Arkansas Math Standards - Arkansas Mathematics Standards

1052 standards, Kindergarten through AP.

Arkansas developed its own math standards covering K-8 through a broad range of high school options: Algebra III, Quantitative Literacy, Technical Math, and more. The variety supports diverse career and college pathways beyond standard college prep tracks.

Kindergarten

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K.CAR Computation & Algebraic Reasoning
K.CAR.1Use objects, fingers, mental images, drawings, sounds, acting out situations, or verbal explanations to represent addition and subtraction from 0 to 10.
K.CAR.2Use objects or drawings to decompose numbers less than or equal to 10 into pairs in more than one way, recording each decomposition.
K.CAR.3Use a drawing or equation to find the number that makes 10 when added to a given number.
K.CAR.4Use manipulatives and various strategies to fluently add and subtract within 10.
K.CAR.5Solve real-world problems involving addition and subtraction within 10, using objects, drawings, or equations to represent the problem.
K.DA Data Analysis
K.DA.1Collect, sort, and organize data into two or three categories, using real-object graphs and picture graphs.
K.GM Geometry & Measurement
K.GM.1Describe the positions of objects and geometric shapes in the environment. Terms include: inside, outside, between, above, below, near, far, under, over, up, down, behind, in front of, next to, to the left of, and to the right of
K.GM.2Name shapes correctly regardless of their orientation or overall size. Shapes include: squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres
K.GM.3Identify two-dimensional attributes of three-dimensional objects.
K.GM.4Analyze and sort a variety of two and three-dimensional shapes using informal language to describe their similarities, differences, and other attributes.
K.GM.5Compose and draw shapes found in the world using objects (e.g., straws, toothpicks, clay balls).
K.GM.6Make direct comparisons of the length, capacity, weight, and temperature of objects, recognizing which object is shorter/longer, lighter/heavier, warmer/cooler, or holds more.
K.GM.7Understand concepts of time, recognizing that clocks and calendars are tools that measure time. Concepts of time include: morning, afternoon, evening, today, yesterday, tomorrow, day, week, month, and year
K.GM.8Identify pennies and dimes by name and value.
K.NPV Number & Place Value
K.NPV.1Count to 100 by ones and tens; count forward by ones from any given number up to 100.
K.NPV.2Count a set of objects up to 20 using one-to-one correspondence, demonstrating that the last number stated indicates the number of objects in the set regardless of the arrangement.
K.NPV.3Identify the position of objects in a set using ordinal numbers (first, second, third, etc.).
K.NPV.4Identify quickly a number of items in a set from 0 to 10 without counting.
K.NPV.5Read, write, and represent whole numbers from 0 to 20.
K.NPV.6Show equivalent forms of whole numbers up to 20 as groups of tens and ones, using manipulatives and drawings.
K.NPV.7Use matching and counting strategies to compare the number of objects in one group to the number of objects in another group (0 to 10) using the terms greater than, less than, or equal.
K.NPV.8Compare two whole numbers, using the terms greater than, less than, or equal.

Grade 1

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1.CAR Computation & Algebraic Reasoning
1.CAR.1Add and subtract fluently within 10 with mastery by the end of first grade.
1.CAR.2Use computational fluency to add and subtract within 20 using manipulatives and/or a variety of strategies.
1.CAR.3Apply properties of operations to add and subtract within 20.
1.CAR.4Use concrete models or drawings to add within 100, including a two-digit number and a one-digit number as well as a two-digit number and a multiple of ten; relate strategy used to a written expression or equation and explain reasoning.
1.CAR.5Demonstrate the relationship between addition and subtraction by solving problems, using an inverse operation.
1.CAR.6Solve real-world problems involving addition and subtraction within 20. Problem types include: adding to, taking from, putting together, taking apart, and comparing with unknowns present throughout the addition and subtraction problem.
1.CAR.7Solve real-world problems involving addition of three whole numbers whose sum is less than or equal to 20.
1.CAR.8Apply understanding of the equal sign to determine if equations involving addition and subtraction are true or false.
1.CAR.9Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.
1.DA Data Analysis
1.DA.1Organize, represent, and interpret data with up to three categories (e.g., tally tables, picture graphs, bar graphs).
1.DA.2Ask and answer questions about the total number represented such as how many in each category and how many more or less in one category compared to another.
1.GM Geometry & Measurement
1.GM.1Understand the difference between defining attributes (e.g., triangles are closed and three-sided shapes) and non-defining attributes (e.g., color, orientation, overall size), using that understanding to build and draw shapes that exhibit defining attributes.
1.GM.2Create a composite shape using two-dimensional or three-dimensional shapes. Two-dimensional include: rectangle, square, trapezoid, triangle, hexagon, half circle, and quarter circle. Three-dimensional include: cube, rectangular prism, cone, and cylinder
1.GM.3Express the length of an object as a whole number of units by laying multiple copies of a shorter object end-to-end, understanding that the length of one object is equal to the number of same-size units that span the object with no gaps or overlaps.
1.GM.4Order three objects by their length, indirectly comparing the lengths of two objects by using a third object.
1.GM.5Tell and write time to the nearest hour and half hour using analog clocks; understand how to read hours and minutes using digital clocks.
1.GM.6Identify coins by name and value, including penny, nickel, dime, and quarter.
1.GM.7Count collections of like coins including pennies, nickels, and dimes to determine their total value up to 100 cents.
1.NPV Number & Place Value
1.NPV.1Count forward and back within 120 by ones and tens from any given whole number.
1.NPV.2Skip count forward by multiples of fives within 120.
1.NPV.3Explain the place value of ones and tens in two-digit numbers, using concrete models, diagrams, numbers, or words.
1.NPV.4Read, write, and represent whole numbers up to 120, using concrete models or drawings, word form, base ten numerals, and expanded form.
1.NPV.5Use concrete models or drawings to subtract multiples of 10 from multiples of 10 (within the range of 10-90), relate the strategy to a written expression or equation, and explain the reasoning used to solve.
1.NPV.6Use mental strategies to find 10 more or 10 less than a given two-digit number.
1.NPV.7Compare two two-digit numbers using symbols (<, =, >) based on the value of tens and ones in the given numbers.
1.NPV.8Partition circles and rectangles into two and four equal shares, describing the shares using the words halves, fourths, and quarters; understand that decomposing into more equal pieces creates smaller pieces.

Grade 2

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2.CAR Computation & Algebraic Reasoning
2.CAR.1Use mental strategies to fluently add and subtract within 20 with mastery by the end of second grade.
2.CAR.2Use computational fluency to add and subtract within 100 using strategies based on place value, properties of operations, or the relationship between addition and subtraction.
2.CAR.3Add up to four two-digit numbers with sums not exceeding 100 using strategies based on place value and properties of operations.
2.CAR.4Use a number line to solve addition and subtraction problems within 100.
2.CAR.5Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
2.CAR.6Use concrete models, drawings, or equations to solve addition and subtraction problems within 1000.
2.CAR.7Solve one and two-step real-world problems involving addition and subtraction within 100 in situations of adding to, taking from, putting together, taking apart, and comparing unknowns in all positions.
2.CAR.8Determine whether a group of objects up to 20 has an odd or even number of members; write an equation to express an even number as a sum of two equal addends.
2.DA Data Analysis
2.DA.1Use bar graphs, picture graphs, and line plots to organize and represent data, interpreting data with up to four categories.
2.DA.2Ask and answer simple put together, take apart, and compare problems, using information presented in the bar graphs, picture graphs, and line plots.
2.GM Geometry & Measurement
2.GM.1Identify, describe, and draw two-dimensional shapes. Shapes include: triangles, regular pentagons, regular hexagons, and quadrilaterals (square, rectangle, trapezoid, parallelogram, rhombus)
2.GM.10Describe relationships of time. Times include: seconds in a minute; minutes in an hour; hours in a day; days in a week; and days, weeks, and months in a year
2.GM.11Solve real-world problems involving addition and subtraction of time intervals in half hours or hours.
2.GM.12Count collections of mixed coins and solve real-world problems involving quarters, dimes, nickels, and pennies within 99ยข and whole dollar amounts.
2.GM.2Identify and describe three-dimensional shapes based on the shape, number of faces, number of edges, and number of vertices. Shapes include: rectangular prisms, cubes, and square-based pyramids
2.GM.3Select appropriate measurement tools to estimate and measure the length of an object to the nearest whole inch or whole centimeters.
2.GM.4Demonstrate how the length of an object does not change, regardless of the units used to measure it, by measuring the length of an object twice; use two different length units, describing how the two measurements relate to the size of the chosen unit.
2.GM.5Measure to determine how much longer or shorter one object is than another, expressing the length difference in terms of a standard length whole unit.
2.GM.6Solve real-world problems involving lengths of the same units, using addition and subtraction within 100.
2.GM.7Solve real-world and mathematical problems to find the perimeter of polygons.
2.GM.8Partition a rectangle into rows and columns of same-size squares, counting the total number of squares to find the area.
2.GM.9Using an analog clock, tell and write time to the nearest five minutes using colon notation and indicate a.m. or p.m.
2.NPV Number & Place Value
2.NPV.1Count within 1,000 forwards and backwards by ones, tens, and hundreds from any given number.
2.NPV.2Identify the value of hundreds, tens, and ones place in a three-digit number.
2.NPV.3Read, write, and represent whole numbers up to 1,000 using concrete models or drawings, number names, and a variety of expanded forms.
2.NPV.4Mentally add 10 or 100 to a given number in the range of 100-900 and mentally subtract 10 or 100 from a given number in the range of 100-900.
2.NPV.5Compare two three-digit numbers using symbols (<, =, >) based on the value of hundreds, tens, and ones in the given numbers.
2.NPV.6Partition circles and rectangles into two, three, or four equal shares, describing the shares using the words halves, thirds, and fourths (or quarters).
2.NPV.7Recognize that equal shares of identical wholes need not have the same shape.

Grade 3

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3.CAR Computation & Algebraic Reasoning
3.CAR.1Use computational fluency to add and subtract three-digit whole numbers, using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
3.CAR.2Use basic fact fluency to multiply and divide whole numbers with mastery by the end of third grade. Knowing all products with factors up to and including 12 and the corresponding division facts from the products with factors up to and including 12. Using strategies such as the relationship between multiplication and division (e.g., Knowing that 8โˆ™5=40, one knows 40 รท 5 =8) or properties of operations.
3.CAR.3Apply properties of operations as strategies to multiply and divide. Properties include: Distributive, Commutative, and Associative Properties of Multiplication
3.CAR.4Use strategies to multiply one-digit numbers by multiples of 10 ranging from 10-90; strategies are based on place value and properties of operations (e.g., 9โˆ™80,5โˆ™60).
3.CAR.5Identify arithmetic patterns including, but not limited to, patterns in an addition or multiplication table, explaining use of properties of operations appropriate to the pattern.
3.CAR.6Solve real-world problems using multiplication and division within 100 involving equal groups, arrays, partitive and measurement division.
3.CAR.7Solve two-step real-word situations using addition, subtraction, multiplication, and division, representing these problems using equations with a symbol standing for an unknown quantity.
3.CAR.8Determine the unknown whole number in a multiplication or division equation relating three whole numbers.
3.CAR.9Understand division as an unknown-factor problem.
3.DA Data Analysis
3.DA.1Represent a data set with multiple categories, using a scaled picture graph, scaled bar graph, and a line plot.
3.DA.2Solve one and two-step problems, using categorical data represented with a scaled picture graph, scaled bar graph, and a line plot.
3.GM Geometry & Measurement
3.GM.1Understand that quadrilaterals in different categories may share attributes; those attributes (e.g., four equivalent sides) can define a larger category (e.g., quadrilaterals) or subcategory (e.g., rhombus and square).
3.GM.10Tell and write time to the nearest minute, using analog clocks.
3.GM.11Solve word problems involving addition and subtraction of time intervals in minutes.
3.GM.2Identify perpendicular and parallel lines, as well as right angles in two-dimensional shapes and real-world surroundings or objects.
3.GM.3Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, identifying and/or drawing examples of quadrilaterals that do not belong to any of these subcategories.
3.GM.4Measure lengths of objects to the nearest half and quarter inch, using a ruler.
3.GM.5Describe area as the number of unit squares that cover a plane figure without gaps and overlaps.
3.GM.6Find the area of a rectangle with whole number side lengths by modeling with unit squares and multiplying the side lengths to show the results are the same.
3.GM.7Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real-world and mathematical problems.
3.GM.8Measure and estimate liquid volumes and masses of objects using standard units.
3.GM.9Solve one-step real-world problems involving liquid volumes and masses of objects in the same units, using all four operations.
3.NPV Number & Place Value
3.NPV.1Round four-digit whole numbers to the nearest 10 or 100, using place value understanding.
3.NPV.10Decompose and compose a non-unit fraction ๐‘Ž/๐‘ as the quantity formed by the sum of unit fractions. Fractions include: denominators 2, 3, 4, 6, and 8
3.NPV.11Use number lines and visual models to recognize and generate equivalent fractions, explaining how they are equivalent in real-world and mathematical situations. Fractions include: denominators 2, 3, 4, 6, and 8
3.NPV.2Identify the value of thousands, hundreds, tens, and ones place in a four-digit number.
3.NPV.3Read and write whole numbers up to 10,000, using base ten numerals, word form, and a variety of expanded forms.
3.NPV.4Compare two four-digit numbers using symbols (<, =, >) based on the value of thousands, hundreds, tens, and ones in the given numbers.
3.NPV.5Compare two fractions with the same numerator or denominator by reasoning about their size based on the same whole; use symbols (<, =, >) and justify the conclusion using visual fraction models, concrete objects, or words.
3.NPV.6Identify fractions as parts of a whole and parts of a collection or set. Fractions include: denominators 2, 3, 4, 6, and 8
3.NPV.7Partition squares, regular hexagons, and equilateral triangles into parts with equal shares, explaining the shares of each part as a unit fraction of the whole. Fractions include: denominators 2, 3, 4, 6, and 8
3.NPV.8Identify and represent a unit fraction as a number on the number line. Fractions include: denominators 2, 3, 4, 6, and 8
3.NPV.9Identify and represent a non-unit fraction as a number on the number line, including fractions greater than one. Fractions include: denominators 2, 3, 4, 6, and 8

Grade 4

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4.CAR Computation & Algebraic Reasoning
4.CAR.1Find the factor pairs for a given number in the range of 1-100, identifying whether a number is prime or composite; determine whether a given whole number in the range of 1-100 is a multiple of a given one-digit number.
4.CAR.10Solve real-word problems involving the multiplication of a fraction by a whole number using visual fraction models or equations. Fractions include: denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100
4.CAR.11Generate a number or shape pattern that follows a given rule, identifying apparent features of the pattern that are not explicit in the rule itself.
4.CAR.2Use computational fluency to add and subtract whole numbers up to 1,000,000 by using strategies and algorithms, including the standard algorithm, with mastery by the end of fourth grade.
4.CAR.3Use strategies based on place value and the properties of operations to multiply four-digit by one-digit whole numbers and two two-digit whole numbers.
4.CAR.4Use strategies based on place value, the properties of operations, and the relationship between multiplication and division to divide whole numbers with four-digits by one-digit divisors; quotients should be with and without whole number remainders.
4.CAR.5Add and subtract fractions, including mixed numbers, with like denominators, using visual fraction models and equations. Fractions include: denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100
4.CAR.6Multiply a fraction by a whole number using visual fraction models and equations. Fractions include: denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100
4.CAR.7Solve real-world problems involving multiplicative comparison, using drawings and/or equations with a symbol for the unknown number, and distinguish between multiplicative comparison and additive comparison.
4.CAR.8Solve multi-step, real-world problems posed with whole numbers and having whole-number answers, using addition, subtraction, multiplication, and division; include problems in which remainders must be interpreted and represent these problems using equations with symbols standing for the unknown quantity.
4.CAR.9Solve real-world problems involving the addition and subtraction of fractions; include mixed numbers with like denominators, using visual fraction models or equations. Fractions include: denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100
4.DA Data Analysis
4.DA.1Collect and interpret data from observations, surveys, and experiments; represent data using frequency tables and scaled bar graphs.
4.DA.2Use a line plot to display a data set of measurements in fractions of a unit, solving problems involving addition and subtraction of fractions with like denominators using data presented in line plots.
4.GM Geometry & Measurement
4.GM.1Identify angles as geometric shapes that are formed where two rays share a common endpoint, understanding that angles are measured with reference to a circle so that an angle that turns through a 1/360 of a circle is called a โ€œone-degree angleโ€ and an angle that turns through ๐‘› one-degree angles is said to have an angle measure of n degree.
4.GM.10Solve real-world problems involving addition and subtraction of money, including the ability to make change.
4.GM.11Solve real-world problems involving distances, liquid volume, and masses of objects, including problems that require expressing measurements given in a larger unit in terms of a smaller unit.
4.GM.2Measure angles in whole-number degrees, using a protractor, drawing angles of specified measure.
4.GM.3Solve real-word problems finding unknown angle measures, using addition and subtraction when an angle is decomposed into non-overlapping parts.
4.GM.4Identify and draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines, identifying these in quadrilaterals and triangles.
4.GM.5Classify two-dimensional figures based on the presence or absence of parallel lines, perpendicular lines, or angles of a specified size, involving quadrilaterals and triangles. Shapes include: quadrilaterals (trapezoid, parallelogram, rectangle, square, rhombus) and triangles (right, acute, obtuse)
4.GM.6Identify and/or draw lines of symmetry for a two-dimensional figure.
4.GM.7Apply the area and perimeter formulas for rectangles and figures composed of two or more rectangles in real-world situations.
4.GM.8Convert measurements of length, weight/mass, and liquid volume within the same system of measurement, metric and customary, expressing measurements from a larger unit in terms of a smaller unit.
4.GM.9Solve real-world problems involving time intervals that may cross the hour.
4.NPV Number & Place Value
4.NPV.1Recognize that a digit in a given place represents ten times what it represents in the place to its right.
4.NPV.10Apply decimal notation for fractions with denominators 10 or 100.
4.NPV.2Read and write whole numbers up to 1,000,000 using base ten numerals, word form, and a variety of expanded forms.
4.NPV.3Use place value understanding to round five-digit and six-digit whole numbers to any place.
4.NPV.4Compare two five-digit whole numbers and six-digit whole numbers, using symbols (<, =, >) to record the results of comparisons.
4.NPV.5Compare two fractions with different numerators and different denominators using symbols (<, =, >) to record the results of comparisons (e.g., by creating common denominators or numerators or by comparing to a benchmark of 0, ยฝ, 1).
4.NPV.6Compare two decimals to the hundredths place, using symbols (<, =, >) to record the results of comparisons.
4.NPV.7Decompose fractions, including fractions greater than one and mixed numbers, into unit fractions, using concrete models, drawings, and/or the number line. Fractions include denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NPV.8Explain why a fraction ๐‘Ž/๐‘ is equivalent to a fraction (๐‘›โˆ™๐‘Ž)/(๐‘›โˆ™๐‘), using visual fraction models, generating equivalent fractions using the principle ๐‘Ž/๐‘ = (๐‘›โˆ™๐‘Ž)/(๐‘›โˆ™๐‘). Fractions include denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NPV.9Add two fractions with denominators of 10 and 100 by expressing the denominator of 10 as an equivalent fraction with a denominator of 100.

Grade 5 Mathematics Standards

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5.CAR Computation & Algebraic Reasoning
5.CAR.1Use computational fluency to multiply multi-digit whole numbers by using strategies and algorithms, including the standard algorithm, with mastery by the end of fifth grade.
5.CAR.10Solve real-world problems involving the division of natural numbers leading to answers in the form of fractions or mixed numbers using visual models and equations.
5.CAR.11Solve real-world problems involving the division of unit fractions by whole numbers and whole numbers by unit fractions, using visual fraction models and equations.
5.CAR.12Evaluate numerical expressions with parentheses or brackets and exponents with the base of ten, using the Order of Operations.
5.CAR.13Write simple expressions that record calculations with numbers, interpreting numerical expressions without evaluating them.
5.CAR.14Generate two numerical patterns given two rules, identifying the relationship between the corresponding terms by graphing the terms in the first quadrant of the coordinate grid.
5.CAR.2Calculate whole number quotients of whole numbers with up to four-digit dividends and two-digit divisors using strategies based on place value, properties of operations, divisibility rules, and the relationship between multiplication and division.
5.CAR.3Add and subtract decimals to the hundredths using concrete models or drawings and strategies based on place value, properties of operations, or the relationship between addition and subtraction.
5.CAR.4Multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, or the relationship between multiplication and division.
5.CAR.5Add and subtract fractions with like and unlike denominators by using equivalent fractions {๐‘Ž/๐‘ = (๐‘› โˆ™ ๐‘Ž)/(๐‘› โˆ™ ๐‘)} to create common denominators; include real-world problems. Fractions include: mixed numbers
5.CAR.6Interpret and solve fractions as division problems, (๐‘Ž/๐‘ = ๐‘Ž รท ๐‘), where ๐‘Ž and ๐‘ are natural numbers.
5.CAR.7Use visual models and equations to multiply whole numbers by fractions and fractions by fractions, including mixed numbers and fractions greater than one.
5.CAR.8Apply previous understanding of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
5.CAR.9Solve and create real-world problems involving multiplication of fractions and mixed numbers.
5.DA Data Analysis
5.DA.1Collect and interpret data from observations, surveys, and experiments; represent data using frequency tables, scaled bar graphs, and scaled line graphs.
5.DA.2Use a line plot to display a data set of measurements in fractions of a unit solving problems involving all four operations with fractions (excluding division of a fraction by fraction) using data presented in line plots.
5.GM Geometry & Measurement
5.GM.1Classify two-dimensional figures in a hierarchy based on properties with the focus on quadrilaterals and triangles when teaching hierarchies. Shapes to include: quadrilaterals (trapezoid, parallelogram, rectangle, square, rhombus, kite) and triangles (right, acute, obtuse, scalene, isosceles, equilateral)
5.GM.2Find the area of a rectangle with fractional and/or mixed number side lengths by using models and multiplying the fractional side lengths showing that both strategies produce the same area.
5.GM.3Measure volumes by counting unit cubes using cubic cm (๐‘๐‘š^3), cubic in (๐‘–๐‘›^3), cubic ft (ft^3), and improvised units (๐‘ข^3).
5.GM.4Solve real-world and mathematical problems involving the volume of rectangular prisms with whole number side lengths by applying the formulas (๐‘‰=๐‘™โˆ™๐‘คโˆ™โ„Ž or ๐‘‰=๐ตโˆ™โ„Ž) and the properties of operations.
5.GM.5Solve real-world problems by calculating volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts.
5.GM.6Convert among different-sized standard measurement units within the same system, including both the metric and customary systems, and solve multi-step, real-world problems using conversions.
5.GM.7Graph points with whole number coordinates on a coordinate plane in the first quadrant, explaining how the coordinates relate to the horizontal and vertical axes to describe the location of points in the plane.
5.GM.8Represent real-world and mathematical problems by graphing points in the first quadrant on a coordinate plane, interpreting coordinate values of points in the context of the situation.
5.NPV Number & Place Value
5.NPV.1Recognize that, in a multi-digit number, a digit in a given place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
5.NPV.2Explain patterns in the number of zeros and/or the decimal point when multiplying or dividing a number by a power of 10, using whole-number exponents to denote powers of 10.
5.NPV.3Read and write decimals to thousandths, using base-ten numerals, word form, and a variety of expanded forms.
5.NPV.4Apply place value understanding to round decimals to any place up to the thousandths.
5.NPV.5Compare two decimals to thousandths based on the value of the digits in each place, using symbols (<, =, >) to record the results of comparisons.
5.NPV.6Use visual models to explain the product of multiplying a whole number by a fraction greater than and less than one.

Grade 6 Mathematics Standards

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6.ALG Algebra
6.ALG.1Read and write expressions in real-world or mathematical problems in which letters stand for numbers.
6.ALG.2Use mathematical terms to identify parts of an expression, including the names of operations, terms, factors, coefficients, variables, and constants.
6.ALG.3Write and evaluate expressions for given values of variables, using order of operations, including expressions with whole number exponents.
6.ALG.4Generate equivalent expressions by applying the associative, commutative, distributive, and identity properties.
6.ALG.5Identify when two expressions are equivalent by using properties of operations including like terms.
6.ALG.6Use substitution to determine if a given value in a specified set makes an equation or inequality true. Include the following inequality symbols: <,>,โ‰ค,โ‰ฅ,โ‰ 
6.ALG.7Write and solve one-step equations in real-world and mathematical problems, involving positive rational numbers and zero.
6.ALG.8Write, solve, and graph one-step inequalities in real-world and mathematical problems.
6.GM Geometry & Measurement
6.GM.1Find the area of triangles, quadrilaterals, and polygons by composing or decomposing to solve real-world and mathematical problems.
6.GM.2Apply the formulas ๐‘‰=๐‘™๐‘คโ„Ž and ๐‘‰=๐ตโ„Ž to find the volume of right rectangular prisms with fractional edge lengths to solve real-world and mathematical problems, including solving for an unknown dimension.
6.GM.3Construct nets of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid, using the nets to find the surface area of these prisms.
6.GM.4Find and graph pairs of rational numbers in all four quadrants of the coordinate plane in real-world and mathematical problems.
6.GM.5Draw polygons in the coordinate plane when given coordinates for the vertices.
6.GM.6Use coordinates to calculate vertical and horizontal distances between points with the same x-coordinate or the same y-coordinate to solve real-world and mathematical problems.
6.GM.7Convert measurements within and between the metric and customary measurement systems to solve real-world and mathematical problems.
6.NCC Number Concepts & Computations
6.NCC.1Explain positive and negative integers as being opposite values or directions and the meaning of 0 in a real-world context.
6.NCC.10Use any standard algorithm to fluently multiply and divide multi-digit decimals and fractions in real-world and mathematical problems.
6.NCC.11Solve real-world and mathematical problems with the greatest common factor of two whole numbers less than or equal to 100.
6.NCC.12Solve real-world and mathematical problems with the least common multiple of two whole numbers less than or equal to 12.
6.NCC.13Use the distributive property and the greatest common factor to rewrite the sum of two whole numbers, 1 through 100.
6.NCC.2Find and plot rational numbers on horizontal and vertical number lines in real-world and mathematical problems.
6.NCC.3Compare rational numbers, using inequalities (<,>,โ‰ค,โ‰ฅ,โ‰ ) and order on a number line.
6.NCC.4Interpret the absolute value of numbers for positive or negative quantities in a real-world context.
6.NCC.5Convert between fractions, decimals, and percents in real-world and mathematical problems.
6.NCC.6Interpret and represent quotients of fractions. Fractions include all forms of fractions.
6.NCC.7Solve problems involving the division of fractions in real-world and mathematical problems. Fractions include all forms of fractions.
6.NCC.8Divide multi-digit numbers fluently in real-world and mathematical problems.
6.NCC.9Use any standard algorithm to fluently add and subtract multi-digit decimals and fractions in real-world and mathematical problems.
6.PR Proportional Relationships
6.PR.1Use precise ratio language and notation to describe a ratio as a relationship between two quantities.
6.PR.2Calculate unit rates to include unit pricing and constant speed.
6.PR.3Give examples of unit rates as a ratio that compares two quantities with different units of measure, limited to non-complex fractions.
6.PR.4Create various representations to compare ratios and find missing values to solve real-world and mathematical problems.
6.PR.5Find a percent of a quantity as a rate per 100 and solve problems involving finding the whole when given a part and the percent.
6.SP Statistics & Probability
6.SP.1Identify the difference between statistical and non-statistical questions and write simple statistical questions that allow variable responses.
6.SP.2Calculate and interpret any measure of center (mean, median, and mode) of a numerical data set.
6.SP.3Determine which measure of center (mean or median) is more appropriate to describe the center of data and justify the choice.
6.SP.4Describe how the mean or median is affected by outliers of a numerical data set.
6.SP.5Calculate and interpret the measure of variation [range and interquartile range (IQR)] of a numerical data set.
6.SP.6Determine which measure of variation (range or interquartile range) is more appropriate to describe the shape; justify the choice.
6.SP.7Represent numerical data on a number line, histogram, and box plot.
6.SP.8Calculate the relative frequency of an interval of data values when given a histogram.
6.SP.9Interpret a box plot to answer statistical questions about a data set.

Grade 7 Mathematics Standards

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7.ALG Algebra
7.ALG.1Generate and justify equivalent expressions, using properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients within mathematical and real-world problems.
7.ALG.2Model and solve fluently two-step equations in real-world or mathematical problems.
7.ALG.3Create, solve, and graph two-step inequalities in real-world and mathematical problems in the forms ๐‘๐‘ฅยฑ๐‘ž>๐‘Ÿ, ๐‘๐‘ฅยฑ๐‘ž<๐‘Ÿ, ๐‘๐‘ฅยฑ๐‘žโ‰ฅ๐‘Ÿ, and ๐‘๐‘ฅยฑ๐‘žโ‰ค๐‘Ÿ.
7.ALG.4Write an equation to express two quantities in terms of the dependent and independent variables.
7.ALG.5Describe the relationship between the dependent and independent variables in an equation using tables and graphs, relating these to the equation.
7.GM Geometry & Measurement
7.GM.1Describe the proportional relationship between the circumference and diameter of a circle.
7.GM.2Use area and circumference formulas of a circle to solve real-world and mathematical problems.
7.GM.3Apply the formulas for the volume and surface area of right rectangular prisms, rectangular pyramids, triangular prisms, and triangular pyramids to solve real-world and mathematical problems.
7.GM.4Describe the two-dimensional figure that results from slicing a three-dimensional figure parallel and perpendicular to the base. Three-dimensional figures include: right rectangular prisms, triangular prisms, and cylinders
7.GM.5Solve multi-step problems involving supplementary, complementary, vertical, and adjacent angles to include solving for an unknown angle in a figure.
7.GM.6Calculate the scale factor, compute the actual lengths from the scale in a drawing, and reproduce a scale drawing using another scale.
7.NCC Number Concepts & Computations
7.NCC.1Represent addition and subtraction of rational numbers in real-world contexts using a variety of forms.
7.NCC.2Model and describe additive inverse in real-world situations to show opposite quantities combine to make 0.
7.NCC.3Demonstrate in real-world contexts the distance between two rational numbers on the number line as the absolute value of their differences.
7.NCC.4Convert a rational number in fraction form to decimal form and recognize that the decimal form of a rational number terminates in 0s or eventually repeats.
7.NCC.5Interpret the products and quotients of rational numbers by describing real-world contexts.
7.NCC.6Apply properties of operations as strategies to fluently add, subtract, multiply, and divide rational numbers.
7.NCC.7Use addition and subtraction with rational numbers in any form to solve multi-step problems in real-world and mathematical contexts.
7.NCC.8Use multiplication and division with rational numbers in any form to solve multi-step problems in real-world and mathematical contexts.
7.NCC.9Apply operations with rational numbers involving the order of operations, involving nested grouping symbols.
7.PR Proportional Relationships
7.PR.1Determine the unit rate (constant of proportionality) from tables, graphs, equations, diagrams, or verbal descriptions of proportional relationships.
7.PR.2Calculate unit rates in real-world contexts that include complex fractions.
7.PR.3Solve multi-step ratio and percent problems in a real-world context, including percent error and percent increase and decrease.
7.PR.4Determine whether two quantities represent proportional relationships by using equivalent ratios in a table and by graphing on a coordinate plane.
7.PR.5Compare two different proportional relationships represented in different forms.
7.PR.6Create equations in the form of ๐‘ฆ=๐‘š๐‘ฅ from tables, verbal descriptions, or graphs.
7.PR.7Given a graph with a proportional relationship, explain the meaning of a point (๐‘ฅ,๐‘ฆ) on the graph, including the origin (0,0) and the unit rate (1,๐‘Ÿ).
7.SP Statistics & Probability
7.SP.1Interpret data displayed in a histogram and box plot to answer questions about the data.
7.SP.10Use theoretical probability of an event in a simple experiment to predict the number of times that an event will occur for a large number of experiments.
7.SP.2Recognize, create, and interpret categorical data in a circle graph.
7.SP.3Graph two numerical data sets and compare their variability. Variability includes: range, interquartile range, or mean absolute deviation
7.SP.4Select an appropriate measure(s) of center or variability and draw valid comparative inferences for two data sets.
7.SP.5Distinguish between a random and non-random sample.
7.SP.6Use a random sampling of a population to draw valid inferences and generalizations of populations.
7.SP.7Determine the sample space of a simple experiment and use the sample space to determine the theoretical probability of a given set of outcomes. Simple experiments include: tossing a fair coin, spinning a fair spinner, rolling a fair dice, picking a random marble from a bag, and selecting a random card from a deck
7.SP.8Recognize that probabilities in a simple experiment can be qualitative descriptors of likelihood: impossible (0), unlikely, neither likely nor unlikely, likely, or certain (1).
7.SP.9Determine experimental probabilities in simple experiments and represent as fractions, decimals, and percents.

Grade 8 Mathematics Standards

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8.ALG Algebra
8.ALG.1Analyze and solve one-variable linear equations with rational coefficients containing solutions with one, zero, or infinitely many solutions.
8.ALG.2Analyze and solve one-variable linear inequalities with rational coefficients.
8.ALG.3Analyze and solve systems of linear equations in the form ๐‘ฆ=๐‘š๐‘ฅ+๐‘ in real-world or mathematical contexts, graphically and algebraically.
8.FN Functions
8.FN.1Graph proportional relationships, interpreting the unit rate as the slope of the graph.
8.FN.2Explain, using similar right triangles, how the slope of a line is the same between two points on a non-vertical line or non-horizontal line. Slope includes: positive, negative, horizontal (zero), and vertical (undefined)
8.FN.3Determine whether a relation is a function or not when given a function map, table, graph, equation, or set of ordered pairs.
8.FN.4Compare the rate of change (slope) and y-intercept (initial value) of two linear functions each represented in different forms. Functions are represented algebraically, graphically, numerically in tables, or by verbal descriptions.
8.FN.5Distinguish between linear and nonlinear functions by comparing graphs and equations.
8.FN.6Determine the rate of change (slope) and y-intercept (initial value) from tables, graphs, equations, and verbal descriptions of linear relationships.
8.FN.7Interpret and explain the meaning of the rate of change (slope) and y-intercept (initial value) of a linear relationship in a real-world context.
8.FN.8Analyze a graph by describing the functional relationships between two quantities.
8.FN.9Sketch a graph that exhibits qualitative features of a function described verbally.
8.GM Geometry & Measurement
8.GM.1Apply the formulas for the volume and surface area of cylinders, cones, and spheres to solve real-world and mathematical problems.
8.GM.10Describe the effects of rotations, reflections, translations, and dilations on two-dimensional figures using coordinates. Rotations include: 90ยฐ, 180ยฐ, and 270ยฐ
8.GM.11Given two similar two-dimensional figures, describe a sequence of transformations that exhibits similarity, including rotations, reflections, translations, and dilations.
8.GM.2Describe the two-dimensional figure that results from slicing a three-dimensional figure parallel and perpendicular to the base. Three-dimensional figures include: pyramids, cones, and spheres
8.GM.3Model or explain an informal proof of the Pythagorean Theorem and its converse.
8.GM.4Apply the Pythagorean Theorem to determine unknown side lengths in right triangles.
8.GM.5Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
8.GM.6Given a figure, draw a congruent figure on a coordinate plane resulting from a rotation, reflection, or translation.
8.GM.7Identify a single transformation used to transform one figure onto another on a coordinate plane. Rotations include: 90ยฐ, 180ยฐ, and 270ยฐ
8.GM.8Given two congruent figures, describe a sequence of transformations that maps one figure to another.
8.GM.9Perform a given sequence of transformations of a figure on the coordinate plane, including rotations, reflections, translations, and dilations. Rotations include: 90ยฐ, 180ยฐ, and 270ยฐ
8.NCC Number Concepts & Computations
8.NCC.1Describe relationships in the real number system (rational and irrational). Numbers relationships to include: decimal expansion for rational and irrational numbers, square roots of nonperfect squares, and cube roots of nonperfect cubes
8.NCC.2Compare the size of irrational numbers and locate them on a number line by finding the rational approximations.
8.NCC.3Know and apply the properties of integer exponents to generate equivalent numerical expressions.
8.NCC.4Write very large and very small numbers in scientific notation using positive and negative exponents.
8.NCC.5Compare numbers written in scientific notation to determine how many times larger or smaller one number is than the other, using real-world and mathematical problems.
8.NCC.6Solve real-world and mathematical problems by performing operations with numbers written in standard and scientific notation.
8.NCC.7Solve equations in the form of ๐‘ฅ^2 = ๐‘ or ๐‘ฅ^3 = ๐‘ where ๐‘ is a positive rational number.
8.NCC.8Evaluate square roots of perfect squares and cube roots of perfect cubes.
8.SP Statistics & Probability
8.SP.1Construct scatter plots using bivariate data; determine if the data displays a linear or nonlinear pattern and positive, negative, or no association.
8.SP.2Construct straight lines to approximately fit data displaying a linear association when presented in scatter plots.
8.SP.3Construct and interpret a relative frequency table, using data from two categorical variables collected from the same subject.
8.SP.4Determine the sample space and use the sample space to determine the theoretical probability of a given set of outcomes for compound experiments, using organized lists, tables, or tree diagrams. Compound experiments include a combination of two different experiments.
8.SP.5Determine theoretical and experimental probabilities of compound experiments.
8.SP.6Use theoretical probability of an event in a compound experiment to predict the number of times that event will occur for a large number of experiments.

HSA

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HSA.APR HSA.APR
HSA.APR.A HSA.APR.A
HSA.APR.A.1Add, subtract, and multiply polynomials. Understand that polynomials, like the integers, are closed under addition, subtraction, and multiplication
HSA.APR.B HSA.APR.B
HSA.APR.B.2Know and apply the Factor and Remainder Theorems: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).
HSA.APR.B.3Identify zeros of polynomials when suitable factorizations are available. Use the zeros to construct a rough graph of the function defined by the polynomial.
HSA.APR.C HSA.APR.C
HSA.APR.C.4Prove polynomial identities and use them to describe numerical relationships. Note: Examples of Polynomial Identities may include but are not limited to the following: (a + b)^2 = a^2 + 2ab + b^2 (Algebra 1); a^2 โ€“ b^2 = (a โ€“ b)(a + b) (Algebra 1); (x^2 + y^2)^2 = (x^2 โ€“ y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples (Algebra 2).
HSA.APR.D HSA.APR.D
HSA.APR.D.6Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), (where a(x) is the dividend, b(x) is the divisor, q(x) is the quotient, and r(x) is the remainder) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
HSA.APR.D.7Add, subtract, multiply, and divide by nonzero rational expressions. Understand that rational expressions, like the integers, are closed under addition, subtraction, and multiplication.
HSA.CED HSA.CED
HSA.CED.A HSA.CED.A
HSA.CED.A.1Create equations and inequalities in one variable and use them to solve problems. Note: Including but not limited to equations arising from: Linear functions, Quadratic functions, Simple rational functions, Exponential functions, Absolute value functions
HSA.CED.A.2Create equations in two or more variables to represent relationships between quantities. Graph equations, in two variables, on a coordinate plane.
HSA.CED.A.3Represent and interpret constraints by equations or inequalities, and by systems of equations and/or inequalities. Interpret solutions as viable or nonviable options in a modeling and/or real-world context.
HSA.CED.A.4Rearrange literal equations using the properties of equality
HSA.REI HSA.REI
HSA.REI.A HSA.REI.A
HSA.REI.A.1Assuming that equations have a solution, construct a solution and justify the reasoning used.
HSA.REI.A.2Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. For example: The area of a square equals 49 square inches. The length of the side is 7 inches. Although -7 is a solution to the equation, x2 = 49, -7 is an extraneous solution.
HSA.REI.B HSA.REI.B
HSA.REI.B.4Solve quadratic equations in one variable.
HSA.REI.C HSA.REI.C
HSA.REI.C.5Solve systems of equations in two variables using substitution and elimination. Understand that the solution to a system of equations will be the same when using substitution and elimination.
HSA.REI.C.6Solve systems of equations algebraically and graphically.
HSA.REI.C.7Solve systems of equations consisting of linear equations and nonlinear equations in two variables algebraically and graphically. For example: Find the points of intersection between y = -3x and y = x^2 + 2.
HSA.REI.C.8(+) Represent a system of linear equations as a single matrix equation in a vector variable.
HSA.REI.C.9(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 ร— 3 or greater).
HSA.REI.D HSA.REI.D
HSA.REI.D.11Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); Find the solutions approximately by: Using technology to graph the functions; Making tables of values; Finding successive approximations. Include cases (but not limited to) where f(x) and/or g(x) are: Linear; Polynomial; Rational; Exponential (Introduction in Algebra 1, Mastery in Algebra 2); Logarithmic functions
HSA.REI.D.12Solve linear inequalities and systems of linear inequalities in two variables by graphing.
HSA.SSE HSA.SSE
HSA.SSE.A HSA.SSE.A
HSA.SSE.A.1Interpret expressions that represent a quantity in terms of its context.
HSA.SSE.A.2Use the structure of an expression to identify ways to rewrite it. For example: See that (x + 3)(x + 3) is the same as (x + 3)^2 OR x^4 โ€“ y^4 as (x^2)^2 - (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 โ€“ y^2)(x^2 + y^2).
HSA.SSE.B HSA.SSE.B
HSA.SSE.B.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

HSF

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HSF.BF HSF.BF
HSF.BF.A HSF.BF.A
HSF.BF.A.1Write a function that describes a relationship between two quantities.
HSF.BF.A.2Write arithmetic and geometric sequences both recursively and with an explicit formula, and translate between the two forms. Use arithmetic and geometric sequences to model situations.
HSF.BF.B HSF.BF.B
HSF.BF.B.3Identify the effect on the graph of replacing f(x) by f(x) + k,k f(x),f(kx),and f(x + k) for specific values of k (k, a constant both positive and negative). Find the value of k given the graphs of the transformed functions. Experiment with multiple transformations and illustrate an explanation of the effects on the graph with or without technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
HSF.BF.B.4Find inverse functions.
HSF.IF HSF.IF
HSF.IF.A HSF.IF.A
HSF.IF.A.3Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example: The Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n + 1) = f(n) + (n โˆ’ 1) for n โ‰ฅ 1.
HSF.IF.B HSF.IF.B
HSF.IF.B.4For a function that models a relationship between two quantities: Interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
HSF.IF.B.5Relate the domain of a function to its graph. Relate the domain of a function to the quantitative relationship it describes. For example: If the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
HSF.IF.B.6Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate the rate of change from a graph.
HSF.IF.C HSF.IF.C
HSF.IF.C.7Graph functions expressed algebraically and show key features of the graph, with and without technology.
HSF.IF.C.8Write expressions for functions in different but equivalent forms to reveal key features of the function.
HSF.LE HSF.LE
HSF.LE.A HSF.LE.A
HSF.LE.A.2Construct linear and exponential equations, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
HSF.LE.A.4Express exponential models as logarithms; Express logarithmic models as exponentials; Use properties of logarithms to simplify and evaluate logarithmic expressions (expanding and/or condensing logarithms as appropriate); Evaluate logarithms with or without technology

HSN

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HSN.CN HSN.CN
HSN.CN.A HSN.CN.A
HSN.CN.A.1Know there is a complex number i such that i^2 = โ€“1, and every complex number has the form a + bi with a and b real.
HSN.CN.A.2Use the relation i^2 = โ€“1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
HSN.CN.A.3Find the conjugate of a complex number. Use conjugates to find quotients of complex numbers.
HSN.CN.C HSN.CN.C
HSN.CN.C.7Solve quadratic equations with real coefficients that have real or complex solutions.
HSN.CN.C.8(+) Extend polynomial identities to the complex numbers. For example: Rewrite x^2 + 4 as (x + 2i)(x - 2i).
HSN.CN.C.9(+) Know the Fundamental Theorem of Algebra; (+) Show that it is true for quadratic polynomials.
HSN.Q HSN.Q
HSN.Q.A HSN.Q.A
HSN.Q.A.2Define appropriate quantities for the purpose of descriptive modeling. (I.E., Use units appropriate to the problem being solved.)
HSN.RN HSN.RN
HSN.RN.A HSN.RN.A
HSN.RN.A.1Explain how extending the properties of integer exponents to rational exponents provides an alternative notation for radicals. For example: We define 5^(4/3) to be the cube root of 5^4 because we want (5^(4/3))^(3/4) = 5 to hold.
HSN.RN.A.2Rewrite expressions involving radicals and rational exponents using the properties of exponents.
HSN.RN.B HSN.RN.B
HSN.RN.B.4Simplify radical expressions. Perform operations (add, subtract, multiply, and divide) with radical expressions. Rationalize denominators and/or numerators
HSN.VM HSN.VM
HSN.VM.C HSN.VM.C
HSN.VM.C.10Understand that: (+) The zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. (+)The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
HSN.VM.C.12(+) Work with 2 ร— 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
HSN.VM.C.6(+) Use matrices to represent and manipulate data (e.g., to represent payoffs or incidence relationships in a network).
HSN.VM.C.7(+) Multiply matrices by scalars to produce new matrices (e.g., as when all of the payoffs in a game are doubled).
HSN.VM.C.8(+) Add, subtract, and multiply matrices of appropriate dimensions.
HSN.VM.C.9(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

HSS

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HSS.IC HSS.IC
HSS.IC.A HSS.IC.A
HSS.IC.A.1Recognize statistics as a process for making inferences about population parameters based on a random sample from that population.
HSS.IC.A.2Compare theoretical and empirical probabilities using simulations (e.g. such as flipping a coin, rolling a number cube, spinning a spinner, and technology).
HSS.IC.B HSS.IC.B
HSS.IC.B.3Recognize the purposes of and differences among sample surveys, experiments, and observational studies. Explain how randomization relates to sample surveys, experiments, and observational studies.
HSS.IC.B.6Read and explain, in context, the validity of data from outside reports by:
HSS.ID HSS.ID
HSS.ID.A HSS.ID.A
HSS.ID.A.4Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators and/or spreadsheets to estimate areas under the normal curve.
HSS.ID.B HSS.ID.B
HSS.ID.B.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

Algebra I Mathematics Standards

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A1.EFE Exponential Functions & Equations
A1.EFE.1Represent and solve real-world problems, using exponential equations in one variable.
A1.EFE.10Write exponential functions that provide a reasonable fit to data and use them to make predictions with technology.
A1.EFE.2Represent real-world problems (growth, decay, and compound interest), using exponential equations.
A1.EFE.3Construct exponential equations from geometric sequences with and without context.
A1.EFE.4Determine the domain and range of exponential functions in mathematical problems.
A1.EFE.5Determine reasonable domain and range values of exponential functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.
A1.EFE.6Interpret the key features of an exponential function that models a relationship between two quantities in a given context.
A1.EFE.7Flexibly use different representations of an exponential function, including graphs, tables, and equations.
A1.EFE.8Interpret the quantities in an exponential equation in the context of a real-world problem, including growth, decay, and compound interest.
A1.EFE.9Graph exponential functions that model real-world problems (growth, decay, and compound interest), showing key attributes.
A1.EX Expressions
A1.EX.1Add, subtract, and multiply polynomials; compare the system of polynomials to the system of integers when performing operations.
A1.EX.2Simplify and perform operations with radical expressions without variables; rationalizing denominators should not include conjugates.
A1.EX.3Simplify algebraic expressions using the laws of exponents.
A1.EX.4Interpret the parts of expressions such as terms, factors, and coefficients in terms of a real-world context.
A1.FN Functions
A1.FN.1Explain that a function assigns each element in the domain to exactly one element in the range.
A1.FN.2Use function notation to represent functions, understanding that if ๐‘“ is a function and ๐‘ฅ is an element of its domain, then ๐‘“(๐‘ฅ) represents the output of ๐‘“ corresponding to the input ๐‘ฅ.
A1.FN.3Graph functions given in function notation, understanding that the graph contains the points (๐‘ฅ,๐‘“(๐‘ฅ)).
A1.FN.4Evaluate functions expressed in function notation for one or more elements in their domains (inputs); use function notation to describe a contextual situation.
A1.FN.5Differentiate between real-world scenarios that can be modeled by exponential or linear functions by determining whether the relationship has a common difference or a common ratio.
A1.FN.6Compare the growth pattern of exponential to linear or quadratic functions using graphs and tables and recognize how exponential growth exceeds other functions.
A1.LFE Linear Functions, Equations, & Inequalities
A1.LFE.1Represent and solve real-world problems, using linear expressions, equations, and inequalities in one variable.
A1.LFE.10Translate among equivalent forms of equations for linear functions, including standard, point-slope, and slope-intercept forms; recognize that each form reveals key features in a given context.
A1.LFE.11Solve systems of linear equations by substitution, elimination, and graphing with and without a real-world context; understand that the solutions will be the same regardless of the method for solving.
A1.LFE.12Solve a system of equations consisting of a linear equation and a quadratic equation in two variables graphically with the assistance of technology.
A1.LFE.13Explain why a solution to the equation ๐‘“(๐‘ฅ)=๐‘”(๐‘ฅ) is the x-coordinate where the y-coordinate of ๐‘“(๐‘ฅ) and ๐‘”(๐‘ฅ) are the same using graphs, tables, or approximations. Include cases where ๐‘“(x) and/or ๐‘”(๐‘ฅ) are linear, quadratic, absolute value, and exponential.
A1.LFE.14Solve linear inequalities and systems of linear inequalities in two variables by graphing.
A1.LFE.15Write linear equations that model the relationship between two quantities and produce a graph of the equation.
A1.LFE.16Graph linear functions expressed as an equation and show intercepts of the graph without technology.
A1.LFE.17Graph absolute value functions expressed as an equation with and without technology, showing intercepts and end behavior.
A1.LFE.18Graph and generalize the effect of transformations on linear and absolute value functions. Transformations include: stretches, compressions, vertical, and horizontal
A1.LFE.19Given the graph of a linear function, explain the effects of the transformation from the parent function, ๐‘ฆ=๐‘ฅ.
A1.LFE.2Construct linear functions from arithmetic sequences with and without context.
A1.LFE.20Write linear functions that provide a reasonable fit to data and use them to make predictions, with and without technology; interpret the slope and y-intercept in context.
A1.LFE.21Calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association.
A1.LFE.22Compare and contrast correlation and causation in real-world problems.
A1.LFE.3Solve linear formulas for a specified variable.
A1.LFE.4Solve linear equations, linear inequalities, and absolute value equations in one variable, including those with rational number coefficients, and variables on both sides of the equal or inequality sign; solve them fluently, explaining the process used.
A1.LFE.5Determine the domain and range of linear functions in mathematical problems.
A1.LFE.6Determine reasonable domain and range values of linear functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.
A1.LFE.7Interpret the key features of a linear and absolute value functions that models a relationship between two quantities in a given context.
A1.LFE.8Flexibly use different representations of a linear function, including graphs, tables, and equations.
A1.LFE.9Calculate and interpret the rate of change of a linear function represented in a table, graph, or as an equation in context of real-world and mathematical problems.
A1.QFE Quadratic Functions & Equations
A1.QFE.1Represent and solve real-world problems using quadratic expressions and equations in one variable.
A1.QFE.10Graph quadratic functions given as an equation or in function notation, labeling key attributes, without technology.
A1.QFE.11Graph and describe the effect of transformations on quadratic functions. Transformations include: stretches, compressions, vertical, and horizontal
A1.QFE.12Given the graph of a quadratic function, explain the effects of the transformation from the parent function, ๐‘ฆ=๐‘ฅ^2.
A1.QFE.13Write quadratic functions that provide a reasonable fit to data and use them to make predictions with technology.
A1.QFE.2Write quadratic equations with real number solutions that model the relationship between two quantities and produce a graph of the equation.
A1.QFE.3Solve quadratic equations with real number solutions, containing one variable, including those with variables on both sides of the equal sign. Equations should be solved by:
A1.QFE.4Determine the domain and range of quadratic functions in mathematical problems.
A1.QFE.5Determine reasonable domain and range values of quadratic functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.
A1.QFE.6Interpret the key features of a quadratic function that models a relationship between two quantities in a given context.
A1.QFE.7Flexibly use different representations of a quadratic function, including graphs, tables, and equations.
A1.QFE.8Explain how each form of a quadratic expression (standard, factored, and vertex form) identifies different key attributes, using the different forms to interpret quantities in context.
A1.QFE.9Use factoring and completing the square to create equivalent forms of quadratic functions to reveal key attributes.
A1.SP Statistics & Probability
A1.SP.1Use box plots and histograms to determine the statistics appropriate to the shape of the data distribution; compare the center and spread of two or more data sets.
A1.SP.2Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points.
A1.SP.3Summarize data from two categorical variables in a frequency table; interpret relative frequencies in the context of the data, recognizing data trends and associations.

Algebra II

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Algebra III

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AR

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AR.3 Students will use mathematical concepts of algebra to explain linear and non-linear applications in real-world scenarios.
AR.3.TM AR.3.TM
AR.3.TM.1Analyze and apply rate of change in terms of real-world scenarios (e.g., rise and run of stair stringers, roof pitch)
AR.3.TM.2Use concepts of systems of equations and inequalities (e.g., tables, graphs, matrix operations, pictorial representations, or algebraic properties) to model and solve real-world scenarios (e.g., compare โ€˜best deal opportunitiesโ€™ with profit and expenses in businesses)
AR.3.TM.3Use linear programming with or without the use of technology to
AR.3.TM.4Collect and organize data, independently and as a collaborative team, to create appropriate graphical representations (e.g., scatterplots, histograms, box plots, circle graphs) of real-world scenarios
AR.3.TM.5Create, interpret, and analyze best-fit models of linear, exponential, and quadratic functions to solve real-world scenarios

Advanced Topics and Modeling in Mathematics

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BF

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Bridge to Algebra II

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Calculus

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CP

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CP.2 CP.2
CP.2.S CP.2.S
CP.2.S.1Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").
CP.2.S.2Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
CP.2.S.3Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
CP.2.S.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. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.
CP.2.S.5Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.
CP.3 CP.3
CP.3.S CP.3.S
CP.3.S.1Find the conditional probability of A given B.
CP.3.S.2Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
CP.3.S.3(+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
CP.3.S.4Use permutations and combinations to compute probabilities of compound events and solve problems.
CP.3.S.5Use visual representations in counting (e.g. combinations, permutations, etc.) including but not limited to:

CS

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CS.2 CS.2
CS.2.AIII CS.2.AIII
CS.2.AIII.1Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers
CS.2.AIII.2Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant; find the equations for the asymptotes of a hyperbola
CS.2.AIII.3Complete the square in order to generate an equivalent form of an equation for a conic section; use that equivalent form to identify key characteristics of the conic section
CS.2.AIII.4Identify, graph, write, and analyze equations of each type of conic section, using properties such as symmetry, intercepts, foci, asymptotes, and eccentricity, and using technology when appropriate
CS.2.AIII.5Solve systems of equations and inequalities involving conics and other types of equations, with and without appropriate technology
CS.5 CS.5
CS.5.PC CS.5.PC
CS.5.PC.1Derive the equation of a circle of given center and radius using the Pythagorean Theorem. Complete the square to find the center and radius of a circle given by an equation.
CS.5.PC.2(+) Derive the equation of a parabola given a focus and directrix.
CS.5.PC.3(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
CS.5.PC.4Find the equations for the asymptotes of a hyperbola
CS.5.PC.5Complete the square in order to generate an equivalent form of an equation for a conic section; use that equivalent form to identify key characteristics of the conic section
CS.5.PC.6Identify, graph, write, and analyze equations of each type of conic section, using properties such as symmetry, intercepts, foci, asymptotes, and eccentricity, and using technology when appropriate
CS.5.PC.7Solve systems of equations and inequalities involving conics and other types of equations, with and without appropriate technology

D

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DMT

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EF

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EF.2 EF.2
EF.2.MAA EF.2.MAA
EF.2.MAA.1Represent constraints by equations or inequalities and by systems of equations and/or inequalities (two and three variable systems); interpret solutions as viable or nonviable options in a modeling context (e.g., represent inequalities describing nutritional and cost constraints on combinations of different foods)
EF.2.MAA.2Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations (e.g., rearrange Ohmโ€™s law V = IR to highlight resistance R)
EF.2.MAA.3Give an informal argument for the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone; use dissection arguments, Cavalieriโ€™s principle, and informal limit arguments
EF.2.MAA.4Give an informal argument using Cavalieriโ€™s principle for the formulas for the volume of a sphere and other solid figures
EF.2.MAA.5Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems

F

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F.1 F.1
F.1.ATMM F.1.ATMM
F.1.ATMM.1Interpret key features of graphs and tables in terms of two quantities for functions beyond the level of quadratic that model a relationship between the quantities
F.1.ATMM.2Graph functions expressed symbolically and show key features of the graph using technology
F.1.ATMM.3Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions
F.1.ATMM.4Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior
F.1.ATMM.5Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available and showing end behavior
F.1.ATMM.6Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude
F.1.ATMM.7Interpret the parameters of functions beyond the level of linear and quadratic in terms of a context
F.1.MAA F.1.MAA
F.1.MAA.1Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers [e.g., the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(nโˆ’1) for n โ‰ฅ 1]
F.1.MAA.10Use the relation i^2 = โ€“1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers
F.1.MAA.11Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers
F.1.MAA.2Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases:
F.1.MAA.3Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function
F.1.MAA.4Compare properties of two functions each represented in a different way: algebraically, graphically, numerically in tables, or by verbal descriptions (e.g., given a graph of one quadratic function and an algebraic expression for another, determine which has the larger maximum)
F.1.MAA.5Write a function that describes a relationship between two quantities:
F.1.MAA.6Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms
F.1.MAA.7Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed
F.1.MAA.8Use inverse functions to solve trigonometric equations that arise in modeling contexts, evaluate the solutions using technology, and interpret them in terms of the context
F.1.MAA.9Know there is a complex number i such that i^2 = โ€“1, and every complex number has the form a + bi with a and b real
F.2 F.2
F.2.ATMM F.2.ATMM
F.2.ATMM.1Model equations in two or more variables to represent relationships between quantities for functions beyond the level of linear and quadratic
F.2.ATMM.2Represent constraints or inequalities using systems of equations and/or inequalities; interpret solutions as viable or non-viable options in a modeling context for functions beyond the level of linear and quadratic
F.2.ATMM.3Compose functions (e.g., If T(y) is the temperature in the atmosphere as a function of height, and h(y) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time)
F.2.ATMM.4Write arithmetic and geometric sequences both recursively and with an explicit formula; use the sequences to model situations and translate between the two forms
F.2.ATMM.5Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed
F.2.ATMM.6Use inverse functions to solve trigonometric equations that arise in modeling context; evaluate the solutions using technology and interpret them in terms of the context
F.6 F.6
F.6.PC F.6.PC
F.6.PC.1Write a function that describes a relationship between two quantities.
F.6.PC.2Find inverse functions.
F.6.PC.3Understand the inverse relationship between exponents and logarithms. Use the inverse relationship between exponents and logarithms to solve problems.
F.7 F.7
F.7.PC F.7.PC
F.7.PC.1Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example: The Fibonacci sequence is defined recursively by (0) = (1) = 1, f(n + 1) = f(n) + (n โˆ’ 1) for n โ‰ฅ 1.
F.7.PC.2Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example: Calculate mortgage payments.
F.7.PC.3(+) Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.
F.7.PC.4For a function that models a relationship between two quantities: Interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Note: Key features may include but not limited to: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
F.7.PC.5Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate the rate of change from a graph.
F.7.PC.6Graph functions expressed algebraically and show key features of the graph, with and without technology.
F.7.PC.7Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
F.7.PC.8Build functions to model real-world applications using algebraic operations on functions and composition, with and without appropriate technology (e.g., profit functions as well as volume and surface area, optimization subject to constraints)

FM

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FM.3 FM.3
FM.3.BTAII FM.3.BTAII
FM.3.BTAII.1Create equations and inequalities in one variable and use them to solve problems. Note: Including but not limited to equations arising from: Linear functions; Quadratic functions; Exponential functions; Absolute value functions
FM.3.BTAII.10Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
FM.3.BTAII.11Write a function that describes a relationship between two quantities.
FM.3.BTAII.12Identify the effect on the graph of replacing f(x) by f(x) + k,k f(x),f(kx),and f(x + k) for specific values of k (k, a constant both positive and negative). Find the value of k given the graphs of the transformed functions. Experiment with multiple transformations and illustrate an explanation of the effects on the graph with or without technology. Include recognizing even and odd functions from their graphs and algebraic representations for them.
FM.3.BTAII.13Solve an equation of the form y = f(x) for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = 2 x^2 or f(x) = (x + 1)/(x โ€“ 1) for x โ‰  1.
FM.3.BTAII.14Define appropriate quantities for the purpose of descriptive modeling (I.E., Use units appropriate to the problem being solved.)
FM.3.BTAII.15Choose a level of accuracy appropriate to limitations on measurement when reporting quantities
FM.3.BTAII.16Solve linear inequalities and systems of linear inequalities in two variables by graphing.
FM.3.BTAII.17Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers [e.g., the Fibonacci sequence is defined recursively by f(0) = f(1) = 1,f(n+1) = f(n) + f(nโˆ’1) for n โ‰ฅ 1]
FM.3.BTAII.18Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another
FM.3.BTAII.19Construct linear and exponential equations, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
FM.3.BTAII.2Create equations in two or more variables to represent relationships between quantities. Graph equations, in two variables, on a coordinate plane.
FM.3.BTAII.20Use the properties of exponents to transform expressions for exponential functions For example: The expression 1.15t can be rewritten as (1.15^(1/12))^(12t) โ‰ˆ 1.012^(12t) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
FM.3.BTAII.3Represent and interpret constraints by equations or inequalities, and by systems of equations and/or inequalities. Interpret solutions as viable or nonviable options in a modeling and/or real-world context.
FM.3.BTAII.4Rearrange literal equations using the properties of equality
FM.3.BTAII.5For a function that models a relationship between two quantities: Interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Note: Key features may include but not limited to: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
FM.3.BTAII.6Relate the domain of a function to its graph. Relate the domain of a function to the quantitative relationship it describes. For example: If the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
FM.3.BTAII.7Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate the rate of change from a graph.
FM.3.BTAII.8Graph functions expressed algebraically and show key features of the graph, with and without technology.
FM.3.BTAII.9Write expressions for functions in different but equivalent forms to reveal key features of the function.

FOP

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FOP.3 FOP.3
FOP.3.AIII FOP.3.AIII
FOP.3.AIII.1Compose functions (e.g., if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time)
FOP.3.AIII.2Verify, by composition, that one function is the inverse of another
FOP.3.AIII.3Read values of an inverse function from a graph or a table, given that the function has an inverse
FOP.3.AIII.4Produce an invertible function from a non-invertible function by restricting the domain
FOP.3.AIII.5Combine standard function types using arithmetic operations (e.g., build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential and relate these functions to the model)
FOP.3.AIII.6Understand the inverse relationship between exponents and logarithms; use this relationship to solve problems involving logarithms and exponents
FOP.3.AIII.7Graph transformations of functions including quadratic, absolute value, square root, cube root, cubic, and step functions; graph piece-wise defined functions including these transformations
FOP.3.AIII.8Determine numerically, graphically, and algebraically if a function is even, odd, or neither

FR

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FR.1 FR.1
FR.1.BTAII FR.1.BTAII
FR.1.BTAII.1Interpret expressions that represent a quantity in terms of its context.
FR.1.BTAII.2Use the structure of an expression to identify ways to rewrite it. For example: See that (x + 3)(x + 3) is the same as (x + 3)^2 OR x^4 โ€“ y^4 as (x^2)^2 - (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 โ€“ y^2)(x^2 + y^2).
FR.1.BTAII.3Add, subtract, and multiply polynomials. Understand that polynomials, like the integers, are closed under addition, subtraction, and multiplication
FR.1.BTAII.4Use various methods to factor quadratic polynomials; understand the relationship between the factored form of a quadratic polynomial and the zeros of a function
FR.1.BTAII.5Identify zeros of polynomials (linear, quadratic) when suitable factorizations are available. Use the zeros to construct a rough graph of the function defined by the polynomial.
FR.1.BTAII.6Solve linear equations, inequalities and absolute value equations in one variable, including equations with coefficients represented by letters.
FR.1.BTAII.7Solve systems of equations in two variables using substitution and elimination. Understand that the solution to a system of equations will be the same when using substitution and elimination.
FR.1.BTAII.8In terms of a context, interpret the parameters (rates of growth or decay, domain and range restrictions where applicable, etc.) in a function.

Geometry Mathematics Standards

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G.5 Students will apply geometric concepts to real-world scenarios.
G.5.TM G.5.TM
G.5.TM.1Identify various geometric figures in order to identify what formulas are needed to solve situational problems (e.g., decompose and rearrange geometric figures)
G.5.TM.2Compute measurements of geometric figures such as area, surface area (including area of sectors), volume, perimeter, and circumference (including arc length) for real-world scenarios
G.5.TM.3Use trigonometric ratios (e.g., sine, cosine, tangent) to calculate angles and lengths of sides in real-world scenarios
G.5.TM.4Analyze how changing dimensions will affect the perimeter, circumference, area, surface area, or volume in real-world scenarios
G.5.TM.5Determine the role angles play in a situational problem (e.g., structural strength and stability, angle straps for lifting, angles used to cut hair)
G.5.TM.6Apply right-triangle relationships using Pythagorean Theorem, special right triangles, and trigonometry in real-world scenarios (e.g., roof construction, building the frame of a car, calculating machined parts)
G.5.TM.7Draw and interpret with or without the use of technology (e.g., house plans, engineering drawings, fashion design)
G.5.TM.8Use cross-sections of three-dimensional shapes to relate to two-dimensional figures
G.5.TM.9Describe the transformation of polygons in the coordinate plane as they relate to real-world scenarios (e.g., cookie cutting, fabric cutting, machine dies)
G.CIR Circles
G.CIR.1Apply the precise definition and standard geometric notation for a circle to understand geometric relationships.
G.CIR.2Recognize and apply relationships between angles, radii, and chords, tangents, and secants including:
G.CIR.3Use the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems.
G.CIR.4Use the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems.
G.CIR.5Explain why the formulas for the area and circumference of a circle work using dissection and informal limit arguments.
G.CIR.6Write the equation of a circle, given the radius and center, where the center is at the origin or another point.
G.CIR.7Identify the center and radius of a circle, given the equation of a circle, where the center is at the origin or another point.
G.CIR.8Apply the equation of a circle to solve real-world problems.
G.GF Geometric Figures
G.GF.1Find the volume and surface area of complex three-dimensional figures composed of prisms, pyramids, cones, cylinders, and spheres.
G.GF.10Calculate the area of triangles and rectangles when given the vertices, including using the distance formula and decomposing figures.
G.GF.11Describe reflectional and rotational symmetry as they apply to a rectangle, parallelogram, trapezoid, or regular polygon.
G.GF.12Calculate probabilities as a proportion of area in a geometric context.
G.GF.2Use three-dimensional geometric figures and their measures to model real-world objects and solve problems.
G.GF.3Explain why the formulas for the volume and surface area of a cylinder, pyramid, and cone work.
G.GF.4Apply the Pythagorean Theorem to determine missing measurements in a three-dimensional figure.
G.GF.5Identify the three-dimensional figure generated by rotating a two-dimensional figure.
G.GF.6Apply theorems about quadrilaterals, including those involving angles, diagonals, and sides to solve problems.
G.GF.7Prove that a given quadrilateral is a parallelogram, rhombus, rectangle, square, kite, or trapezoid, and apply these relationships to solve problems.
G.GF.8Prove and apply theorems about triangles including:
G.GF.9Calculate the perimeter of polygons when given the vertices, including using the distance formula.
G.LA Lines & Angles
G.LA.1Use precise definitions and standard geometric notation for angles, perpendicular lines, parallel lines, and line segments based on the undefined notions of point, line, and distance along a line.
G.LA.2Make formal geometric constructions with a variety of tools and methods including:
G.LA.3Determine the point that cuts a line segment into a specified ratio on a number line and a coordinate plane, including finding the midpoint.
G.LA.4Derive the distance and midpoint formulas and use the formulas, including the slope formula, to verify geometric relationships on a coordinate plane.
G.LA.5Prove and apply slope criteria of parallel and perpendicular lines to solve problems.
G.LA.6Write an equation of a line that is parallel or perpendicular to a given line and passing through a given point.
G.LA.7Prove and apply theorems about lines and angles including:
G.RT Right Triangles
G.RT.1Apply the properties of special right triangles (30ยฐ-60ยฐ-90ยฐ and 45ยฐ-45ยฐ-90ยฐ) to solve real-world and mathematical problems.
G.RT.2Prove and apply the Pythagorean Theorem and its converse.
G.RT.3Explain how the definitions for trigonometric ratios are developed by similarity and how the side ratios in right triangles are properties of the angles in the triangle.
G.RT.4Explain the relationship between the sine and cosine of complementary angles and use them to solve problems.
G.RT.5Determine the sine, cosine, and tangent ratios of acute angles given the side lengths of right triangles.
G.RT.6Use trigonometric ratios (sine, cosine, and tangent) to calculate missing side lengths and angle measures in a right triangle, including applications of angles of elevation and depression; include real-world and mathematical problems.
G.SC Similarities & Congruence
G.SC.1Given two figures, apply the definition of similarity in terms of a dilation to identify similar figures, proportional sides, and corresponding congruent angles.
G.SC.2Develop and apply the criteria of similarity for triangles (AA~, SAS~, and SSS~) to solve problems and prove geometric relationships.
G.SC.3Use transformations to prove all circles are similar.
G.SC.4Explain, using rigid motion transformations, why two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G.SC.5Develop and apply the criteria for triangle congruence (ASA, SAS, AAS, SSS, and HL) to solve problems and prove geometric relationships.
G.TRF Transformations
G.TRF.1Describe rotations, reflections, and translations as functions that take points in the coordinate plane as inputs and give other points as outputs; write in prime notation.
G.TRF.2Compare transformations that preserve distance and angle (rotations, reflections, and translations) to those that do not (dilations) to develop definitions for congruence and similarity.
G.TRF.3Apply understanding of angles, circles, perpendicular lines, parallel lines, and line segments to develop definitions for rotations, reflections, and translations.
G.TRF.4Use geometric constructions to represent rotations, reflections, translations, and dilations in the plane with a variety of tools and methods.
G.TRF.5Given two congruent figures, identify the sequence of transformations that maps one figure to another.

I

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I.3 I.3
I.3.C I.3.C
I.3.C.1Define the definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval โˆซ{a to b} fโ€™(x)dx = f(b) โ€“ f(a)
I.3.C.2Determine the area between two curves, and identify the definite integral as the area of the region bounded by two curves
I.3.C.3Apply the Fundamental Theorem of Calculus to solve contextual models that represent real-world phenomena
I.3.C.4Compute indefinite integrals
I.3.C.5Determine the antiderivative of a function using rules of basic differentiation, and solve problems using the techniques of anti-differentiation
I.3.C.6Estimate definite integrals by using Riemann sums and trapezoidal sums, and identify the definite integral as a limit of Riemann sums
I.3.C.7Explore and apply different integration techniques

IC

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IF

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IF.4 IF.4
IF.4.AIII IF.4.AIII
IF.4.AIII.1Graph rational functions identifying zeros and asymptotes when suitable factorizations are available; show end behavior
IF.4.AIII.2Analyze and interpret polynomial functions numerically, graphically, and algebraically, identifying key characteristics such as intercepts, end behavior, domain and range, relative and absolute maximum and minimum, as well as intervals over which the function increases and decreases
IF.4.AIII.3Analyze and interpret rational functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes (vertical, horizontal, and slant), end behavior, point discontinuities, intercepts, and domain and range
IF.4.AIII.4Analyze and interpret exponential functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes, end behavior, intercepts, and domain and range
IF.4.AIII.5Analyze and interpret logarithmic functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes, end behavior, intercepts, and domain and range
IF.4.AIII.6Build functions to model real-world applications using algebraic operations on functions and composition of functions, with and without appropriate technology [e.g., profit functions as well as volume and surface area (optimization subject to constraints)]

LC

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LC.1 LC.1
LC.1.C LC.1.C
LC.1.C.1Identify vertical asymptotes in rational and logarithmic functions by identifying locations where the function value approaches infinity; estimate limits numerically and graphically; calculate limits analytically:
LC.1.C.2Calculate infinite limits and use the result to identity vertical asymptotes in rational and logarithmic functions
LC.1.C.3Calculate limits at infinity and use the result to identify horizontal asymptotes in rational and exponential functions
LC.1.C.4Calculate limits at infinity and use the result to identify unbounded behavior in rational, exponential, and logarithmic functions
LC.1.C.5Identify and classify graphically, algebraically, and numerically if a discontinuity is removable or non-removable; identify the three conditions that must exist in order for a function to be continuous at x = a:
LC.1.C.6Apply the Intermediate Value Theorem for continuous functions

M

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M.1 M.1
M.1.QL M.1.QL
M.1.QL.1Demonstrate understanding of the meaning of a solution and identify when insufficient information is given to solve a problem
M.1.QL.2Analyze mathematical models, describe limitations, and suggest improvements
M.1.QL.3Use mathematical models created with spreadsheets or other tools to: estimate solutions for contextual questions; identify patterns; identify how changing parameters affect results.
M.1.QL.4Use mathematical models to make decisions about purchases (e.g., buying a vehicle, home improvement, fashion trends).
M.1.QL.5Create and use mathematical models for bivariate data sets to: answer questions; draw conclusions; make decisions
M.4 Students will apply measurement and use measurement tools in real-world scenarios.
M.4.TM M.4.TM
M.4.TM.1Convert between and within the metric system and the U.S. customary system in real-world scenarios
M.4.TM.2Apply accurate readings of both metric and the U.S. customary measuring devices to a problem situation
M.4.TM.3Select and use appropriate measuring devices (e.g., rulers, tape measures, calipers, gauges) and understand the limitations of such devices (e.g., flat surfaces, curved surfaces) for real-world scenarios
M.4.TM.4Determine and use appropriate unit labels (e.g., length, distance, area, surface area, volume, weight, voltage, resistance, pressure, density) for real-world scenarios

Mathematical Applications and Algorithms

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MD

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MD.4 MD.4
MD.4.S MD.4.S
MD.4.S.1(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
MD.4.S.2(+) Calculate the expected value of a random variable. (+) Interpret the expected value of a random variable as the mean of the probability distribution.
MD.4.S.3(+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated. (+) Find the expected value. For example: Find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.
MD.4.S.4(+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically. (+) Find the expected value. For example: Find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?
MD.5 MD.5
MD.5.S MD.5.S
MD.5.S.1(+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
MD.5.S.2(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
MD.5.S.3(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

MO

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MO.1 MO.1
MO.1.AIII MO.1.AIII
MO.1.AIII.1Use matrices to represent and manipulate data (e.g., to represent payoffs or incidence relationships in a network)
MO.1.AIII.2Multiply matrices by scalars to produce new matrices (e.g., as when all of the payoffs in a game are doubled)
MO.1.AIII.3Add, subtract, and multiply matrices of appropriate dimensions
MO.1.AIII.4Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties
MO.1.AIII.5Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers; the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse
MO.1.AIII.6Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector; work with matrices as transformations of vectors
MO.1.AIII.7Work with 2 X 2 matrices as transformations of the plane; interpret the absolute value of the determinant in terms of area
MO.1.AIII.8Represent a system of linear equations as a single matrix equation in a vector variable
MO.1.AIII.9Find the inverse of a matrix if it exists; use the inverse to solve systems of linear equations using technology for matrices of dimension 3 X 3 or greater
MO.4 MO.4
MO.4.ATMM MO.4.ATMM
MO.4.ATMM.1Use matrices to represent and manipulate data (e.g., to represent payoffs or incidence relationships in a network)
MO.4.ATMM.2Multiply matrices by scalars to produce new matrices (e.g., all the payoffs in a game are doubled)
MO.4.ATMM.3Add, subtract, and multiply matrices of appropriate dimensions
MO.4.ATMM.4Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties
MO.4.ATMM.5Understand that zero and identity matrices play a role in matrix addition and multiplication similar to 0 and 1 in real numbers; the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse
MO.4.ATMM.6Represent a system of linear equations as a single matrix equation in a vector variable
MO.4.ATMM.7Find the inverse of a matrix if it exists, and use it to solve systems of linear equations; utilize technology to find the inverse of matrices with dimensions of 3 x 3 or greater

MPM

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MPM.2 Students will use mathematical processes and models to acquire, demonstrate, and communicate mathematical understanding in real-world scenarios.
MPM.2.TM MPM.2.TM
MPM.2.TM.1Apply mathematics to problems arising in everyday life, workplace, and society
MPM.2.TM.2Use mathematical processes with algebraic formulas (e.g., literal equations), numerical techniques, and graphs to solve real-world scenarios
MPM.2.TM.3Create mathematical models and use problem-solving skills, independently and as a collaborative team, for real-world scenarios to
MPM.2.TM.4Select appropriate tools (e.g., real objects, manipulatives, paper and pencil, technology) and techniques (e.g., mental math, estimation, number sense) to solve problems
MPM.2.TM.5Demonstrate effective use of resources (e.g., faculty, other students, reference materials, industry resources, the internet)
MPM.2.TM.6Use precise mathematical language and multiple representations (e.g., symbols, diagrams, graphs, written language) to communicate, independently and as a collaborative team, written or orally (e.g., reports, presentations, demonstrations), mathematical ideas or solutions to real-world scenarios

NPR

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NPR.1 Students will use number sense and proportional reasoning in real-world scenarios to make and communicate decisions in order to draw conclusions.
NPR.1.TM NPR.1.TM
NPR.1.TM.1Use estimation to identify the most reasonable mathematical solution
NPR.1.TM.2Use estimation and precision in real-world scenarios
NPR.1.TM.3Solve real world-problems and interpret results involving calculations with percentages, decimals, and fractions
NPR.1.TM.4Recognize, set up, and solve proportions from real-world scenarios
NPR.1.TM.5Utilize real-world scenarios requiring interpretation and comparison of various representations of rates, ratios, and proportions including scale drawings
NPR.1.TM.6Compare magnitudes of numbers in context in different forms (e.g., place value, Richter scale, scientific notation, powers of 10)
NPR.1.TM.7Use dimensional analysis to solve problems involving multiple units of measurement (e.g., convert between and within the metric system and the U.S. customary system, determine miles per gallon, appropriate dosages of medicine)

NQ

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NQ.1 NQ.1
NQ.1.PC NQ.1.PC
NQ.1.PC.1Find the conjugate of a complex number. Use conjugates to find quotients of complex numbers. (+)Use conjugates to find moduli.
NQ.1.PC.2(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers). (+) Explain why the rectangular and polar forms of a given complex number represent the same number.
NQ.1.PC.3(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; (+) Use properties of geometrical representation for computation. For example: (-1 + iโˆš3)^3 = 8 because (-1 + โˆš3 i) has modulus 2 and argument 120ยฐ.
NQ.1.PC.4(+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
NQ.2 NQ.2
NQ.2.PC NQ.2.PC
NQ.2.PC.1(+) Recognize vector quantities as having both magnitude and direction. (+) Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).
NQ.2.PC.2(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
NQ.2.PC.3Solve problems involving velocity and other quantities that can be represented by vectors.
NQ.2.PC.4(+) Add and subtract vectors.
NQ.2.PC.5(+) Multiply a vector by a scalar.
NQ.2.PC.6(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. (+) Work with matrices as transformations of vectors.

NR

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NR.2 NR.2
NR.2.QL NR.2.QL
NR.2.QL.1Solve real world problems and interpret results involving calculations with percentages, decimals, and fractions: conversions; percent change (absolute vs relative); percent of quantities
NR.2.QL.2Use estimation in real world situations: know when; know how; know why
NR.2.QL.3Identify appropriate numeric benchmarks (e.g., use 10% as an estimation for 12%) for estimating calculations. Identify appropriate contextual benchmarks (e.g., population for Arkansas, the United States, and the world) to compare to other numbers (e.g., reasonableness of statistical claims, giving context to numbers)
NR.2.QL.4Compare magnitudes of numbers in context in different forms (e.g., millions, billions, trillions, national debt, Richter scale, scientific notation)
NR.2.QL.5Use dimensional analysis to solve problems involving multiple units of measurement (e.g., converting between currencies, determine miles per gallon, appropriate dosages of medicine)
NR.2.QL.6Solve real world problems requiring interpretation and comparison of various representations of rates and ratios
NR.2.QL.7Distinguish between proportional and non-proportional real world situations

Pre-Calculus

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PD

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PF

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PF.4 PF.4
PF.4.QL PF.4.QL
PF.4.QL.1Represent and analyze mathematical models for various types of income (e.g., commission, salary, hourly wage, overtime)
PF.4.QL.2Represent and analyze various types of income deductions (e.g., federal and state income taxes, Social Security, Medicare taxes, pre-tax deductions) and employment forms (W-2, W-4, I-9)
PF.4.QL.3Analyze expenses to create a household budget utilizing food, shelter, transportation, utilities, insurance, savings, and other expenses (charitable giving)
PF.4.QL.4Analyze various investment instruments for: purposes; advantages; disadvantages; risks (e.g., savings, checking accounts, certificates of deposit, stocks, social security, individual retirement accounts, bonds, annuities)
PF.4.QL.5Analyze the characteristics of various types of loans (e.g., credit cards, personal loans, student loans, auto financing, mortgages)
PF.4.QL.6Apply appropriate models to determine the impact of the relationship among loan rates, the term of a loan, the principle amount of a loan, and payments (e.g., amortization table, spreadsheet, compound interest, annual interest rates, continuous rates)
PF.4.QL.7Examine consumer protection, bankruptcy, and debt and credit management services for ways in which they affect household budgeting

PI

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PI.6 PI.6
PI.6.MAA PI.6.MAA
PI.6.MAA.1Create, edit, and execute a program utilizing an array in a programmable calculator and spreadsheet application
PI.6.MAA.2Create, edit, and execute programs using recursions and loops in a programmable calculator and spreadsheet application
PI.6.MAA.3Create, edit, and execute programs to calculate mathematical formulas (e.g., quadratic formula, volume of a simple solid)
PI.6.MAA.4Develop functional programs from algorithms developed from the mathematical models
PI.6.MAA.5Create programs using various display modes including tables and graphs
PI.6.MAA.6Locate, categorize, and implement programming commands
PI.6.MAA.7Use subroutines to reduce keystrokes and memory use
PI.6.MAA.8Use a spreadsheet application to sort data using various methods (e.g., bubble, quick, shell)

PS

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PS.4 PS.4
PS.4.MAA PS.4.MAA
PS.4.MAA.1Analyze and interpret graphs, charts, and tables in the design and implementation of a computer program
PS.4.MAA.2Write an algorithm to solve mathematical problems using formulas, equations, and functions
PS.4.MAA.3Analyze and interpret truth tables from basic statements using Boolean operators (AND, OR, XOR, and NOT)
PS.4.MAA.4Write an algorithm from a mathematical model
PS.5 PS.5
PS.5.ATMM PS.5.ATMM
PS.5.ATMM.1Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions
PS.5.ATMM.2Calculate the expected value of a random variable; interpret it as the mean of the probability distribution
PS.5.ATMM.3Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value (e.g., find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices; find the expected grade under various grading schemes)
PS.5.ATMM.4Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value (e.g., find a current data distribution on the number of TV sets per household in the United States and calculate the expected number of sets per household; how many TV sets would you expect to find in 100 randomly selected households?)
PS.5.ATMM.5Find the expected payoff for a game of chance (e.g., find the expected winnings from a state lottery or a game at a fast-food restaurant)
PS.5.ATMM.6Evaluate and compare strategies on the basis of expected values (e.g., compare a high-deductible versus a low-deductible automobile insurance policy using various but reasonable chances of having a minor or major accident)

Quantitative Literacy

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RF

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RF.2 RF.2
RF.2.BTAII RF.2.BTAII
RF.2.BTAII.1Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); Find the solutions approximately by: Using technology to graph the functions; Making tables of values; Finding successive approximations. Include cases (but not limited to) where f(x) and/or g(x) are: Linear, Polynomial, Absolute value, Exponential
RF.2.BTAII.2Graph functions expressed algebraically and show key features of the graph, with and without technology.
RF.2.BTAII.3Explain how extending the properties of integer exponents to rational exponents provides an alternative notation for radicals. For example: We define 5^(4/3) to be the cube root of 5^4 because we want (5^(4/3))^(3/4) = 5 to hold.
RF.2.BTAII.4Rewrite expressions involving radicals and rational exponents using the properties of exponents
RF.2.BTAII.5Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or any polynomial function.
RF.2.BTAII.6Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
RF.2.BTAII.7Solve quadratic equations in one variable.
RF.2.BTAII.8Solve systems of equations consisting of linear equations and nonlinear equations in two variables algebraically and graphically. For example: Find the points of intersection between y = -3x and y = x^2 + 2.

Statistics

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SEM

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SEM.3 SEM.3
SEM.3.MAA SEM.3.MAA
SEM.3.MAA.1Represent a system of linear equations as a single matrix equation in a vector variable
SEM.3.MAA.2Find the inverse of a matrix if it exists and use it to solve systems of linear equations; use technology for matrices of dimension 3 ร— 3 or greater
SEM.3.MAA.3Use matrices to represent and manipulate data (e.g., to represent payoffs or incidence relationships in a network)
SEM.3.MAA.4Multiply matrices by scalars to produce new matrices (e.g., as when all of the payoffs in a game are doubled)
SEM.3.MAA.5Add, subtract, and multiply matrices of appropriate dimensions
SEM.3.MAA.6Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation but still satisfies the associative and distributive properties
SEM.3.MAA.7Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers; the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse
SEM.3.MAA.8Work with 2 ร— 2 matrices as transformations of the plane and interpret the absolute value of the determinant in terms of area

SP

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SP.3 SP.3
SP.3.QL SP.3.QL
SP.3.QL.1Create and use charts, tables, and graphs of real world data (with and without technology)
SP.3.QL.2Analyze charts, tables and graphs of real world data. Interpret charts, tables and graphs of real world data. Compare charts, tables and graphs of real world data
SP.3.QL.3Analyze statistical information from studies, surveys, and polls to make informed judgements as to the validity of claims or conclusions (e.g., bias, limitations, sampling, causation vs correlation, misuse of statistics)
SP.3.QL.4Make decisions about data summarized numerically using measures of center: compare measures of center of two or more data sets; interpret the differences in context; justify the use of a chosen measure
SP.3.QL.5Use probabilities to make and justify decisions about risks in everyday life (e.g., types of investments, taking medication, selecting car insurance, playing the lottery)
SP.3.QL.6Evaluate the validity of claims based on experimental and theoretical probabilities
SP.3.QL.7Apply rules of counting and probability to compute probabilities of compound real world events: addition rule; multiplication rule; Fundamental Counting Principle; permutation and combinations; visual representations (e.g., Venn diagrams, tree diagrams, lists, two-way tables)
SP.4 SP.4
SP.4.BTAII SP.4.BTAII
SP.4.BTAII.1Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets
SP.4.BTAII.2Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
SP.4.BTAII.3Compute (using technology) and interpret the correlation coefficient of a linear fit.

SS

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T

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T.3 T.3
T.3.PC T.3.PC
T.3.PC.1Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
T.3.PC.2Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed around the unit circle.
T.3.PC.3(+) Use special right triangles to determine geometrically the exact values of sine, cosine, tangent for ฯ€/3, ฯ€/4, ฯ€/6, and ฯ€/2. (+) Use the unit circle to express the values of sine, cosine, and tangent for ฯ€-x, ฯ€+x, and 2ฯ€-x in terms of their exact values for x where x is any real number.
T.3.PC.4(+) Develop the Pythagorean identity, sin^2(ฮธ) + cos^2(ฮธ) = 1. (+) Given sin(ฮธ) , cos(ฮธ), or tan(ฮธ) and the quadrant of the angle, use the Pythagorean identity to find the remaining trigonometric functions.
T.3.PC.5(+) Develop the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
T.3.PC.6Derive the formula A = (ยฝ)ab sin C for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
T.3.PC.7Prove the Law of Sines and the Law of Cosines and use them to solve problems.
T.3.PC.8(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.
T.3.PC.9Define and use reciprocal functions, cosecant, secant, and cotangent to solve problems.
T.4 T.4
T.4.PC T.4.PC
T.4.PC.1Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions
T.4.PC.2Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
T.4.PC.3(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
T.4.PC.4(+) Use inverse functions to: Solve trigonometric equations that arise in modeling context(s); Evaluate the solutions of trigonometric equations, with or without technology, and Interpret the solutions of trigonometric equations in terms of the context(s).
T.4.PC.5Recognize that some trigonometric equations have infinitely many solutions and be able to state a general formula to represent the infinite solutions

Technical Math for College and Career

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V

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V.3 V.3
V.3.ATMM V.3.ATMM
V.3.ATMM.1Recognize vector quantities as having both magnitude and direction; represent vector quantities by directed line segments and use appropriate symbols for vector and their magnitudes (e.g., v,|v|,||v||,v)
V.3.ATMM.2Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point
V.3.ATMM.3Solve problems involving velocity and other quantities that can be represented by vectors
V.3.ATMM.4Add vectors end-to-end, component-wise, and by the parallelogram rule; understand that the magnitude of a sum of two vectors is typically not the sum of magnitudes
V.3.ATMM.5Determine the magnitude and direction of the sum of two given vectors in magnitude and direction form
V.3.ATMM.6Understand vector subtraction; v - w as v + (-w), where โ€“w is the additive inverse of w, with the same magnitude as w pointing in the opposite direction; represent vector subtraction graphically by connecting the tips in the appropriate order and perform vector subtraction component-wise
V.3.ATMM.7Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise [e.g., as c(vx,vy) = (c vx ,c vy)]
V.3.ATMM.8Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v; compute the direction of cv knowing that when the |c|v โ‰  0, the direction cv is either along v (for c > 0 ) or against v (c < 0)

AP Calculus Learning Objectives

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

AP Statistics Learning Objectives

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

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