Missouri Math Standards

816 standards, Kindergarten through AP.

Kindergarten

K.DS Data and Statistics
K.DS.A Classify objects and count the number of objects in each category.
K.DS.A.1Classify objects into given categories; count the number of objects in each category.
K.DS.A.2Compare category counts using appropriate language.
K.GM Geometry and Measurement
K.GM.A Reason with shapes and their attributes.
K.GM.A.1Describe several measureable attributes of objects.
K.GM.A.2Compare the measurable attributes of two objects.
K.GM.B Work with time and money.
K.GM.B.3Demonstrate an understanding of concepts of time and devices that measure time.
K.GM.B.4Name the days of the week.
K.GM.B.5Identify pennies, nickels, dimes and quarters.
K.GM.C Analyze squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders and spheres.
K.GM.C.10Compose simple shapes to form larger shapes using manipulatives.
K.GM.C.6Identify shapes and describe objects in the environment using names of shapes, recognizing the name stays the same regardless of orientation or size.
K.GM.C.7Describe the relative positions of objects in space.
K.GM.C.8Identify and describe the attribute of shapes, and use the attributes to sort a collection of shapes.
K.GM.C.9Draw or model simple two-dimensional shapes.
K.NBT Number Sense and Operations in Base Ten
K.NBT.A A Work with numbers 11 – 19 to gain foundations for place value.
K.NBT.A.1Compose and decompose numbers from 11 to 19 into sets of tens with additional ones.
K.NS Number Sense
K.NS.A Know the number names and the count sequence.
K.NS.A.1Count to 100 by ones and tens.
K.NS.A.2Count forward beginning from a given number between 1 and 20.
K.NS.A.3Count backward from a given number between 10 and 1.
K.NS.A.4Read and write numerals and represent a number of objects from 0 to 20.
K.NS.B Understand the relationship between numbers and quantities; connect counting to cardinality.
K.NS.B.5Say the number names when counting objects, in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
K.NS.B.6Demonstrate that the last number name said tells the number of objects counted and the number of objects is the same regardless of their arrangement or the order in which they were counted.
K.NS.B.7Demonstrate that each successive number name refers to a quantity that is one larger than the previous number.
K.NS.B.8Recognize, without counting, the quantity of groups up to 5 objects arranged in common patterns.
K.NS.B.9Demonstrate that a number can be used to represent “how many” are in a set.
K.NS.C Compare numbers.
K.NS.C.10Compare two or more sets of objects and identify which set is equal to, more than or less than the other.
K.NS.C.11Compare two numerals, between 1 and 10, and determine which is more than or less than the other.
K.RA Relationships and Algebraic Thinking
K.RA.A Understand addition as putting together or adding to, and understand subtraction as taking apart or taking from.
K.RA.A.1Represent addition and subtraction within 10.
K.RA.A.2Demonstrate fluency for addition and subtraction within 5.
K.RA.A.3Decompose numbers less than or equal to 10 in more than one way.
K.RA.A.4Make 10 for any number from 1 to 9.

Grade 1

1.DS Data and Statistics
1.DS.A Represent and interpret data.
1.DS.A.1Collect, organize and represent data with up to three categories.
1.DS.A.2Draw conclusions from object graphs, picture graphs, T-charts and tallies.
1.GM Geometry and Measurement
1.GM.A Reason with shapes and their attributes.
1.GM.A.1Distinguish between defining attributes versus non-defining attributes; build and draw shapes that possess defining attributes.
1.GM.A.2Compose and decompose two- and three-dimensional shapes to build an understanding of part-whole relationships and the properties of the original and composite shapes.
1.GM.A.3Recognize two- and three-dimensional shapes from different perspectives and orientations.
1.GM.A.4Partition circles and rectangles into two or four equal shares, and describe the shares and the wholes verbally.
1.GM.B Measure lengths in non-standard units.
1.GM.B.5Order three or more objects by length.
1.GM.B.6Compare the lengths of two objects indirectly by using a third object.
1.GM.B.7Demonstrate the ability to measure length or distance using objects.
1.GM.C Work with time and money.
1.GM.C.8Tell and write time in hours and half-hours using analog and digital clocks.
1.GM.C.9Know the value of a penny, nickel, dime and quarter.
1.NBT Number Sense and Operations in Base Ten
1.NBT.A Understand place value of two-digit numbers.
1.NBT.A.1Understand that 10 can be thought of as a bundle of 10 ones – called a “ten”.
1.NBT.A.2Understand two-digit numbers are composed of ten(s) and one(s).
1.NBT.A.3Compare two two-digit numbers using the symbols >, = or <.
1.NBT.A.4Count by 10s to 120 starting at any number.
1.NBT.B Use place value understanding to add and subtract.
1.NBT.B.5Add within 100.
1.NBT.B.6Calculate 10 more or 10 less than a given number mentally without having to count.
1.NBT.B.7Add or subtract a multiple of 10 from another two-digit number, and justify the solution.
1.NS Number Sense
1.NS.A Understand and use numbers up to 120.
1.NS.A.1Count to 120, starting at any number less than 120.
1.NS.A.2Read and write numerals and represent a number of objects with a written numeral.
1.NS.A.3Count backward from a given number between 20 and 1.
1.NS.A.4Count by 5s to 100 starting at any multiple of five.
1.RA Relationships and Algebraic Thinking
1.RA.A Represent and solve problems involving addition and subtraction.
1.RA.A.1Use addition and subtraction within 20 to solve problems.
1.RA.A.2Solve problems that call for addition of three whole numbers whose sum is within 20.
1.RA.A.3Develop the meaning of the equal sign and determine if equations involving addition and subtraction are true or false.
1.RA.A.4Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.
1.RA.B Understand and apply properties of operations and the relationship between addition and subtraction.
1.RA.B.5Use properties as strategies to add and subtract.
1.RA.B.6Demonstrate that subtraction can be solved as an unknown-addend problem.
1.RA.C Add and subtract within 20.
1.RA.C.7Add and subtract within 20.
1.RA.C.8Demonstrate fluency with addition and subtraction within 10.

Grade 2

2.DS Data and Statistics
2.DS.A Represent and interpret data.
2.DS.A.1Create a line plot to represent a set of numeric data, given a horizontal scale marked in whole numbers.
2.DS.A.2Generate measurement data to the nearest whole unit, and display the data in a line plot.
2.DS.A.3Draw a picture graph or a bar graph to represent a data set with up to four categories.
2.DS.A.4Solve problems using information presented in line plots, picture graphs and bar graphs.
2.DS.A.5Draw conclusions from line plots, picture graphs and bar graphs.
2.GM Geometry and Measurement
2.GM.A Reason with shapes and their attributes.
2.GM.A.1Recognize and draw shapes having specified attributes, such as a given number of angles or sides.
2.GM.A.1aIdentify triangles, quadrilaterals, pentagons, hexagons, circles and cubes.
2.GM.A.1bIdentify the faces of three-dimensional objects.
2.GM.A.2Partition a rectangle into rows and columns of same-size squares and count to find the total number of squares.
2.GM.A.3Partition circles and rectangles into two, three or four equal shares, and describe the shares and the whole.
2.GM.A.3aDemonstrate that equal shares of identical wholes need not have the same shape.
2.GM.B Measure and estimate lengths in standard units.
2.GM.B.4Measure the length of an object by selecting and using appropriate tools.
2.GM.B.5Analyze the results of measuring the same object with different units.
2.GM.B.6Estimate lengths using units of inches, feet, yards, centimeters and meters.
2.GM.B.7Measure to determine how much longer one object is than another.
2.GM.C Relate addition and subtraction to length.
2.GM.C.8Use addition and subtraction within 100 to solve problems involving lengths that are given in the same units.
2.GM.C.9Represent whole numbers as lengths on a number line, and represent whole-number sums and differences within 100 on a number line.
2.GM.D Work with time and money.
2.GM.D.10Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
2.GM.D.11Describe a time shown on a digital clock as representing hours and minutes, and relate a time shown on a digital clock to the same time on an analog clock.
2.GM.D.12Find the value of combinations of dollar bills, quarters, dimes, nickels and pennies, using $ and ¢ appropriately.
2.GM.D.13Find combinations of coins that equal a given amount.
2.NBT Number Sense and Operations in Base Ten
2.NBT.A Understand place value of three digit numbers.
2.NBT.A.1Understand three-digit numbers are composed of hundreds, tens and ones.
2.NBT.A.2Understand that 100 can be thought of as 10 tens – called a “hundred”.
2.NBT.A.3Count within 1000 by 1s, 10s and 100s starting with any number.
2.NBT.A.4Read and write numbers to 1000 using number names, base-ten numerals and expanded form.
2.NBT.A.5Compare two three-digit numbers using the symbols >, = or <.
2.NBT.B Use place value understanding and properties of operations to add and subtract.
2.NBT.B.10Add or subtract mentally 10 or 100 to or from a given number within 1000.
2.NBT.B.6Demonstrate fluency with addition and subtraction within 100.
2.NBT.B.7Add up to four two-digit numbers.
2.NBT.B.8Add or subtract within 1000, and justify the solution.
2.NBT.B.9Use the relationship between addition and subtraction to solve problems.
2.NBT.C Represent and solve problems involving addition and subtraction.
2.NBT.C.11Write and solve problems involving addition and subtraction within 100.
2.RA Relationships and Algebraic Thinking
2.RA.A Add and subtract within 20.
2.RA.A.1Demonstrate fluency with addition and subtraction within 20.
2.RA.B Develop foundations for multiplication and division.
2.RA.B.2Determine if a set of objects has an odd or even number of members.
2.RA.B.2aCount by 2s to 100 starting with any even number.
2.RA.B.2bExpress even numbers as pairings/groups of 2, and write an expression to represent the number using addends of 2.
2.RA.B.2cExpress even numbers as being composed of equal groups and write an expression to represent the number with 2 equal addends.
2.RA.B.3Find the total number of objects arranged in a rectangular array with up to 5 rows and 5 columns, and write an equation to represent the total as a sum of equal addends.

Grade 3

3.DS Data and Statistics
3.DS.A Represent and analyze data.
3.DS.A.1Create frequency tables, scaled picture graphs and bar graphs to represent a data set with several categories.
3.DS.A.2Solve one- and two-step problems using information presented in bar and/or picture graphs.
3.DS.A.3Create a line plot to represent data.
3.DS.A.4Use data shown in a line plot to answer questions.
3.GM Geometry and Measurement
3.GM.A Reason with shapes and their attributes.
3.GM.A.1Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category.
3.GM.A.2Distinguish rhombuses and rectangles as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to these subcategories.
3.GM.A.3Partition shapes into parts with equal areas, and express the area of each part as a unit fraction of the whole.
3.GM.B Solve problems involving the measurement of time, liquid volumes and weights of objects.
3.GM.B.4Tell and write time to the nearest minute.
3.GM.B.5Estimate time intervals in minutes.
3.GM.B.6Solve problems involving addition and subtraction of minutes.
3.GM.B.7Measure or estimate length, liquid volume and weight of objects.
3.GM.B.8Use the four operations to solve problems involving lengths, liquid volumes or weights given in the same units.
3.GM.C Understand concepts of area.
3.GM.C.10Label area measurements with squared units.
3.GM.C.11Demonstrate that tiling a rectangle to find the area and multiplying the side lengths result in the same value.
3.GM.C.12Multiply whole-number side lengths to solve problems involving the area of rectangles.
3.GM.C.13Find rectangular arrangements that can be formed for a given area.
3.GM.C.14Decompose a rectangle into smaller rectangles to find the area of the original rectangle.
3.GM.C.9Calculate area by using unit squares to cover a plane figure with no gaps or overlaps.
3.GM.D Understand concepts of perimeter.
3.GM.D.15Solve problems involving perimeters of polygons.
3.GM.D.16Understand that rectangles can have equal perimeters but different areas, or rectangles can have equal areas but different perimeters.
3.NBT Number Sense and Operations in Base Ten
3.NBT.A Use place value understanding and properties of operations to perform multi-digit arithmetic.
3.NBT.A.1Round whole numbers to the nearest 10 or 100.
3.NBT.A.2Read, write and identify whole numbers within 100,000 using base ten numerals, number names and expanded form.
3.NBT.A.3Demonstrate fluency with addition and subtraction within 1000.
3.NBT.A.4Multiply whole numbers by multiples of 10 in the range 10-90.
3.NF Number Sense and Operations in Fractions
3.NF.A Develop understanding of fractions as numbers.
3.NF.A.1Understand a unit fraction as the quantity formed by one part when a whole is partitioned into equal parts.
3.NF.A.2Understand that when a whole is partitioned equally, a fraction can be used to represent a portion of the whole.
3.NF.A.2aDescribe the numerator as representing the number of pieces being considered.
3.NF.A.2bDescribe the denominator as the number of pieces that make the whole.
3.NF.A.3Represent fractions on a number line.
3.NF.A.3aUnderstand the whole is the interval from 0 to 1.
3.NF.A.3bUnderstand the whole is partitioned into equal parts.
3.NF.A.3cUnderstand a fraction represents the endpoint of the length a given number of partitions from 0.
3.NF.A.4Demonstrate that two fractions are equivalent if they are the same size, or the same point on a number line.
3.NF.A.5Recognize and generate equivalent fractions using visual models, and justify why the fractions are equivalent.
3.NF.A.6Compare two fractions with the same numerator or denominator using the symbols >, = or <, and justify the solution.
3.NF.A.7Explain why fraction comparisons are only valid when the two fractions refer to the same whole.
3.RA Relationships and Algebraic Thinking
3.RA.A Represent and solve problems involving multiplication and division.
3.RA.A.1Interpret products of whole numbers.
3.RA.A.2Interpret quotients of whole numbers.
3.RA.A.3Describe in words or drawings a problem that illustrates a multiplication or division situation.
3.RA.A.4Use multiplication and division within 100 to solve problems.
3.RA.A.5Determine the unknown number in a multiplication or division equation relating three whole numbers.
3.RA.B Understand properties of multiplication and the relationship between multiplication and division.
3.RA.B.6Apply properties of operations as strategies to multiply and divide.
3.RA.C Multiply and divide within 100.
3.RA.C.7Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers.
3.RA.C.8Demonstrate fluency with products within 100.
3.RA.D Use the four operations to solve word problems.
3.RA.D.10Interpret the reasonableness of answers using mental computation and estimation strategies including rounding.
3.RA.D.9Write and solve two-step problems involving variables using any of the four operations.
3.RA.E Identify and explain arithmetic patterns.
3.RA.E.11Identify arithmetic patterns and explain the patterns using properties of operations.

Grade 4

4.DS Data and Statistics
4.DS.A Represent and analyze data.
4.DS.A.1Create a frequency table and/or line plot to display measurement data.
4.DS.A.2Solve problems involving addition and subtraction by using information presented in a data display.
4.DS.A.3Analyze the data in a frequency table, line plot, bar graph or picture graph.
4.GM Geometry and Measurement
4.GM.A Classify 2-dimensional shapes by properties of their lines and angles.
4.GM.A.1Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines.
4.GM.A.2Classify two-dimensional shapes by their sides and/or angles.
4.GM.A.3Construct lines of symmetry for a two-dimensional figure.
4.GM.B Understand the concepts of angle and measure angles.
4.GM.B.4Identify and estimate angles and their measure.
4.GM.B.5Draw and measure angles in whole-number degrees using a protractor.
4.GM.C Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
4.GM.C.6Know relative sizes of measurement units within one system of units.
4.GM.C.6aConvert measurements in a larger unit in terms of a smaller unit.
4.GM.C.7Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money.
4.GM.C.8Apply the area and perimeter formulas for rectangles to solve problems.
4.NBT Number Sense and Operations in Base Ten
4.NBT.A Use place value understanding and properties of operations to perform multi-digit arithmetic with numbers up to one million.
4.NBT.A.1Round multi-digit whole numbers to any place.
4.NBT.A.2Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form.
4.NBT.A.3Compare two multi-digit numbers using the symbols >, = or <, and justify the solution.
4.NBT.A.4Understand that in a multi-digit whole number, a digit represents 10 times what it would represents in the place to its right.
4.NBT.A.5Demonstrate fluency with addition and subtraction of whole numbers.
4.NBT.A.6Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution.
4.NBT.A.7Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution.
4.NF Number Sense and Operations in Fractions
4.NF.A Extend understanding of fraction equivalence and ordering. (Limit denominators to 2, 3, 4, 5, 6, 8, 10, 12 and 100.)
4.NF.A.1Explain and/or illustrate why two fractions are equivalent.
4.NF.A.2Recognize and generate equivalent fractions.
4.NF.A.3Compare two fractions using the symbols >, = or <, and justify the solution.
4.NF.B Extend understanding of operations on whole numbers to fraction operations.
4.NF.B.4Understand addition and subtraction of fractions as joining/composing and separating/decomposing parts referring to the same whole.
4.NF.B.5Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification.
4.NF.B.6Solve problems involving adding and subtracting fractions and mixed numbers with like denominators.
4.NF.B.7Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
4.NF.B.8Solve problems involving multiplication of a fraction by a whole number.
4.NF.C Understand decimal notation for fractions, and compare decimal fractions. (Denominators of 10 or 100)
4.NF.C.10Understand that fractions and decimals are equivalent representations of the same quantity.
4.NF.C.11Read, write and identify decimals to the hundredths place using number names, base ten numerals and expanded form.
4.NF.C.12Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution.
4.NF.C.9Use decimal notation for fractions with denominators of 10 or 100.
4.RA Relationships and Algebraic Thinking
4.RA.A Use the four operations with whole numbers to solve problems.
4.RA.A.1Multiply or divide to solve problems involving a multiplicative comparison.
4.RA.A.2Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer.
4.RA.A.3Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution.
4.RA.B Work with factors and multiples.
4.RA.B.4Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number.
4.RA.B.5Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100.
4.RA.C Generate and analyze patterns.
4.RA.C.6Generate a number pattern that follows a given rule.
4.RA.C.7Use words or mathematical symbols to express a rule for a given pattern.

Grade 5

5.DS Data and Statistics
5.DS.A Represent and analyze data.
5.DS.A.1Create a line graph to represent a data set, and analyze the data to answer questions and solve problems.
5.DS.A.2Create a line plot to represent a given or generated data set, and analyze the data to answer questions and solve problems, recognizing the outliers and generating the median.
5.GM Geometry and Measurement
5.GM.A Classify two- and three-dimensional geometric shapes.
5.GM.A.1Understand that attributes belonging to a category of figures also belong to all subcategories.
5.GM.A.2Classify figures in a hierarchy based on properties.
5.GM.A.3Analyze and describe the properties of prisms and pyramids.
5.GM.B Understand and compute volume.
5.GM.B.4Understand the concept of volume and recognize that volume is measured in cubic units.
5.GM.B.4aDescribe a cube with edge length 1 unit as a “unit cube” and is said to have “one cubic unit” of volume and can be used to measure volume.
5.GM.B.4bUnderstand that the volume of a right rectangular prism can be found by stacking multiple layers of the base.
5.GM.B.5Apply the formulas V = l × w × h and V = B × h for volume of right rectangular prisms with whole-number edge lengths.
5.GM.C Graph points on the Cartesian coordinate plane within the first quadrant to solve problems.
5.GM.C.6Define a first quadrant Cartesian coordinate system.
5.GM.C.6aRepresent the axes as scaled perpendicular number lines that both intersect at 0, the origin.
5.GM.C.6bIdentify any point on the Cartesian coordinate plane by its ordered pair coordinates.
5.GM.C.6cDefine the first number in an ordered pair as the horizontal distance from the origin.
5.GM.C.6dDefine the second number in an ordered pair as the vertical distance from the origin.
5.GM.C.7Plot and interpret points in the first quadrant of the Cartesian coordinate plane.
5.GM.D Solve problems involving measurement and conversions within a measurement system.
5.GM.D.8Convert measurements of capacity, length and weight within a given measurement system.
5.GM.D.9Solve multi-step problems that require measurement conversions.
5.NBT Number Sense and Operations in Base Ten
5.NBT.A Use place value system understanding to perform operations with multi-digit whole numbers to billions and decimals to thousandths.
5.NBT.A.1Read, write and identify numbers from billions to thousandths using number names, base ten numerals and expanded form.
5.NBT.A.2Compare two numbers from billions to thousandths using the symbols >, = or <, and justify the solution.
5.NBT.A.3Understand that in a multi-digit number, a digit represents 1/10 times what it would represents in the place to its left.
5.NBT.A.4Evaluate the value of powers of 10 and understand the relationship to the place value system.
5.NBT.A.5Round numbers from billions to thousandths place.
5.NBT.A.6Add and subtract multi-digit whole numbers and decimals to the thousandths place, and justify the solution.
5.NBT.A.7Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution.
5.NBT.A.8Divide multi-digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four-digit dividends, and justify the solution.
5.NF Number Sense and Operations in Fractions
5.NF.A Understand the relationship between fractions and decimals (denominators that are factors of 100).
5.NF.A.1Understand that parts of a whole can be expressed as fractions and/or decimals.
5.NF.A.2Convert decimals to fractions and fractions to decimals.
5.NF.A.3Compare and order fractions and/or decimals to the thousandths place using the symbols >, = or <, and justify the solution.
5.NF.B Perform operations and solve problems with fractions and decimals.
5.NF.B.4Estimate results of sums, differences and products with fractions and decimals to the thousandths.
5.NF.B.5Justify the reasonableness of a product when multiplying with fractions.
5.NF.B.5aEstimate the size of the product based on the size of the two factors.
5.NF.B.5bExplain why multiplying a given number by a fraction greater than 1 results in a product larger than the given number.
5.NF.B.5cExplain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.
5.NF.B.5dExplain why multiplying the numerator and denominator by the same number is equivalent to multiplying the fraction by 1.
5.NF.B.6Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution.
5.NF.B.7Extend the concept of multiplication to multiply a fraction or whole number by a fraction.
5.NF.B.7aRecognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths.
5.NF.B.7bCalculate and interpret the product of a fraction by a whole number and a whole number by a fraction.
5.NF.B.7cCalculate and interpret the product of two fractions less than one.
5.NF.B.8Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations.
5.NF.B.8aCalculate and interpret the quotient of a unit fraction by a non-zero whole number.
5.NF.B.8bCalculate and interpret the quotient of a whole number by a unit fraction.
5.RA Relationships and Algebraic Thinking
5.RA.A Represent and analyze patterns and relationships.
5.RA.A.1Investigate the relationship between two numeric patterns.
5.RA.A.1aGenerate two numeric patterns given two rules.
5.RA.A.1bTranslate two numeric patterns into two sets of ordered pairs.
5.RA.A.1cGraph numeric patterns on the Cartesian coordinate plane.
5.RA.A.1dIdentify the relationship between two numeric patterns.
5.RA.A.2Write a rule to describe or explain a given numeric pattern.
5.RA.B Write and interpret numerical expressions.
5.RA.B.3Write, evaluate and interpret numeric expressions using the order of operations.
5.RA.B.4Translate written expressions into algebraic expressions.
5.RA.C Use the four operations to represent and solve problems.
5.RA.C.5Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals.

Grade 6

6.DSP Data Analysis, Statistics and Probability
6.DSP.A Develop understanding of statistical variability.
6.DSP.A.1Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
6.DSP.A.2Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape.
6.DSP.A.3Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number.
6.DSP.B Summarize and describe distributions.
6.DSP.B.4Display and interpret data.
6.DSP.B.4aUse dot plots, histograms and box plots to display and interpret numerical data.
6.DSP.B.4bCreate and interpret circle graphs.
6.DSP.B.5Summarize numerical data sets in relation to the context.
6.DSP.B.5aReport the number of observations.
6.DSP.B.5bDescribe the nature of the attribute under investigation, including how it was measured and its units of measurement.
6.DSP.B.5cGive quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data.
6.DSP.B.5dAnalyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data.
6.EEI Expressions, Equations and Inequalities
6.EEI.A Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EEI.A.1Describe the difference between an expression and an equation.
6.EEI.A.2Create and evaluate expressions involving variables and whole number exponents.
6.EEI.A.2aIdentify parts of an expression using mathematical terminology.
6.EEI.A.2bEvaluate expressions at specific values of the variables.
6.EEI.A.2cEvaluate non-negative rational number expressions.
6.EEI.A.2dWrite and evaluate algebraic expressions.
6.EEI.A.2eUnderstand the meaning of the variable in the context of the situation.
6.EEI.A.3Identify and generate equivalent algebraic expressions using mathematical properties.
6.EEI.B Reason about and solve one-variable equations and inequalities.
6.EEI.B.4Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true.
6.EEI.B.5Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true.
6.EEI.B.6Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation.
6.EEI.B.7Solve one-step linear equations in one variable involving non-negative rational numbers.
6.EEI.B.8Recognize that inequalities may have infinitely many solutions.
6.EEI.B.8aWrite an inequality of the form x > c, x < c, x ≥ c, or x ≤ c to represent a constraint or condition.
6.EEI.B.8bGraph the solution set of an inequality.
6.EEI.C Represent and analyze quantitative relationships between dependent and independent variables.
6.EEI.C.9Identify and describe relationships between two variables that change in relationship to one another.
6.EEI.C.9aWrite an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable.
6.EEI.C.9bAnalyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other.
6.GM Geometry and Measurement
6.GM.A Solve problems involving area, surface area and volume.
6.GM.A.1Find the area of polygons by composing or decomposing the shapes into rectangles or triangles.
6.GM.A.2Find the volume of right rectangular prisms.
6.GM.A.2aUnderstand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base.
6.GM.A.2bApply V = l * w * h and V = Bh to find the volume of right rectangular prisms.
6.GM.A.3Solve problems by graphing points in all four quadrants of the Cartesian coordinate plane.
6.GM.A.3aUnderstand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane.
6.GM.A.3bRecognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
6.GM.A.3cFind distances between points with the same first coordinate or the same second coordinate.
6.GM.A.3dConstruct polygons in the Cartesian coordinate plane.
6.GM.A.4Solve problems using nets.
6.GM.A.4aRepresent three-dimensional figures using nets made up of rectangles and triangles.
6.GM.A.4bUse nets to find the surface area of three-dimensional figures whose sides are made up of rectangles and triangles.
6.NS Number Sense and Operations
6.NS.A Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
6.NS.A.1Compute and interpret quotients of positive fractions.
6.NS.A.1aSolve problems involving division of fractions by fractions.
6.NS.B Compute with non-negative multi-digit numbers, and find common factors and multiples.
6.NS.B.2Demonstrate fluency with division of multi-digit whole numbers.
6.NS.B.3Demonstrate fluency with addition, subtraction, multiplication and division of decimals.
6.NS.B.4Find common factors and multiples.
6.NS.B.4aFind the greatest common factor (GCF) and the least common multiple (LCM).
6.NS.B.4bUse the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers.
6.NS.C Apply and extend previous understandings of numbers to the system of rational numbers.
6.NS.C.5Use positive and negative numbers to represent quantities.
6.NS.C.6Locate a rational number as a point on the number line.
6.NS.C.6aLocate rational numbers on a horizontal or vertical number line.
6.NS.C.6bWrite, interpret and explain problems of ordering of rational numbers.
6.NS.C.6cUnderstand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line.
6.NS.C.7Understand that the absolute value of a rational number is its distance from 0 on the number line.
6.NS.C.8Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3).
6.RP Ratios and Proportional Relationships
6.RP.A Understand and use ratios to solve problems.
6.RP.A.1Understand a ratio as a comparison of two quantities and represent these comparisons.
6.RP.A.2Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate.
6.RP.A.3Solve problems involving ratios and rates.
6.RP.A.3aCreate tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane.
6.RP.A.3bSolve unit rate problems.
6.RP.A.3cSolve percent problems.
6.RP.A.3dConvert measurement units within and between two systems of measurement.

Grade 7

7.DSP Data Analysis, Statistics and Probability
7.DSP.A Use random sampling to draw inferences about a population.
7.DSP.A.1Understand that statistics can be used to gain information about a population by examining a sample of the population.
7.DSP.A.1aUnderstand that a sample is a subset of a population.
7.DSP.A.1bUnderstand that generalizations from a sample are valid only if the sample is representative of the population.
7.DSP.A.1cUnderstand that random sampling is used to produce representative samples and support valid inferences.
7.DSP.A.2Use data from multiple samples to draw inferences about a population and investigate variability in estimates of the characteristic of interest.
7.DSP.B Draw informal comparative inferences about two populations.
7.DSP.B.3Analyze different data distributions using statistical measures.
7.DSP.B.4Compare the numerical measures of center, measures of frequency and measures of variability from two random samples to draw inferences about the population.
7.DSP.C Develop, use and evaluate probability models.
7.DSP.C.5Investigate the probability of chance events.
7.DSP.C.5aDetermine probabilities of simple events.
7.DSP.C.5bUnderstand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.
7.DSP.C.6Investigate the relationship between theoretical and experimental probabilities for simple events.
7.DSP.C.6aPredict outcomes using theoretical probability.
7.DSP.C.6bPerform experiments that model theoretical probability.
7.DSP.C.6cCompare theoretical and experimental probabilities.
7.DSP.C.7Explain possible discrepancies between a developed probability model and observed frequencies.
7.DSP.C.7aDevelop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
7.DSP.C.7bDevelop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
7.DSP.C.8Find probabilities of compound events using organized lists, tables, tree diagrams and simulations.
7.DSP.C.8aRepresent the sample space of a compound event.
7.DSP.C.8bDesign and use a simulation to generate frequencies for compound events.
7.EEI Expressions, Equations and Inequalities
7.EEI.A Use properties of operations to generate equivalent expressions.
7.EEI.A.1Apply properties of operations to simplify and to factor linear algebraic expressions with rational coefficients.
7.EEI.A.2Understand how to use equivalent expressions to clarify quantities in a problem.
7.EEI.B Solve problems using numerical and algebraic expressions and equations.
7.EEI.B.3Solve multi-step problems posed with rational numbers.
7.EEI.B.3aConvert between equivalent forms of the same number.
7.EEI.B.3bAssess the reasonableness of answers using mental computation and estimation strategies.
7.EEI.B.4Write and/or solve linear equations and inequalities in one variable.
7.EEI.B.4aWrite and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers.
7.EEI.B.4bWrite and/or solve two-step equations of the form px + q = r and p(x + q) = r, where p, q and r are rational numbers, and interpret the meaning of the solution in the context of the problem.
7.EEI.B.4cWrite, solve and/or graph inequalities of the form px + q > r or px + q < r, where p, q and r are rational numbers.
7.GM Geometry and Measurement
7.GM.A Draw and describe geometrical figures and describe the relationships between them.
7.GM.A.1Solve problems involving scale drawings of real objects and geometric figures, including computing actual lengths and areas from a scale drawing and reproducing the drawing at a different scale.
7.GM.A.2Use a variety of tools to construct geometric shapes.
7.GM.A.2aDetermine if provided constraints will create a unique triangle through construction.
7.GM.A.2bConstruct special quadrilaterals given specific parameters.
7.GM.A.3Describe two-dimensional cross sections of pyramids, prisms, cones and cylinders.
7.GM.A.4Understand the concepts of circles.
7.GM.A.4aAnalyze the relationships among the circumference, the radius, the diameter, the area and Pi in a circle.
7.GM.A.4bKnow and apply the formulas for circumference and area of circles to solve problems.
7.GM.B Apply and extend previous understanding of angle measure, area and volume.
7.GM.B.5Use angle properties to write and solve equations for an unknown angle.
7.GM.B.6Understand the relationship between area, surface area and volume.
7.GM.B.6aFind the area of triangles, quadrilaterals and other polygons composed of triangles and rectangles.
7.GM.B.6bFind the volume and surface area of prisms, pyramids and cylinders.
7.NS Number Sense and Operations
7.NS.A Apply and extend previous understandings of operations to add, subtract, multiply and divide rational numbers.
7.NS.A.1Apply and extend previous understandings of numbers to add and subtract rational numbers.
7.NS.A.1aAdd and subtract rational numbers.
7.NS.A.1bRepresent addition and subtraction on a horizontal or vertical number line.
7.NS.A.1cDescribe situations and show that a number and its opposite have a sum of 0 (additive inverses).
7.NS.A.1dUnderstand subtraction of rational numbers as adding the additive inverse.
7.NS.A.1eDetermine the distance between two rational numbers on the number line is the absolute value of their difference.
7.NS.A.1fInterpret sums and differences of rational numbers.
7.NS.A.2Apply and extend previous understandings of numbers to multiply and divide rational numbers.
7.NS.A.2aMultiply and divide rational numbers.
7.NS.A.2bDetermine that a number and its reciprocal have a product of 1 (multiplicative inverse).
7.NS.A.2cUnderstand that every quotient of integers (with non-zero divisor) is a rational number.
7.NS.A.2dConvert a rational number to a decimal.
7.NS.A.2eUnderstand that all rational numbers can be written as fractions or decimal numbers that terminate or repeat.
7.NS.A.2fInterpret products and quotients of rational numbers by describing real-world contexts.
7.NS.A.3Solve problems involving the four arithmetic operations with rational numbers.
7.RP Ratios and Proportional Relationships
7.RP.A Analyze proportional relationships and use them to solve problems.
7.RP.A.1Compute unit rates, including those that involve complex fractions, with like or different units.
7.RP.A.2Recognize and represent proportional relationships between quantities.
7.RP.A.2aDetermine when two quantities are in a proportional relationship.
7.RP.A.2bIdentify and/or compute the constant of proportionality (unit rate).
7.RP.A.2cExplain what a point (x, y) on the graph of a proportional relationship means in terms of the situation.
7.RP.A.2dRecognize that the graph of any proportional relationship will pass through the origin.
7.RP.A.3Solve problems involving ratios, rates, percentages and proportional relationships.

Grade 8

8.DSP Data Analysis, Statistics and Probability
8.DSP.A Investigate patterns of association in bivariate data.
8.DSP.A.1Construct and interpret scatter plots of bivariate measurement data to investigate patterns of association between two quantities.
8.DSP.A.2Generate and use a trend line for bivariate data, and informally assess the fit of the line.
8.DSP.A.3Interpret the parameters of a linear model of bivariate measurement data to solve problems.
8.DSP.A.4Understand the patterns of association in bivariate categorical data displayed in a two-way table.
8.DSP.A.4aConstruct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.
8.DSP.A.4bUse relative frequencies calculated for rows or columns to describe possible association between the two variables.
8.EEI Expressions, Equations and Inequalities
8.EEI.A Work with radicals and integer exponents.
8.EEI.A.1Know and apply the properties of integer exponents to generate equivalent expressions.
8.EEI.A.2Investigate concepts of square and cube roots.
8.EEI.A.2aSolve equations of the form x^2 = p and x^3 = p, where p is a positive rational number.
8.EEI.A.2bEvaluate square roots of perfect squares less than or equal to 625 and cube roots of perfect cubes less than or equal to 1000.
8.EEI.A.2cRecognize that square roots of non-perfect squares are irrational.
8.EEI.A.3Express very large and very small quantities in scientific notation and approximate how many times larger one is than the other.
8.EEI.A.4Use scientific notation to solve problems.
8.EEI.A.4aPerform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.
8.EEI.A.4bUse scientific notation and choose units of appropriate size for measurements of very large or very small quantities.
8.EEI.B Understand the connections between proportional relationships, lines and linear equations.
8.EEI.B.5Graph proportional relationships.
8.EEI.B.5aInterpret the unit rate as the slope of the graph.
8.EEI.B.5bCompare two different proportional relationships.
8.EEI.B.6Apply concepts of slope and y-intercept to graphs, equations and proportional relationships.
8.EEI.B.6aExplain why the slope (m) is the same between any two distinct points on a non-vertical line in the Cartesian coordinate plane.
8.EEI.B.6bDerive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
8.EEI.C Analyze and solve linear equations and inequalities and pairs of simultaneous linear equations.
8.EEI.C.7Solve linear equations and inequalities in one variable.
8.EEI.C.7aCreate and identify linear equations with one solution, infinitely many solutions or no solutions.
8.EEI.C.7bSolve linear equations and inequalities with rational number coefficients, including equations and inequalities whose solutions require expanding expressions using the distributive property and combining like terms.
8.EEI.C.8Analyze and solve systems of linear equations.
8.EEI.C.8aGraph systems of linear equations and recognize the intersection as the solution to the system.
8.EEI.C.8bExplain why solution(s) to a system of two linear equations in two variables correspond to point(s) of intersection of the graphs.
8.EEI.C.8cExplain why systems of linear equations can have one solution, no solution or infinitely many solutions.
8.EEI.C.8dSolve systems of two linear equations.
8.F Functions
8.F.A Define, evaluate and compare functions.
8.F.A.1Explore the concept of functions. (The use of function notation is not required.)
8.F.A.1aUnderstand that a function assigns to each input exactly one output.
8.F.A.1bDetermine if a relation is a function.
8.F.A.1cGraph a function.
8.F.A.2Compare characteristics of two functions each represented in a different way.
8.F.A.3Investigate the differences between linear and nonlinear functions.
8.F.A.3aInterpret the equation y = mx + b as defining a linear function, whose parameters are the slope (m) and the y-intercept (b).
8.F.A.3bRecognize that the graph of a linear function has a constant rate of change.
8.F.A.3cGive examples of nonlinear functions.
8.F.B Use functions to model relationships between quantities.
8.F.B.4Use functions to model linear relationships between quantities.
8.F.B.4aExplain the parameters of a linear function based on the context of a problem.
8.F.B.4bDetermine the parameters of a linear function.
8.F.B.4cDetermine the x-intercept of a linear function.
8.F.B.5Describe the functional relationship between two quantities from a graph or a verbal description.
8.GM Geometry and Measurement
8.GM.A Understand congruence and similarity using physical models, transparencies or geometry software.
8.GM.A.1Verify experimentally the congruence properties of rigid transformations.
8.GM.A.1aVerify that angle measure, betweeness, collinearity and distance are preserved under rigid transformations.
8.GM.A.1bInvestigate if orientation is preserved under rigid transformations.
8.GM.A.2Understand that two-dimensional figures are congruent if a series of rigid transformations can be performed to map the pre-image to the image.
8.GM.A.2aDescribe a possible sequence of rigid transformations between two congruent figures.
8.GM.A.3Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.
8.GM.A.4Understand that two-dimensional figures are similar if a series of transformations (rotations, reflections, translations and dilations) can be performed to map the pre-image to the image.
8.GM.A.4aDescribe a possible sequence of transformations between two similar figures.
8.GM.A.5Explore angle relationships and establish informal arguments.
8.GM.A.5aDerive the sum of the interior angles of a triangle.
8.GM.A.5bExplore the relationship between the interior and exterior angles of a triangle.
8.GM.A.5cConstruct and explore the angles created when parallel lines are cut by a transversal.
8.GM.A.5dUse the properties of similar figures to solve problems.
8.GM.B Understand and apply the Pythagorean Theorem.
8.GM.B.6Use models to demonstrate a proof of the Pythagorean Theorem and its converse.
8.GM.B.7Use the Pythagorean Theorem to determine unknown side lengths in right triangles in problems in two- and three-dimensional contexts.
8.GM.B.8Use the Pythagorean Theorem to find the distance between points in a Cartesian coordinate system.
8.GM.C Solve problems involving volume of cones, pyramids and spheres.
8.GM.C.9Solve problems involving surface area and volume.
8.GM.C.9aUnderstand the concept of surface area and find surface area of pyramids.
8.GM.C.9bUnderstand the concepts of volume and find the volume of pyramids, cones and spheres.
8.NS Number Sense and Operations
8.NS.A Know that there are numbers that are not rational, and approximate them by rational numbers.
8.NS.A.1Explore the real number system.
8.NS.A.1aKnow the differences between rational and irrational numbers.
8.NS.A.1bUnderstand that all rational numbers have a decimal expansion that terminates or repeats.
8.NS.A.1cConvert decimals which repeat into fractions and fractions into repeating decimals.
8.NS.A.1dGenerate equivalent representations of rational numbers.
8.NS.A.2Estimate the value and compare the size of irrational numbers and approximate their locations on a number line.

Algebra 1

A1.APR Arithmetic with Polynomials and Rational Expressions
A1.APR.A Perform operations on polynomials.
A1.APR.A.1Add, subtract and multiply polynomials, and understand that polynomials follow the same general rules of arithmetic and are closed under these operations.
A1.APR.A.2Divide polynomials by monomials.
A1.BF Building Functions
A1.BF.A Build new functions from existing functions (limited to linear, quadratic and exponential).
A1.BF.A.1Analyze the effect of translations and scale changes on functions.
A1.CED Creating Equations
A1.CED.A Create equations that describe linear, quadratic and exponential relationships.
A1.CED.A.1Create equations and inequalities in one variable and use them to model and/or solve problems.
A1.CED.A.2Create and graph linear, quadratic and exponential equations in two variables.
A1.CED.A.3Represent constraints by equations or inequalities and by systems of equations or inequalities, and interpret the data points as a solution or non-solution in a modeling context.
A1.CED.A.4Solve literal equations and formulas for a specified variable that highlights a quantity of interest.
A1.DS Data and Statistical Analysis
A1.DS.A Summarize, represent and interpret data.
A1.DS.A.1Analyze and interpret graphical displays of data.
A1.DS.A.2Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets.
A1.DS.A.3Interpret differences in shape, center and spreads in the context of the data sets, accounting for possible effects of outliers.
A1.DS.A.4Summarize data in two-way frequency tables.
A1.DS.A.4aInterpret relative frequencies in the context of the data.
A1.DS.A.4bRecognize possible associations and trends in the data.
A1.DS.A.5Construct a scatter plot of bivariate quantitative data describing how the variables are related; determine and use a function that models the relationship.
A1.DS.A.5aConstruct a linear function to model bivariate data represented on a scatter plot that minimizes residuals.
A1.DS.A.5bConstruct an exponential function to model bivariate data represented on a scatter plot that minimizes residuals.
A1.DS.A.6Interpret the slope (rate of change) and the y-intercept (constant term) of a linear model in the context of the data.
A1.DS.A.7Determine and interpret the correlation coefficient for a linear association.
A1.DS.A.8Distinguish between correlation and causation.
A1.IF Interpreting Functions
A1.IF.A Understand the concept of a function and use function notation.
A1.IF.A.1Understand that a function from one set (domain) to another set (range) assigns to each element of the domain exactly one element of the range.
A1.IF.A.1aRepresent a function using function notation.
A1.IF.A.1bUnderstand that the graph of a function labeled 𝑓 is the set of all ordered pairs (𝑥, y) that satisfy the equation 𝑦=f(𝑥).
A1.IF.A.2Use function notation to evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
A1.IF.B Interpret linear, quadratic and exponential functions in terms of the context.
A1.IF.B.3Using tables, graphs and verbal descriptions, interpret key characteristics of a function that models the relationship between two quantities.
A1.IF.B.4Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes.
A1.IF.B.5Determine the average rate of change of a function over a specified interval and interpret the meaning.
A1.IF.B.6Interpret the parameters of a linear or exponential function in terms of the context.
A1.IF.C Analyze linear, quadratic and exponential functions using different representations.
A1.IF.C.7Graph functions expressed symbolically and identify and interpret key features of the graph.
A1.IF.C.8Translate between different but equivalent forms of a function to reveal and explain properties of the function and interpret these in terms of a context.
A1.IF.C.9Compare the properties of two functions given different representations.
A1.LQE Linear, Quadratic and Exponential Models
A1.LQE.A Construct and compare linear, quadratic and exponential models and solve problems.
A1.LQE.A.1Distinguish between situations that can be modeled with linear or exponential functions.
A1.LQE.A.1aDetermine that linear functions change by equal differences over equal intervals.
A1.LQE.A.1bRecognize exponential situations in which a quantity grows or decays by a constant percent rate per unit interval.
A1.LQE.A.2Describe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.
A1.LQE.A.3Construct linear, quadratic and exponential equations given graphs, verbal descriptions or tables.
A1.LQE.B Use arithmetic and geometric sequences.
A1.LQE.B.4Write arithmetic and geometric sequences in recursive and explicit forms, and use them to model situations and translate between the two forms.
A1.LQE.B.5Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the set of integers.
A1.LQE.B.6Find the terms of sequences given an explicit or recursive formula.
A1.NQ Number and Quantity
A1.NQ.A Extend and use properties of rational exponents.
A1.NQ.A.1Explain how the meaning of rational exponents extends from the properties of integer exponents.
A1.NQ.A.2Rewrite expressions involving radicals and rational exponents using the properties of exponents. Limit to rational exponents with a numerator of 1.
A1.NQ.B Use units to solve problems.
A1.NQ.B.3Use units of measure as a way to understand and solve problems involving quantities.
A1.NQ.B.3aIdentify, label and use appropriate units of measure within a problem.
A1.NQ.B.3bConvert units and rates.
A1.NQ.B.3cUse units within problems.
A1.NQ.B.3dChoose and interpret the scale and the origin in graphs and data displays.
A1.NQ.B.4Define and use appropriate quantities for representing a given context or problem.
A1.NQ.B.5Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
A1.REI Reasoning with Equations and Inequalities
A1.REI.A Understand solving equations as a process, and solve equations and inequalities in one variable.
A1.REI.A.1Explain how each step taken when solving an equation or inequality in one variable creates an equivalent equation or inequality that has the same solution(s) as the original.
A1.REI.A.2Solve problems involving quadratic equations.
A1.REI.A.2aUse the method of completing the square to create an equivalent quadratic equation.
A1.REI.A.2bDerive the quadratic formula.
A1.REI.A.2cAnalyze different methods of solving quadratic equations.
A1.REI.B Solve systems of equations.
A1.REI.B.3Solve a system of linear equations algebraically and/or graphically.
A1.REI.B.4Solve a system consisting of a linear equation and a quadratic equation algebraically and/or graphically.
A1.REI.B.5Justify that the technique of linear combination produces an equivalent system of equations.
A1.REI.C Represent and solve linear and exponential equations and inequalities graphically.
A1.REI.C.6Explain that the graph of an equation in two variables is the set of all its solutions plotted in the Cartesian coordinate plane.
A1.REI.C.7Graph the solution to a linear inequality in two variables.
A1.REI.C.8Solve problems involving a system of linear inequalities.
A1.SSE Seeing Structure in Expressions
A1.SSE.A Interpret and use structure.
A1.SSE.A.1Interpret the contextual meaning of individual terms or factors from a given problem that utilizes formulas or expressions.
A1.SSE.A.2Analyze the structure of polynomials to create equivalent expressions or equations.
A1.SSE.A.3Choose and produce equivalent forms of a quadratic expression or equations to reveal and explain properties.
A1.SSE.A.3aFind the zeros of a quadratic function by rewriting it in factored form.
A1.SSE.A.3bFind the maximum or minimum value of a quadratic function by completing the square.

Algebra 2

A2.APR Arithmetic with Polynomials and Rational Expressions
A2.APR.A Perform operations on polynomials and rational expressions.
A2.APR.A.1Extend the knowledge of factoring to include factors with complex coefficients.
A2.APR.A.2Understand the Remainder Theorem and use it to solve problems.
A2.APR.A.3Find the least common multiple of two or more polynomials.
A2.APR.A.4Add, subtract, multiply and divide rational expressions.
A2.APR.A.5Identify zeros of polynomials when suitable factorizations are available, and use the zeros to sketch the function defined by the polynomial.
A2.BF Building Functions
A2.BF.A Create new functions from existing functions.
A2.BF.A.1Create new functions by applying the four arithmetic operations and composition of functions (modifying the domain and range as necessary).
A2.BF.A.2Derive inverses of functions, and compose the inverse with the original function to show that the functions are inverses.
A2.BF.A.3Describe the effects of transformations algebraically and graphically, creating vertical and horizontal translations, vertical and horizontal reflections and dilations (expansions/compressions) for linear, quadratic, cubic, square and cube root, absolute value, exponential and logarithmic functions.
A2.DS Data and Statistical Analysis
A2.DS.A Make inferences and justify conclusions.
A2.DS.A.1Analyze how random sampling could be used to make inferences about population parameters.
A2.DS.A.2Determine whether a specified model is consistent with a given data set.
A2.DS.A.3Describe and explain the purposes, relationship to randomization and differences among sample surveys, experiments and observational studies.
A2.DS.A.4Use data from a sample to estimate characteristics of the population and recognize the meaning of the margin of error in these estimates.
A2.DS.A.5Describe and explain how the relative sizes of a sample and the population affect the margin of error of predictions.
A2.DS.A.6Analyze decisions and strategies using probability concepts.
A2.DS.A.7Evaluate reports based on data.
A2.DS.B Fit a data set to a normal distribution.
A2.DS.B.8Know and use the characteristics of normally distributed data sets; predict what percentage of the data will be above or below a given value that is a multiple of standard deviations above or below the mean.
A2.DS.B.9Fit a data set to a distribution using its mean and standard deviation to determine whether the data is approximately normally distributed.
A2.FM Modeling
A2.FM.A Use functions to model real-world problems.
A2.FM.A.1Create functions and use them to solve applications of quadratic and exponential function model problems.
A2.IF Interpreting Functions
A2.IF.A Use and interpret functions.
A2.IF.A.1Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.
A2.IF.A.2Translate between equivalent forms of functions.
A2.NQ Number and Quantity
A2.NQ.A Extend and use the relationship between rational exponents and radicals.
A2.NQ.A.1Extend the system of powers and roots to include rational exponents.
A2.NQ.A.2Create and recognize equivalent expressions involving radical and exponential forms of expressions.
A2.NQ.A.3Add, subtract, multiply and divide radical expressions.
A2.NQ.A.4Solve equations involving rational exponents and/or radicals and identify situations where extraneous solutions may result.
A2.NQ.B Use complex numbers.
A2.NQ.B.5Represent complex numbers.
A2.NQ.B.6Add, subtract, multiply and divide complex numbers.
A2.NQ.B.7Know and apply the Fundamental Theorem of Algebra.
A2.REI Reasoning with Equations and Inequalities
A2.REI.A Solve equations and inequalities.
A2.REI.A.1Create and solve equations and inequalities, including those that involve absolute value.
A2.REI.A.2Solve rational equations where numerators and denominators are polynomials and where extraneous solutions may result.
A2.REI.B Solve general systems of equations and inequalities.
A2.REI.B.3Create and solve systems of equations that may include non-linear equations and inequalities.
A2.SSE Seeing Structure in Expressions
A2.SSE.A Define and use logarithms.
A2.SSE.A.1Develop the definition of logarithms based on properties of exponents.
A2.SSE.A.2Use the inverse relationship between exponents and logarithms to solve exponential and logarithmic equations.
A2.SSE.A.3Use properties of logarithms to solve equations or find equivalent expressions.
A2.SSE.A.4Understand why logarithmic scales are used, and use them to solve problems.

Geometry

G.C Circles
G.C.A Understand and apply theorems about circles.
G.C.A.1Prove that all circles are similar using similarity transformations.
G.C.A.2Identify and describe relationships among inscribed angles, radii and chords of circles.
G.C.A.3Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
G.C.B Find arc lengths and areas of sectors of circles.
G.C.B.4Derive the formula for the length of an arc of a circle.
G.C.B.5Derive the formula for the area of a sector of a circle.
G.CO Congruence
G.CO.A Experiment with transformations in the plane.
G.CO.A.1Define angle, circle, perpendicular line, parallel line, line segment and ray based on the undefined notions of point, line, distance along a line and distance around a circular arc.
G.CO.A.2Represent transformations in the plane, and describe them as functions that take points in the plane as inputs and give other points as outputs.
G.CO.A.3Describe the rotational symmetry and lines of symmetry of two-dimensional figures.
G.CO.A.4Develop definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.
G.CO.A.5Demonstrate the ability to rotate, reflect or translate a figure, and determine a possible sequence of transformations between two congruent figures.
G.CO.B Understand congruence in terms of rigid motions.
G.CO.B.6Develop the definition of congruence in terms of rigid motions.
G.CO.B.7Develop the criteria for triangle congruence from the definition of congruence in terms of rigid motions.
G.CO.C Prove geometric theorems.
G.CO.C.10Prove theorems about polygons.
G.CO.C.8Prove theorems about lines and angles.
G.CO.C.9Prove theorems about triangles.
G.CO.D Make geometric constructions.
G.CO.D.11Construct geometric figures using various tools and methods.
G.CP Conditional Probability and Rules of Probability
G.CP.A Understand independence and conditional probability and use them to interpret data.
G.CP.A.1Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections or complements of other events.
G.CP.A.2Understand the definition of independent events and use it to solve problems.
G.CP.A.3Calculate conditional probabilities of events.
G.CP.A.4Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
G.CP.A.5Recognize and explain the concepts of conditional probability and independence in a context.
G.CP.A.6Apply and interpret the Addition Rule for calculating probabilities.
G.CP.A.7Apply and Interpret the general Multiplication Rule in a uniform probability model.
G.CP.A.8Use permutations and combinations to solve problems.
G.GMD Geometric Measurement and Dimension
G.GMD.A Explain volume formulas and use them to solve problems.
G.GMD.A.1Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid and cone.
G.GMD.A.2Use volume formulas for cylinders, pyramids, cones, spheres and composite figures to solve problems.
G.GMD.B Visualize relationships between two-dimensional and three-dimensional objects.
G.GMD.B.3Identify the shapes of two-dimensional cross-sections of three-dimensional objects.
G.GMD.B.4Identify three-dimensional objects generated by transformations of two-dimensional objects.
G.GPE Exploring Geometric Properties with Equations
G.GPE.A Translate between the geometric description and the equation for a conic section.
G.GPE.A.1Derive the equation of a circle.
G.GPE.A.2Derive the equation of a parabola given a focus and directrix.
G.GPE.B Use coordinates to prove geometric theorems algebraically.
G.GPE.B.3Use coordinates to prove geometric theorems algebraically.
G.GPE.B.4Prove the slope criteria for parallel and perpendicular lines and use them to solve problems.
G.GPE.B.5Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
G.GPE.B.6Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.
G.MG Modeling with Geometry
G.MG.A Apply geometric concepts in modeling situations.
G.MG.A.1Use geometric shapes, their measures and their properties to describe objects.
G.MG.A.2Apply concepts of density based on area and volume in modeling situations.
G.MG.A.3Apply geometric methods to solve design mathematical modeling problems.
G.SRT Similarity, Right Triangles, and Trigonometry
G.SRT.A Understand similarity in terms of similarity transformations.
G.SRT.A.1Construct and analyze scale changes of geometric figures.
G.SRT.A.2Use the definition of similarity to decide if figures are similar and to solve problems involving similar figures.
G.SRT.A.3Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
G.SRT.B Prove theorems involving similarity.
G.SRT.B.4Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
G.SRT.C Define trigonometric ratios, and solve problems involving right triangles.
G.SRT.C.5Understand that side ratios in right triangles define the trigonometric ratios for acute angles.
G.SRT.C.6Explain and use the relationship between the sine and cosine of complementary angles.
G.SRT.C.7Use trigonometric ratios and the Pythagorean Theorem to solve right triangles.
G.SRT.C.8Derive the formula A = 1/2 ab sin(C) for the area of a triangle.

AP Calculus Learning Objectives

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

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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