Florida Math Standards - B.E.S.T.

884 standards, Kindergarten through AP.

Benchmarks for Excellent Student Thinking (B.E.S.T.), adopted in 2020, replaced Common Core with a structure organized by benchmarks within consistent domains (NSO, AR, GR, and others). The format prioritizes benchmark level clarity while keeping domains stable across grade bands.

Kindergarten

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MA.K.AR Algebraic Reasoning
MA.K.AR.1 Represent and solve addition problems with sums between 0 and 10 and subtraction problems using related facts.
MA.K.AR.1.1For any number from 1 to 9, find the number that makes 10 when added to the given number.
MA.K.AR.1.2Given a number from 0 to 10, find the different ways it can be represented as the sum of two numbers.
MA.K.AR.1.3Solve addition and subtraction real-world problems using objects, drawings or equations to represent the problem.
MA.K.AR.2 Develop an understanding of the equal sign.
MA.K.AR.2.1Explain why addition or subtraction equations are true using objects or drawings.
MA.K.DP Data Analysis and Probability
MA.K.DP.1 Develop an understanding for collecting, representing and comparing data.
MA.K.DP.1.1Collect and sort objects into categories and compare the categories by counting the objects in each category. Report the results verbally, with a written numeral or with drawings.
MA.K.GR Geometric Reasoning
MA.K.GR.1 Identify, compare and compose two- and three-dimensional figures.
MA.K.GR.1.1Identify two- and three-dimensional figures regardless of their size or orientation. Figures are limited to circles, triangles, rectangles, squares, spheres, cubes, cones and cylinders.
MA.K.GR.1.2Compare two-dimensional figures based on their similarities, differences and positions. Sort two-dimensional figures based on their similarities and differences. Figures are limited to circles, triangles, rectangles and squares.
MA.K.GR.1.3Compare three-dimensional figures based on their similarities, differences and positions. Sort three-dimensional figures based on their similarities and differences. Figures are limited to spheres, cubes, cones and cylinders.
MA.K.GR.1.4Find real-world objects that can be modeled by a given two- or three-dimensional figure. Figures are limited to circles, triangles, rectangles, squares, spheres, cubes, cones and cylinders.
MA.K.GR.1.5Combine two-dimensional figures to form a given composite figure. Figures used to form a composite shape are limited to triangles, rectangles and squares.
MA.K.M Measurement
MA.K.M.1 Identify and compare measurable attributes of objects.
MA.K.M.1.1Identify the attributes of a single object that can be measured such as length, volume or weight.
MA.K.M.1.2Directly compare two objects that have an attribute which can be measured in common. Express the comparison using language to describe the difference.
MA.K.M.1.3Express the length of an object, up to 20 units long, as a whole number of lengths by laying non-standard objects end to end with no gaps or overlaps.
MA.K.NSO Number Sense and Operations
MA.K.NSO.1 Develop an understanding for counting using objects in a set.
MA.K.NSO.1.1Given a group of up to 20 objects, count the number of objects in that group and represent the number of objects with a written numeral. State the number of objects in a rearrangement of that group without recounting.
MA.K.NSO.1.2Given a number from 0 to 20, count out that many objects.
MA.K.NSO.1.3Identify positions of objects within a sequence using the words “first,” “second,” “third,” “fourth” or “fifth.”
MA.K.NSO.1.4Compare the number of objects from 0 to 20 in two groups using the terms less than, equal to or greater than.
MA.K.NSO.2 Recite number names sequentially within 100 and develop an understanding for place value.
MA.K.NSO.2.1Recite the number names to 100 by ones and by tens. Starting at a given number, count forward within 100 and backward within 20.
MA.K.NSO.2.2Represent whole numbers from 10 to 20, using a unit of ten and a group of ones, with objects, drawings and expressions or equations.
MA.K.NSO.2.3Locate, order and compare numbers from 0 to 20 using the number line and terms less than, equal to or greater than.
MA.K.NSO.3 Develop an understanding of addition and subtraction operations with one-digit whole numbers.
MA.K.NSO.3.1Explore addition of two whole numbers from 0 to 10, and related subtraction facts.
MA.K.NSO.3.2Add two one-digit whole numbers with sums from 0 to 10 and subtract using related facts with procedural reliability.

Grade 1

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MA.1.AR Algebraic Reasoning
MA.1.AR.1 Solve addition problems with sums between 0 and 20 and subtraction problems using related facts.
MA.1.AR.1.1Apply properties of addition to find a sum of three or more whole numbers.
MA.1.AR.1.2Solve addition and subtraction real-world problems using objects, drawings or equations to represent the problem.
MA.1.AR.2 Develop an understanding of the relationship between addition and subtraction.
MA.1.AR.2.1Restate a subtraction problem as a missing addend problem using the relationship between addition and subtraction.
MA.1.AR.2.2Determine and explain if equations involving addition or subtraction are true or false.
MA.1.AR.2.3Determine the unknown whole number in an addition or subtraction equation, relating three whole numbers, with the unknown in any position.
MA.1.DP Data Analysis and Probability
MA.1.DP.1 Collect, represent and interpret data using pictographs and tally marks.
MA.1.DP.1.1Collect data into categories and represent the results using tally marks or pictographs.
MA.1.DP.1.2Interpret data represented with tally marks or pictographs by calculating the total number of data points and comparing the totals of different categories.
MA.1.FR Fractions
MA.1.FR.1 Develop an understanding of fractions by partitioning shapes into halves and fourths.
MA.1.FR.1.1Partition circles and rectangles into two and four equal-sized parts. Name the parts of the whole using appropriate language including halves or fourths.
MA.1.GR Geometric Reasoning
MA.1.GR.1 Identify and analyze two- and three-dimensional figures based on their defining attributes.
MA.1.GR.1.1Identify, compare and sort two- and three-dimensional figures based on their defining attributes. Figures are limited to circles, semi-circles, triangles, rectangles, squares, trapezoids, hexagons, spheres, cubes, rectangular prisms, cones and cylinders.
MA.1.GR.1.2Sketch two-dimensional figures when given defining attributes. Figures are limited to triangles, rectangles, squares and hexagons.
MA.1.GR.1.3Compose and decompose two- and three-dimensional figures. Figures are limited to semi-circles, triangles, rectangles, squares, trapezoids, hexagons, cubes, rectangular prisms, cones and cylinders.
MA.1.GR.1.4Given a real-world object, identify parts that are modeled by two- and three-dimensional figures. Figures are limited to semi-circles, triangles, rectangles, squares and hexagons, spheres, cubes, rectangular prisms, cones and cylinders.
MA.1.M Measurement
MA.1.M.1 Compare and measure the length of objects.
MA.1.M.1.1Estimate the length of an object to the nearest inch. Measure the length of an object to the nearest inch or centimeter.
MA.1.M.1.2Compare and order the length of up to three objects using direct and indirect comparison.
MA.1.M.2 Tell time and identify the value of coins and combinations of coins and dollar bills.
MA.1.M.2.1Using analog and digital clocks, tell and write time in hours and half-hours.
MA.1.M.2.2Identify pennies, nickels, dimes and quarters, and express their values using the ¢ symbol. State how many of each coin equal a dollar.
MA.1.M.2.3Find the value of combinations of pennies, nickels and dimes up to one dollar, and the value of combinations of one, five and ten dollar bills up to $100. Use the ¢ and $ symbols appropriately.
MA.1.NSO Number Sense and Operations
MA.1.NSO.1 Extend counting sequences and understand the place value of two-digit numbers.
MA.1.NSO.1.1Starting at a given number, count forward and backwards within 120 by ones. Skip count by 2s to 20 and by 5s to 100.
MA.1.NSO.1.2Read numbers from 0 to 100 written in standard form, expanded form and word form. Write numbers from 0 to 100 using standard form and expanded form.
MA.1.NSO.1.3Compose and decompose two-digit numbers in multiple ways using tens and ones. Demonstrate each composition or decomposition with objects, drawings and expressions or equations.
MA.1.NSO.1.4Plot, order and compare whole numbers up to 100.
MA.1.NSO.2 Develop an understanding of addition and subtraction operations with one- and two-digit numbers.
MA.1.NSO.2.1Recall addition facts with sums to 10 and related subtraction facts with automaticity.
MA.1.NSO.2.2Add two whole numbers with sums from 0 to 20, and subtract using related facts with procedural reliability.
MA.1.NSO.2.3Identify the number that is one more, one less, ten more and ten less than a given two-digit number.
MA.1.NSO.2.4Explore the addition of a two-digit number and a one-digit number with sums to 100.
MA.1.NSO.2.5Explore subtraction of a one-digit number from a two-digit number.

Grade 2

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MA.2.AR Algebraic Reasoning
MA.2.AR.1 Solve addition problems with sums between 0 and 100 and related subtraction problems.
MA.2.AR.1.1Solve one- and two-step addition and subtraction real-world problems.
MA.2.AR.2 Demonstrate an understanding of equality and addition and subtraction.
MA.2.AR.2.1Determine and explain whether equations involving addition and subtraction are true or false.
MA.2.AR.2.2Determine the unknown whole number in an addition or subtraction equation, relating three or four whole numbers, with the unknown in any position.
MA.2.AR.3 Develop an understanding of multiplication.
MA.2.AR.3.1Represent an even number using two equal groups or two equal addends. Represent an odd number using two equal groups with one left over or two equal addends plus 1.
MA.2.AR.3.2Use repeated addition to find the total number of objects in a collection of equal groups. Represent the total number of objects using rectangular arrays and equations.
MA.2.DP Data Analysis and Probability
MA.2.DP.1 Collect, categorize, represent and interpret data using appropriate titles, labels and units.
MA.2.DP.1.1Collect, categorize and represent data using tally marks, tables, pictographs or bar graphs. Use appropriate titles, labels and units.
MA.2.DP.1.2Interpret data represented with tally marks, tables, pictographs or bar graphs including solving addition and subtraction problems.
MA.2.FR Fractions
MA.2.FR.1 Develop an understanding of fractions.
MA.2.FR.1.1Partition circles and rectangles into two, three or four equal-sized parts. Name the parts using appropriate language, and describe the whole as two halves, three thirds or four fourths.
MA.2.FR.1.2Partition rectangles into two, three or four equal-sized parts in two different ways showing that equal-sized parts of the same whole may have different shapes.
MA.2.GR Geometric Reasoning
MA.2.GR.1 Identify and analyze two-dimensional figures and identify lines of symmetry.
MA.2.GR.1.1Identify and draw two-dimensional figures based on their defining attributes. Figures are limited to triangles, rectangles, squares, pentagons, hexagons and octagons.
MA.2.GR.1.2Categorize two-dimensional figures based on the number and length of sides, number of vertices, whether they are closed or not and whether the edges are curved or straight.
MA.2.GR.1.3Identify line(s) of symmetry for a two-dimensional figure.
MA.2.GR.2 Describe perimeter and find the perimeter of polygons.
MA.2.GR.2.1Explore perimeter as an attribute of a figure by placing unit segments along the boundary without gaps or overlaps. Find perimeters of rectangles by counting unit segments.
MA.2.GR.2.2Find the perimeter of a polygon with whole-number side lengths. Polygons are limited to triangles, rectangles, squares and pentagons.
MA.2.M Measurement
MA.2.M.1 Measure the length of objects and solve problems involving length.
MA.2.M.1.1Estimate and measure the length of an object to the nearest inch, foot, yard, centimeter or meter by selecting and using an appropriate tool.
MA.2.M.1.2Measure the lengths of two objects using the same unit and determine the difference between their measurements.
MA.2.M.1.3Solve one- and two-step real-world measurement problems involving addition and subtraction of lengths given in the same units.
MA.2.M.2 Tell time and solve problems involving money.
MA.2.M.2.1Using analog and digital clocks, tell and write time to the nearest five minutes using a.m. and p.m. appropriately. Express portions of an hour using the fractional terms half an hour, half past, quarter of an hour, quarter after and quarter til.
MA.2.M.2.2Solve one- and two-step addition and subtraction real-world problems involving either dollar bills within $100 or coins within 100¢ using $ and ¢ symbols appropriately.
MA.2.NSO Number Sense and Operations
MA.2.NSO.1 Understand the place value of three-digit numbers.
MA.2.NSO.1.1Read and write numbers from 0 to 1,000 using standard form, expanded form and word form.
MA.2.NSO.1.2Compose and decompose three-digit numbers in multiple ways using hundreds, tens and ones. Demonstrate each composition or decomposition with objects, drawings and expressions or equations.
MA.2.NSO.1.3Plot, order and compare whole numbers up to 1,000.
MA.2.NSO.1.4Round whole numbers from 0 to 100 to the nearest 10.
MA.2.NSO.2 Add and subtract two- and three-digit whole numbers.
MA.2.NSO.2.1Recall addition facts with sums to 20 and related subtraction facts with automaticity.
MA.2.NSO.2.2Identify the number that is ten more, ten less, one hundred more and one hundred less than a given three-digit number.
MA.2.NSO.2.3Add two whole numbers with sums up to 100 with procedural reliability. Subtract a whole number from a whole number, each no larger than 100, with procedural reliability.
MA.2.NSO.2.4Explore the addition of two whole numbers with sums up to 1,000. Explore the subtraction of a whole number from a whole number, each no larger than 1,000.

Grade 3

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MA.3.AR Algebraic Reasoning
MA.3.AR.1 Solve multiplication and division problems.
MA.3.AR.1.1Apply the distributive property to multiply a one-digit number and two-digit number. Apply properties of multiplication to find a product of one-digit whole numbers.
MA.3.AR.1.2Solve one- and two-step real-world problems involving any of four operations with whole numbers.
MA.3.AR.2 Develop an understanding of equality and multiplication and division.
MA.3.AR.2.1Restate a division problem as a missing factor problem using the relationship between multiplication and division.
MA.3.AR.2.2Determine and explain whether an equation involving multiplication or division is true or false.
MA.3.AR.2.3Determine the unknown whole number in a multiplication or division equation, relating three whole numbers, with the unknown in any position.
MA.3.AR.3 Identify numerical patterns, including multiplicative patterns.
MA.3.AR.3.1Determine and explain whether a whole number from 1 to 1,000 is even or odd.
MA.3.AR.3.2Determine whether a whole number from 1 to 144 is a multiple of a given one-digit number.
MA.3.AR.3.3Identify, create and extend numerical patterns.
MA.3.DP Data Analysis and Probability
MA.3.DP.1 Collect, represent and interpret numerical and categorical data.
MA.3.DP.1.1Collect and represent numerical and categorical data with whole-number values using tables, scaled pictographs, scaled bar graphs or line plots. Use appropriate titles, labels and units.
MA.3.DP.1.2Interpret data with whole-number values represented with tables, scaled pictographs, circle graphs, scaled bar graphs or line plots by solving one- and two-step problems.
MA.3.FR Fractions
MA.3.FR.1 Understand fractions as numbers and represent fractions.
MA.3.FR.1.1Represent and interpret unit fractions in the form 1/n as the quantity formed by one part when a whole is partitioned into n equal parts.
MA.3.FR.1.2Represent and interpret fractions, including fractions greater than one, in the form of m/n as the result of adding the unit fraction 1/n to itself m times.
MA.3.FR.1.3Read and write fractions, including fractions greater than one, using standard form, numeral-word form and word form.
MA.3.FR.2 Order and compare fractions and identify equivalent fractions.
MA.3.FR.2.1Plot, order and compare fractional numbers with the same numerator or the same denominator.
MA.3.FR.2.2Identify equivalent fractions and explain why they are equivalent.
MA.3.GR Geometric Reasoning
MA.3.GR.1 Describe and identify relationships between lines and classify quadrilaterals.
MA.3.GR.1.1Describe and draw points, lines, line segments, rays, intersecting lines, perpendicular lines and parallel lines. Identify these in two-dimensional figures.
MA.3.GR.1.2Identify and draw quadrilaterals based on their defining attributes. Quadrilaterals include parallelograms, rhombi, rectangles, squares and trapezoids.
MA.3.GR.1.3Draw line(s) of symmetry in a two-dimensional figure and identify line-symmetric two-dimensional figures.
MA.3.GR.2 Solve problems involving the perimeter and area of rectangles.
MA.3.GR.2.1Explore area as an attribute of a two-dimensional figure by covering the figure with unit squares without gaps or overlaps. Find areas of rectangles by counting unit squares.
MA.3.GR.2.2Find the area of a rectangle with whole-number side lengths using a visual model and a multiplication formula.
MA.3.GR.2.3Solve mathematical and real-world problems involving the perimeter and area of rectangles with whole-number side lengths using a visual model and a formula.
MA.3.GR.2.4Solve mathematical and real-world problems involving the perimeter and area of composite figures composed of non-overlapping rectangles with whole-number side lengths.
MA.3.M Measurement
MA.3.M.1 Measure attributes of objects and solve problems involving measurement.
MA.3.M.1.1Select and use appropriate tools to measure the length of an object, the volume of liquid within a beaker and temperature.
MA.3.M.1.2Solve real-world problems involving any of the four operations with whole-number lengths, masses, weights, temperatures or liquid volumes.
MA.3.M.2 Tell and write time and solve problems involving time.
MA.3.M.2.1Using analog and digital clocks tell and write time to the nearest minute using a.m. and p.m. appropriately.
MA.3.M.2.2Solve one- and two-step real-world problems involving elapsed time.
MA.3.NSO Number Sense and Operations
MA.3.NSO.1 Understand the place value of four-digit numbers.
MA.3.NSO.1.1Read and write numbers from 0 to 10,000 using standard form, expanded form and word form.
MA.3.NSO.1.2Compose and decompose four-digit numbers in multiple ways using thousands, hundreds, tens and ones. Demonstrate each composition or decomposition using objects, drawings and expressions or equations.
MA.3.NSO.1.3Plot, order and compare whole numbers up to 10,000.
MA.3.NSO.1.4Round whole numbers from 0 to 1,000 to the nearest 10 or 100.
MA.3.NSO.2 Add and subtract multi-digit whole numbers. Build an understanding of multiplication and division operations.
MA.3.NSO.2.1Add and subtract multi-digit whole numbers including using a standard algorithm with procedural fluency.
MA.3.NSO.2.2Explore multiplication of two whole numbers with products from 0 to 144, and related division facts.
MA.3.NSO.2.3Multiply a one-digit whole number by a multiple of 10, up to 90, or a multiple of 100, up to 900, with procedural reliability.
MA.3.NSO.2.4Multiply two whole numbers from 0 to 12 and divide using related facts with procedural reliability.

Grade 4

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MA.4.AR Algebraic Reasoning
MA.4.AR.1 Represent and solve problems involving the four operations with whole numbers and fractions.
MA.4.AR.1.1Solve real-world problems involving multiplication and division of whole numbers including problems in which remainders must be interpreted within the context.
MA.4.AR.1.2Solve real-world problems involving addition and subtraction of fractions with like denominators, including mixed numbers and fractions greater than one.
MA.4.AR.1.3Solve real-world problems involving multiplication of a fraction by a whole number or a whole number by a fraction.
MA.4.AR.2 Demonstrate an understanding of equality and operations with whole numbers.
MA.4.AR.2.1Determine and explain whether an equation involving any of the four operations with whole numbers is true or false.
MA.4.AR.2.2Given a mathematical or real-world context, write an equation involving multiplication or division to determine the unknown whole number with the unknown in any position.
MA.4.AR.3 Recognize numerical patterns, including patterns that follow a given rule.
MA.4.AR.3.1Determine factor pairs for a whole number from 0 to 144. Determine whether a whole number from 0 to 144 is prime, composite or neither.
MA.4.AR.3.2Generate, describe and extend a numerical pattern that follows a given rule.
MA.4.DP Data Analysis and Probability
MA.4.DP.1 Collect, represent and interpret data and find the mode, median and range of a data set.
MA.4.DP.1.1Collect and represent numerical data, including fractional values, using tables, stem-and-leaf plots or line plots.
MA.4.DP.1.2Determine the mode, median or range to interpret numerical data including fractional values, represented with tables, stem-and-leaf plots or line plots.
MA.4.DP.1.3Solve real-world problems involving numerical data.
MA.4.FR Fractions
MA.4.FR.1 Develop an understanding of the relationship between different fractions and the relationship between fractions and decimals.
MA.4.FR.1.1Model and express a fraction, including mixed numbers and fractions greater than one, with the denominator 10 as an equivalent fraction with the denominator 100.
MA.4.FR.1.2Use decimal notation to represent fractions with denominators of 10 or 100, including mixed numbers and fractions greater than 1, and use fractional notation with denominators of 10 or 100 to represent decimals.
MA.4.FR.1.3Identify and generate equivalent fractions, including fractions greater than one. Describe how the numerator and denominator are affected when the equivalent fraction is created.
MA.4.FR.1.4Plot, order and compare fractions, including mixed numbers and fractions greater than one, with different numerators and different denominators.
MA.4.FR.2 Build a foundation of addition, subtraction and multiplication operations with fractions.
MA.4.FR.2.1Decompose a fraction, including mixed numbers and fractions greater than one, into a sum of fractions with the same denominator in multiple ways. Demonstrate each decomposition with objects, drawings and equations.
MA.4.FR.2.2Add and subtract fractions with like denominators, including mixed numbers and fractions greater than one, with procedural reliability.
MA.4.FR.2.3Explore the addition of a fraction with denominator of 10 to a fraction with denominator of 100 using equivalent fractions.
MA.4.FR.2.4Extend previous understanding of multiplication to explore the multiplication of a fraction by a whole number or a whole number by a fraction.
MA.4.GR Geometric Reasoning
MA.4.GR.1 Draw, classify and measure angles.
MA.4.GR.1.1Informally explore angles as an attribute of two-dimensional figures. Identify and classify angles as acute, right, obtuse, straight or reflex.
MA.4.GR.1.2Estimate angle measures. Using a protractor, measure angles in whole-number degrees and draw angles of specified measure in whole-number degrees. Demonstrate that angle measure is additive.
MA.4.GR.1.3Solve real-world and mathematical problems involving unknown whole-number angle measures. Write an equation to represent the unknown.
MA.4.GR.2 Solve problems involving the perimeter and area of rectangles.
MA.4.GR.2.1Solve perimeter and area mathematical and real-world problems, including problems with unknown sides, for rectangles with whole-number side lengths.
MA.4.GR.2.2Solve problems involving rectangles with the same perimeter and different areas or with the same area and different perimeters.
MA.4.M Measurement
MA.4.M.1 Measure the length of objects and solve problems involving measurement.
MA.4.M.1.1Select and use appropriate tools to measure attributes of objects.
MA.4.M.1.2Convert within a single system of measurement using the units: yards, feet, inches; kilometers, meters, centimeters, millimeters; pounds, ounces; kilograms, grams; gallons, quarts, pints, cups; liter, milliliter; and hours, minutes, seconds.
MA.4.M.2 Solve problems involving time and money.
MA.4.M.2.1Solve two-step real-world problems involving distances and intervals of time using any combination of the four operations.
MA.4.M.2.2Solve one- and two-step addition and subtraction real-world problems involving money using decimal notation.
MA.4.NSO Number Sense and Operations
MA.4.NSO.1 Understand place value for multi-digit numbers.
MA.4.NSO.1.1Express how the value of a digit in a multi-digit whole number changes if the digit moves one place to the left or right.
MA.4.NSO.1.2Read and write multi-digit whole numbers from 0 to 1,000,000 using standard form, expanded form and word form.
MA.4.NSO.1.3Plot, order and compare multi-digit whole numbers up to 1,000,000.
MA.4.NSO.1.4Round whole numbers from 0 to 10,000 to the nearest 10, 100 or 1,000.
MA.4.NSO.1.5Plot, order and compare decimals up to the hundredths.
MA.4.NSO.2 Build an understanding of operations with multi-digit numbers including decimals.
MA.4.NSO.2.1Recall multiplication facts with factors up to 12 and related division facts with automaticity.
MA.4.NSO.2.2Multiply two whole numbers, up to three digits by up to two digits, with procedural reliability.
MA.4.NSO.2.3Multiply two whole numbers, each up to two digits, including using a standard algorithm with procedural fluency.
MA.4.NSO.2.4Divide a whole number up to four digits by a one-digit whole number with procedural reliability. Represent remainders as fractional parts of the divisor.
MA.4.NSO.2.5Explore the multiplication and division of multi-digit whole numbers using estimation, rounding and place value.
MA.4.NSO.2.6Identify the number that is one-tenth more, one-tenth less, one-hundredth more and one-hundredth less than a given number.
MA.4.NSO.2.7Explore the addition and subtraction of multi-digit numbers with decimals to the hundredths.

Grade 5

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MA.5.AR Algebraic Reasoning
MA.5.AR.1 Solve problems involving the four operations with whole numbers and fractions.
MA.5.AR.1.1Solve multi-step real-world problems involving any combination of the four operations with whole numbers, including problems in which remainders must be interpreted within the context.
MA.5.AR.1.2Solve real-world problems involving the addition, subtraction or multiplication of fractions, including mixed numbers and fractions greater than 1.
MA.5.AR.1.3Solve real-world problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.
MA.5.AR.2 Demonstrate an understanding of equality, the order of operations and equivalent numerical expressions.
MA.5.AR.2.1Translate written real-world and mathematical descriptions into numerical expressions and numerical expressions into written mathematical descriptions.
MA.5.AR.2.2Evaluate multi-step numerical expressions using order of operations.
MA.5.AR.2.3Determine and explain whether an equation involving any of the four operations is true or false.
MA.5.AR.2.4Given a mathematical or real-world context, write an equation involving any of the four operations to determine the unknown whole number with the unknown in any position.
MA.5.AR.3 Analyze patterns and relationships between inputs and outputs.
MA.5.AR.3.1Given a numerical pattern, identify and write a rule that can describe the pattern as an expression.
MA.5.AR.3.2Given a rule for a numerical pattern, use a two-column table to record the inputs and outputs.
MA.5.DP Data Analysis and Probability
MA.5.DP.1 Collect, represent and interpret data and find the mean, mode, median or range of a data set.
MA.5.DP.1.1Collect and represent numerical data, including fractional and decimal values, using tables, line graphs or line plots.
MA.5.DP.1.2Interpret numerical data, with whole-number values, represented with tables or line plots by determining the mean, mode, median or range.
MA.5.FR Fractions
MA.5.FR.1 Interpret a fraction as an answer to a division problem.
MA.5.FR.1.1Given a mathematical or real-world problem, represent the division of two whole numbers as a fraction.
MA.5.FR.2 Perform operations with fractions.
MA.5.FR.2.1Add and subtract fractions with unlike denominators, including mixed numbers and fractions greater than 1, with procedural reliability.
MA.5.FR.2.2Extend previous understanding of multiplication to multiply a fraction by a fraction, including mixed numbers and fractions greater than 1, with procedural reliability.
MA.5.FR.2.3When multiplying a given number by a fraction less than 1 or a fraction greater than 1, predict and explain the relative size of the product to the given number without calculating.
MA.5.FR.2.4Extend previous understanding of division to explore the division of a unit fraction by a whole number and a whole number by a unit fraction.
MA.5.GR Geometric Reasoning
MA.5.GR.1 Classify two-dimensional figures and three-dimensional figures based on defining attributes.
MA.5.GR.1.1Classify triangles or quadrilaterals into different categories based on shared defining attributes. Explain why a triangle or quadrilateral would or would not belong to a category.
MA.5.GR.1.2Identify and classify three-dimensional figures into categories based on their defining attributes. Figures are limited to right pyramids, right prisms, right circular cylinders, right circular cones and spheres.
MA.5.GR.2 Find the perimeter and area of rectangles with fractional or decimal side lengths.
MA.5.GR.2.1Find the perimeter and area of a rectangle with fractional or decimal side lengths using visual models and formulas.
MA.5.GR.3 Solve problems involving the volume of right rectangular prisms.
MA.5.GR.3.1Explore volume as an attribute of three-dimensional figures by packing them with unit cubes without gaps. Find the volume of a right rectangular prism with whole-number side lengths by counting unit cubes.
MA.5.GR.3.2Find the volume of a right rectangular prism with whole-number side lengths using a visual model and a formula.
MA.5.GR.3.3Solve real-world problems involving the volume of right rectangular prisms, including problems with an unknown edge length, with whole-number edge lengths using a visual model or a formula. Write an equation with a variable for the unknown to represent the problem.
MA.5.GR.4 Plot points and represent problems on the coordinate plane.
MA.5.GR.4.1Identify the origin and axes in the coordinate system. Plot and label ordered pairs in the first quadrant of the coordinate plane.
MA.5.GR.4.2Represent mathematical and real-world problems by plotting points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation.
MA.5.M Measurement
MA.5.M.1 Convert measurement units to solve multi-step problems.
MA.5.M.1.1Solve multi-step real-world problems that involve converting measurement units to equivalent measurements within a single system of measurement.
MA.5.M.2 Solve problems involving money.
MA.5.M.2.1Solve multi-step real-world problems involving money using decimal notation.
MA.5.NSO Number Sense and Operations
MA.5.NSO.1 Understand the place value of multi-digit numbers with decimals to the thousandths place.
MA.5.NSO.1.1Express how the value of a digit in a multi-digit number with decimals to the thousandths changes if the digit moves one or more places to the left or right.
MA.5.NSO.1.2Read and write multi-digit numbers with decimals to the thousandths using standard form, word form and expanded form.
MA.5.NSO.1.3Compose and decompose multi-digit numbers with decimals to the thousandths in multiple ways using the values of the digits in each place. Demonstrate the compositions or decompositions using objects, drawings and expressions or equations.
MA.5.NSO.1.4Plot, order and compare multi-digit numbers with decimals up to the thousandths.
MA.5.NSO.1.5Round multi-digit numbers with decimals to the thousandths to the nearest hundredth, tenth or whole number.
MA.5.NSO.2 Add, subtract, multiply and divide multi-digit numbers.
MA.5.NSO.2.1Multiply multi-digit whole numbers including using a standard algorithm with procedural fluency.
MA.5.NSO.2.2Divide multi-digit whole numbers, up to five digits by two digits, including using a standard algorithm with procedural fluency. Represent remainders as fractions.
MA.5.NSO.2.3Add and subtract multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency.
MA.5.NSO.2.4Explore the multiplication and division of multi-digit numbers with decimals to the hundredths using estimation, rounding and place value.
MA.5.NSO.2.5Multiply and divide a multi-digit number with decimals to the tenths by one-tenth and one-hundredth with procedural reliability.

Grade 6

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MA.6.AR Algebraic Reasoning
MA.6.AR.1 Apply previous understanding of arithmetic expressions to algebraic expressions.
MA.6.AR.1.1Given a mathematical or real-world context, translate written descriptions into algebraic expressions and translate algebraic expressions into written descriptions.
MA.6.AR.1.2Translate a real-world written description into an algebraic inequality in the form of x>a, x<a, x>=a, or x<= a. Represent the inequality on a number line.
MA.6.AR.1.3Evaluate algebraic expressions using substitution and order of operations.
MA.6.AR.1.4Apply the properties of operations to generate equivalent algebraic expressions with integer coefficients.
MA.6.AR.2 Develop an understanding for solving equations and inequalities. Write and solve one-step equations in one variable.
MA.6.AR.2.1Given an equation or inequality and a specified set of integer values, determine which values make the equation or inequality true or false.
MA.6.AR.2.2Write and solve one-step equations in one variable within a mathematical or real-world context using addition and subtraction, where all terms and solutions are integers.
MA.6.AR.2.3Write and solve one-step equations in one variable within a mathematical or real-world context using multiplication and division, where all terms and solutions are integers.
MA.6.AR.2.4Determine the unknown decimal or fraction in an equation involving any of the four operations, relating three numbers, with the unknown in any position.
MA.6.AR.3 Understand ratio and unit rate concepts and use them to solve problems.
MA.6.AR.3.1Given a real-world context, write and interpret ratios to show the relative sizes of two quantities using appropriate notation: a/b, a to b, or a:b where b not equal to 0.
MA.6.AR.3.2Given a real-world context, determine a rate for a ratio of quantities with different units. Calculate and interpret the corresponding unit rate.
MA.6.AR.3.3Extend previous understanding of fractions and numerical patterns to generate or complete a two- or three-column table to display equivalent part-to-part ratios and part-to-part-to-whole ratios.
MA.6.AR.3.4Apply ratio relationships to solve mathematical and real-world problems involving percentages using the relationship between two quantities.
MA.6.AR.3.5Solve mathematical and real-world problems involving ratios, rates and unit rates, including comparisons, mixtures, ratios of lengths and conversions within the same measurement system.
MA.6.DP Data Analysis and Probability
MA.6.DP.1 Develop an understanding of statistics and determine measures of center and measures of variability. Summarize statistical distributions graphically and numerically.
MA.6.DP.1.1Recognize and formulate a statistical question that would generate numerical data.
MA.6.DP.1.2Given a numerical data set within a real-world context, find and interpret mean, median, mode and range.
MA.6.DP.1.3Given a box plot within a real-world context, determine the minimum, the lower quartile, the median, the upper quartile and the maximum. Use this summary of the data to describe the spread and distribution of the data.
MA.6.DP.1.4Given a histogram or line plot within a real-world context, qualitatively describe and interpret the spread and distribution of the data, including any symmetry, skewness, gaps, clusters, outliers and the range.
MA.6.DP.1.5Create box plots and histograms to represent sets of numerical data within real-world contexts.
MA.6.DP.1.6Given a real-world scenario, determine and describe how changes in data values impact measures of center and variation.
MA.6.GR Geometric Reasoning
MA.6.GR.1 Apply previous understanding of the coordinate plane to solve problems.
MA.6.GR.1.1Extend previous understanding of the coordinate plane to plot rational number ordered pairs in all four quadrants and on both axes. Identify the x- or y-axis as the line of reflection when two ordered pairs have an opposite x- or y- coordinate.
MA.6.GR.1.2Find distances between ordered pairs, limited to the same x-coordinate or the same y-coordinate, represented on the coordinate plane.
MA.6.GR.1.3Solve mathematical and real-world problems by plotting points on a coordinate plane, including finding the perimeter or area of a rectangle.
MA.6.GR.2 Model and solve problems involving two-dimensional figures and three-dimensional figures.
MA.6.GR.2.1Derive a formula for the area of a right triangle using a rectangle. Apply a formula to find the area of a triangle.
MA.6.GR.2.2Solve mathematical and real-world problems involving the area of quadrilaterals and composite figures by decomposing them into triangles or rectangles.
MA.6.GR.2.3Solve mathematical and real-world problems involving the volume of right rectangular prisms with positive rational number edge lengths using a visual model and a formula.
MA.6.GR.2.4Given a mathematical or real-world context, find the surface area of right rectangular prisms and right rectangular pyramids using the figure’s net.
MA.6.NSO Number Sense and Operations
MA.6.NSO.1 Extend knowledge of numbers to negative numbers and develop an understanding of absolute value.
MA.6.NSO.1.1Extend previous understanding of numbers to define rational numbers. Plot, order and compare rational numbers.
MA.6.NSO.1.2Given a mathematical or real-world context, represent quantities that have opposite direction using rational numbers. Compare them on a number line and explain the meaning of zero within its context.
MA.6.NSO.1.3Given a mathematical or real-world context, interpret the absolute value of a number as the distance from zero on a number line. Find the absolute value of rational numbers.
MA.6.NSO.1.4Solve mathematical and real-world problems involving absolute value, including the comparison of absolute value.
MA.6.NSO.2 Add, subtract, multiply and divide positive rational numbers.
MA.6.NSO.2.1Multiply and divide positive multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency.
MA.6.NSO.2.2Extend previous understanding of multiplication and division to compute products and quotients of positive fractions by positive fractions, including mixed numbers, with procedural fluency.
MA.6.NSO.2.3Solve multi-step real-world problems involving any of the four operations with positive multi-digit decimals or positive fractions, including mixed numbers.
MA.6.NSO.3 Apply properties of operations to rewrite numbers in equivalent forms.
MA.6.NSO.3.1Given a mathematical or real-world context, find the greatest common factor and least common multiple of two whole numbers.
MA.6.NSO.3.2Rewrite the sum of two composite whole numbers having a common factor, as a common factor multiplied by the sum of two whole numbers.
MA.6.NSO.3.3Evaluate positive rational numbers and integers with natural number exponents.
MA.6.NSO.3.4Express composite whole numbers as a product of prime factors with natural number exponents.
MA.6.NSO.3.5Rewrite positive rational numbers in different but equivalent forms including fractions, terminating decimals and percentages.
MA.6.NSO.4 Extend understanding of operations with integers.
MA.6.NSO.4.1Apply and extend previous understandings of operations with whole numbers to add and subtract integers with procedural fluency.
MA.6.NSO.4.2Apply and extend previous understandings of operations with whole numbers to multiply and divide integers with procedural fluency.

Grade 7

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MA.7.AR Algebraic Reasoning
MA.7.AR.1 Rewrite algebraic expressions in equivalent forms.
MA.7.AR.1.1Apply properties of operations to add and subtract linear expressions with rational coefficients.
MA.7.AR.1.2Determine whether two linear expressions are equivalent.
MA.7.AR.2 Write and solve equations and inequalities in one variable.
MA.7.AR.2.1Write and solve one-step inequalities in one variable within a mathematical context and represent solutions algebraically or graphically.
MA.7.AR.2.2Write and solve two-step equations in one variable within a mathematical or real-world context, where all terms are rational numbers.
MA.7.AR.3 Use percentages and proportional reasoning to solve problems.
MA.7.AR.3.1Apply previous understanding of percentages and ratios to solve multi-step real-world percent problems.
MA.7.AR.3.2Apply previous understanding of ratios to solve real-world problems involving proportions.
MA.7.AR.3.3Solve mathematical and real-world problems involving the conversion of units across different measurement systems.
MA.7.AR.4 Analyze and represent two-variable proportional relationships.
MA.7.AR.4.1Determine whether two quantities have a proportional relationship by examining a table, graph or written description.
MA.7.AR.4.2Determine the constant of proportionality within a mathematical or real-world context given a table, graph or written description of a proportional relationship.
MA.7.AR.4.3Given a mathematical or real-world context, graph proportional relationships from a table, equation or a written description.
MA.7.AR.4.4Given any representation of a proportional relationship, translate the representation to a written description, table or equation.
MA.7.AR.4.5Solve real-world problems involving proportional relationships.
MA.7.DP Data Analysis and Probability
MA.7.DP.1 Represent and interpret numerical and categorical data.
MA.7.DP.1.1Determine an appropriate measure of center or measure of variation to summarize numerical data, represented numerically or graphically, taking into consideration the context and any outliers.
MA.7.DP.1.2Given two numerical or graphical representations of data, use the measure(s) of center and measure(s) of variability to make comparisons, interpret results and draw conclusions about the two populations.
MA.7.DP.1.3Given categorical data from a random sample, use proportional relationships to make predictions about a population.
MA.7.DP.1.4Use proportional reasoning to construct, display and interpret data in circle graphs.
MA.7.DP.1.5Given a real-world numerical or categorical data set, choose and create an appropriate graphical representation.
MA.7.DP.2 Develop an understanding of probability. Find and compare experimental and theoretical probabilities.
MA.7.DP.2.1Determine the sample space for a simple experiment.
MA.7.DP.2.2Given the probability of a chance event, interpret the likelihood of it occurring. Compare the probabilities of chance events.
MA.7.DP.2.3Find the theoretical probability of an event related to a simple experiment.
MA.7.DP.2.4Use a simulation of a simple experiment to find experimental probabilities and compare them to theoretical probabilities.
MA.7.GR Geometric Reasoning
MA.7.GR.1 Solve problems involving two-dimensional figures, including circles.
MA.7.GR.1.1Apply formulas to find the areas of trapezoids, parallelograms and rhombi.
MA.7.GR.1.2Solve mathematical or real-world problems involving the area of polygons or composite figures by decomposing them into triangles or quadrilaterals.
MA.7.GR.1.3Explore the proportional relationship between circumferences and diameters of circles. Apply a formula for the circumference of a circle to solve mathematical and real-world problems.
MA.7.GR.1.4Explore and apply a formula to find the area of a circle to solve mathematical and real-world problems.
MA.7.GR.1.5Solve mathematical and real-world problems involving dimensions and areas of geometric figures, including scale drawings and scale factors.
MA.7.GR.2 Solve problems involving three-dimensional figures, including right circular cylinders.
MA.7.GR.2.1Given a mathematical or real-world context, find the surface area of a right circular cylinder using the figure’s net.
MA.7.GR.2.2Solve real-world problems involving surface area of right circular cylinders.
MA.7.GR.2.3Solve mathematical and real-world problems involving volume of right circular cylinders.
MA.7.NSO Number Sense and Operations
MA.7.NSO.1 Rewrite numbers in equivalent forms.
MA.7.NSO.1.1Know and apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions, limited to whole-number exponents and rational number bases.
MA.7.NSO.1.2Rewrite rational numbers in different but equivalent forms including fractions, mixed numbers, repeating decimals and percentages to solve mathematical and real-world problems.
MA.7.NSO.2 Add, subtract, multiply and divide rational numbers.
MA.7.NSO.2.1Solve mathematical problems using multi-step order of operations with rational numbers including grouping symbols, whole-number exponents and absolute value.
MA.7.NSO.2.2Add, subtract, multiply and divide rational numbers with procedural fluency.
MA.7.NSO.2.3Solve real-world problems involving any of the four operations with rational numbers.

Grade 8

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MA.8.AR Algebraic Reasoning
MA.8.AR.1 Generate equivalent algebraic expressions.
MA.8.AR.1.1Apply the Laws of Exponents to generate equivalent algebraic expressions, limited to integer exponents and monomial bases.
MA.8.AR.1.2Apply properties of operations to multiply two linear expressions with rational coefficients.
MA.8.AR.1.3Rewrite the sum of two algebraic expressions having a common monomial factor as a common factor multiplied by the sum of two algebraic expressions.
MA.8.AR.2 Solve multi-step one-variable equations and inequalities.
MA.8.AR.2.1Solve multi-step linear equations in one variable, with rational number coefficients. Include equations with variables on both sides.
MA.8.AR.2.2Solve two-step linear inequalities in one variable and represent solutions algebraically and graphically.
MA.8.AR.2.3Given an equation in the form of x^2 = p and x^3 = q, where p is a whole number and q is an integer, determine the real solutions.
MA.8.AR.3 Extend understanding of proportional relationships to two-variable linear equations.
MA.8.AR.3.1Determine if a linear relationship is also a proportional relationship.
MA.8.AR.3.2Given a table, graph or written description of a linear relationship, determine the slope.
MA.8.AR.3.3Given a table, graph or written description of a linear relationship, write an equation in slope-intercept form.
MA.8.AR.3.4Given a mathematical or real-world context, graph a two-variable linear equation from a written description, a table or an equation in slope-intercept form.
MA.8.AR.3.5Given a real-world context, determine and interpret the slope and y-intercept of a two-variable linear equation from a written description, a table, a graph or an equation in slope-intercept form.
MA.8.AR.4 Develop an understanding of two-variable systems of equations.
MA.8.AR.4.1Given a system of two linear equations and a specified set of possible solutions, determine which ordered pairs satisfy the system of linear equations.
MA.8.AR.4.2Given a system of two linear equations represented graphically on the same coordinate plane, determine whether there is one solution, no solution or infinitely many solutions.
MA.8.AR.4.3Given a mathematical or real-world context, solve systems of two linear equations by graphing.
MA.8.DP Data Analysis and Probability
MA.8.DP.1 Represent and investigate numerical bivariate data.
MA.8.DP.1.1Given a set of real-world bivariate numerical data, construct a scatter plot or a line graph as appropriate for the context.
MA.8.DP.1.2Given a scatter plot within a real-world context, describe patterns of association.
MA.8.DP.1.3Given a scatter plot with a linear association, informally fit a straight line.
MA.8.DP.2 Represent and find probabilities of repeated experiments.
MA.8.DP.2.1Determine the sample space for a repeated experiment.
MA.8.DP.2.2Find the theoretical probability of an event related to a repeated experiment.
MA.8.DP.2.3Solve real-world problems involving probabilities related to single or repeated experiments, including making predictions based on theoretical probability.
MA.8.F Functions
MA.8.F.1 Define, evaluate and compare functions.
MA.8.F.1.1Given a set of ordered pairs, a table, a graph or mapping diagram, determine whether the relationship is a function. Identify the domain and range of the relation.
MA.8.F.1.2Given a function defined by a graph or an equation, determine whether the function is a linear function. Given an input-output table, determine whether it could represent a linear function.
MA.8.F.1.3Analyze a real-world written description or graphical representation of a functional relationship between two quantities and identify where the function is increasing, decreasing or constant.
MA.8.GR Geometric Reasoning
MA.8.GR.1 Develop an understanding of the Pythagorean Theorem and angle relationships involving triangles.
MA.8.GR.1.1Apply the Pythagorean Theorem to solve mathematical and real-world problems involving unknown side lengths in right triangles.
MA.8.GR.1.2Apply the Pythagorean Theorem to solve mathematical and real-world problems involving the distance between two points in a coordinate plane.
MA.8.GR.1.3Use the Triangle Inequality Theorem to determine if a triangle can be formed from a given set of sides. Use the converse of the Pythagorean Theorem to determine if a right triangle can be formed from a given set of sides.
MA.8.GR.1.4Solve mathematical problems involving the relationships between supplementary, complementary, vertical or adjacent angles.
MA.8.GR.1.5Solve problems involving the relationships of interior and exterior angles of a triangle.
MA.8.GR.1.6Develop and use formulas for the sums of the interior angles of regular polygons by decomposing them into triangles.
MA.8.GR.2 Understand similarity and congruence using models and transformations.
MA.8.GR.2.1Given a preimage and image generated by a single transformation, identify the transformation that describes the relationship.
MA.8.GR.2.2Given a preimage and image generated by a single dilation, identify the scale factor that describes the relationship.
MA.8.GR.2.3Describe and apply the effect of a single transformation on two-dimensional figures using coordinates and the coordinate plane.
MA.8.GR.2.4Solve mathematical and real-world problems involving proportional relationships between similar triangles.
MA.8.NSO Number Sense and Operations
MA.8.NSO.1 Solve problems involving rational numbers, including numbers in scientific notation, and extend the understanding of rational numbers to irrational numbers.
MA.8.NSO.1.1Extend previous understanding of rational numbers to define irrational numbers within the real number system. Locate an approximate value of a numerical expression involving irrational numbers on a number line.
MA.8.NSO.1.2Plot, order and compare rational and irrational numbers, represented in various forms.
MA.8.NSO.1.3Extend previous understanding of the Laws of Exponents to include integer exponents. Apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions, limited to integer exponents and rational number bases, with procedural fluency.
MA.8.NSO.1.4Express numbers in scientific notation to represent and approximate very large or very small quantities. Determine how many times larger or smaller one number is compared to a second number.
MA.8.NSO.1.5Add, subtract, multiply and divide numbers expressed in scientific notation with procedural fluency.
MA.8.NSO.1.6Solve real-world problems involving operations with numbers expressed in scientific notation.
MA.8.NSO.1.7Solve multi-step mathematical and real-world problems involving the order of operations with rational numbers including exponents and radicals.

Grades 9-12

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MA.912.AR High School: Algebraic Reasoning
MA.912.AR.1 Interpret and rewrite algebraic expressions and equations in equivalent forms.
MA.912.AR.1.1Identify and interpret parts of an equation or expression that represent a quantity in terms of a mathematical or real-world context, including viewing one or more of its parts as a single entity.
MA.912.AR.1.10Solve mathematical and real-world problems involving addition, subtraction, multiplication or division of rational algebraic expressions.
MA.912.AR.1.11Apply the Binomial Theorem to create equivalent polynomial expressions.
MA.912.AR.1.2Rearrange equations or formulas to isolate a quantity of interest.
MA.912.AR.1.3Add, subtract and multiply polynomial expressions with rational number coefficients.
MA.912.AR.1.4Divide a polynomial expression by a monomial expression with rational number coefficients.
MA.912.AR.1.5Divide polynomial expressions using long division, synthetic division or algebraic manipulation.
MA.912.AR.1.6Solve mathematical and real-world problems involving addition, subtraction, multiplication or division of polynomials.
MA.912.AR.1.7Rewrite a polynomial expression as a product of polynomials over the real number system.
MA.912.AR.1.8Rewrite a polynomial expression as a product of polynomials over the real or complex number system.
MA.912.AR.1.9Apply previous understanding of rational number operations to add, subtract, multiply and divide rational algebraic expressions.
MA.912.AR.10 Solve problems involving sequences and series.
MA.912.AR.10.1Given a mathematical or real-world context, write and solve problems involving arithmetic sequences.
MA.912.AR.10.2Given a mathematical or real-world context, write and solve problems involving geometric sequences.
MA.912.AR.10.3Recognize and apply the formula for the sum of a finite arithmetic series to solve mathematical and real-world problems.
MA.912.AR.10.4Recognize and apply the formula for the sum of a finite or an infinite geometric series to solve mathematical and real-world problems.
MA.912.AR.10.5Given a mathematical or real-world context, write a sequence using function notation, defined explicitly or recursively, to represent relationships between quantities from a written description.
MA.912.AR.10.6Given a mathematical or real-world context, find the domain of a given sequence defined recursively or explicitly.
MA.912.AR.2 Write, solve and graph linear equations, functions and inequalities in one and two variables.
MA.912.AR.2.1Given a real-world context, write and solve one-variable multi-step linear equations.
MA.912.AR.2.2Write a linear two-variable equation to represent the relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context.
MA.912.AR.2.3Write a linear two-variable equation for a line that is parallel or perpendicular to a given line and goes through a given point.
MA.912.AR.2.4Given a table, equation or written description of a linear function, graph that function, and determine and interpret its key features.
MA.912.AR.2.5Solve and graph mathematical and real-world problems that are modeled with linear functions. Interpret key features and determine constraints in terms of the context.
MA.912.AR.2.6Given a mathematical or real-world context, write and solve one-variable linear inequalities, including compound inequalities. Represent solutions algebraically or graphically.
MA.912.AR.2.7Write two-variable linear inequalities to represent relationships between quantities from a graph or a written description within a mathematical or real-world context.
MA.912.AR.2.8Given a mathematical or real-world context, graph the solution set to a two-variable linear inequality.
MA.912.AR.3 Write, solve and graph quadratic equations, functions and inequalities in one and two variables.
MA.912.AR.3.1Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real number system.
MA.912.AR.3.10Given a mathematical or real-world context, graph the solution set to a two-variable quadratic inequality.
MA.912.AR.3.2Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real and complex number systems.
MA.912.AR.3.3Given a mathematical or real-world context, write and solve one-variable quadratic inequalities over the real number system. Represent solutions algebraically or graphically.
MA.912.AR.3.4Write a quadratic function to represent the relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context.
MA.912.AR.3.5Given the x-intercepts and another point on the graph of a quadratic function, write the equation for the function.
MA.912.AR.3.6Given an expression or equation representing a quadratic function, determine the vertex and zeros and interpret them in terms of a real-world context.
MA.912.AR.3.7Given a table, equation or written description of a quadratic function, graph that function, and determine and interpret its key features.
MA.912.AR.3.8Solve and graph mathematical and real-world problems that are modeled with quadratic functions. Interpret key features and determine constraints in terms of the context.
MA.912.AR.3.9Given a mathematical or real-world context, write two-variable quadratic inequalities to represent relationships between quantities from a graph or a written description.
MA.912.AR.4 Write, solve and graph absolute value equations, functions and inequalities in one and two variables.
MA.912.AR.4.1Given a mathematical or real-world context, write and solve one-variable absolute value equations.
MA.912.AR.4.2Given a mathematical or real-world context, write and solve one-variable absolute value inequalities. Represent solutions algebraically or graphically.
MA.912.AR.4.3Given a table, equation or written description of an absolute value function, graph that function and determine its key features.
MA.912.AR.4.4Solve and graph mathematical and real-world problems that are modeled with absolute value functions. Interpret key features and determine constraints in terms of the context.
MA.912.AR.5 Write, solve and graph exponential and logarithmic equations and functions in one and two variables.
MA.912.AR.5.1Solve one-variable exponential equations using the properties of exponents.
MA.912.AR.5.2Solve one-variable equations involving logarithms or exponential expressions. Interpret solutions as viable in terms of the context and identify any extraneous solutions.
MA.912.AR.5.3Given a mathematical or real-world context, classify an exponential function as representing growth or decay.
MA.912.AR.5.4Write an exponential function to represent a relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context.
MA.912.AR.5.5Given an expression or equation representing an exponential function, reveal the constant percent rate of change per unit interval using the properties of exponents. Interpret the constant percent rate of change in terms of a real-world context.
MA.912.AR.5.6Given a table, equation or written description of an exponential function, graph that function and determine its key features.
MA.912.AR.5.7Solve and graph mathematical and real-world problems that are modeled with exponential functions. Interpret key features and determine constraints in terms of the context.
MA.912.AR.5.8Given a table, equation or written description of a logarithmic function, graph that function and determine its key features.
MA.912.AR.5.9Solve and graph mathematical and real-world problems that are modeled with logarithmic functions. Interpret key features and determine constraints in terms of the context.
MA.912.AR.6 Solve and graph polynomial equations and functions in one and two variables.
MA.912.AR.6.1Given a mathematical or real-world context, when suitable factorization is possible, solve one-variable polynomial equations of degree 3 or higher over the real and complex number systems.
MA.912.AR.6.2Explain and apply the Remainder Theorem to solve mathematical and real-world problems.
MA.912.AR.6.3Explain and apply theorems for polynomials to solve mathematical and real-world problems.
MA.912.AR.6.4Given a table, equation or written description of a polynomial function of degree 3 or higher, graph that function and determine its key features.
MA.912.AR.6.5Sketch a rough graph of a polynomial function of degree 3 or higher using zeros, multiplicity and knowledge of end behavior.
MA.912.AR.6.6Solve and graph mathematical and real-world problems that are modeled with polynomial functions of degree 3 or higher. Interpret key features and determine constraints in terms of the context.
MA.912.AR.7 Solve and graph radical equations and functions in one and two variables.
MA.912.AR.7.1Solve one-variable radical equations. Interpret solutions as viable in terms of context and identify any extraneous solutions.
MA.912.AR.7.2Given a table, equation or written description of a square root or cube root function, graph that function and determine its key features.
MA.912.AR.7.3Solve and graph mathematical and real-world problems that are modeled with square root or cube root functions. Interpret key features and determine constraints in terms of the context.
MA.912.AR.7.4Solve and graph mathematical and real-world problems that are modeled with radical functions. Interpret key features and determine constraints in terms of the context.
MA.912.AR.8 Solve and graph rational equations and functions in one and two variables.
MA.912.AR.8.1Write and solve one-variable rational equations. Interpret solutions as viable in terms of the context and identify any extraneous solutions.
MA.912.AR.8.2Given a table, equation or written description of a rational function, graph that function and determine its key features.
MA.912.AR.8.3Solve and graph mathematical and real-world problems that are modeled with rational functions. Interpret key features and determine constraints in terms of the context.
MA.912.AR.9 Write and solve a system of two- and three-variable equations and inequalities that describe quantities or relationships.
MA.912.AR.9.1Given a mathematical or real-world context, write and solve a system of two-variable linear equations algebraically or graphically.
MA.912.AR.9.10Solve and graph mathematical and real-world problems that are modeled with piecewise functions. Interpret key features and determine constraints in terms of the context.
MA.912.AR.9.2Given a mathematical or real-world context, solve a system consisting of a two-variable linear equation and a non-linear equation algebraically or graphically.
MA.912.AR.9.3Given a mathematical or real-world context, solve a system consisting of two-variable linear or non-linear equations algebraically or graphically.
MA.912.AR.9.4Graph the solution set of a system of two-variable linear inequalities.
MA.912.AR.9.5Graph the solution set of a system of two-variable inequalities.
MA.912.AR.9.6Given a real-world context, represent constraints as systems of linear equations or inequalities. Interpret solutions to problems as viable or non-viable options.
MA.912.AR.9.7Given a real-world context, represent constraints as systems of linear and non-linear equations or inequalities. Interpret solutions to problems as viable or non-viable options.
MA.912.AR.9.8Solve real-world problems involving linear programming in two variables.
MA.912.AR.9.9Given a mathematical or real-world context, solve a system of three-variable linear equations algebraically.
MA.912.C High School: Calculus
MA.912.C.1 Develop an understanding for limits and continuity. Determine limits and continuity.
MA.912.C.1.1Demonstrate understanding of the concept of a limit and estimate limits from graphs and tables of values.
MA.912.C.1.10Given the graph of a function, identify whether a function is continuous at a point. If not, identify the type of discontinuity for the given function.
MA.912.C.1.11Apply the Intermediate Value Theorem and the Extreme Value Theorem.
MA.912.C.1.2Determine the value of a limit if it exists algebraically using limits of sums, differences, products, quotients and compositions of continuous functions.
MA.912.C.1.3Find limits of rational functions that are undefined at a point.
MA.912.C.1.4Find one-sided limits.
MA.912.C.1.5Find limits at infinity.
MA.912.C.1.6Decide when a limit is infinite and use limits involving infinity to describe asymptotic behavior.
MA.912.C.1.7Find special limits by using the Squeeze Theorem or algebraic manipulation.
MA.912.C.1.8Find limits of indeterminate forms using L'Hôpital's Rule.
MA.912.C.1.9Define continuity in terms of limits.
MA.912.C.2 Develop an understanding for and determine derivatives.
MA.912.C.2.1State, understand and apply the definition of derivative. Apply and interpret derivatives geometrically and numerically.
MA.912.C.2.10Apply the Mean Value Theorem.
MA.912.C.2.2Interpret the derivative as an instantaneous rate of change or as the slope of the tangent line.
MA.912.C.2.3Prove the rules for finding derivatives of constants, sums, products, quotients and the Chain Rule.
MA.912.C.2.4Apply the rules for finding derivatives of constants, sums, products, quotients and the Chain Rule to solve problems with functions limited to algebraic, trigonometric, inverse trigonometric, logarithmic and exponential.
MA.912.C.2.5Find the derivatives of implicitly defined functions.
MA.912.C.2.6Find derivatives of inverse functions.
MA.912.C.2.7Find second derivatives and derivatives of higher order.
MA.912.C.2.8Find derivatives using logarithmic differentiation.
MA.912.C.2.9Demonstrate and use the relationship between differentiability and continuity.
MA.912.C.3 Apply derivatives to solve problems.
MA.912.C.3.1Find the slope of a curve at a point, including points at which there are vertical tangent lines.
MA.912.C.3.10Model and solve problems involving rates of change, including related rates.
MA.912.C.3.2Find an equation for the tangent line to a curve at a point and use it to make local linear approximation.
MA.912.C.3.3Determine where a function is decreasing and increasing using its derivative.
MA.912.C.3.4Find local and absolute maximum and minimum points of a function.
MA.912.C.3.5Determine the concavity and points of inflection of a function using its second derivative.
MA.912.C.3.6Sketch graphs by using first and second derivatives. Compare the corresponding characteristics of the graphs of f, f', and f".
MA.912.C.3.7Solve optimization problems using derivatives.
MA.912.C.3.8Find average and instantaneous rates of change. Explain the instantaneous rate of change as the limit of the average rate of change. Interpret a derivative as a rate of change in applications, including velocity, speed and acceleration.
MA.912.C.3.9Find the velocity and acceleration of a particle moving in a straight line.
MA.912.C.4 Develop an understanding for and determine integrals.
MA.912.C.4.1Interpret a definite integral as a limit of Riemann sums. Calculate the values of Riemann sums over equal subdivisions using left, right and midpoint evaluation points.
MA.912.C.4.2Apply Riemann sums, the Trapezoidal Rule and technology to approximate definite integrals of functions represented algebraically, geometrically and by tables of values.
MA.912.C.4.3Interpret a definite integral of the rate of change of a quantity over an interval as the change of the quantity over the interval.
MA.912.C.4.4Evaluate definite integrals by using the Fundamental Theorem of Calculus.
MA.912.C.4.5Analyze function graphs by using derivative graphs and the Fundamental Theorem of Calculus.
MA.912.C.4.6Evaluate or solve problems using the properties of definite integrals. Properties are limited to the following:
MA.912.C.4.7Evaluate definite and indefinite integrals by using integration by substitution.
MA.912.C.5 Apply integrals to solve problems.
MA.912.C.5.1Find specific antiderivatives using initial conditions, including finding velocity functions from acceleration functions, finding position functions from velocity functions and solving applications related to motion along a line.
MA.912.C.5.2Solve separable differential equations.
MA.912.C.5.3Solve differential equations of the form dy/dt = ky as applied to growth and decay problems.
MA.912.C.5.4Display a graphic representation of the solution to a differential equation by using slope fields, and locate particular solutions to the equation.
MA.912.C.5.5Find the area between a curve and the x-axis or between two curves by using definite integrals.
MA.912.C.5.6Find the average value of a function over a closed interval by using definite integrals.
MA.912.C.5.7Find the volume of a figure with known cross-sectional area, including figures of revolution, by using definite integrals.
MA.912.DP High School: Data Analysis and Probability
MA.912.DP.1 Summarize, represent and interpret categorical and numerical data with one and two variables.
MA.912.DP.1.1Given a set of data, select an appropriate method to represent the data, depending on whether it is numerical or categorical data and on whether it is univariate or bivariate.
MA.912.DP.1.2Interpret data distributions represented in various ways. State whether the data is numerical or categorical, whether it is univariate or bivariate and interpret the different components and quantities in the display.
MA.912.DP.1.3Explain the difference between correlation and causation in the contexts of both numerical and categorical data.
MA.912.DP.1.4Estimate a population total, mean or percentage using data from a sample survey; develop a margin of error through the use of simulation.
MA.912.DP.1.5Interpret the margin of error of a mean or percentage from a data set. Interpret the confidence level corresponding to the margin of error.
MA.912.DP.2 Solve problems involving univariate and bivariate numerical data.
MA.912.DP.2.1For two or more sets of numerical univariate data, calculate and compare the appropriate measures of center and measures of variability, accounting for possible effects of outliers. Interpret any notable features of the shape of the data distribution.
MA.912.DP.2.2Use 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.
MA.912.DP.2.3Estimate population percentages from data that has been fit to the normal distribution.
MA.912.DP.2.4Fit a linear function to bivariate numerical data that suggests a linear association and interpret the slope and y-intercept of the model. Use the model to solve real-world problems in terms of the context of the data.
MA.912.DP.2.5Given a scatter plot that represents bivariate numerical data, assess the fit of a given linear function by plotting and analyzing residuals.
MA.912.DP.2.6Given a scatter plot with a line of fit and residuals, determine the strength and direction of the correlation. Interpret strength and direction within a real-world context.
MA.912.DP.2.7Compute the correlation coefficient of a linear model using technology. Interpret the strength and direction of the correlation coefficient.
MA.912.DP.2.8Fit a quadratic function to bivariate numerical data that suggests a quadratic association and interpret any intercepts or the vertex of the model. Use the model to solve real-world problems in terms of the context of the data.
MA.912.DP.2.9Fit an exponential function to bivariate numerical data that suggests an exponential association. Use the model to solve real-world problems in terms of the context of the data.
MA.912.DP.3 Solve problems involving categorical data.
MA.912.DP.3.1Construct a two-way frequency table summarizing bivariate categorical data. Interpret joint and marginal frequencies and determine possible associations in terms of a real-world context.
MA.912.DP.3.2Given marginal and conditional relative frequencies, construct a two-way relative frequency table summarizing categorical bivariate data.
MA.912.DP.3.3Given a two-way relative frequency table or segmented bar graph summarizing categorical bivariate data, interpret joint, marginal and conditional relative frequencies in terms of a real-world context.
MA.912.DP.3.4Given a relative frequency table, construct and interpret a segmented bar graph.
MA.912.DP.3.5Solve real-world problems involving univariate and bivariate categorical data.
MA.912.DP.4 Use and interpret independence and probability.
MA.912.DP.4.1Describe events as subsets of a sample space using characteristics, or categories, of the outcomes, or as unions, intersections or complements of other events.
MA.912.DP.4.10Given a mathematical or real-world situation, calculate the appropriate permutation or combination.
MA.912.DP.4.2Determine if events A and B are independent by calculating the product of their probabilities.
MA.912.DP.4.3Calculate the conditional probability of two events and interpret the result in terms of its context.
MA.912.DP.4.4Interpret the independence of two events using conditional probability.
MA.912.DP.4.5Given a two-way table containing data from a population, interpret the joint and marginal relative frequencies as empirical probabilities and the conditional relative frequencies as empirical conditional probabilities. Use those probabilities to determine whether characteristics in the population are approximately independent.
MA.912.DP.4.6Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
MA.912.DP.4.7Apply the addition rule for probability, taking into consideration whether the events are mutually exclusive, and interpret the result in terms of the model and its context.
MA.912.DP.4.8Apply the general multiplication rule for probability, taking into consideration whether the events are independent, and interpret the result in terms of the context.
MA.912.DP.4.9Apply the addition and multiplication rules for counting to solve mathematical and real-world problems, including problems involving probability.
MA.912.DP.5 Determine methods of data collection and make inferences from collected data.
MA.912.DP.5.1Distinguish between a population parameter and a sample statistic.
MA.912.DP.5.10Determine whether differences between parameters are significant using simulations.
MA.912.DP.5.11Evaluate reports based on data from diverse media, print and digital resources by interpreting graphs and tables; evaluating data-based arguments; determining whether a valid sampling method was used; or interpreting provided statistics.
MA.912.DP.5.2Explain how random sampling produces data that is representative of a population.
MA.912.DP.5.3Compare and contrast sampling methods.
MA.912.DP.5.4Generate multiple samples or simulated samples of the same size to measure the variation in estimates or predictions.
MA.912.DP.5.5Determine if a specific model is consistent within a given process by analyzing the data distribution from a data-generating process.
MA.912.DP.5.6Determine the appropriate design, survey, experiment or observational study, based on the purpose. Articulate the types of questions appropriate for each type of design.
MA.912.DP.5.7Compare and contrast surveys, experiments and observational studies.
MA.912.DP.5.8Draw inferences about two populations using data and statistical analysis from two random samples.
MA.912.DP.5.9Compare two treatments using data from an experiment in which the treatments are assigned randomly.
MA.912.DP.6 Use probability distributions to solve problems.
MA.912.DP.6.1Define a random variable for a quantity of interest by assigning a numerical value to each individual outcome in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
MA.912.DP.6.2Develop a probability distribution for a discrete random variable using theoretical probabilities. Find the expected value and interpret it as the mean of the discrete distribution.
MA.912.DP.6.3Develop a probability distribution for a discrete random variable using empirical probabilities. Find the expected value and interpret it as the mean of the discrete distribution.
MA.912.DP.6.4Given a binomial distribution, calculate and interpret the expected value. Solve real-world problems involving binomial distributions.
MA.912.DP.6.5Solve real-world problems involving geometric distributions.
MA.912.DP.6.6Solve real-world problems involving Poisson distributions.
MA.912.DP.6.7Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values and standard deviations. Evaluate and compare strategies on the basis of the calculated expected values and standard deviations.
MA.912.DP.6.8Apply probabilities to make fair decisions, such as drawing from lots or using a random number generator.
MA.912.F High School: Functions
MA.912.F.1 Understand, compare and analyze properties of functions.
MA.912.F.1.1Given an equation or graph that defines a function, determine the function type. Given an input-output table, determine a function type that could represent it.
MA.912.F.1.2Given a function represented in function notation, evaluate the function for an input in its domain. For a real-world context, interpret the output.
MA.912.F.1.3Calculate and interpret the average rate of change of a real-world situation represented graphically, algebraically or in a table over a specified interval.
MA.912.F.1.4Write an algebraic expression that represents the difference quotient of a function. Calculate the numerical value of the difference quotient at a given pair of points.
MA.912.F.1.5Compare key features of linear functions each represented algebraically, graphically, in tables or written descriptions.
MA.912.F.1.6Compare key features of linear and nonlinear functions each represented algebraically, graphically, in tables or written descriptions.
MA.912.F.1.7Compare key features of two functions each represented algebraically, graphically, in tables or written descriptions.
MA.912.F.1.8Determine whether a linear, quadratic or exponential function best models a given real-world situation.
MA.912.F.1.9Determine whether a function is even, odd or neither when represented algebraically, graphically or in a table.
MA.912.F.2 Identify and describe the effects of transformations on functions. Create new functions given transformations.
MA.912.F.2.1Identify the effect on the graph or table of a given function after replacing f(x) by f(x)+k,kf(x), f(kx) and f(x+k) for specific values of k.
MA.912.F.2.2Identify the effect on the graph of a given function of two or more transformations defined by adding a real number to the x- or y- values or multiplying the x- or y- values by a real number.
MA.912.F.2.3Given the graph or table of f(x) and the graph or table of f(x)+k,kf(x), f(kx) and f(x+k), state the type of transformation and find the value of the real number k.
MA.912.F.2.4Given the graph or table of values of two or more transformations of a function, state the type of transformation and find the values of the real number that defines the transformation.
MA.912.F.2.5Given a table, equation or graph that represents a function, create a corresponding table, equation or graph of the transformed function defined by adding a real number to the x- or y-values or multiplying the x- or y-values by a real number.
MA.912.F.3 Create new functions from existing functions.
MA.912.F.3.1Given a mathematical or real-world context, combine two functions, limited to linear and quadratic, using arithmetic operations. When appropriate, include domain restrictions for the new function.
MA.912.F.3.2Given a mathematical or real-world context, combine two or more functions, limited to linear, quadratic, exponential and polynomial, using arithmetic operations. When appropriate, include domain restrictions for the new function.
MA.912.F.3.3Solve mathematical and real-world problems involving functions that have been combined using arithmetic operations.
MA.912.F.3.4Represent the composition of two functions algebraically or in a table. Determine the domain and range of the composite function.
MA.912.F.3.5Solve mathematical and real-world problems involving composite functions.
MA.912.F.3.6Determine whether an inverse function exists by analyzing tables, graphs and equations.
MA.912.F.3.7Represent the inverse of a function algebraically, graphically or in a table. Use composition of functions to verify that one function is the inverse of the other.
MA.912.F.3.8Produce an invertible function from a non-invertible function by restricting the domain.
MA.912.F.3.9Solve mathematical and real-world problems involving inverse functions.
MA.912.FL High School: Financial Literacy
MA.912.FL.1 Build mathematical foundations for financial literacy.
MA.912.FL.1.1Extend previous knowledge of operations of fractions, percentages and decimals to solve real-world problems involving money and business.
MA.912.FL.1.2Extend previous knowledge of ratios and proportional relationships to solve real-world problems involving money and business.
MA.912.FL.1.3Solve real-world problems involving weighted averages using spreadsheets and other technology.
MA.912.FL.2 Develop an understanding of basic accounting and economic principles.
MA.912.FL.2.1Given assets and liabilities, calculate net worth using spreadsheets and other technology.
MA.912.FL.2.2Solve real-world problems involving profits, costs and revenues using spreadsheets and other technology.
MA.912.FL.2.3Explain how consumer price index (CPI), gross domestic product (GDP), stock indices, unemployment rate and trade deficit are calculated. Interpret their value in terms of the context.
MA.912.FL.2.4Given current exchange rates, convert between currencies. Solve real-world problems involving exchange rates.
MA.912.FL.2.5Develop budgets that fit within various incomes using spreadsheets and other technology.
MA.912.FL.2.6Given a real-world scenario, complete and calculate federal income tax using spreadsheets and other technology.
MA.912.FL.3 Describe the advantages and disadvantages of short-term and long-term purchases.
MA.912.FL.3.1Compare simple, compound and continuously compounded interest over time.
MA.912.FL.3.10Analyze credit scores qualitatively. Explain how short-term and long-term purchases, including deferred payments, may increase or decrease credit scores. Explain how credit scores influence buying power.
MA.912.FL.3.11Given a real-world scenario, establish a plan to pay off debt.
MA.912.FL.3.12Given fixed costs, per item costs and selling price, determine the break-even point for sales volume.
MA.912.FL.3.2Solve real-world problems involving simple, compound and continuously compounded interest.
MA.912.FL.3.3Solve real-world problems involving present value and future value of money
MA.912.FL.3.4Explain the relationship between simple interest and linear growth. Explain the relationship between compound interest and exponential growth and the relationship between continuously compounded interest and exponential growth.
MA.912.FL.3.5Compare the advantages and disadvantages of using cash versus personal financing options.
MA.912.FL.3.6Calculate the finance charges and total amount due on a bill using various forms of credit using estimation, spreadsheets and other technology.
MA.912.FL.3.7Compare the advantages and disadvantages of different types of student loans by manipulating a variety of variables and calculating the total cost using spreadsheets and other technology.
MA.912.FL.3.8Calculate using spreadsheets and other technology the total cost of purchasing consumer durables over time given different monthly payments, down payments, financing options and fees.
MA.912.FL.3.9Compare the advantages and disadvantages of different types of mortgage loans by manipulating a variety of variables and calculating fees and total cost using spreadsheets and other technology.
MA.912.FL.4 Describe the advantages and disadvantages of financial and investment plans, including insurances.
MA.912.FL.4.1Calculate and compare various options, deductibles and fees for various types of insurance policies using spreadsheets and other technology.
MA.912.FL.4.2Compare the advantages and disadvantages for adding on a one-time warranty to a purchase using spreadsheets and other technology.
MA.912.FL.4.3Compare the advantages and disadvantages of various retirement savings plans using spreadsheets and other technology.
MA.912.FL.4.4Collect, organize and interpret data to determine an effective retirement savings plan to meet personal financial goals using spreadsheets and other technology.
MA.912.FL.4.5Compare different ways that portfolios can be diversified in investments.
MA.912.FL.4.6Simulate the purchase of a stock portfolio with a set amount of money, and evaluate its worth over time considering gains, losses and selling, taking into account any associated fees.
MA.912.GR High School: Geometric Reasoning
MA.912.GR.1 Prove and apply geometric theorems to solve problems.
MA.912.GR.1.1Prove relationships and theorems about lines and angles. Solve mathematical and real-world problems involving postulates, relationships and theorems of lines and angles.
MA.912.GR.1.2Prove triangle congruence or similarity using Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, Angle-Angle and Hypotenuse-Leg.
MA.912.GR.1.3Prove relationships and theorems about triangles. Solve mathematical and real-world problems involving postulates, relationships and theorems of triangles.
MA.912.GR.1.4Prove relationships and theorems about parallelograms. Solve mathematical and real-world problems involving postulates, relationships and theorems of parallelograms.
MA.912.GR.1.5Prove relationships and theorems about trapezoids. Solve mathematical and real-world problems involving postulates, relationships and theorems of trapezoids.
MA.912.GR.1.6Solve mathematical and real-world problems involving congruence or similarity in two-dimensional figures.
MA.912.GR.2 Apply properties of transformations to describe congruence or similarity.
MA.912.GR.2.1Given a preimage and image, describe the transformation and represent the transformation algebraically using coordinates.
MA.912.GR.2.2Identify transformations that do or do not preserve distance.
MA.912.GR.2.3Identify a sequence of transformations that will map a given figure onto itself or onto another congruent or similar figure.
MA.912.GR.2.4Determine symmetries of reflection, symmetries of rotation and symmetries of translation of a geometric figure.
MA.912.GR.2.5Given a geometric figure and a sequence of transformations, draw the transformed figure on a coordinate plane.
MA.912.GR.2.6Apply rigid transformations to map one figure onto another to justify that the two figures are congruent.
MA.912.GR.2.7Justify the criteria for triangle congruence using the definition of congruence in terms of rigid transformations.
MA.912.GR.2.8Apply an appropriate transformation to map one figure onto another to justify that the two figures are similar.
MA.912.GR.2.9Justify the criteria for triangle similarity using the definition of similarity in terms of non-rigid transformations.
MA.912.GR.3 Use coordinate geometry to solve problems or prove relationships.
MA.912.GR.3.1Determine the weighted average of two or more points on a line.
MA.912.GR.3.2Given a mathematical context, use coordinate geometry to classify or justify definitions, properties and theorems involving circles, triangles or quadrilaterals.
MA.912.GR.3.3Use coordinate geometry to solve mathematical and real-world geometric problems involving lines, circles, triangles and quadrilaterals.
MA.912.GR.3.4Use coordinate geometry to solve mathematical and real-world problems on the coordinate plane involving perimeter or area of polygons.
MA.912.GR.4 Use geometric measurement and dimensions to solve problems.
MA.912.GR.4.1Identify the shapes of two-dimensional cross-sections of three-dimensional figures.
MA.912.GR.4.2Identify three-dimensional objects generated by rotations of two-dimensional figures.
MA.912.GR.4.3Extend previous understanding of scale drawings and scale factors to determine how dilations affect the area of two-dimensional figures and the surface area or volume of three-dimensional figures.
MA.912.GR.4.4Solve mathematical and real-world problems involving the area of two-dimensional figures.
MA.912.GR.4.5Solve mathematical and real-world problems involving the volume of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres.
MA.912.GR.4.6Solve mathematical and real-world problems involving the surface area of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres.
MA.912.GR.5 Make formal geometric constructions with a variety of tools and methods.
MA.912.GR.5.1Construct a copy of a segment or an angle.
MA.912.GR.5.2Construct the bisector of a segment or an angle, including the perpendicular bisector of a line segment.
MA.912.GR.5.3Construct the inscribed and circumscribed circles of a triangle.
MA.912.GR.5.4Construct a regular polygon inscribed in a circle. Regular polygons are limited to triangles, quadrilaterals and hexagons.
MA.912.GR.5.5Given a point outside a circle, construct a line tangent to the circle that passes through the given point.
MA.912.GR.6 Use properties and theorems related to circles.
MA.912.GR.6.1Solve mathematical and real-world problems involving the length of a secant, tangent, segment or chord in a given circle.
MA.912.GR.6.2Solve mathematical and real-world problems involving the measures of arcs and related angles.
MA.912.GR.6.3Solve mathematical problems involving triangles and quadrilaterals inscribed in a circle.
MA.912.GR.6.4Solve mathematical and real-world problems involving the arc length and area of a sector in a given circle.
MA.912.GR.6.5Apply transformations to prove that all circles are similar.
MA.912.GR.7 Apply geometric and algebraic representations of conic sections.
MA.912.GR.7.1Given a conic section, describe how it can result from the slicing of two cones.
MA.912.GR.7.2Given a mathematical or real-world context, derive and create the equation of a circle using key features.
MA.912.GR.7.3Graph and solve mathematical and real-world problems that are modeled with an equation of a circle. Determine and interpret key features in terms of the context.
MA.912.GR.7.4Given a mathematical or real-world context, derive and create the equation of a parabola using key features.
MA.912.GR.7.5Graph and solve mathematical and real-world problems that are modeled with an equation of a parabola. Determine and interpret key features in terms of the context.
MA.912.GR.7.6Given a mathematical or real-world context, derive and create the equation of an ellipse using key features.
MA.912.GR.7.7Graph and solve mathematical and real-world problems that are modeled with an equation of an ellipse. Determine and interpret key features in terms of the context.
MA.912.GR.7.8Given a mathematical or real-world context, derive and create the equation of a hyperbola using key features.
MA.912.GR.7.9Graph and solve mathematical and real-world problems that are modeled with an equation of a hyperbola. Determine and interpret key features in terms of the context.
MA.912.LT High School: Logic and Discrete Theory
MA.912.LT.1 Apply recursive methods to solve problems.
MA.912.LT.1.1Apply recursive and iterative thinking to solve problems.
MA.912.LT.1.2Solve problems involving recurrence relations.
MA.912.LT.1.3Apply mathematical induction in a variety of applications.
MA.912.LT.2 Apply optimization and techniques from Graph Theory to solve problems.
MA.912.LT.2.1Define and explain the basic concepts of Graph Theory.
MA.912.LT.2.2Solve problems involving paths in graphs.
MA.912.LT.2.3Solve scheduling problems using critical path analysis and Gantt charts. Create a schedule using critical path analysis.
MA.912.LT.2.4Apply graph coloring techniques to solve problems.
MA.912.LT.2.5Apply spanning trees, rooted trees, binary trees and decision trees to solve problems.
MA.912.LT.2.6Solve problems concerning optimizing resource usage using bin-packing techniques.
MA.912.LT.2.7Solve problems involving optimal strategies in Game Theory.
MA.912.LT.3 Apply techniques from Election Theory and Fair Division Theory to solve problems.
MA.912.LT.3.1Define and explain the basic concepts of Election Theory and voting.
MA.912.LT.3.2Analyze election data using election theory techniques. Explain how Arrow’s Impossibility Theorem may be related to the fairness of the outcome of the election.
MA.912.LT.3.3Decide voting power within a group using weighted voting techniques. Provide real-world examples of weighted voting and its pros and cons.
MA.912.LT.3.4Solve problems using fair division and apportionment techniques.
MA.912.LT.4 Develop an understanding of the fundamentals of propositional logic, arguments and methods of proof.
MA.912.LT.4.1Translate propositional statements into logical arguments using propositional variables and logical connectives.
MA.912.LT.4.10Judge the validity of arguments and give counterexamples to disprove statements.
MA.912.LT.4.2Determine truth values of simple and compound statements using truth tables.
MA.912.LT.4.3Identify and accurately interpret “if…then,” “if and only if,” “all” and “not” statements. Find the converse, inverse and contrapositive of a statement.
MA.912.LT.4.4Represent logic operations, such as AND, OR, NOT, NOR, and XOR, using logical symbolism to solve problems.
MA.912.LT.4.5Determine whether two propositions are logically equivalent.
MA.912.LT.4.6Apply methods of direct and indirect proof and determine whether a logical argument is valid.
MA.912.LT.4.7Identify and give examples of undefined terms; axioms; theorems; proofs, including proofs using mathematical induction; and inductive and deductive reasoning.
MA.912.LT.4.8Construct proofs, including proofs by contradiction.
MA.912.LT.4.9Construct logical arguments using laws of detachment, syllogism, tautology, contradiction and Euler Diagrams.
MA.912.LT.5 Apply properties from Set Theory to solve problems.
MA.912.LT.5.1Given two sets, determine whether the two sets are equivalent and whether one set is a subset of another. Given one set, determine its power set.
MA.912.LT.5.2Given a relation on two sets, determine whether the relation is a function, determine the inverse of the relation if it exists and identify if the relation is bijective.
MA.912.LT.5.3Partition a set into disjoint subsets and determine an equivalence class given the equivalence relation on a set.
MA.912.LT.5.4Perform the set operations of taking the complement of a set and the union, intersection, difference and product of two sets.
MA.912.LT.5.5Explore relationships and patterns and make arguments about relationships between sets using Venn Diagrams.
MA.912.LT.5.6Prove set relations, including DeMorgan’s Laws and equivalence relations.
MA.912.NSO High School: Number Sense and Operations
MA.912.NSO.1 Generate equivalent expressions and perform operations with expressions involving exponents, radicals or logarithms.
MA.912.NSO.1.1Extend previous understanding of the Laws of Exponents to include rational exponents. Apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions involving rational exponents.
MA.912.NSO.1.2Generate equivalent algebraic expressions using the properties of exponents.
MA.912.NSO.1.3Generate equivalent algebraic expressions involving radicals or rational exponents using the properties of exponents.
MA.912.NSO.1.4Apply previous understanding of operations with rational numbers to add, subtract, multiply and divide numerical radicals.
MA.912.NSO.1.5Add, subtract, multiply and divide algebraic expressions involving radicals.
MA.912.NSO.1.6Given a numerical logarithmic expression, evaluate and generate equivalent numerical expressions using the properties of logarithms or exponents.
MA.912.NSO.1.7Given an algebraic logarithmic expression, generate an equivalent algebraic expression using the properties of logarithms or exponents.
MA.912.NSO.2 Represent and perform operations with expressions within the complex number system.
MA.912.NSO.2.1Extend previous understanding of the real number system to include the complex number system. Add, subtract, multiply and divide complex numbers.
MA.912.NSO.2.2Represent addition, subtraction, multiplication and conjugation of complex numbers geometrically on the complex plane.
MA.912.NSO.2.3Calculate the distance and midpoint between two numbers on the complex coordinate plane.
MA.912.NSO.2.4Solve mathematical and real-world problems involving complex numbers represented algebraically or on the coordinate plane.
MA.912.NSO.2.5Represent complex numbers on the complex plane in rectangular and polar forms.
MA.912.NSO.2.6Rewrite complex numbers to trigonometric form. Multiply complex numbers in trigonometric form.
MA.912.NSO.3 Represent and perform operations with vectors.
MA.912.NSO.3.1Apply appropriate notation and symbols to represent vectors in the plane as directed line segments. Determine the magnitude and direction of a vector in component form.
MA.912.NSO.3.2Represent vectors in component form, linear form or trigonometric form. Rewrite vectors from one form to another.
MA.912.NSO.3.3Solve mathematical and real-world problems involving velocity and other quantities that can be represented by vectors.
MA.912.NSO.3.4Solve mathematical and real-world problems involving vectors in two dimensions using the dot product and vector projections.
MA.912.NSO.3.5Solve mathematical and real-world problems involving vectors in three dimensions using the dot product and cross product.
MA.912.NSO.3.6Multiply a vector by a scalar algebraically or graphically.
MA.912.NSO.3.7Compute the magnitude and direction of a vector scalar multiple.
MA.912.NSO.3.8Add and subtract vectors algebraically or graphically.
MA.912.NSO.3.9Given the magnitude and direction of two or more vectors, determine the magnitude and direction of their sum.
MA.912.NSO.4 Represent and perform operations with matrices.
MA.912.NSO.4.1Given a mathematical or real-world context, represent and manipulate data using matrices.
MA.912.NSO.4.2Given a mathematical or real-world context, represent and solve a system of two- or three-variable linear equations using matrices.
MA.912.NSO.4.3Solve mathematical and real-world problems involving addition, subtraction and multiplication of matrices.
MA.912.NSO.4.4Solve mathematical and real-world problems using the inverse and determinant of matrices.
MA.912.T High School: Trigonometry
MA.912.T.1 Define and use trigonometric ratios, identities or functions to solve problems.
MA.912.T.1.1Define trigonometric ratios for acute angles in right triangles.
MA.912.T.1.2Solve mathematical and real-world problems involving right triangles using trigonometric ratios and the Pythagorean Theorem.
MA.912.T.1.3Apply the Law of Sines and the Law of Cosines to solve mathematical and real-world problems involving triangles.
MA.912.T.1.4Solve mathematical problems involving finding the area of a triangle given two sides and the included angle.
MA.912.T.1.5Prove Pythagorean Identities. Apply Pythagorean Identities to calculate trigonometric ratios and to solve problems.
MA.912.T.1.6Prove the Double-Angle, Half-Angle, Angle Sum and Difference formulas for sine, cosine, and tangent. Apply these formulas to solve problems.
MA.912.T.1.7Simplify expressions using trigonometric identities.
MA.912.T.1.8Solve mathematical and real-world problems involving one-variable trigonometric ratios.
MA.912.T.2 Extend trigonometric functions to the unit circle.
MA.912.T.2.1Given any positive or negative angle measure in degrees or radians, identify its corresponding angle measure between 0° and 360° or between 0 and 2π. Convert between degrees and radians.
MA.912.T.2.2Define the six basic trigonometric functions for all real numbers by identifying corresponding angle measures and using right triangles drawn in the unit circle.
MA.912.T.2.3Determine the values of the six basic trigonometric functions for 0, π/6, π/3 and π/4 and their multiples using special triangles.
MA.912.T.2.4Use the unit circle to express the values of sine, cosine and tangent for π-x, π+x, and 2π-x in terms of their values for x, where x is any real number.
MA.912.T.2.5Given angles measured in radians or degrees, calculate the values of the six basic trigonometric functions using the unit circle, trigonometric identities or technology.
MA.912.T.3 Graph and apply trigonometric relations and functions.
MA.912.T.3.1Given a mathematical or real-world context, choose sine, cosine or tangent trigonometric functions to model periodic phenomena with specified amplitude, frequency, horizontal shift and midline.
MA.912.T.3.2Given a table, equation or written description of a trigonometric function, graph that function and determine key features.
MA.912.T.3.3Solve and graph mathematical and real-world problems that are modeled with trigonometric functions. Interpret key features and determine constraints in terms of the context.
MA.912.T.4 Extend rectangular coordinates and equations to polar and parametric forms.
MA.912.T.4.1Define and plot polar coordinates. Convert between polar coordinates and rectangular coordinates with and without the use of technology.
MA.912.T.4.2Represent equations given in rectangular coordinates in terms of polar coordinates. Represent equations given in polar coordinates in terms of rectangular coordinates.
MA.912.T.4.3Graph equations in the polar coordinate plane with and without the use of graphing technology.
MA.912.T.4.4Identify and graph special polar equations, including circles, cardioids, limacons, rose curves and lemniscates.
MA.912.T.4.5Sketch the graph of a curve in the plane represented parametrically, indicating the direction of motion.
MA.912.T.4.6Convert from a parametric representation of a plane curve to a rectangular equation, and convert from a rectangular equation to a parametric representation of a plane curve.
MA.912.T.4.7Apply parametric equations to model applications involving motion in the plane.

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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