like ATO (Arrays, Tools, Operations), NSBT (Number Sense, Base Ten), and NSF (Number Sense, Fractions). Grades 6-8 shift to domains like EEI (Equations and Expressions), NS (Number Systems), and RP (Ratios and Proportional Relationships).

Kindergarten

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K.DPSR Data, Probability, and Statistical Reasoning
K.DPSR.1 Collect and organize data and communicate through multiple representations.
K.DPSR.1.1Sort pictures or objects into at least two categories. Count to determine how many are in each category. Limit to 20 pictures or objects.
K.DPSR.1.2Answer questions about data organized in a t-chart, object graph, or picture graph.
K.MGSR Measurement, Geometry, and Spatial Reasoning
K.MGSR.1 Describe and compare objects in real-world situations using units of length, weight, money, and time.
K.MGSR.1.1Identify a penny, nickel, dime, and quarter.
K.MGSR.1.2Directly compare two objects using words including shorter, longer, taller, lighter, and heavier.
K.MGSR.2 Analyze, describe, and manipulate shapes to make sense of their relationships in mathematical and real-world situations.
K.MGSR.2.1Identify and describe the attributes of triangles, squares, rectangles, circles, cubes, and spheres to include everyday situations.
K.MGSR.2.2Describe relative positions of objects by appropriately using terms including below, above, beside, between, inside, outside, in front of, or behind.
K.NR Numerical Reasoning
K.NR.1 Represent multi-digit numbers in a variety of ways to build the foundation for place value understanding.
K.NR.1.1Read, write, and represent the numerals 0 to 20 and represent the written numeral with concrete models.
K.NR.1.2Compose and decompose numbers from 11 to 19 into tens and ones by using concrete objects, pictorial models, or drawings to demonstrate understanding that the teen numbers are composed of one set of ten ones and a few more ones.
K.NR.2 Demonstrate and explain the relationship between numbers and quantities.
K.NR.2.1Count forward by ones and tens to 100 and backward from 10 by ones.
K.NR.2.2Subitize a quantity of up to 10 objects in an organized arrangement without counting, explaining how one grouped the objects within the set to determine the total quantity.
K.NR.2.3Given a group of up to 20 objects, count the number of objects in that group and represent the number of objects with a written numeral. State the number of objects in a rearrangement of that group without recounting.
K.NR.2.4Given a number from 0 to 20, count out that many objects.
K.NR.3 Demonstrate the ability to compare quantities of objects and numerals representing quantities of objects.
K.NR.3.1Compare up to 10 objects in one set to another set of up to 10 objects using the phrases more than, fewer than, or the same as.
K.PAFR Patterns, Algebra, and Functional Reasoning
K.PAFR.1 Develop an understanding of the relationship between addition and subtraction to solve problems.
K.PAFR.1.1Add and subtract number combinations within 5.
K.PAFR.1.2Create a sum of 10 using objects and drawings when given one of two addends 0–9, to include real-world situations.
K.PAFR.1.3Compose and decompose numbers up to 10 in different ways. Record using objects or drawings.
K.PAFR.1.4Solve add-to/joining, take-from/separating, part-part-whole (total unknown), part-part-whole (both addends unknown) real-world situations to find sums and differences within 10.
K.PAFR.2 Recognize, describe, extend, and create patterns.
K.PAFR.2.1Describe, extend, and create (to the next term) simple repeating patterns in the form of AB, AAB, ABB, and ABC.

Grade 1

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1.DPSR Data, Probability, and Statistical Reasoning
1.DPSR.1 Create and answer survey questions, collect and analyze data, and communicate through multiple representations.
1.DPSR.1.1Sort pictures or objects into at least three categories (not to exceed 10 items in each category).
1.DPSR.1.2Create survey questions and collect data with up to three categories. Create charts and graphs with a single unit scale to display the data. Use the graph to draw conclusions. Limit to one-step add-to, take-from, and part-part-whole questions.
1.MGSR Measurement, Geometry, and Spatial Reasoning
1.MGSR.1 Describe, estimate, measure, and compare objects in real-world situations using units of length, weight, money, and time.
1.MGSR.1.1Order three objects by length from shortest to longest and longest to shortest using direct comparison.
1.MGSR.1.2Use nonstandard physical objects to estimate and then measure the length of an item as the number of same size units of length with no gaps or overlaps.
1.MGSR.1.3Use analog and digital clocks to tell and record time to the hour and half hour.
1.MGSR.1.4Identify and write the values of a coin or a bill using a ¢ symbol for coin values or $ symbol for bills. Limit to penny, nickel, dime, quarter, one-dollar bill, five-dollar bill, and ten-dollar bill.
1.MGSR.1.5Count a collection of like coins to determine the total value of the set. Limit to pennies, nickels, and dimes with values not to exceed a dollar.
1.MGSR.2 Analyze, describe, and manipulate shapes to make sense of their relationships in mathematical and real-world situations.
1.MGSR.2.1Sort a mixed set of polygons and describe the reasoning used while sorting the polygons.
1.MGSR.2.2Identify and describe the attributes of two-dimensional shapes and three-dimensional shapes. Limit to triangle, square, rectangle, rhombus, hexagon, circle, cone, cube, cylinder, square pyramid, and sphere.
1.MGSR.2.3Identify and describe a given shape in everyday situations to include two-dimensional shapes and three-dimensional shapes. Limit to triangle, square, rectangle, rhombus, hexagon, circle, cone, cube, cylinder, square pyramid, and sphere.
1.MGSR.2.4Classify shapes as two-dimensional/flat or three-dimensional/solid and explain the reasoning using formal mathematical language. Limit to triangle, square, rectangle, rhombus, hexagon, circle, cone, cube, cylinder, square pyramid, and sphere.
1.MGSR.2.5Analyze and compare a pair of two-dimensional shapes or a pair of three-dimensional shapes of assorted sizes and orientations using formal mathematical language. Limit to triangle, square, rectangle, rhombus, hexagon, circle, cone, cube, cylinder, square pyramid, and sphere.
1.NR Numerical Reasoning
1.NR.1 Represent multi-digit numbers in a variety of ways to build place value understanding.
1.NR.1.1Read, write, and represent numbers to 100 using concrete models, drawings, standard form, base ten language, and equations in expanded form.
1.NR.1.2Represent and explain that whole numbers 1 through 99 are organized into groups of tens and ones, and a digit has a different value depending on its placement.
1.NR.1.3Compose and decompose whole numbers from 1 through 99 in more than one way using tens and ones. Explain and demonstrate each composition or decomposition with the use of concrete models, drawings, and/or equations.
1.NR.1.4Apply place value reasoning to identify the number that is one more and one less, ten more, and ten less than a given number with up to two digits.
1.NR.2 Explain the relationship between numbers and quantities.
1.NR.2.1Count by ones forward or backward starting at any number up to 120 making accurate decade transitions.
1.NR.2.2Skip count by fives and tens from any multiple of five to 100, identifying place value patterns in the sequence.
1.NR.3 Demonstrate the ability to compare quantities of objects and numerals representing quantities of objects.
1.NR.3.1Compare representations of two numbers up to 100 using the phrases is greater than, is less than, or is equal to (the same value as).
1.NR.4 Represent partitioned shapes in multiple ways using part-whole relationships.
1.NR.4.1Partition in multiple ways squares, rectangles, and circles into two or four equal-sized parts. Name the pieces as halves and fourths.
1.PAFR Patterns, Algebra, and Functional Reasoning
1.PAFR.1 Understand and apply properties of operations and the relationship between addition and subtraction to solve problems.
1.PAFR.1.1Determine and explain if an equation within 10 is true using a variety of equation formats.
1.PAFR.1.2Compose and decompose numbers less than or equal to 20 in more than one way. Record each composition or decomposition as an equation.
1.PAFR.1.3Solve add-to, take-from, and part-part-whole real-world situations to find sums and differences within 20. Situations include result or change unknown, both addends unknown, and total or one part unknown.
1.PAFR.1.4Add and subtract number combinations flexibly and accurately within 10.
1.PAFR.1.5Apply and explain the Commutative Property of Addition to find the sum (through 20) of the two addends and explain that the value does not change when the order of the two numbers changes.
1.PAFR.1.6Determine an unknown number in addition and subtraction equations within 10.
1.PAFR.1.7Find the sum of a two-digit number and a one-digit number or a two-digit number and a multiple of 10 (1–99) using concrete models, drawings, and strategies that reflect place value understanding, the inverse relationship of addition and subtraction, and the properties of the operations to justify the sum.
1.PAFR.1.8Find the difference between two numbers that are multiples of 10, both in the range 10–90, and write the corresponding equation. Explain the reasoning used.
1.PAFR.2 Recognize, describe, extend, and create patterns.
1.PAFR.2.1Create, describe, and extend (to the next term) a growing shape pattern.
1.PAFR.2.2Create, describe, and extend (to three terms within a sequence) repeating patterns using AB, AAB, ABB, and ABC type patterns.

Grade 2

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2.DPSR Data, Probability, and Statistical Reasoning
2.DPSR.1 Create and answer survey questions, collect and analyze data, and communicate through multiple representations.
2.DPSR.1.1Create a survey question and collect data with up to four categories. Create tally charts, picture graphs, dot plots, and bar graphs with a single-unit scale to read the graph, answer questions, and draw conclusions. Limit to one-step add-to, take-from, part-part-whole, and comparison questions.
2.MGSR Measurement, Geometry, and Spatial Reasoning
2.MGSR.1 Describe, estimate, measure, and compare objects in real-world situations using units of length, weight, currency, and time.
2.MGSR.1.1Select and use appropriate tools to estimate and measure the length of an object or distance to the nearest customary unit. Limit to inches, feet, and yards.
2.MGSR.1.2Use analog and digital clocks to tell and record time in five-minute intervals, identifying AM and PM.
2.MGSR.1.3Determine the value of mixed sets of coins or bills in mathematical and real-world situations and record the value using a ¢ or $ symbol. Limit to pennies, nickels, dimes, and quarters up to a dollar; one-dollar bills, five-dollar bills, ten-dollar bills, and twenty-dollar bills up to $100, and add-to or take-from problem types.
2.MGSR.2 Analyze, describe, and manipulate shapes to make sense of their relationships in mathematical and real-world situations.
2.MGSR.2.1Identify and describe a given shape in everyday situations to include two-dimensional shapes and three-dimensional shapes. Limit to triangle, quadrilateral, pentagon, hexagon, octagon, circle, cone, cube, cylinder, rectangular prism, square pyramid, and sphere.
2.MGSR.2.2Classify shapes as polygons or non-polygons and defend that determination based on their attributes.
2.MGSR.2.3Classify two-dimensional shapes as triangles or quadrilaterals and justify each classification.
2.NR Numerical Reasoning
2.NR.1 Represent multi-digit numbers in a variety of ways to build place value understanding.
2.NR.1.1Read, write, and represent numbers up to 999 using concrete models, drawings, standard form, base ten language, and equations in expanded form.
2.NR.1.2Represent and explain that whole numbers 1 through 999 are organized into groups of hundreds, tens, and ones, and a digit has a different value depending on its placement.
2.NR.1.3Compose and decompose whole numbers from 1 through 999 in more than one way using hundreds, tens, and ones. Explain and demonstrate each composition or decomposition with the use of concrete models, drawings, and equations.
2.NR.1.4Apply place value reasoning to identify the number that is 10 more, 10 less, 100 more, and 100 less than a given three-digit number through 999.
2.NR.2 Explain the relationship between numbers and quantities.
2.NR.2.1Count forward and backward by ones, tens, and hundreds from any number within 999 and identify patterns in the sequence.
2.NR.3 Demonstrate the ability to compare quantities of objects and numerals representing quantities of objects.
2.NR.3.1Compare representations of whole numbers up to 999 and write a comparison statement using words and symbols. Limit to is equal to (=), is less than (<), and/or is greater than (>).
2.NR.3.2When given a two-digit number, identify which multiple of 10 the number is closest to.
2.NR.4 Represent and compare partitioned shapes in multiple ways using part-whole relationships.
2.NR.4.1Partition in multiple ways squares, rectangles, and circles into two or four equal sized parts, and describe the parts using the words halves, fourths, a half of, and a fourth of (not quarters).
2.NR.4.2Explain that when partitioning a square, rectangle, or circle into two or four equal parts, the parts become smaller as the number of parts increases.
2.PAFR Patterns, Algebra, and Functional Reasoning
2.PAFR.1 Understand and apply properties of operations and the relationship between addition and subtraction to solve problems.
2.PAFR.1.1Use a strategy to accurately find sums and differences of two-digit numbers within 100 and justify the sum or difference.
2.PAFR.1.2Determine and explain if an equation (within 20) is true using a variety of equation formats.
2.PAFR.1.3Solve one-step add-to, take-from, part-part-whole, and additive comparison real-world situations through 99 with the unknown in any position.
2.PAFR.1.4For any number from 0 to 99, find the number that makes 100 when added to the given number.
2.PAFR.1.5Add and subtract number combinations flexibly and accurately within 20.
2.PAFR.1.6Apply the Associative Property of Addition to find the sum (through 20) of three addends and explain that the value can be found using various grouping strategies.
2.PAFR.1.7Determine the unknown number in addition and subtraction equations within 20, with the unknown in any position.
2.PAFR.1.8Sort a collection of 20 or fewer objects into two groups to determine if the number of objects is even or odd.
2.PAFR.1.9Find the total number of objects arranged in equal groups or in a rectangular array and write an addition equation to express the total as a sum (up to 25) of equal addends.
2.PAFR.2 Recognize, describe, extend, and create patterns.
2.PAFR.2.1Describe, extend, and create a growing shape pattern with up to three terms within a sequence.
2.PAFR.2.2Create, describe, and extend an appropriate one-step rule for number patterns using addition and subtraction within 100.

Grade 3

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3.DPSR Data, Probability, and Statistical Reasoning
3.DPSR.1 Collect and analyze data and communicate through multiple representations.
3.DPSR.1.1Collect and organize categorical and numerical data based on observations, surveys, experiments, and investigations with whole number values using tables, scaled picture graphs, scaled bar graphs, or dot plots. Use titles and labels. Limit scales to multiples of 1, 2, 5, and 10.
3.DPSR.1.2Solve one-step, real-world situations using whole number data represented in tables, scaled picture graphs, scaled bar graphs, or dot plots. Limit scales to multiples of 1, 2, 5, and 10.
3.DPSR.2 Represent the probability of simple events and determine possible outcomes.
3.DPSR.2.1Identify the possible outcomes of a simple event.
3.MGSR Measurement, Geometry, and Spatial Reasoning
3.MGSR.1 Solve area and perimeter problems in real-world and mathematical situations.
3.MGSR.1.1Determine the area of squares and rectangles presented in relevant problems by covering the space with square units and counting the total number of units needed.
3.MGSR.1.2Determine the perimeter of regular and irregular triangles and quadrilaterals with known side lengths.
3.MGSR.1.3Determine if a real-world situation is an example of the need for finding the area or the perimeter of a figure.
3.MGSR.2 Estimate and measure using units of length, liquid volume, currency, and intervals of time.
3.MGSR.2.1Determine the value of any collection of coins, not to exceed $5. Write the amount in the form of dollars and cents using the decimal notation. Limit to penny, nickel, dime, and quarter.
3.MGSR.2.2Use analog and digital clocks to tell and record time to 1-minute intervals, identifying AM and PM.
3.MGSR.2.3Solve problems involving addition and subtraction of time intervals to determine elapsed time to the nearest half hour.
3.MGSR.2.4Estimate and measure length/distance to the nearest half inch and nearest whole centimeter.
3.MGSR.2.5Determine which unit of liquid volume is most appropriate to measure in real-world situations. Limit to fluid ounces, cups, pints, quarts, gallons, milliliters, and liters.
3.MGSR.3 Extend geometric reasoning to attributes of polygons and/or polyhedrons.
3.MGSR.3.1Describe and draw right, acute, obtuse, and straight angles. Identify these angle types in two-dimensional figures including triangles and quadrilaterals.
3.MGSR.3.2Identify, describe, and draw points, lines, line segments, rays, intersecting lines, perpendicular lines, and parallel lines. Identify these in two-dimensional figures.
3.NR Numerical Reasoning
3.NR.1 Represent and compare numbers using relationships within the base ten number system.
3.NR.1.1Read, write, and represent whole numbers through the thousands period (0 to 999,999) on a number line and in standard form, base ten language, word form, and equations in expanded form.
3.NR.1.2Compose and decompose 4-digit whole numbers in multiple ways using thousands, hundreds, tens, and ones.
3.NR.1.3Compare two whole numbers up to 999,999 based on the place value of the digits using the symbols for is equal to (=), is less than (<), or is greater than (>).
3.NR.1.4Round whole numbers from 0 to 1,000 to the nearest 10 or 100.
3.NR.2 Represent and compare fractions in multiple ways using part-whole relationships.
3.NR.2.1Identify unit fractions as the quantity formed by one part when a whole is partitioned into 2, 3, 4, 6, or 8 equal-sized parts. Express each part as a unit fraction of the whole.
3.NR.2.2Represent fractions from 0 to 1 using concrete, set, area, and linear models, and write them in standard form and word form. Limit denominators to 2, 3, 4, 6, and 8.
3.NR.2.3Express whole numbers as fractions and identify fractions that are equivalent to whole numbers. Limit denominators to 1, 2, 3, 4, 6, and 8.
3.NR.2.4Compose fractions between the whole numbers 0 and 5 using unit fractions. Record the composition as a mixed number or fraction greater than 1. Limit denominators to 2, 3, 4, 6, and 8.
3.NR.2.5Recognize two fractions are equivalent. Limit denominators to 2, 3, 4, 6, and 8, and fractions should be limited to fractions between 0 and 1.
3.NR.2.6Compare two fractions with the same numerator or same denominator based on the same size whole by reasoning about their size. Use the symbols for is equal to (=), is less than (<), or is greater than (>). Limit denominators to 2, 3, 4, 6, and 8, and fractions should be limited to fractions between 0 and 1.
3.PAFR Patterns, Algebra, and Functional Reasoning
3.PAFR.1 Use multiple representations to reason and solve problems involving operational properties of whole numbers.
3.PAFR.1.1Use a strategy to compute sums and differences up to 1,000.
3.PAFR.1.2Multiply whole numbers (factors 0–10) and divide whole numbers (divisors 1–10) using a model and write a corresponding equation.
3.PAFR.1.3Multiply two whole numbers from 0 to 10 and divide using related facts flexibly and accurately.
3.PAFR.2 Use reasoning to represent and solve algebraic and numerical situations.
3.PAFR.2.1Determine the unknown whole number in a multiplication or division real-world situation relating three whole numbers when the unknown is a missing factor, product, dividend, divisor, or quotient.
3.PAFR.2.2Solve one- and two-step real-world situations using addition and subtraction up to 1,000.
3.PAFR.2.3Identify, create, and extend numerical patterns to determine the next three terms in an addition or subtraction sequence.
3.PAFR.2.4Recognize that a whole number is a multiple of each of its factors 1–10.

Grade 4

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4.DPSR Data, Probability, and Statistical Reasoning
4.DPSR.1 Create questions, collect and analyze data, and communicate interpretations through multiple representations.
4.DPSR.1.1Collect and organize numerical and categorical data based on observations, investigations, surveys, and experiments using tables, scaled bar graphs, or dot plots. Use titles and labels. Scales to include whole numbers, halves, and fourths.
4.DPSR.1.2Solve one-step, real-world situations using whole number and fractional data represented in tables, scaled picture graphs, scaled bar graphs, or dot plots. Limit to like denominators of 2, 3, 4, 5, 6, 8, and 10.
4.DPSR.2 Represent the probability of simple events and determine possible outcomes.
4.DPSR.2.1Determine the possible outcomes of a simple event and record the probability as certain, possible, or impossible.
4.MGSR Measurement, Geometry, and Spatial Reasoning
4.MGSR.1 Solve area and perimeter problems in real-world and mathematical situations.
4.MGSR.1.1Apply perimeter formulas for rectangles to solve real-world situations including finding the perimeter, given the side lengths, and finding an unknown side length.
4.MGSR.1.2Apply area formulas for rectangles to solve real-world situations. Use square units to label area measurements.
4.MGSR.2 Estimate and measure using units of length, liquid volume, weight, currency, and intervals of time.
4.MGSR.2.1Calculate the value of a collection of coins and bills in real-world situations to determine whether there is enough money to make a purchase. Justify based on comparison of money amounts.
4.MGSR.2.2Solve real-world situations involving addition and subtraction of time intervals within 60 minutes to find elapsed time, start time, or end time.
4.MGSR.2.3Measure length to the nearest quarter inch.
4.MGSR.2.4Measure weight in customary units and metric units to the nearest whole unit. Limit to ounces, pounds, grams, and kilograms.
4.MGSR.2.5Convert customary units of length, weight, and liquid volume from a larger unit to a smaller unit, given direct comparisons of the two measurements and/or the unit equivalencies within a single system of measurement. Limit to inches, feet, yards, ounces, pounds, fluid ounces, cups, pints, quarts, and gallons when given unit equivalences.
4.MGSR.3 Extend geometric reasoning to attributes of polygons and/or polyhedrons.
4.MGSR.3.1Classify triangles according to side length (isosceles, equilateral, scalene) and angle measure (acute, obtuse, right, equiangular).
4.MGSR.3.2Classify quadrilaterals in a hierarchy based on their shared attributes.
4.NR Numerical Reasoning
4.NR.1 Represent and compare numbers using relationships within the base ten number system.
4.NR.1.1Read and write whole numbers through the millions period (0 to 999,999,999) in word, standard, and equations in expanded form.
4.NR.1.2Estimate sums, differences, products, and quotients of multi-digit whole numbers, using rounding and place value to determine the reasonableness of real-world problem solutions. Write an equation for the estimate.
4.NR.1.3Order whole numbers within 999,999 (no more than 3) in ascending or descending order and record the comparison(s) using symbols for is less than (<) and/or is greater than (>).
4.NR.2 Represent and compare fractions in multiple ways using part-whole relationships.
4.NR.2.1Represent fractions with denominators of 10 and 100 in words, models, and decimal notations.
4.NR.2.2Compare decimal numbers to the hundredths using the benchmarks 0, 0.5, and 1.0, concrete area, and linear models. Use the symbols for is equal to (=), is less than (<), and/or is greater than (>).
4.NR.2.3Generate equivalent fractions, including fractions greater than 1, using multiple representations. Limit fractions to denominators of 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 50, and 100.
4.NR.2.4Represent the composition and decomposition of fractions with the same denominator, including mixed numbers and fractions greater than 1, using multiple representations. Limit fractions to denominators of 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 50, and 100.
4.NR.2.5Explain and demonstrate how a mixed number is equivalent to a fraction greater than 1 and how a fraction greater than 1 is equivalent to a mixed number. Limit fractions to denominators of 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 50, and 100.
4.NR.2.6Compare fractions and mixed numbers with like and unlike denominators applying benchmark fractions such as 0, 1/2, and 1 using the symbols for is equal to (=), is less than (<), or is greater than (>). Limit fractions to denominators of 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 50, and 100.
4.PAFR Patterns, Algebra, and Functional Reasoning
4.PAFR.1 Use multiple representations to reason and solve problems involving operational properties of whole numbers and decimals.
4.PAFR.1.1Use a strategy to accurately compute sums and differences of whole numbers up to 100,000 and justify the sum or difference.
4.PAFR.1.2Compute the product of a one-digit whole number times a multiple of 10 (from 10 to 90) and 100 (from 100 to 900) based on place value and properties of operations.
4.PAFR.1.3Decompose numbers by the value of each digit to multiply whole numbers up to four digits by a one-digit number and two 2-digit whole numbers.
4.PAFR.1.4Use a strategy to divide up to a four-digit dividend by a one-digit divisor, with and without remainders. Justify the calculation.
4.PAFR.2 Use multiple representations to reason and solve problems involving operational properties of fractions.
4.PAFR.2.1Use a strategy to accurately compute sums and differences of fractions with like denominators and justify the reasonableness of the answer. Limit denominators to 2, 3, 4, 5, 6, 8, 10, 12, 25, and 100.
4.PAFR.2.2Use fraction and decimal equivalencies to add and subtract tenths and hundredths, to include mixed numbers and fractions greater than 1.
4.PAFR.2.3Represent and compute the product of a whole number times a unit fraction. Limit denominators to 2, 3, 4, 5, 6, 8, 10, 12, 25, and 100.
4.PAFR.2.4Interpret a fraction as an equal sharing division situation, where a quantity (the numerator) is divided into equal parts (the denominator) to include real-world situations.
4.PAFR.3 Use reasoning to represent and solve algebraic and numerical situations.
4.PAFR.3.1Find all factor pairs for a whole number in the range 1–50. Determine whether the whole number is prime or composite.
4.PAFR.3.2Describe and extend a numerical pattern that follows a rule using function tables and real-world situations.
4.PAFR.3.3Solve real-world situations involving multiplicative comparison situations and write equations to represent the problem using a variable for the unknown.
4.PAFR.3.4Solve two-step, real-world situations using the four operations involving whole number answers. Represent the problem using an equation with a variable as the unknown in any position.

Grade 5

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5.DPSR Data, Probability, and Statistical Reasoning
5.DPSR.1 Create questions, collect and analyze data, and communicate through multiple representations.
5.DPSR.1.1Describe data by determining the range and mode, including whole numbers, fractional data, and decimal data. Limit fractions to denominators of 2, 3, 4, 5, 6, 8, and 10, and limit decimals to decimals through the hundredths place.
5.DPSR.1.2Solve two-step, real-world situations using whole number and fractional data represented in tables, line graphs, scaled bar graphs, or dot plots. Limit fractions to denominators of 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 50, and 100.
5.DPSR.1.3Analyze categorical and numerical data in graphical displays to make predictions or draw conclusions. Limit displays to tables, bar graphs, dot plots, line graphs, and circle graphs with scales of whole numbers, halves, fourths, and eighths.
5.DPSR.2 Represent the probability of simple events and determine possible outcomes.
5.DPSR.2.1Represent the probability of a simple event as 0, a fraction, or 1. Limit fractions to denominators of 2, 3, 4, 5, 6, 8, 10, 20, and 25.
5.MGSR Measurement, Geometry, and Spatial Reasoning
5.MGSR.1 Solve area, perimeter, and volume problems in real-world and mathematical situations.
5.MGSR.1.1Solve problems involving area and perimeter of composite figures by decomposing with rectangles.
5.MGSR.1.2Estimate and measure the volume of a right rectangular prism with whole-number side lengths by filling it with unit cubes.
5.MGSR.2 Convert within a given measurement system and measure length.
5.MGSR.2.1Given the unit equivalencies, convert within a single system of measurement from larger units to smaller units and smaller units to larger units for length, weight, liquid volume, and time. Use these conversions in solving real-world situations. Limit units to inches, feet, yards, ounces, pounds, fluid ounces, cups, pints, quarts, gallons, seconds, minutes, hours, milli-, centi-, kilo-, and base units (grams, liters, meters).
5.MGSR.2.2Estimate and measure lengths to the nearest eighth of an inch or nearest millimeter.
5.MGSR.3 Graph on the coordinate plane.
5.MGSR.3.1Identify the origin, x-axis, and y-axis in the coordinate system. Write, plot, and label ordered pairs, including values in a function table, in the first quadrant of the coordinate plane.
5.MGSR.3.2Represent mathematical and real-world situations by graphing, labeling, and interpreting points in the first quadrant of the coordinate plane.
5.NR Numerical Reasoning
5.NR.1 Represent and compare numbers using relationships within the base ten number system.
5.NR.1.1Read, write, and represent multi-digit numbers from 0 to 999 with decimals to the thousandths place. Use pictorial, word, standard, or expanded form with fraction or decimal notation.
5.NR.1.2Explain how the value of a digit in a multi-digit number changes if the digit moves one or more places to the left or right in the base ten system. Include decimals to the thousandths place.
5.NR.1.3Round decimal numbers up to 999 with decimals to the thousandths place to the nearest hundredth, tenth, or whole number.
5.NR.1.4Use patterns to explain the exponents when multiplying and dividing by powers of 10, not to exceed the thousandths place.
5.NR.2 Represent and compare fractions in multiple ways.
5.NR.2.1Compare fractions and mixed numbers with like and unlike denominators of 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, and 100 using equivalence to create a common denominator. Use the symbols for is less than (<), is more than (>), or is equal to (=) to record the comparison.
5.PAFR Patterns, Algebra, and Functional Reasoning
5.PAFR.1 Use multiple representations to reason and solve problems involving operational properties of whole numbers and decimals.
5.PAFR.1.1Use a strategy to compute the product of a two- or three-digit factor times a two-digit factor to include real-world situations.
5.PAFR.1.2Use a strategy to compute the quotient of a multi-digit whole number dividend divided by a two-digit whole number divisor, with and without remainders, to include real-world situations. Limit the dividend to four digits.
5.PAFR.1.3Use a strategy to compute sums and differences of decimal numbers to the hundredths.
5.PAFR.1.4Use a strategy to multiply a one-digit whole number by a decimal to the hundredths and divide a decimal to the hundredths (dividend) by a one-digit whole number (divisor). Justify the calculation.
5.PAFR.2 Use multiple representations to reason and solve problems involving operational properties of fractions.
5.PAFR.2.1Use a strategy to compute sums and differences of fractions and mixed numbers with unlike denominators and justify the sum or difference to include real-world situations. Limit denominators to 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 50, and 100.
5.PAFR.2.2Use a strategy to multiply a fraction by a fraction or a fraction by a whole to include real-world situations. Limit denominators to 2, 3, 4, 5, 6, 8, 10, and 12.
5.PAFR.2.3Interpret and represent the division of a whole number dividend by a unit fraction divisor and a unit fraction dividend by a whole number divisor and apply to real-world situations. Limit denominators to 2, 3, 4, 5, 6, 8, 10, and 12.
5.PAFR.3 Use reasoning to represent and solve algebraic and numerical situations.
5.PAFR.3.1Determine the least common multiple (LCM) to find a common denominator. Limit denominators to 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 50, and 100.
5.PAFR.3.2Determine the greatest common factor (GCF) of two numbers both less than or equal to 50 to simplify a fraction into its standard form.
5.PAFR.3.3Identify a rule that can describe the pattern from the data of a function table and write it as an expression.
5.PAFR.3.4Translate a two-step real-world situation into a numerical expression using parentheses as grouping symbols and evaluate the expression.

Grade 6

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6.DPSR Data, Probability, and Statistical Reasoning
6.DPSR.1 Analyze data sets to identify their statistical elements.
6.DPSR.1.1Identify the sample size for a numerical set of data in mathematical and real-world situations.
6.DPSR.1.2Create box plots to represent numerical data sets in mathematical and real-world situations.
6.DPSR.1.3Use the shape of the graph to determine whether median or mode best describes the data set.
6.DPSR.1.4Calculate and interpret the median, mode, range, interquartile range in mathematical and real-world situations.
6.DPSR.2 Calculate and interpret probability.
6.DPSR.2.1Given the probability of a random event, expressed as a number from 0 to 1, state the likelihood of the event occurring.
6.DPSR.2.2Find the probability of simple events in mathematical and real-world situations. Limit denominators to 2, 4, 5, 8, 10, 20, 25, 50, 100, and 200.
6.DPSR.2.3Given the probability of an event, identify and calculate the complement of that event.
6.MGSR Measurement, Geometry, and Spatial Reasoning
6.MGSR.1 Determine the measurements of geometric figures.
6.MGSR.1.1Find the area of a triangle, square, rectangle, parallelogram, and trapezoid.
6.MGSR.1.2Create nets to represent three-dimensional shapes.
6.MGSR.1.3Calculate the surface area of right rectangular prisms, right triangular prisms, right rectangular pyramids, and right triangular pyramids using two-dimensional nets.
6.MGSR.1.4Find the area of composite figures by decomposing them into triangles and rectangles to solve mathematical and real-world situations.
6.MGSR.1.5Calculate the volume of a right rectangular prism using the formula (V = Bh) in mathematical and real-world situations.
6.MGSR.2 Determine angle and/or side relationships.
6.MGSR.2.1Determine if two angles are complementary or supplementary.
6.MGSR.2.2Determine the measure of angles using a protractor.
6.MGSR.3 Graph on the coordinate plane.
6.MGSR.3.1Plot ordered pairs in all four quadrants and identify points on a graph by writing ordered pairs.
6.MGSR.3.2Graph a polygon on a coordinate plane given the coordinates of the vertices.
6.NR Numerical Reasoning
6.NR.1 Translate among multiple representations of rational numbers.
6.NR.1.1Convert positive rational numbers into equivalent forms among terminating decimals, fractions (including mixed numbers), and percentages. Limit fractions to denominators of 2, 4, 5, 8, 10, 20, 25, 50, 100, and 200.
6.NR.2 Utilize rational numbers in mathematical and real-world situations.
6.NR.2.1Compare two positive rational numbers and write statements using the symbols for is equal to (=), is not equal to (≠), is less than (<), and/or is greater than (>) in mathematical and real-world situations. Limit fractions to denominators of 2, 4, 5, 8, 10, 20, 25, 50, 100, and 200.
6.NR.2.2Sort a set of positive rational numbers in ascending and/or descending order in mathematical and real-world situations. Limit sets to no more than 5 numbers. Limit fractions to denominators of 2, 4, 5, 8, 10, 20, 25, 50, 100, and 200.
6.NR.2.3Represent quantities with integers in real-world situations and explain the meaning of zero.
6.NR.2.4Identify and compare the opposite value and absolute value of positive and negative rational numbers.
6.PAFR Patterns, Algebra, and Functional Reasoning
6.PAFR.1 Use tables, graphs, verbal descriptions, or equations to represent a function.
6.PAFR.1.1Use tables, graphs, verbal descriptions, and equations to represent the relationship between independent and dependent variables of functions.
6.PAFR.1.2Identify the independent and dependent variable of a function in mathematical and real-world situations.
6.PAFR.2 Write, simplify, and evaluate algebraic expressions; write and solve algebraic equations and inequalities.
6.PAFR.2.1Identify parts of an algebraic expression using the mathematical terms sum, difference, term, variable, product, factor, quotient, coefficient, and constant.
6.PAFR.2.2Write and evaluate numerical expressions containing powers. Limit to positive whole number bases and positive whole number exponents.
6.PAFR.2.3Evaluate numerical expressions with positive whole number bases and positive whole number exponents using the Order of Operations.
6.PAFR.2.4Write and evaluate expressions using variables to represent quantities in mathematical and real-world situations.
6.PAFR.2.5Write and solve one-step equations and inequalities with one variable involving positive rational numbers in mathematical and real-world situations.
6.PAFR.2.6Interpret the concept of a ratio as the relationship between two quantities, including part-to-part and part-to-whole.
6.PAFR.2.7Explain the relationship between ratios and rates, including unit rates.
6.PAFR.2.8Solve ratio and rate problems in real-world situations.
6.PAFR.2.9Use one-step dimensional analysis to convert units within the metric or customary systems.
6.PAFR.3 Apply mathematical patterns, properties, and algorithms to the set of rational numbers to find sums, differences, products, and quotients and to write equivalent expressions.
6.PAFR.3.1Represent the solutions of inequalities on a number line and explain that the solution set may contain an infinite number of solutions. Limited to the symbols for is less than (<) and is greater than (>).
6.PAFR.3.2Identify the multiplicative inverse of a number and multiply multiplicative inverses to find their product is equal to 1.
6.PAFR.3.3Identify the additive inverse of a number and add additive inverses to find their sum is equal to zero.
6.PAFR.3.4Apply the properties of operations to create equivalent algebraic expressions and justify the properties used. Limit properties to the Identity, Inverse, Commutative, Associative, and Distributive Properties.
6.PAFR.3.5Add, subtract, multiply, and divide integers in mathematical and real-world situations.
6.PAFR.3.6Add, subtract, multiply, and divide positive fractions, including mixed numbers in mathematical and real-world situations.
6.PAFR.3.7Add, subtract, multiply, and divide multi-digit positive decimals, up to the thousandths place, to solve problems in mathematical and real-world situations.

Grade 7

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7.DPSR Data, Probability, and Statistical Reasoning
7.DPSR.1 Analyze data sets to identify their statistical elements.
7.DPSR.1.1Create stem-and-leaf plots to represent numerical data sets in mathematical and real-world situations.
7.DPSR.1.2Use the shape of the graph to select the measure of center (mean, median, or mode) that best describes the data set.
7.DPSR.1.3Calculate and interpret the measures of center (mean, median, mode) and spread (mean absolute deviation, interquartile range, range) in mathematical and real-world situations.
7.DPSR.1.4Create histograms to represent data sets and interpret histograms to answer questions or draw conclusions about data sets.
7.DPSR.2 Calculate and interpret probability.
7.DPSR.2.1Identify the sample space for a simple event.
7.DPSR.2.2Calculate and interpret the theoretical probability of a simple random event.
7.DPSR.2.3Calculate and interpret the experimental probability of a random event related to a simple experiment.
7.DPSR.2.4Compare and contrast the experimental and theoretical probabilities for a simple experiment.
7.MGSR Measurement, Geometry, and Spatial Reasoning
7.MGSR.1 Determine the measurements of geometric figures.
7.MGSR.1.1Identify the parts of a circle. Limit the parts to center, radius, diameter, and chord.
7.MGSR.1.2Describe the relationship between the radius, diameter, and circumference of a circle.
7.MGSR.1.3Solve mathematical and real-world situations involving circumference or area of circles.
7.MGSR.1.4Determine if three given side lengths can form a triangle using the Triangle Inequality Theorem.
7.MGSR.1.5In mathematical and real-world situations, find the volume of right prisms and right pyramids having triangular or quadrilateral bases.
7.MGSR.1.6In mathematical and real-world situations, find the surface area of right prisms and right pyramids having triangular or quadrilateral bases.
7.MGSR.2 Determine angle and/or side relationships.
7.MGSR.2.1Determine the measure of the third angle given the measure of the other two angles of a triangle using the Triangle Sum Theorem.
7.MGSR.2.2Solve mathematical and real-world situations involving dimensions and areas of geometric figures including scale drawings and scale factors.
7.MGSR.2.3Identify the relationships and measures among angles formed by two intersecting lines, given the measure of one angle. Limit to supplementary, complementary, vertical, and adjacent relationships.
7.MGSR.2.4Write and solve equations to solve mathematical and real-world situations involving the relationships among angles formed by two intersecting lines. Limit to supplementary, complementary, vertical, and adjacent relationships.
7.MGSR.3 Graph on the coordinate plane.
7.MGSR.3.1Find distances between ordered pairs on the coordinate plane, limited to the same x-coordinate or the same y-coordinate.
7.NR Numerical Reasoning
7.NR.1 Translate among multiple representations of rational numbers.
7.NR.1.1Convert rational numbers into equivalent forms among fractions (including mixed numbers), decimals, and percentages. Exclude the conversion of repeating decimals to fractions.
7.NR.2 Utilize rational numbers in mathematical and real-world situations.
7.NR.2.1Compare two rational numbers and write statements using is equal to (=), is not equal to (≠), is less than (<), is greater than (>), is greater than or equal to (≥), and/or is less than or equal to (≤) in mathematical and real-world situations.
7.PAFR Patterns, Algebra, and Functional Reasoning
7.PAFR.1 Use tables, graphs, verbal descriptions, or equations to represent a function.
7.PAFR.1.1Apply proportional reasoning to solve problems in mathematical and real-world situations involving ratios and percentages.
7.PAFR.1.2Create a model with functions that address a proportional relationship in real-world situations.
7.PAFR.1.3Identify the constant of proportionality within proportional relationships.
7.PAFR.2 Write, simplify, and evaluate algebraic expressions; write and solve algebraic equations and inequalities.
7.PAFR.2.1Write and solve multi-step equations and inequalities in one variable involving rational numbers in mathematical and real-world situations.
7.PAFR.2.2Write and evaluate expressions in one variable that model mathematical and real-world situations.
7.PAFR.2.3Compute unit rates, including those involving complex fractions with like or different units.
7.PAFR.2.4Use dimensional analysis to convert units between metric and customary systems.
7.PAFR.3 Apply mathematical patterns, properties, and algorithms to the set of rational numbers to find sums, differences, products, and quotients and to write equivalent expressions.
7.PAFR.3.1Simplify numerical expressions that include integer exponents using the laws of exponents: the Product of Powers, Quotient of Powers, Power of a Power, Power of a Product, Power of a Quotient, Zero Power, and Negative Exponent.
7.PAFR.3.2Identify linear expressions that are equivalent.
7.PAFR.3.3Recognize that algebraic expressions may have a variety of equivalent forms and determine an appropriate form for a given real-world situation.
7.PAFR.3.4Factor linear expressions with integer coefficients using the greatest common factor (GCF).
7.PAFR.3.5Apply all operations with rational numbers to solve problems in mathematical and real-world situations.

Grade 8

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8.DPSR Data, Probability, and Statistical Reasoning
8.DPSR.1 Analyze data sets to identify their statistical elements.
8.DPSR.1.1Create and analyze scatterplots to represent numerical data sets in mathematical and real-world situations.
8.DPSR.1.2Draw inferences about two populations utilizing representative random samples of comparisons of the shape of the distribution, measures of center, and measures of variability. Limit measures to mean, median, mode, range, mean absolute deviation, and interquartile range.
8.DPSR.1.3Describe how adding and deleting data throughout the data set can affect the mean, median, mode, and distribution of the data set.
8.DPSR.1.4For two data sets (numerical or graphical), compare and interpret the centers, spreads, and overlap of data to draw inferences about data in mathematical and real-world situations. Limit displays to double line graphs, back-to-back stem-and-leaf plots, and double box plots.
8.DPSR.2 Calculate and interpret probability.
8.DPSR.2.1Determine the sample space for a compound event.
8.DPSR.2.2Calculate and interpret the probability of compound independent and dependent events.
8.MGSR Measurement, Geometry, and Spatial Reasoning
8.MGSR.1 Determine the measurements of geometric figures.
8.MGSR.1.1Given the geometric formulas, find the volume of cones, cylinders, and spheres in mathematical and real-world situations.
8.MGSR.1.2Find the distance between any two points in the coordinate plane using the Pythagorean Theorem.
8.MGSR.1.3Given the Pythagorean Theorem, determine unknown side lengths in right triangles in mathematical and real-world situations.
8.MGSR.1.4Determine if a given set of sides forms a right triangle.
8.MGSR.2 Determine angle and/or side relationships.
8.MGSR.2.1Determine missing angle measurements created when parallel lines are cut by a transversal.
8.MGSR.2.2Determine if two-dimensional figures are congruent or similar.
8.MGSR.2.3Identify the congruent corresponding angles of similar polygons.
8.MGSR.2.4Discover and apply the Exterior Angle Theorem of triangles to find a missing angle.
8.MGSR.2.5Apply proportional reasoning to find the missing side lengths of two similar figures.
8.MGSR.3 Graph on a coordinate plane.
8.MGSR.3.1Identify the transformation as rotation, reflection, and/or translation. Limit rotations to multiples of 90 degrees centered on the origin.
8.MGSR.3.2Identify congruent angles and congruent line segments of a preimage and its image.
8.MGSR.3.3Translate geometric figures vertically and/or horizontally.
8.MGSR.3.4Reflect geometric figures with respect to the x-axis and/or y-axis.
8.MGSR.3.5Rotate geometric figures 90, 180, and 270 degrees, both clockwise and counterclockwise, about the origin of a coordinate plane.
8.MGSR.3.6Create a dilation using a given scale factor and describe the effect of a dilation.
8.MGSR.3.7Describe the effect of a series of transformations, including dilations, translations, rotations, and reflections, on two-dimensional figures using coordinates on the coordinate plane.
8.NR Numerical Reasoning
8.NR.1 Translate among multiple representations of rational numbers.
8.NR.1.1Convert any form of a rational number to any other form including fractions (mixed numbers), decimals, and percentages.
8.NR.2 Utilize real numbers in mathematical and real-world situations.
8.NR.2.1Compare real numbers and write statements using is equal to (=), is not equal to (≠), is less than (<), is greater than (>), is greater than or equal to (≥), or is less than or equal to (≤).
8.NR.2.2Classify and order the subsets of real numbers in the number system including natural, whole, integer, rational, and irrational numbers.
8.PAFR Patterns, Algebra, and Functional Reasoning
8.PAFR.1 Determine if a table, graph, verbal description, or equation represents a function and describe its characteristics.
8.PAFR.1.1Define an equation in slope-intercept form (y = mx + b) as being a linear function.
8.PAFR.1.2Identify and describe the constant rate of change and the y-intercept of a linear function.
8.PAFR.1.3Determine if a graph, table, mapping, or verbal description is a function (linear or nonlinear) or not a function.
8.PAFR.1.4Describe the key features of given functions, including domain, range, intervals of increasing or decreasing, constant, discrete, continuous, and intercepts.
8.PAFR.1.5Use multiple representations including mappings, tables, graphs, verbal description, and equations (only when linear) of two functions to compare the functions and draw conclusions.
8.PAFR.1.6Translate among the multiple representations, including mappings, tables, graphs, verbal description, and equations (only when linear) of a function.
8.PAFR.2 Write, simplify, and evaluate algebraic expressions; write and solve algebraic equations and inequalities.
8.PAFR.2.1Solve multi-step one-variable equations and inequalities with variables on both sides with rational coefficients.
8.PAFR.2.2Describe single-variable equations as having one solution, no solution, or an infinite number of solutions.
8.PAFR.2.3Identify the rate of change for a linear function as the slope of the line.
8.PAFR.2.4Explain why the slope, m, is the same between any two distinct points on a linear graph.
8.PAFR.2.5Given a table or a graph, identify the slope and the y-intercept of a line and write a linear equation to express that line.
8.PAFR.3 Apply mathematical patterns, properties, and algorithms to the set of rational numbers to find sums, differences, products, and quotients and to write equivalent expressions.
8.PAFR.3.1Analyze patterns of perfect squares and perfect cubes to evaluate square roots and cube roots. Limit to square roots less than or equal to 400 and cube roots less than or equal to 1,000.
8.PAFR.3.2Approximate non-perfect square roots and cube roots to nearest tenth. Limit to square roots less than or equal to 400 and cube roots less than or equal to 1,000.
8.PAFR.3.3Apply laws of exponents to simplify algebraic expressions involving no more than three variables and integer exponents.

Geometry with Statistics

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GS.DPSR Data, Probability, and Statistical Reasoning
GS.DPSR.1 Summarize, represent, and interpret data on two categorical and quantitative variables.
GS.DPSR.1.1Represent data for two quantitative variables on a scatterplot and describe how the variables are related.
GS.DPSR.1.2Use two representative points from the data to find an approximate line of fit and compare it to the line of best fit.
GS.DPSR.1.3Conduct an investigation for a statistical question, interpret statistical significance in the context of a situation, and answer investigative questions appropriately.
GS.DPSR.2 Analyze and interpret models for two quantitative variables.
GS.DPSR.2.1Distinguish between correlation and causation.
GS.DPSR.3 Solve problems involving the probability of compound events in real-world situations.
GS.DPSR.3.1Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events.
GS.DPSR.3.2Apply the Addition Rule to find the probability of both mutually exclusive and not mutually exclusive events and interpret the answers in context.
GS.DPSR.3.3Apply the Multiplication Rule to determine the probability of independent events and interpret the answers in context.
GS.MGSR Measurement, Geometry, and Spatial Reasoning
GS.MGSR.1 Compute area and volume of figures by determining how the figure might be obtained from simpler figures by dissection and recombination.
GS.MGSR.1.1Apply area and volume formulas of two- and three-dimensional figures to solve real-world situations.
GS.MGSR.1.2Identify the shape of a two-dimensional cross-section of a three-dimensional figure.
GS.MGSR.1.3Use cross-sections of three-dimensional figures to model and solve mathematical and real-world situations.
GS.MGSR.2 Apply rigid geometric transformations to figures, describing their attributes and symmetries.
GS.MGSR.2.1Describe the results of transformations on a given figure using geometric terminology from the definitions of the transformations.
GS.MGSR.2.2Describe and apply a sequence of transformations that maps a preimage onto its image.
GS.MGSR.3 Determine that two figures are congruent by demonstrating that a rigid motion or a sequence of rigid motions maps one figure onto the other.
GS.MGSR.3.1Identify types of symmetry of polygons, including line, point, rotational, and self-congruence, and use symmetry to analyze mathematical situations.
GS.MGSR.3.2Demonstrate that triangles and quadrilaterals are congruent by a combination of translations, rotations, and reflections.
GS.MGSR.3.3Recognize the criteria for showing triangles are congruent using a sequence of rigid motions that map one triangle to another and justify that the two triangles are congruent by applying the Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions.
GS.MGSR.4 Determine that two figures are similar by demonstrating a similarity transformation or a sequence of similarity transformations that maps one figure onto the other.
GS.MGSR.4.1Demonstrate experimentally the properties of dilations given by a center and a scale factor.
GS.MGSR.4.2Justify experimentally that a dilation of a line segment is longer or shorter, given the ratio.
GS.MGSR.4.3Recognize that the criteria for showing triangles are similar using a similarity transformation that maps one figure to the other and justify the two triangles are similar by applying the Angle-Angle, Side-Side-Side, and Side-Angle-Side similarity conditions.
GS.MGSR.5 Demonstrate whether a conjecture or theorem is true or false using a variety of algebraic and geometric explanations.
GS.MGSR.5.1Justify and apply the attributes of angle relationships/lines in mathematical and real-world situations.
GS.MGSR.5.2Apply the attributes of triangles in mathematical and real-world situations.
GS.MGSR.5.3Apply the attributes of quadrilaterals, including diagonals, sides, and angles, to prove that a given quadrilateral is a parallelogram in mathematical and real-world situations.
GS.MGSR.6 Discover and apply relationships in similar right triangles.
GS.MGSR.6.1Discover and apply the converse of the Pythagorean Theorem.
GS.MGSR.6.2Discover and apply the constant ratios of the sides in 30-60-90 and 45-45-90 right triangles.
GS.MGSR.6.3Define the trigonometric ratios using the properties of similar right triangles.
GS.MGSR.6.4Determine the sine, cosine, and tangent of an acute angle in a right triangle in the context of mathematical and real-world situations.
GS.MGSR.6.5Apply trigonometric ratios (sine, cosine, tangent) and the Pythagorean Theorem to solve right triangle problems in real-life situations.
GS.MGSR.7 Investigate and apply relationships among segments and angles in circles.
GS.MGSR.7.1Use angle and segment relationships in circles to solve mathematical and real-world situations.
GS.MGSR.7.2Investigate and apply relationships in circles, inscribed angles, radii, secants, and chords; among inscribed angles, central angles, and circumscribed angles; and between radii and tangents to circles.
GS.NR Numerical Reasoning
GS.NR.1 Represent all points on the number line as irrational and rational numbers in the real number system.
GS.NR.1.1Rewrite numerical expressions of irrational and rational numbers involving radicals, including addition, subtraction, multiplication, and division, to recognize geometric patterns.
GS.PAFR Patterns, Algebra, and Functional Reasoning
GS.PAFR.1 Analyze the structure of an equation or inequality to determine an efficient strategy to find a solution, if one exists, then justify the solution.
GS.PAFR.1.1Discover and apply the formulas for the length of an arc and the area of a sector in a circle to develop mathematical models and solve mathematical and real-world situations.
GS.PAFR.1.2Analyze and apply the derivations of the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone to model real phenomena and solve mathematical and real-world situations.
GS.PAFR.2 Interpret the structure of expressions, equations, and inequalities to analyze and make predictions in different contexts.
GS.PAFR.2.1Apply surface area and volume formulas for prisms, cylinders, pyramids, cones, spheres, and/or compositions of figures to solve problems and justify results.
GS.PAFR.2.2Analyze slopes of lines to determine whether lines are parallel, perpendicular, or neither.
GS.PAFR.2.3Determine the equation of a line passing through a given point that is parallel or perpendicular to a given line.
GS.PAFR.3 Determine the exact or approximate solutions of equations and inequalities using graphs on the coordinate plane.
GS.PAFR.3.1Use coordinates to prove simple geometric theorems algebraically.
GS.PAFR.3.2Determine distance and midpoint of segments in a coordinate plane to find areas of triangles and quadrilaterals, when given coordinates.

Algebra 1

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A1.DPSR Data, Probability, and Statistical Reasoning
A1.DPSR.1 Use statistical reasoning to summarize, represent, and interpret data on two categorical and quantitative variables.
A1.DPSR.1.1Summarize categorical data in two-way frequency tables, interpret relative frequencies in real-world situations, and informally determine possible associations and trends in the data.
A1.DPSR.1.2Summarize quantitative data in a table and on a scatterplot and describe how the variables are associated. Limit to linear data.
A1.DPSR.1.3Find a linear function for a scatterplot that suggests a linear association.
A1.DPSR.1.4For linear associations, use technology to determine the correlation coefficient, evaluate the strength of the association, and find the line of best fit.
A1.DPSR.2 Analyze and interpret models for two categorical and quantitative variables.
A1.DPSR.2.1Use two-way frequency tables to make inferences and interpret the data in terms of real-world or mathematical situations.
A1.DPSR.2.2Interpret the slope and the intercept of a linear model in the context of the data.
A1.DPSR.2.3Use a linear model to interpolate and extrapolate unknown values close to the data set.
A1.MGSR Measurement, Geometry, and Spatial Reasoning
A1.MGSR.1 Use geometric concepts and measurement opportunities to model mathematical and real-world situations.
A1.MGSR.1.1Identify any limitations specific to a real-world situation.
A1.NR Numerical Reasoning
A1.NR.1 Represent all points on the number line as irrational and rational numbers in the real number system.
A1.NR.1.1Rewrite numerical and algebraic expressions of irrational and rational numbers involving radicals, including addition, subtraction, multiplication, and division. Limit to square and cube roots.
A1.NR.2 Represent exponents and radical expressions in different ways.
A1.NR.2.1Translate between rational exponents and radical expressions of irrational and rational numbers. Use properties of addition, subtraction, multiplication, and division to simplify radical and rational expressions. Limit to square and cube roots.
A1.PAFR Patterns, Algebra, and Functional Reasoning
A1.PAFR.1 Transform and/or solve equations and expressions in one variable that model real-world and mathematical situations, interpret the solutions, and determine whether they are reasonable.
A1.PAFR.1.1Transform an equation in one variable to create new equations that have the same solution as the original and justify the steps taken.
A1.PAFR.1.2Solve literal equations and formulas for a specified variable including equations and formulas that arise in a variety of disciplines.
A1.PAFR.1.3Solve mathematical and real-world situations using linear, quadratic, exponential (same bases), and linear absolute value equations in one variable.
A1.PAFR.1.4Add, subtract, and multiply polynomials with initial terms up to a degree of 2.
A1.PAFR.2 Create, solve, and transform equations and inequalities in two or more variables to represent relationships between quantities and graph the equations on coordinate axes using appropriate labels, units, and scales.
A1.PAFR.2.1Transform linear, quadratic, exponential, and linear absolute value functions to equivalent forms to identify slope and y-intercept for linear, vertex, and roots (if any) for quadratic and linear absolute value, and y-intercept for exponential.
A1.PAFR.2.2Solve quadratic equations by completing the square, factoring, and the quadratic formula, explaining the connection between the zeros of the function derived from the equation, its linear factors (if it factors), the x-intercepts of its graph (if they exist), and the solutions (if any) to the corresponding quadratic equation.
A1.PAFR.2.3Solve and graph linear, quadratic, exponential, and linear absolute value equations given in tabular, symbolic, and/or verbal forms using intercepts, domain and range, intervals of increasing and decreasing, vertex (maximum and minimum), end-behavior, and symmetry, and interpret these in terms of mathematical and real-world situations.
A1.PAFR.2.4Create, solve, and graph linear inequalities in two variables.
A1.PAFR.2.5Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
A1.PAFR.2.6Create symbolic representations of linear and exponential functions, including arithmetic and geometric sequences, given graphs, verbal descriptions, and tables.
A1.PAFR.2.7Use graphs to obtain exact and/or approximate solutions of equations, inequalities, and systems of linear equations in two variables (given or obtained by using technology).
A1.PAFR.2.8Solve an equation of the form f(x) = g(x) graphically by identifying the x-coordinate(s) of the point(s) of intersection of the graphs of y = f(x) and y = g(x).
A1.PAFR.2.9Solve systems of linear equations algebraically and graphically.
A1.PAFR.2.10Analyze the growth/decay rate between linear and exponential functions specifically between consecutive integers.
A1.PAFR.3 Represent and interpret functions symbolically and graphically.
A1.PAFR.3.1Recognize that f(x) denotes the output of function f that corresponds to the input x, and this corresponds to the set of all the ordered pairs (x, y) that satisfy the equation y = f(x) both tabularly and graphically.
A1.PAFR.3.2Use the definition of a function to analyze the domain and range of a function in relation to its graph, mapping, table, verbal, and/or symbolic description and, where applicable, using interval and set notation.
A1.PAFR.3.3Translate among graphical, tabular, verbal, and symbolic representations in function notation, to identify intercepts, intervals where the function is increasing, decreasing, constant, maximums and minimums, and symmetries and explain their meanings in real-world and mathematical situations.
A1.PAFR.3.4Interpret how lead coefficients impact the shape of a function's graph.
A1.PAFR.4 Reason with parent functions in varying representations to find families of functions that all have similar distinguishing attributes common to the family and use common characteristics to aid in rewriting and identifying linear, linear absolute value, quadratic, and exponential functions.
A1.PAFR.4.1Describe the effect of the transformations kf(x), f(x) + k, f(x - k), and combinations of such transformations on the graph of parent function y = f(x) for any real number k; find the value of k given the graphs; and write the equation of a transformed parent function given its graph.
A1.PAFR.4.2Given a real-world or mathematical situation, determine the parent graph that best models the situation.
A1.PAFR.4.3Given different representations of two different functions, compare key features including intercepts, domain and range, intervals of increasing and decreasing, constant, average rate of change, and maximum and minimum values.

Algebra 2 with Probability

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A2P.DPSR Data, Probability, and Statistical Reasoning
A2P.DPSR.1 Understand independence and conditional probability and use them to interpret data.
A2P.DPSR.1.1Describe events as subsets of a sample space using characteristics or categories of the outcomes, or as unions, intersections, or complements of other events.
A2P.DPSR.1.2Explain whether two events, A and B, are independent if and only if the probability of A and B occurring together is the product of their probabilities and use this characterization to determine if they are independent.
A2P.DPSR.1.3Determine whether the conditional probability of A given B as P(A and B)/P(B) and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B in mathematical and real-world situations.
A2P.DPSR.1.4Recognize and explain the concepts of conditional probability and independence.
A2P.DPSR.2 Use the rules of probability to compute probabilities of compound events in a uniform probability model.
A2P.DPSR.2.1Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A and interpret the answer in terms of the model.
A2P.DPSR.2.2Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B) and interpret the answer in terms of the model.
A2P.DPSR.2.3Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)*P(B|A) = P(B)*P(A|B) and interpret the answer in terms of the model.
A2P.DPSR.2.4Use permutations and combinations to determine the number of possible outcomes in a sample space.
A2P.MGSR Measurement, Geometry, and Spatial Reasoning
A2P.MGSR.1 Explore and analyze sine and cosine functions using the unit circle, right triangle definitions, and models of periodic phenomena.
A2P.MGSR.1.1Build the unit circle for sine and cosine functions using right triangle definitions.
A2P.MGSR.1.2Use models of periodic phenomena to evaluate and analyze the graph of sine and cosine functions.
A2P.NR Numerical Reasoning
A2P.NR.1 Recognize that the complex number system extends the real number system to allow for solution to all polynomial equations.
A2P.NR.1.1Understand that there is an imaginary unit i such that i^2 = -1 and explain the structure of a complex number as a + bi, where a and b are real.
A2P.NR.1.2Add, subtract, and multiply complex numbers.
A2P.NR.2 Represent and manipulate data using matrices.
A2P.NR.2.1Perform operations with matrices including addition, subtraction, and scalar multiplication.
A2P.PAFR Patterns, Algebra, and Functional Reasoning
A2P.PAFR.1 Explore and analyze quadratic and polynomial functions and inequalities and use them to model real-world situations.
A2P.PAFR.1.1Graph, identify roots, and analyze quadratic functions in mathematical and real-world situations.
A2P.PAFR.1.2Solve quadratic inequalities that model mathematical and real-world situations.
A2P.PAFR.1.3Graph and analyze polynomial functions in mathematical and real-world situations.
A2P.PAFR.1.4Solve polynomial inequalities that model mathematical and real-world situations.
A2P.PAFR.1.5Recognize perfect squares and perfect cubes and use them to describe the structure of polynomials.
A2P.PAFR.2 Explore and analyze rational and radical functions and use them to model real-world phenomena.
A2P.PAFR.2.1Graph rational and radical functions and describe their key features. Limit to square roots and cube roots only.
A2P.PAFR.2.2Perform arithmetic operations on rational expressions, including problems in context, and express rational expressions in irreducible form.
A2P.PAFR.2.3Create and solve rational and radical equations in one variable, including those that model real-life situations, and verify solutions to identify extraneous solutions if they appear.
A2P.PAFR.3 Explore and analyze exponential functions and use them to model real-world phenomena.
A2P.PAFR.3.1Create, solve, and graph exponential functions, including those that model real-life situations.
A2P.PAFR.3.2Find the sum of the terms of arithmetic and geometric sequences.
A2P.PAFR.4 Reason with parent functions to find families of functions that all have similar distinguishing attributes common to the family and use common characteristics to aid in rewriting and identifying functions.
A2P.PAFR.4.1Identify the effect on the graph of replacing f(x) by kf(x), f(x)+k, f(x-k), f(kx) for any real number k including multiple transformations; write an equation of a transformed parent function given its graph. Extend to equations involving rational, polynomial, radical, exponential, and piecewise.
A2P.PAFR.5 Explore and analyze piecewise functions and linear absolute value inequalities and use them to model real-world phenomena.
A2P.PAFR.5.1Graph piecewise functions and describe their key features.
A2P.PAFR.5.2Solve linear absolute value inequalities.
A2P.PAFR.6 Represent and interpret functions symbolically and graphically.
A2P.PAFR.6.1Find the inverse of functions and verify graphically.
A2P.PAFR.6.2Calculate and interpret the average rate of change of the function over a specified interval, given a function in graphical, symbolic, or numerical form.
A2P.PAFR.6.3Use linear programming to solve systems of equations and inequalities by addressing the constraints that arise in real-world situations.

Pre-Calculus

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PC.MGSR Measurement, Geometry, and Spatial Reasoning
PC.MGSR.1 Analyze the behaviors of conic sections and polar coordinates to model mathematical and real-world situations.
PC.MGSR.1.1Identify and graph different conic sections given the equations in standard form.
PC.MGSR.1.2Identify different conic sections in general form and complete the square to convert the equation of a conic section into standard form.
PC.MGSR.1.3Define polar coordinates and relate polar coordinates to Cartesian coordinates.
PC.MGSR.2 Solve problems and model periodic phenomena with trigonometric expressions and functions.
PC.MGSR.2.1Determine the area of a triangle to solve problems.
PC.MGSR.2.2Prove and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.
PC.MGSR.2.3Derive the formulas for the length of an arc and the area of a sector in a circle and apply these formulas to solve mathematical and real-world situations.
PC.MGSR.2.4Determine geometrically the values of the sine, cosine, and tangent for π/6, π/4, and π/3 by special triangles, and use the unit circle to express the values of sine, cosine, and tangent for π-x, π+x, and 2π-x in terms of their values for x, where x is any real number.
PC.MGSR.2.5Define the six trigonometric ratios in terms of x, y, and r using the unit circle centered at the origin of the coordinate plane and interpret radian measures of angles as a rotation both counterclockwise and clockwise around the unit circle.
PC.MGSR.2.6Explain symmetry, both odd and even, and periodicity of trigonometric functions.
PC.NR Numerical Reasoning
PC.NR.1 Represent and manipulate data using matrices.
PC.NR.1.1Identify the identity and zero matrices for any dimension and add, subtract, and multiply matrices.
PC.NR.1.2Find the additive and multiplicative inverses of square matrices.
PC.NR.1.3Explain the role of the determinant in determining if a square matrix has a multiplicative inverse.
PC.NR.1.4Find the determinant of a square matrix if and only if the matrix has a multiplicative inverse.
PC.NR.2 Represent and model with vector quantities.
PC.NR.2.1Represent vector quantities as directed line segments and represent magnitude and direction of vectors in component form.
PC.NR.2.2Find the components of a vector by adding and subtracting vectors on a coordinate plane using a variety of methods.
PC.NR.2.3Solve problems, including real-life situations, that can be represented by vectors.
PC.NR.2.4Add and subtract vectors and multiply vectors by a scalar to find the resultant vector.
PC.NR.3 Represent complex numbers and their operations on the complex plane.
PC.NR.3.1Represent complex numbers on the complex plane in rectangular and polar form, including real and imaginary numbers, and explain why the rectangular and polar forms of a given complex number represent the same number.
PC.NR.3.2Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.
PC.PAFR Patterns, Algebra, and Functional Reasoning
PC.PAFR.1 Build new functions from existing functions to solve mathematical and real-world situations.
PC.PAFR.1.1Combine and compose functions algebraically, tabularly, and graphically.
PC.PAFR.1.2Find the inverse of functions and verify algebraically, numerically, and graphically.
PC.PAFR.1.3Compare the key features of a function and its inverse function and use the relationship to model real-world situations and solve problems.
PC.PAFR.1.4Graph and describe the effect on the graph f(x) of f(x)+k, f(x-k), kf(x), and f(kx), for specific values of both negative and positive values of k.
PC.PAFR.2 Explore and analyze the behaviors of rational and piecewise functions to model contextual mathematical problems.
PC.PAFR.2.1Graph rational functions and describe their key features.
PC.PAFR.2.2Solve rational equations and inequalities in one variable and explain when extraneous solutions may arise.
PC.PAFR.2.3Transform rational expressions in different forms.
PC.PAFR.2.4Graph piecewise-defined functions, including step functions and absolute value functions, and describe their key features.
PC.PAFR.3 Explore and analyze structures and patterns for radical functions and use radical expressions, equations, and functions to model real-life phenomena.
PC.PAFR.3.1Transform radical expressions as expressions with rational exponents and extend the properties of integer exponents to rational exponents.
PC.PAFR.3.2Solve radical equations and describe how extraneous solutions may arise.
PC.PAFR.3.3Analyze and graph radical functions.
PC.PAFR.4 Explore and analyze structures and patterns for exponential and logarithmic functions and use exponential and logarithmic expressions, equations, and functions to model real-life phenomena.
PC.PAFR.4.1Graph logarithmic functions and describe their key features.
PC.PAFR.4.2Use the definition of a logarithm, logarithmic properties, and the inverse relationship between exponential and logarithmic functions to solve problems, including real-life context.
PC.PAFR.4.3Model real-life situations and solve problems involving exponential and logarithmic functions.
PC.PAFR.5 Explore and analyze structures and patterns of trigonometric functions and use trigonometric functions to model real-life phenomena.
PC.PAFR.5.1Graph trigonometric functions and their inverses and describe their key features.
PC.PAFR.5.2Restrict the domain of a trigonometric function to define the six inverse trigonometric functions, graph the inverse function, and evaluate inverse trigonometric expressions.
PC.PAFR.5.3Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions and interpret them in terms of the context.
PC.PAFR.6 Manipulate, prove, and apply trigonometric identities and equations to solve contextual mathematical problems.
PC.PAFR.6.1Apply the fundamental trigonometric identities to simplify expressions and verify other identities.
PC.PAFR.6.2Apply the sum, difference, double-angle, and half-angle formulas for sine, cosine, and tangent and use them to solve problems.
PC.PAFR.6.3Model real-life situations and solve problems involving trigonometric equations.
PC.PAFR.7 Represent data with matrices, perform mathematical operations, and solve systems of linear equations for mathematical problems.
PC.PAFR.7.1Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically, and understand that such systems may have zero, one, or two solutions.
PC.PAFR.7.2Solve an equation of the form f(x)=g(x) graphically by identifying the x-coordinate(s) of the point(s) of intersection of the graphs of y=f(x) and y=g(x).
PC.PAFR.7.3Represent a system of linear equations as a single matrix equation in a vector variable.

Calculus

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C.MGSR Measurement, Geometry, and Spatial Reasoning
C.MGSR.1 Explain the concept of the integral of a function geometrically, numerically, analytically, and contextually.
C.MGSR.1.1Explain how the definite integral is used to solve area problems.
C.MGSR.1.2Approximate definite integrals by a finite sum.
C.MGSR.1.3Interpret the definite integral as a limit of Riemann sums.
C.MGSR.1.4Explain the relationship between the integral and derivative as expressed in both parts of the Fundamental Theorem of Calculus. Interpret the relationship in terms of rates of change.
C.MGSR.2 Apply theorems and rules of integration to solve mathematical and real-world situations.
C.MGSR.2.1Apply the Fundamental Theorem of Calculus to solve mathematical and real-world situations.
C.MGSR.2.2Explain graphically and verbally the properties of the definite integral. Apply these properties to evaluate basic definite integrals.
C.MGSR.2.3Evaluate integrals using substitution.
C.NR Numerical Reasoning
C.NR.1 Apply the concepts of a limit graphically, numerically, analytically, and contextually.
C.NR.1.1Estimate and verify limits using tables, graphs of functions, and technology.
C.NR.1.2Calculate limits—including one-sided limits—algebraically, using direct substitution, simplification, rationalization, and the limit laws for constant multiples, sums, differences, products, and quotients.
C.NR.1.3Calculate infinite limits and limits at infinity and use those limits to identify the asymptotes.
C.PAFR Patterns, Algebra, and Functional Reasoning
C.PAFR.1 Apply the definition and graphical interpretation of continuity of a function.
C.PAFR.1.1Apply the definition of continuity of a function at a point to solve problems.
C.PAFR.1.2Classify discontinuities as removable, jump, or infinite. Justify that classification using the definition of continuity.
C.PAFR.1.3Understand the Intermediate Value Theorem and apply the theorem to prove the existence of solutions of equations arising in mathematical and real-world situations.
C.PAFR.2 Understand the concept of the derivative of a function geometrically, numerically, analytically, and verbally.
C.PAFR.2.1Interpret the value of the derivative of a function as the slope of the corresponding tangent line.
C.PAFR.2.2Interpret the value of the derivative as an instantaneous rate of change in a variety of real-world contexts such as velocity and population growth.
C.PAFR.2.3Approximate the derivative graphically by finding the slope of the tangent line drawn to a curve at a given point and numerically by using the difference quotient.
C.PAFR.2.4Explain graphically and analytically the relationship between differentiability and continuity.
C.PAFR.2.5Explain graphically and analytically the relationship between the average rate of change and the instantaneous rate of change.
C.PAFR.2.6Use the definition of the derivative to determine the derivatives of various functions.
C.PAFR.3 Apply the rules of differentiation to functions.
C.PAFR.3.1Identify and apply the derivatives of constant, power, trigonometric, inverse trigonometric, exponential, and logarithmic functions.
C.PAFR.3.2Use the constant multiple, sum, difference, product, quotient, and chain rules to find the derivatives of functions.
C.PAFR.3.3Apply methods of implicit and logarithmic differentiation.
C.PAFR.4 Apply theorems and rules of differentiation to solve mathematical and real-world situations.
C.PAFR.4.1Explain the mathematical and real-world meanings of the Extreme Value Theorem and the Mean Value Theorem.
C.PAFR.4.2Write an equation of a line tangent to the graph of a function at a point.
C.PAFR.4.3Explain the relationship between the increasing/decreasing behavior of f and the signs of f′. Use the relationship to generate a graph of f given the graph of f′, and vice versa, and to identify relative and absolute extrema of f.
C.PAFR.4.4Explain the relationships among the concavity of the graph of f, the increasing/decreasing behavior of f′ and the signs of f′′. Use those relationships to generate graphs of f, f′, and f′′ given any one of them and identify the points of inflection of f.
C.PAFR.4.5Solve a variety of real-world situations involving related rates, optimization, linear approximation, and rates of change.

Reasoning in Mathematics

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RM.DPSR Data, Probability, and Statistical Reasoning
RM.DPSR.1 Apply statistical reasoning to complete investigations.
RM.DPSR.1.1Formulate a statistical question and develop a statistical method to address questions/studies through exploration of the research cycle.
RM.DPSR.1.2Write and identify a null hypothesis and an alternative hypothesis, as well as what makes up an experimental study.
RM.DPSR.1.3Identify the population of interest and the variables to be used in each study. Determine the appropriate sampling design, sampling technique, and statistical analysis for each research question.
RM.DPSR.2 Analyze data of a statistical experiment.
RM.DPSR.2.1Compare and contrast categorical and quantitative data.
RM.DPSR.2.2Identify the variable of interest, interpret a variety of graphical displays (particularly histograms and box plots), and estimate center, spread, shape, outliers, and unusual features.
RM.DPSR.2.3Analyze histograms in depth, analyzing the effect of changing the bin size (also known as interval width).
RM.DPSR.2.4Analyze the appropriateness and usefulness of the chosen measure of center and of the graphical display.
RM.DPSR.2.5Analyze the shape, spread, and unusual features of data sets and identify limitations based on data collection.
RM.DPSR.3 Explore the sources of variability in sampling methods.
RM.DPSR.3.1Analyze possible sources of variability in the data, including biased sampling methods (such as non-representative sampling and under coverage) and biased statistics, as well as natural and induced variability.
RM.DPSR.3.2Identify and explore various possible sources of statistical bias (such as response bias, nonresponse bias, and observer effect) and examine the effects of statistical bias on the generalizability of results.
RM.MGSR Measurement, Geometry, and Spatial Reasoning
RM.MGSR.1 Identify transformations using matrices.
RM.MGSR.1.1Use matrices to organize information and identify matrices that can be used to describe geometric transformations.
RM.MGSR.1.2Represent figures using matrices and explore ways of determining different transformations (translations, reflection, rotations, dilations, or combinations).
RM.MGSR.2 Analyze truth tables to validate real-world situations.
RM.MGSR.2.1Analyze truth tables to determine and verify the validity of arguments.
RM.MGSR.2.2Create arguments and statements to validate arguments.
RM.NR Numerical Reasoning
RM.NR.1 Analyze numerical data through estimation and approximation in real-world situations.
RM.NR.1.1Use various numerical techniques when estimating and calculating very large and small values.
RM.NR.1.2Apply proportional reasoning with aspect ratios.
RM.NR.1.3Use weighted averages and sums.
RM.NR.1.4Investigate and validate identification numbers.
RM.NR.2 Analyze present and future value of investments involving interest.
RM.NR.2.1Compare and contrast the nominal interest rate with the annual percentage rate (APR).
RM.NR.2.2Determine the future value of an investment, given the present value.
RM.NR.3 Analyze real-world scenarios involving credit card debt and loans.
RM.NR.3.1Determine the monthly payment to retire a debt at a fixed rate.
RM.NR.3.2Compare and contrast different credit card offers using minimum payments.
RM.PAFR Patterns, Algebra, and Functional Reasoning
RM.PAFR.1 Analyze regression of linear functions.
RM.PAFR.1.1Compute and analyze the correlation coefficient of data to determine the strength of the linear model.
RM.PAFR.1.2Analyze data that follow a linear pattern using recursively defined rules and compare those rules to explicit function rules.
RM.PAFR.2 Analyze step and piecewise functions in real-world situations.
RM.PAFR.2.1Explore step and piecewise functions to make predictions and decisions about a variety of mathematical and real-world situations.
RM.PAFR.3 Analyze data that follow an exponential pattern using the idea of a common ratio between consecutive values.
RM.PAFR.3.1Find recursive rules to model data and make connections between the recursive rule and the explicit function rule of the exponential relationship.

Applications and Modeling

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AM.DPSR Data, Probability, and Statistical Reasoning
AM.DPSR.1 Summarize and interpret data represented in tables or graphs to make predictions.
AM.DPSR.1.1Summarize and interpret trends to make predictions in real-world situations.
AM.DPSR.1.2Calculate and explain pay scale based on occupational outlook projections.
AM.DPSR.1.3Calculate and explain operating costs, including cost of materials, supplies, equipment, license fees, and insurance fees.
AM.DPSR.1.4Construct and analyze charts that reflect current demographics in various industries.
AM.DPSR.2 Solve problems involving probability and probability models, and use expected value to make informed decisions in real-world situations.
AM.DPSR.2.1Determine the probability of simple and compound events in real-world situations.
AM.DPSR.2.2Use probabilities to make and justify decisions about risk in real-world situations.
AM.DPSR.2.3Calculate and analyze the expected value of a probability model (binominal, normal, and Poisson distributions) for a real-world situation to make decisions about fairness, payoff, and risk.
AM.MGSR Measurement, Geometry, and Spatial Reasoning
AM.MGSR.1 Apply trigonometric principles to solve real-world geometric situations involving inaccessible distances.
AM.MGSR.1.1Apply sine, cosine, and tangent ratios and the Law of Sines and the Law of Cosines to discover distances.
AM.MGSR.2 Critique the appropriateness of measurements in terms of precision, accuracy, and approximate error.
AM.MGSR.2.1Determine dimensions by scaling plans or blueprints.
AM.MGSR.2.2Apply knowledge of fractions for reading a ruler to 1/16 inch to interpreting blueprints and measuring materials.
AM.MGSR.2.3Compare the metric and the British imperial systems of measurements used in industry.
AM.MGSR.3 Apply two- and three-dimensional representations, geometric transformations, and scale models in planning, designing, and constructing solutions to real-world situations.
AM.MGSR.3.1Calculate lengths utilizing the Pythagorean Theorem.
AM.MGSR.3.2Apply the concepts of area, volume, scale factors, and scale drawings to applied problems for a specific project.
AM.MGSR.3.3Determine the level of precision and the appropriate tools for taking measurements in constructing a two-dimensional visual representation of a three-dimensional object or structure.
AM.MGSR.3.4Apply Heron's Formula for finding the area of a triangular region.
AM.MGSR.4 Apply two- and three-dimensional representations in coordinate systems to find solutions to real-world situations.
AM.MGSR.4.1Plot coordinates on a three-dimensional Cartesian coordinate system and use relationships between coordinates to solve design problems.
AM.MGSR.4.2Use technology and other tools to explore the results of simple transformations using three-dimensional coordinates, including translations in the x, y, and/or z directions; rotations of 90 degrees, 180 degrees, or 270 degrees about the x, y, and z axes; reflections over the xy, yz, and xz planes; and dilations from the origin.
AM.MGSR.5 Use vectors and matrices to represent, organize, and describe data to solve problems in mathematical and real-world situations.
AM.MGSR.5.1Apply vectors to mathematical and real-world situations by recognizing vectors as mathematical objects having both magnitude and direction.
AM.MGSR.5.2Use and apply matrices to represent geometric transformations in real-world situations.
AM.NR Numerical Reasoning
AM.NR.1 Solve problems using fractions, percents, and ratios for real-world situations involving linear, quadratic, exponential, and absolute functions.
AM.NR.1.1Apply numerical reasoning to real-world situations involving percent increase and decrease.
AM.PAFR Patterns, Algebra, and Functional Reasoning
AM.PAFR.1 Create and analyze mathematical models to make decisions on real-world situations.
AM.PAFR.1.1Use exponential functions to model change in a variety of financial situations.
AM.PAFR.1.2Compare the various means of paying for an automobile, including leasing, purchasing by cash, and purchasing by loan.
AM.PAFR.1.3Use sequences to represent simple and compound interest and depreciation.
AM.PAFR.2 Analyze and solve application-based problems relating to direct, inverse, and joint variation.
AM.PAFR.2.1Apply variations to mathematical and real-world situations to describe troubleshooting in business and industrial applications.
AM.PAFR.2.2Utilize mathematical skills for troubleshooting in business and industrial applications.
AM.PAFR.3 Analyze and apply linear programming to mathematical and real-world situations.
AM.PAFR.3.1Calculate the values of the variables that maximize or minimize the objective function, given four or more constraints.

Statistical Modeling

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SM.DPSR Data, Probability, and Statistical Reasoning
SM.DPSR.1 Communicate using descriptive and inferential statistics by collecting, critiquing, analyzing, and interpreting real-world data.
SM.DPSR.1.1Calculate and interpret z-scores as a measure of relative standing to standardize units.
SM.DPSR.1.2Approximate percentages using the Empirical Rule and z-scores for normally distributed data.
SM.DPSR.1.3Using simulations taken from a given population, model sample-to-sample variability in sampling distributions of a statistic.
SM.DPSR.1.4Construct and compare confidence intervals of different models to make conclusions about reliability given a margin of error.
SM.DPSR.1.5Summarize and evaluate reports based on data for appropriateness of study design, analysis methods, and statistical measures used.
SM.DPSR.2 Formulate investigative statistical questions that can be answered using data.
SM.DPSR.2.1Formulate investigative statistical questions about a population using samples taken from the population.
SM.DPSR.2.2Formulate comparative and associative investigative statistical questions for surveys and observational studies to compare two or more groups or to investigate the association of two or more variables.
SM.DPSR.2.3Formulate comparative and associative investigative statistical questions for experiments to compare two or more groups or to investigate the association of two or more variables.
SM.DPSR.2.4Formulate inferential investigative statistical questions regarding association and prediction.
SM.DPSR.2.5Formulate investigative statistical questions for two variables.
SM.DPSR.3 Design and implement a plan to collect data to address the investigative statistical question.
SM.DPSR.3.1Apply an appropriate data-collection plan when collecting data for the investigative statistical question of interest.
SM.DPSR.3.2Distinguish between sample surveys, observational studies, and experiments.
SM.DPSR.3.3Design sample surveys, experiments, and observational studies using statistical methods.
SM.DPSR.3.4Differentiate between random selection and random assignment and identify their impact on generalizing.
SM.DPSR.3.5Examine potential sources and effects of bias and confounding variables.
SM.DPSR.3.6Describe and comply with the ethical use of data.
SM.DPSR.3.7Identify when data can be generalized to a target population.
SM.DPSR.4 Use appropriate graphical and numerical methods to analyze data.
SM.DPSR.4.1Describe quantitative and categorical data.
SM.DPSR.4.2Summarize and describe relationships between two variables.
SM.DPSR.4.3Describe the relationship between two quantitative variables by interpreting correlation (r) and a least-square regression line (using technology).
SM.DPSR.4.4Assess the fit of a linear model by plotting and analyzing residuals, including the squares of the residuals, to improve its fit.
SM.DPSR.4.5Calculate and interpret the p-value for a population proportion and/or population mean.
SM.DPSR.4.6Use simulated sampling distributions to describe the sample-to-sample variability of sample statistics.
SM.DPSR.4.7Use simulations to investigate associations between two categorical variables and to compare groups.
SM.DPSR.5 Interpret the results of the analysis by making connections to the investigative statistical question.
SM.DPSR.5.1Use statistical evidence from analyses to answer investigative statistical questions.
SM.DPSR.5.2Determine the possible impact of extreme data points, missing values, or incorrect values on the results.
SM.DPSR.5.3Use and interpret the p-value to determine whether the estimate for a population parameter is reasonable.
SM.DPSR.5.4Interpret a given margin of error corresponding to an estimate of a population parameter.
SM.DPSR.5.5Explain the impact of multiple variables on one another.

Discrete Mathematics

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DM.DPSR Data, Probability, and Statistical Reasoning
DM.DPSR.1 Analyze, model, and solve problems involving fair outcomes.
DM.DPSR.1.1Investigate and describe the results of various election methods.
DM.DPSR.1.2Explain fairness and equity in relation to the paradoxes of voting.
DM.DPSR.1.3Solve apportionment problems using a variety of methods.
DM.DPSR.1.4Compare voting methods to determine the most appropriate method for the situation.
DM.DPSR.1.5Determine power indexes for weighted voting systems.
DM.MGSR Measurement, Geometry, and Spatial Reasoning
DM.MGSR.1 Use graph theory to model relationships and solve problems.
DM.MGSR.1.1Distinguish between inductive and deductive reasoning.
DM.MGSR.1.2Determine statements and rephrase them symbolically.
DM.MGSR.1.3Use negation, disjunction, and conjunction to determine if statements are logically equivalent.
DM.MGSR.1.4Write statements in words and symbolically using converse, inverse, and contrapositive.
DM.MGSR.1.5Verify arguments and syllogisms.
DM.MGSR.1.6Represent real-world situations using a vertex-edge graph.
DM.MGSR.1.7Test graphs and digraphs for paths and circuits.
DM.NR Numerical Reasoning
DM.NR.1 Investigate principles of set theory.
DM.NR.1.1Define basic terms and concepts in set theory.
DM.NR.1.2Compare sets with appropriate language and notation.
DM.NR.1.3Determine and explain the cardinality of sets.
DM.NR.2 Analyze numbers with different bases in real-world situations.
DM.NR.2.1Perform arithmetic operations using modular arithmetic properties.
DM.NR.2.2Solve problems involving modular arithmetic in real-world situations.
DM.NR.2.3Explain and apply binary and hexadecimal number systems.
DM.NR.3 Determine the number of ways an event can occur.
DM.NR.3.1Calculate combinations and permutations.
DM.PAFR Patterns, Algebra, and Functional Reasoning
DM.PAFR.1 Classify and compare objects using estimation and sets for real-world situations.
DM.PAFR.1.1Use estimation to get an approximate answer in real-world situations.
DM.PAFR.1.2Perform operations on sets.
DM.PAFR.2 Develop an understanding of and carry out proofs by mathematical induction using the Principle of Mathematical Induction.
DM.PAFR.2.1Create mathematical induction proofs using the Principle of Mathematical Induction.
DM.PAFR.3 Use matrices to model and solve mathematical and real-world situations.
DM.PAFR.3.1Manipulate matrices using addition, subtraction, multiplication, inverse, and power properties.
DM.PAFR.3.2Write and evaluate matrices drawn from real-world situations.

AP Calculus Learning Objectives

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CB.Calc.LIM Limits
CB.Calc.LIM-1 Reasoning with definitions, theorems, and properties can be used to justify claims about limits.
CB.Calc.LIM-1.ARepresent limits analytically using correct notation.
CB.Calc.LIM-1.BInterpret limits expressed in analytic notation.
CB.Calc.LIM-1.CEstimate limits of functions.
CB.Calc.LIM-1.DDetermine the limits of functions using limit theorems.
CB.Calc.LIM-1.EDetermine the limits of functions using equivalent expressions for the function or the squeeze theorem.
CB.Calc.LIM-2 Reasoning with definitions, theorems, and properties can be used to justify claims about continuity.
CB.Calc.LIM-2.AJustify conclusions about continuity at a point using the definition.
CB.Calc.LIM-2.BDetermine intervals over which a function is continuous.
CB.Calc.LIM-2.CDetermine values of x or solve for parameters that make discontinuous functions continuous, if possible.
CB.Calc.LIM-2.DInterpret the behavior of functions using limits involving infinity.
CB.Calc.LIM-3 The derivative of a function is defined as the limit of a difference quotient.
CB.Calc.LIM-3.AInterpret a limit as a definition of a derivative.
CB.Calc.LIM-4 L'Hospital's Rule allows us to determine the limits of some indeterminate forms.
CB.Calc.LIM-4.ADetermine limits of functions that result in indeterminate forms.
CB.Calc.LIM-5 Definite integrals can be approximated using geometric and numerical methods.
CB.Calc.LIM-5.AApproximate a definite integral using geometric and numerical methods.
CB.Calc.LIM-5.BInterpret the limiting case of the Riemann sum as a definite integral.
CB.Calc.LIM-5.CRepresent the limiting case of the Riemann sum as a definite integral.
CB.Calc.LIM-6 Improper integrals can be determined using limits of definite integrals.
CB.Calc.LIM-6.AEvaluate an improper integral or determine that the integral diverges.
CB.Calc.LIM-7 The behavior of a convergent or divergent series can be determined or estimated.
CB.Calc.LIM-7.ADetermine whether a series converges or diverges.
CB.Calc.LIM-7.BApproximate the sum of a series.
CB.Calc.LIM-8 Power series and Taylor series can represent functions.
CB.Calc.LIM-8.ARepresent a function at a point as a Taylor polynomial.
CB.Calc.LIM-8.BApproximate function values using a Taylor polynomial.
CB.Calc.LIM-8.CDetermine the error bound associated with a Taylor polynomial approximation.
CB.Calc.LIM-8.DDetermine the radius of convergence and interval of convergence for a power series.
CB.Calc.LIM-8.ERepresent a function as a Taylor series or a Maclaurin series.
CB.Calc.LIM-8.FInterpret Taylor series and Maclaurin series.
CB.Calc.LIM-8.GRepresent a given function as a power series.
CB.Calc.CHA Change
CB.Calc.CHA-1 The derivative of a function is the instantaneous rate of change of the function.
CB.Calc.CHA-1.AInterpret the rate of change at an instant in terms of average rates of change over intervals containing that instant.
CB.Calc.CHA-2 Derivatives can be computed using definitions and rules.
CB.Calc.CHA-2.ADetermine average rates of change using difference quotients.
CB.Calc.CHA-2.BRepresent the derivative of a function as the limit of a difference quotient.
CB.Calc.CHA-2.CDetermine the equation of a line tangent to a curve at a given point.
CB.Calc.CHA-2.DEstimate derivatives.
CB.Calc.CHA-3 Derivatives can be used to model rates of change in applied contexts.
CB.Calc.CHA-3.AInterpret the meaning of a derivative in context.
CB.Calc.CHA-3.BCalculate rates of change in applied contexts.
CB.Calc.CHA-3.CInterpret rates of change in applied contexts.
CB.Calc.CHA-3.DCalculate related rates in applied contexts.
CB.Calc.CHA-3.EInterpret related rates in applied contexts.
CB.Calc.CHA-3.FApproximate a value on a curve using the equation of a tangent line.
CB.Calc.CHA-3.GCalculate derivatives of parametric functions.
CB.Calc.CHA-3.HCalculate derivatives of vector-valued functions.
CB.Calc.CHA-4 Integrals can be used to model accumulation and net change in applied contexts.
CB.Calc.CHA-4.AInterpret the meaning of areas associated with the graph of a rate of change in context.
CB.Calc.CHA-4.BDetermine the average value of a function using definite integrals.
CB.Calc.CHA-4.CDetermine values for positions and rates of change using definite integrals in problems involving rectilinear motion.
CB.Calc.CHA-4.DInterpret the meaning of a definite integral in accumulation problems.
CB.Calc.CHA-4.EDetermine net change using definite integrals in applied contexts.
CB.Calc.CHA-5 Definite integrals can be used to calculate areas, volumes, and lengths.
CB.Calc.CHA-5.ACalculate areas in the plane using the definite integral.
CB.Calc.CHA-5.BCalculate volumes of solids with known cross sections using definite integrals.
CB.Calc.CHA-5.CCalculate volumes of solids of revolution using definite integrals.
CB.Calc.CHA-5.DCalculate areas of regions defined by polar curves using definite integrals.
CB.Calc.CHA-6 Arc length can be calculated using definite integrals.
CB.Calc.CHA-6.ADetermine the length of a curve in the plane defined by a function, using a definite integral.
CB.Calc.CHA-6.BDetermine the length of a curve in the plane defined by parametric functions, using a definite integral.
CB.Calc.FUN Analysis of Functions
CB.Calc.FUN-1 Existence theorems can be used to draw conclusions about the behavior of functions.
CB.Calc.FUN-1.AExplain the behavior of a function on an interval using the Intermediate Value Theorem.
CB.Calc.FUN-1.BJustify conclusions about functions by applying the Mean Value Theorem over an interval.
CB.Calc.FUN-1.CJustify conclusions about functions by applying the Extreme Value Theorem.
CB.Calc.FUN-2 A function's derivative, when it exists, can be used to determine whether the function is increasing or decreasing.
CB.Calc.FUN-2.AExplain the relationship between differentiability and continuity.
CB.Calc.FUN-3 Derivatives can be calculated for various types of functions.
CB.Calc.FUN-3.ACalculate derivatives of familiar functions.
CB.Calc.FUN-3.BCalculate derivatives of products and quotients of differentiable functions.
CB.Calc.FUN-3.CCalculate derivatives of compositions of differentiable functions.
CB.Calc.FUN-3.DCalculate derivatives of implicitly defined functions.
CB.Calc.FUN-3.ECalculate derivatives of inverse and inverse trigonometric functions.
CB.Calc.FUN-3.FDetermine higher order derivatives of a function.
CB.Calc.FUN-3.GCalculate derivatives of functions written in polar coordinates.
CB.Calc.FUN-4 A function's derivative can be used to understand function behavior.
CB.Calc.FUN-4.AJustify conclusions about the behavior of a function based on the behavior of its derivatives.
CB.Calc.FUN-4.BCalculate minimum and maximum values in applied contexts or analysis of functions.
CB.Calc.FUN-4.CInterpret minimum and maximum values calculated in applied contexts.
CB.Calc.FUN-4.DDetermine critical points of implicit relations.
CB.Calc.FUN-4.EJustify conclusions about the behavior of an implicitly defined function based on evidence from its derivatives.
CB.Calc.FUN-5 The Fundamental Theorem of Calculus connects differentiation and integration.
CB.Calc.FUN-5.ARepresent accumulation functions using definite integrals.
CB.Calc.FUN-6 Recognizing and applying techniques for antidifferentiation.
CB.Calc.FUN-6.ACalculate a definite integral using areas and properties of definite integrals.
CB.Calc.FUN-6.BEvaluate definite integrals analytically using the Fundamental Theorem of Calculus.
CB.Calc.FUN-6.CDetermine antiderivatives of functions and indefinite integrals, using knowledge of derivatives.
CB.Calc.FUN-6.DUse substitution and rearrangements into equivalent forms, such as long division and completing the square, for integrands requiring these techniques.
CB.Calc.FUN-6.EUse integration by parts for integrands requiring this technique.
CB.Calc.FUN-6.FUse integration by linear partial fractions for integrands requiring this technique.
CB.Calc.FUN-7 Solving differential equations allows us to model rates of change.
CB.Calc.FUN-7.AInterpret verbal statements of problems as differential equations involving a derivative expression.
CB.Calc.FUN-7.BVerify solutions to differential equations.
CB.Calc.FUN-7.CEstimate solutions to differential equations.
CB.Calc.FUN-7.DDetermine general solutions to differential equations.
CB.Calc.FUN-7.EDetermine particular solutions to differential equations.
CB.Calc.FUN-7.FInterpret the meaning of a differential equation and its variables in context.
CB.Calc.FUN-7.GDetermine general and particular solutions for problems involving differential equations in context.
CB.Calc.FUN-7.HInterpret the meaning of the logistic growth model in context.
CB.Calc.FUN-8 Solutions to differential equations can model motion in the plane.
CB.Calc.FUN-8.ADetermine a particular solution given a rate vector and initial conditions.
CB.Calc.FUN-8.BDetermine values for positions and rates of change in problems involving planar motion.

AP Statistics Learning Objectives

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CB.Stats.VAR Variation and Distribution
CB.Stats.VAR-1 Exploring data through asking and answering statistical questions.
CB.Stats.VAR-1.AIdentify questions to be answered, based on variation in one-variable data.
CB.Stats.VAR-1.BIdentify variables in a set of data.
CB.Stats.VAR-1.CClassify types of variables.
CB.Stats.VAR-1.DIdentify questions to be answered about possible relationships in data.
CB.Stats.VAR-1.EIdentify questions to be answered about data collection methods.
CB.Stats.VAR-1.FIdentify questions suggested by patterns in data.
CB.Stats.VAR-1.GIdentify questions suggested by variation in statistics for samples collected from the same population.
CB.Stats.VAR-1.HIdentify questions suggested by variation in the shapes of distributions of samples taken from the same population.
CB.Stats.VAR-1.IIdentify questions suggested by probabilities of errors in statistical inference.
CB.Stats.VAR-1.JIdentify questions suggested by variation between observed and expected counts in categorical data.
CB.Stats.VAR-1.KIdentify questions suggested by variation in scatter plots.
CB.Stats.VAR-2 Normal distributions and comparing data.
CB.Stats.VAR-2.ACompare a data distribution to the normal distribution model.
CB.Stats.VAR-2.BDetermine proportions and percentiles from a normal distribution.
CB.Stats.VAR-2.CCompare measures of relative position in data sets.
CB.Stats.VAR-3 Designing and analyzing experiments.
CB.Stats.VAR-3.AIdentify the components of an experiment.
CB.Stats.VAR-3.BDescribe elements of a well-designed experiment.
CB.Stats.VAR-3.CCompare experimental designs and methods.
CB.Stats.VAR-3.DExplain why a particular experimental design is appropriate.
CB.Stats.VAR-3.EInterpret the results of a well-designed experiment.
CB.Stats.VAR-4 Probability rules and calculations.
CB.Stats.VAR-4.ACalculate probabilities for events and their complements.
CB.Stats.VAR-4.BInterpret probabilities for events.
CB.Stats.VAR-4.CExplain why two events are (or are not) mutually exclusive.
CB.Stats.VAR-4.DCalculate conditional probabilities.
CB.Stats.VAR-4.ECalculate probabilities for independent events and for the union of two events.
CB.Stats.VAR-5 Discrete random variables and probability distributions.
CB.Stats.VAR-5.ARepresent the probability distribution for a discrete random variable.
CB.Stats.VAR-5.BInterpret a probability distribution.
CB.Stats.VAR-5.CCalculate parameters for a discrete random variable.
CB.Stats.VAR-5.DInterpret parameters for a discrete random variable.
CB.Stats.VAR-5.ECalculate parameters for linear combinations of random variables.
CB.Stats.VAR-5.FDescribe the effects of linear transformations of parameters of random variables.
CB.Stats.VAR-6 Normal distributions and hypothesis testing for proportions.
CB.Stats.VAR-6.ACalculate the probability that a particular value lies in a given interval of a normal distribution.
CB.Stats.VAR-6.BDetermine the interval associated with a given area in a normal distribution.
CB.Stats.VAR-6.CDetermine the appropriateness of using the normal distribution to approximate probabilities for unknown distributions.
CB.Stats.VAR-6.DIdentify the null and alternative hypotheses for a population proportion.
CB.Stats.VAR-6.EIdentify an appropriate testing method for a population proportion.
CB.Stats.VAR-6.FVerify the conditions for making statistical inferences when testing a population proportion.
CB.Stats.VAR-6.GCalculate an appropriate test statistic and p-value for a population proportion.
CB.Stats.VAR-6.HIdentify the null and alternative hypotheses for a difference of two population proportions.
CB.Stats.VAR-6.IIdentify an appropriate testing method for the difference of two population proportions.
CB.Stats.VAR-6.JVerify the conditions for making statistical inferences when testing a difference of two population proportions.
CB.Stats.VAR-6.KCalculate an appropriate test statistic for the difference of two population proportions.
CB.Stats.VAR-7 t-distributions and hypothesis testing for means and regression.
CB.Stats.VAR-7.ADescribe t-distributions.
CB.Stats.VAR-7.BIdentify an appropriate testing method for a population mean with unknown sigma, including the mean difference between values in matched pairs.
CB.Stats.VAR-7.CIdentify the null and alternative hypotheses for a population mean with unknown sigma, including the mean difference between values in matched pairs.
CB.Stats.VAR-7.DVerify the conditions for the test for a population mean, including the mean difference between values in matched pairs.
CB.Stats.VAR-7.ECalculate an appropriate test statistic for a population mean, including the mean difference between values in matched pairs.
CB.Stats.VAR-7.FIdentify an appropriate selection of a testing method for a difference of two population means.
CB.Stats.VAR-7.GIdentify the null and alternative hypotheses for a difference of two population means.
CB.Stats.VAR-7.HVerify the conditions for the significance test for the difference of two population means.
CB.Stats.VAR-7.ICalculate an appropriate test statistic for a difference of two means.
CB.Stats.VAR-7.JIdentify the appropriate selection of a testing method for a slope of a regression model.
CB.Stats.VAR-7.KIdentify appropriate null and alternative hypotheses for a slope of a regression model.
CB.Stats.VAR-7.LVerify the conditions for the significance test for the slope of a regression model.
CB.Stats.VAR-7.MCalculate an appropriate test statistic for the slope of a regression model.
CB.Stats.VAR-8 Chi-square distributions and tests.
CB.Stats.VAR-8.ADescribe chi-square distributions.
CB.Stats.VAR-8.BIdentify the null and alternative hypotheses in a test for a distribution of proportions in a set of categorical data.
CB.Stats.VAR-8.CIdentify an appropriate testing method for a distribution of proportions in a set of categorical data.
CB.Stats.VAR-8.DCalculate expected counts for the chi-square test for goodness of fit.
CB.Stats.VAR-8.EVerify the conditions for making statistical inferences when testing goodness of fit for a chi-square distribution.
CB.Stats.VAR-8.FCalculate the appropriate statistic for the chi-square test for goodness of fit.
CB.Stats.VAR-8.GDetermine the p-value for the chi-square test for goodness of fit.
CB.Stats.VAR-8.HCalculate expected counts for two-way tables of categorical data.
CB.Stats.VAR-8.IIdentify the null and alternative hypotheses for a chi-square test for homogeneity or independence.
CB.Stats.VAR-8.JIdentify an appropriate testing method for comparing distributions in two-way tables of categorical data.
CB.Stats.VAR-8.KVerify the conditions for making statistical inferences when testing a chi-square distribution for independence or homogeneity.
CB.Stats.VAR-8.LCalculate the appropriate statistic for a chi-square test for homogeneity or independence.
CB.Stats.VAR-8.MDetermine the p-value for a chi-square test for independence or homogeneity.
CB.Stats.UNC Uncertainty and Inference
CB.Stats.UNC-1 Representing and describing categorical and quantitative data.
CB.Stats.UNC-1.ARepresent categorical data using frequency or relative frequency tables.
CB.Stats.UNC-1.BDescribe categorical data represented in frequency or relative tables.
CB.Stats.UNC-1.CRepresent categorical data graphically.
CB.Stats.UNC-1.DDescribe categorical data represented graphically.
CB.Stats.UNC-1.ECompare multiple sets of categorical data.
CB.Stats.UNC-1.FClassify types of quantitative variables.
CB.Stats.UNC-1.GRepresent quantitative data graphically.
CB.Stats.UNC-1.HDescribe the characteristics of quantitative data distributions.
CB.Stats.UNC-1.ICalculate measures of center and position for quantitative data.
CB.Stats.UNC-1.JCalculate measures of variability for quantitative data.
CB.Stats.UNC-1.KExplain the selection of a particular measure of center and/or variability for describing a set of quantitative data.
CB.Stats.UNC-1.LRepresent summary statistics for quantitative data graphically.
CB.Stats.UNC-1.MDescribe summary statistics of quantitative data represented graphically.
CB.Stats.UNC-1.NCompare graphical representations for multiple sets of quantitative data.
CB.Stats.UNC-1.OCompare summary statistics for multiple sets of quantitative data.
CB.Stats.UNC-1.PCompare numerical and graphical representations for two categorical variables.
CB.Stats.UNC-1.QCalculate statistics for two categorical variables.
CB.Stats.UNC-1.RCompare statistics for two categorical variables.
CB.Stats.UNC-1.SRepresent bivariate quantitative data using scatterplots.
CB.Stats.UNC-2 Probability and simulation.
CB.Stats.UNC-2.AEstimate probabilities using simulation.
CB.Stats.UNC-3 Random variables and sampling distributions.
CB.Stats.UNC-3.AEstimate probabilities of binomial random variables using data from a simulation.
CB.Stats.UNC-3.BCalculate probabilities for a binomial distribution.
CB.Stats.UNC-3.CCalculate parameters for a binomial distribution.
CB.Stats.UNC-3.DInterpret probabilities and parameters for a binomial distribution.
CB.Stats.UNC-3.ECalculate probabilities for geometric random variables.
CB.Stats.UNC-3.FCalculate parameters of a geometric distribution.
CB.Stats.UNC-3.GInterpret probabilities and parameters for a geometric distribution.
CB.Stats.UNC-3.HEstimate sampling distributions using simulation.
CB.Stats.UNC-3.IExplain why an estimator is or is not unbiased.
CB.Stats.UNC-3.JCalculate estimates for a population parameter.
CB.Stats.UNC-3.KDetermine parameters of a sampling distribution for sample proportions.
CB.Stats.UNC-3.LDetermine whether a sampling distribution for a sample proportion can be described as approximately normal.
CB.Stats.UNC-3.MInterpret probabilities and parameters for a sampling distribution for a sample proportion.
CB.Stats.UNC-3.NDetermine parameters of a sampling distribution for a difference in sample proportions.
CB.Stats.UNC-3.ODetermine whether a sampling distribution for a difference of sample proportions can be described as approximately normal.
CB.Stats.UNC-3.PInterpret probabilities and parameters for a sampling distribution for a difference in proportions.
CB.Stats.UNC-3.QDetermine parameters of a sampling distribution for a sample mean.
CB.Stats.UNC-3.RDetermine whether a sampling distribution of a sample mean can be described as approximately normal.
CB.Stats.UNC-3.SInterpret probabilities and parameters for a sampling distribution for a sample mean.
CB.Stats.UNC-3.TDetermine parameters of a sampling distribution for a difference in sample means.
CB.Stats.UNC-3.UDetermine whether a sampling distribution of a difference in sample means can be described as approximately normal.
CB.Stats.UNC-3.VInterpret probabilities and parameters for a sampling distribution for a difference in sample means.
CB.Stats.UNC-4 Confidence intervals for proportions and means.
CB.Stats.UNC-4.AIdentify an appropriate confidence interval procedure for a population proportion.
CB.Stats.UNC-4.BVerify the conditions for calculating confidence intervals for a population proportion.
CB.Stats.UNC-4.CDetermine the margin of error for a given sample size and an estimate for the sample size that will result in a given margin of error for a population proportion.
CB.Stats.UNC-4.DCalculate an appropriate confidence interval for a population proportion.
CB.Stats.UNC-4.ECalculate an interval estimate based on a confidence interval for a population proportion.
CB.Stats.UNC-4.FInterpret a confidence interval for a population proportion.
CB.Stats.UNC-4.GJustify a claim based on a confidence interval for a population proportion.
CB.Stats.UNC-4.HIdentify the relationships between sample size, width of a confidence interval, confidence level, and margin of error for a population proportion.
CB.Stats.UNC-4.IIdentify an appropriate confidence interval procedure for a comparison of population proportions.
CB.Stats.UNC-4.JVerify the conditions for calculating confidence intervals for a difference between population proportions.
CB.Stats.UNC-4.KCalculate an appropriate confidence interval for a comparison of population proportions.
CB.Stats.UNC-4.LCalculate an interval estimate based on a confidence interval for a difference of proportions.
CB.Stats.UNC-4.MInterpret a confidence interval for a difference of proportions.
CB.Stats.UNC-4.NJustify a claim based on a confidence interval for a difference of proportions.
CB.Stats.UNC-4.OIdentify an appropriate confidence interval procedure for a population mean, including the mean difference between values in matched pairs.
CB.Stats.UNC-4.PVerify the conditions for calculating confidence intervals for a population mean, including the mean difference between values in matched pairs.
CB.Stats.UNC-4.QDetermine the margin of error for a given sample size for a one-sample t-interval.
CB.Stats.UNC-4.RCalculate an appropriate confidence interval for a population mean, including the mean difference between values in matched pairs.
CB.Stats.UNC-4.SInterpret a confidence interval for a population mean, including the mean difference between values in matched pairs.
CB.Stats.UNC-4.TJustify a claim based on a confidence interval for a population mean, including the mean difference between values in matched pairs.
CB.Stats.UNC-4.UIdentify the relationships between sample size, width of a confidence interval, confidence level, and margin of error for a population mean.
CB.Stats.UNC-4.VIdentify an appropriate confidence interval procedure for a difference of two population means.
CB.Stats.UNC-4.WVerify the conditions for calculating confidence intervals for the difference of two population means.
CB.Stats.UNC-4.XDetermine the margin of error for the difference of two population means.
CB.Stats.UNC-4.YCalculate an appropriate confidence interval for a difference of two population means.
CB.Stats.UNC-4.ZInterpret a confidence interval for a difference of population means.
CB.Stats.UNC-5 Errors in statistical inference.
CB.Stats.UNC-5.AIdentify Type I and Type II errors.
CB.Stats.UNC-5.BCalculate the probability of a Type I and Type II errors.
CB.Stats.UNC-5.CIdentify factors that affect the probability of errors in significance testing.
CB.Stats.UNC-5.DInterpret Type I and Type II errors.
CB.Stats.DAT Data Analysis
CB.Stats.DAT-1 Bivariate data analysis and linear regression.
CB.Stats.DAT-1.ADescribe the characteristics of a scatter plot.
CB.Stats.DAT-1.BDetermine the correlation for a linear relationship.
CB.Stats.DAT-1.CInterpret the correlation for a linear relationship.
CB.Stats.DAT-1.DCalculate a predicted response value using a linear regression model.
CB.Stats.DAT-1.ERepresent differences between measured and predicted responses using residual plots.
CB.Stats.DAT-1.FDescribe the form of association of bivariate data using residual plots.
CB.Stats.DAT-1.GEstimate parameters for the least-squares regression line model.
CB.Stats.DAT-1.HInterpret coefficients for the least-squares regression line model.
CB.Stats.DAT-1.IIdentify influential points in regression.
CB.Stats.DAT-1.JCalculate a predicted response using a least-squares regression line for a transformed data set.
CB.Stats.DAT-2 Studies, sampling, and sources of bias.
CB.Stats.DAT-2.AIdentify the type of a study.
CB.Stats.DAT-2.BIdentify appropriate generalizations and determinations based on observational studies.
CB.Stats.DAT-2.CIdentify a sampling method, given a description of a study.
CB.Stats.DAT-2.DExplain why a particular sampling method is or is not appropriate for a given situation.
CB.Stats.DAT-2.EIdentify potential sources of bias in sampling methods.
CB.Stats.DAT-3 Interpreting and justifying conclusions from significance tests.
CB.Stats.DAT-3.AInterpret the p-value of a significance test for a population proportion.
CB.Stats.DAT-3.BJustify a claim about the population based on the results of a significance test for a population proportion.
CB.Stats.DAT-3.CInterpret the p-value of a significance test for a difference of population proportions.
CB.Stats.DAT-3.DJustify a claim about the population based on the results of a significance test for a difference of population proportions.
CB.Stats.DAT-3.EInterpret the p-value of a significance test for a population mean, including the mean difference between values in matched pairs.
CB.Stats.DAT-3.FJustify a claim about the population based on the results of a significance test for a population mean.
CB.Stats.DAT-3.GInterpret the p-value of a significance test for a difference of population means.
CB.Stats.DAT-3.HJustify a claim about the population based on the results of a significance test for a difference of two population means in context.
CB.Stats.DAT-3.IInterpret the p-value for the chi-square test for goodness of fit.
CB.Stats.DAT-3.JJustify a claim about the population based on the results of a chi-square test for goodness of fit.
CB.Stats.DAT-3.KInterpret the p-value for the chi-square test for homogeneity or independence.
CB.Stats.DAT-3.LJustify a claim about the population based on the results of a chi-square test for homogeneity or independence.
CB.Stats.DAT-3.MInterpret the p-value of a significance test for the slope of a regression model.
CB.Stats.DAT-3.NJustify a claim about the population based on the results of a significance test for the slope of a regression model.

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