Oklahoma Math Standards - Oklahoma Academic Standards for Mathematics

736 standards, Kindergarten through AP.

Oklahoma adopted its own Academic Standards for Mathematics in 2016, covering K-8 plus traditional high school courses: Pre-Algebra, Algebra I and II, Geometry, Precalculus, and Statistics/Probability. Foundational elementary skills feed into multiple secondary pathways.

Kindergarten (K)

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K.A Algebraic Reasoning & Algebra (A)
K.A.1 Duplicate patterns in a variety of contexts.
K.A.1.1Sort and group up to 10 objects into a set based upon characteristics such as color, size, and shape. Explain verbally what the objects have in common.
K.A.1.2Recognize, duplicate, complete, and extend repeating, increasing, and decreasing patterns in a variety of contexts (i.e., shape, color, size, objects, sounds, movement).
K.D Data & Probability (D)
K.D.1 Collect, organize, and interpret categorical data.
K.D.1.1Collect and organize information about objects and events in the environment.
K.D.1.2Use categorical data to create real-object graphs and pictographs.
K.D.1.3Draw conclusions from real-object graphs and pictographs.
K.GM Geometry & Measurement (GM)
K.GM.1 Recognize and sort basic two-dimensional shapes; use two-dimensional and three-dimensional shapes to represent real-world objects.
K.GM.1.1Recognize squares, circles, triangles, and rectangles.
K.GM.1.2Sort two-dimensional objects using characteristics such as shape and size.
K.GM.1.3Identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably, such as the number of corners/vertices and the number of sides/edges.
K.GM.1.4Use smaller two-dimensional shapes to fill in the outline of a larger two-dimensional shape.
K.GM.1.5Compose larger, undefined shapes and structures using three-dimensional objects.
K.GM.1.6Use basic shapes and spatial reasoning to represent objects in the real world.
K.GM.2 Compare and order objects according to location and measurable attributes.
K.GM.2.1Use words to compare objects according to length, size, weight, position, and location.
K.GM.2.2Order up to 6 objects using measurable attributes, such as length and weight.
K.GM.2.3Identify more than one shared attribute between objects, and sort objects into sets.
K.GM.2.4Compare the number of objects needed to fill two different containers.
K.GM.3 Tell time as it relates to daily life.
K.GM.3.1Develop an awareness of simple time concepts within daily life, using age-appropriate vocabulary (e.g., yesterday, today, tomorrow, morning, afternoon, night).
K.N Numbers & Operations (N)
K.N.1 Understand the relationship between quantities and whole numbers.
K.N.1.1Count aloud forward in sequence to 100 by 1s and 10s.
K.N.1.2Recognize that a number can be used to represent how many objects are in a set up to 10.
K.N.1.3Use ordinal numbers to represent the position of an object in a sequence up to 10.
K.N.1.4Recognize without counting (subitize) the quantity of a small group of objects in organized and random arrangements up to 10.
K.N.1.5Count forward, with and without objects, from any given number up to 20.
K.N.1.6Read, write, discuss, and represent whole numbers from 0 to at least 20. Representations may include numerals, pictures, real-object and pictographs, spoken words, and manipulatives.
K.N.1.7Find a number that is 1 more or 1 less than a given number up to 10.
K.N.1.8Compare and order whole numbers from 0 to 10 with and without objects, using the vocabulary "more than,” “less than,” or “equal to.”
K.N.2 Develop conceptual understanding with addition and subtraction (up to 10) using objects and pictures.
K.N.2.1Compose and decompose numbers up to 10 using objects and pictures.
K.N.3 Understand the relationship between whole numbers and fractions through fair share.
K.N.3.1Distribute a set of objects into at least two smaller equal sets.
K.N.4 Identify coins by name.
K.N.4.1Identify pennies, nickels, dimes, and quarters by name.

First Grade (1)

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1.A Algebraic Reasoning & Algebra (A)
1.A.1 Identify patterns found in real-world and mathematical problems.
1.A.1.1Identify, create, complete, and extend repeating, increasing, and decreasing patterns in a variety of contexts (e.g., quantity, numbers, or shapes).
1.D Data & Probability (D)
1.D.1 Collect, organize, and interpret categorical and numerical data.
1.D.1.1Collect, sort, and organize data in up to three categories using representations (e.g., tally marks, tables, Venn diagrams).
1.D.1.2Use data to create pictographs and bar graphs that demonstrate one-to-one correspondence.
1.D.1.3Draw conclusions from pictographs and bar graphs.
1.GM Geometry & Measurement (GM)
1.GM.1 Recognize and compose two- and three-dimensional shapes.
1.GM.1.1Identify regular and irregular trapezoids and hexagons by pointing to the shape when given the name.
1.GM.1.2Compose larger, defined shapes using smaller two-dimensional shapes.
1.GM.1.3Compose structures with three-dimensional shapes.
1.GM.1.4Recognize three-dimensional shapes such as cubes, cones, cylinders, pyramids, and spheres.
1.GM.2 Select and use nonstandard and standard units to describe length and volume/capacity.
1.GM.2.1Use nonstandard and standard measuring tools to measure the length of objects.
1.GM.2.2Illustrate that the length of an object is the number of same-size units of length that, when laid end-to-end with no gaps or overlaps, reach from one end of the object to the other.
1.GM.2.3Measure the same object/distance with units of two different lengths, and describe how and why the measurements differ.
1.GM.2.4Describe a length to the nearest whole unit using a number with standard and nonstandard units.
1.GM.2.5Use standard and nonstandard tools to identify volume/capacity. Compare and sort containers that hold more, less, or the same amount.
1.GM.3 Describe and measure concepts of time.
1.GM.3.1Tell time to the hour and half-hour (analog and digital).
1.GM.3.2Describe and measure calendar time by days, weeks, months, and years.
1.N Numbers & Operations (N)
1.N.1 Count, compare, and represent whole numbers up to 100, with an emphasis on grouping in terms of tens and ones.
1.N.1.1Recognize numbers to 20 without counting (subitize) the quantity of structured arrangements.
1.N.1.2Use concrete representations to describe whole numbers between 10 and 100 in terms of tens and ones. Know that 10 is equivalent to 10 ones and 100 is equivalent to 10 tens.
1.N.1.3Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, words, addition and subtraction, pictures, tally marks, number lines, and manipulatives.
1.N.1.4Count forward, with objects, from any given number up to 100 by 1s, 2s, 5s and 10s.
1.N.1.5Count forward, without objects, by multiples of 1s, 2s, 5s, and 10s, up to 100.
1.N.1.6Find a number that is 10 more or 10 less than a given number up to 100.
1.N.1.7Compare and order whole numbers from 0 to 100.
1.N.1.8Use knowledge of number relationships to locate the position of a given whole number, up to 20, on an open number line.
1.N.1.9Use words such as “more than,” “less than,” and “equal to” to describe the relative value of numbers.
1.N.2 Solve addition and subtraction problems with sums and minuends of up to 10 in real-world and mathematical contexts.
1.N.2.1Represent and solve problems using addition and subtraction with sums and minuends of up to 10.
1.N.2.2Determine if equations involving addition and subtraction are true.
1.N.2.3Demonstrate fluency with basic facts of addition and subtraction with sums and minuends of up to 10.
1.N.3 Develop foundational ideas for fractions.
1.N.3.1Partition a regular polygon using physical models and recognize when those parts are equal.
1.N.3.2Partition (fair share) sets of objects into two and three equal groups.
1.N.4 Identify coins and their values.
1.N.4.1Identify pennies, nickels, dimes, and quarters by name and value.
1.N.4.2Write a number with the cent symbol to describe the value of a coin.
1.N.4.3Determine the value of a collection of pennies, nickels, or dimes up to one dollar, counting by 1s, 5s, and 10s.

Second Grade (2)

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2.A Algebraic Reasoning & Algebra (A)
2.A.1 Describe the relationship found in patterns to solve real-world and mathematical problems.
2.A.1.1Represent, create, describe, complete, and extend increasing and decreasing patterns with quantity and numbers in a variety of contexts.
2.A.1.2Represent and describe repeating patterns involving shapes in a variety of contexts.
2.A.2 Use number sentences involving unknowns to represent and solve real-world and mathematical problems.
2.A.2.1Use objects and number lines to represent number sentences.
2.A.2.2Generate models and situations to represent number sentences and vice versa.
2.A.2.3Apply the commutative property, identity property, and number sense to find values for unknowns that make addition and subtraction number sentences true or false.
2.D Data & Probability (D)
2.D.1 Collect, organize, and interpret data.
2.D.1.1Explain that the length of a bar in a bar graph and the number of objects in a pictograph represents the number of data points for a given category.
2.D.1.2Organize a collection of data with up to four categories using pictographs and bar graphs in intervals of 1s, 2s, 5s or 10s.
2.D.1.3Write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one.
2.D.1.4Draw conclusions and make predictions from information in a pictograph and bar graph.
2.GM Geometry & Measurement (GM)
2.GM.1 Analyze attributes of two- and three-dimensional figures and develop generalizations about their properties.
2.GM.1.1Recognize regular and irregular trapezoids and hexagons.
2.GM.1.2Describe, compare, and classify two-dimensional figures according to their geometric attributes.
2.GM.1.3Compose and decompose two-dimensional shapes using triangles, squares, hexagons, trapezoids, and rhombi.
2.GM.1.4Sort three-dimensional shapes based on attributes such as number of faces, vertices, and edges.
2.GM.1.5Recognize right angles and classify angles as smaller or larger than a right angle.
2.GM.2 Understand length as a measurable attribute and explore capacity.
2.GM.2.1Explain the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object.
2.GM.2.2Explain the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest whole unit.
2.GM.2.3Explore how varying shapes and styles of containers can have the same capacity.
2.GM.3 Tell time to the quarter hour.
2.GM.3.1Distinguish between a.m. and p.m.
2.GM.3.2Read and write time to the quarter hour on an analog and digital clock.
2.N Numbers & Operations (N)
2.N.1 Compare and represent whole numbers up to 1,000 with an emphasis on place value and equality.
2.N.1.1Read, write, discuss, and represent whole numbers up to 1,000. Representations should include, but are not limited to, numerals, words, pictures, tally marks, number lines, and manipulatives.
2.N.1.2Use knowledge of number relationships to locate the position of a given whole number, up to 100, on an open number line.
2.N.1.3Use place value to describe whole numbers between 10 and 1,000 in terms of hundreds, tens, and ones, including written, standard, and expanded forms. Know that 10 is equivalent to 10 ones and 100 is equivalent to 10 tens.
2.N.1.4Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number.
2.N.1.5Use objects to determine whether a number is even or odd.
2.N.1.6Use place value understanding to round numbers to the nearest ten and nearest hundred (up to 1,000). Recognize when to round in real-world situations.
2.N.1.7Use place value to compare and order whole numbers up to 1,000 using comparative language, numbers, and symbols (e.g., 425 > 276, 73 < 107, page 351 comes after page 350, 753 is between 700 and 800).
2.N.2 Add and subtract one- and two-digit numbers in real-world and mathematical problems.
2.N.2.1Use the relationship between addition and subtraction to generate basic facts with sums and minuends of up to 20.
2.N.2.2Demonstrate fluency with basic facts of addition and subtraction with sums and minuends of up to 20.
2.N.2.3Estimate sums and differences up to 100.
2.N.2.4Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers.
2.N.2.5Solve addition and subtraction problems involving whole numbers up to two digits.
2.N.2.6Use concrete models and structured arrangements, such as repeated addition, arrays, and ten frames to develop an understanding of multiplication.
2.N.3 Explore the foundational ideas of fractions.
2.N.3.1Identify the parts of a set and area that represent fractions for halves, thirds, and fourths.
2.N.3.2Construct equal-sized portions through fair sharing (length, set, and area models for halves, thirds, and fourths).
2.N.4 Determine the value of a set of coins.
2.N.4.1Determine the value of a collection of coins up to one dollar using the cent symbol.
2.N.4.2Use a combination of coins to represent a given amount of money up to one dollar.

Third Grade (3)

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3.A Algebraic Reasoning & Algebra (A)
3.A.1 Describe and create representations of numerical and geometric patterns.
3.A.1.1Create, describe, and extend patterns involving addition, subtraction, or multiplication to solve problems in a variety of contexts.
3.A.1.2Describe the rule (limited to a single operation) for a pattern from an input/output table or function machine involving addition, subtraction, or multiplication.
3.A.1.3Explore and develop visual representations of increasing and decreasing geometric patterns and construct the next steps.
3.A.2 Use number sentences involving multiplication and unknowns to represent and solve real-world and mathematical problems.
3.A.2.1Use number sense with the properties of addition, subtraction, and multiplication, to find unknowns (represented by symbols) in one-step equations. Generate real-world situations to represent number sentences.
3.A.2.2Identify, represent, and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems.
3.D Data & Probability (D)
3.D.1 Collect, organize, and analyze data.
3.D.1.1Collect and organize a data set with multiple categories using a frequency table, line plot, pictograph, or bar graph with scaled intervals.
3.D.1.2Solve one- and two-step problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals.
3.GM Geometry & Measurement (GM)
3.GM.1 Analyze and use geometric attributes to describe and create polygons and three-dimensional figures in various contexts.
3.GM.1.2Build a three-dimensional figure using unit cubes when shown a picture of a three-dimensional shape.
3.GM.1.3Classify angles within a polygon as acute, right, obtuse, and straight.
3.GM.2 Understand measurable attributes of real-world and mathematical objects using various tools.
3.GM.2.1Find the perimeter of a polygon, given whole number lengths of the sides, using a variety of models.
3.GM.2.2Analyze why length and width are multiplied to find the area of a rectangle by decomposing the rectangle into one unit by one unit squares and viewing these as rows and columns to determine the area.
3.GM.2.3Count cubes systematically to identify the number of cubes needed to pack the whole or half of a three-dimensional structure.
3.GM.2.4Find the area of two-dimensional figures by counting the total number of same-size unit squares that fill the shape without gaps or overlaps.
3.GM.2.5Choose an appropriate measurement instrument and measure the length of objects to the nearest whole centimeter or whole meter.
3.GM.2.6Choose an appropriate measurement instrument and measure the length of objects to the nearest whole yard, whole foot, or half inch.
3.GM.2.7Use an analog thermometer to determine temperature to the nearest degree in Fahrenheit and Celsius.
3.GM.3 Solve problems by telling time to the nearest five-minute interval.
3.GM.3.1Read and write time to the nearest five-minute interval (analog and digital).
3.GM.3.2Determine the solutions to problems involving addition and subtraction of time in intervals of five minutes, up to one hour, using pictorial models, number line diagrams, or other tools.
3.GM 1 3.GM 1
3.GM 1.1Sort three-dimensional shapes based on attributes.
3.N Numbers & Operations (N)
3.N.1 Compare and represent whole numbers up to 100,000 with an emphasis on place value and equality.
3.N.1.1Read, write, discuss, and represent whole numbers up to 100,000. Representations should include but are not limited to numerals, words, pictures, number lines, and manipulatives (e.g., 350 = 3 hundreds, 5 tens = 35 tens = 3 hundreds, 4 tens, 10 ones).
3.N.1.2Use place value to describe whole numbers between 1,000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones, including written, standard, and expanded forms.
3.N.1.3Applying knowledge of place values, use mental strategies (no written computations) to find 100 more or 100 less than a given number, 1,000 more or 1,000 less than a given number, and 10,000 more or 10,000 less than a given number, up to a five-digit number.
3.N.1.4Use place value to compare and order whole numbers, up to 100,000, using comparative language, numbers, and symbols.
3.N.1.5Use place value understanding to round numbers to the nearest thousand, ten-thousand and hundred thousand.
3.N.2 Solve real-world and mathematical problems using addition, subtraction, multiplication, and division.
3.N.2.1Represent multiplication facts by modeling a variety of approaches (e.g., manipulatives, repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, skip counting).
3.N.2.2Demonstrate fluency with multiplication facts using factors up to 10.
3.N.2.3Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract up to five-digit numbers (answer not to exceed 100,000).
3.N.2.4Recognize when to round numbers and apply understanding to estimate sums and differences to the nearest ten thousand, thousand, hundred, and ten.
3.N.2.5Use addition and subtraction to solve problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction and the context of the problem to assess the reasonableness of results.
3.N.2.6Represent division facts and divisibility by modeling a variety of approaches (e.g., repeated subtraction, equal sharing, forming equal groups) to show the relationship between multiplication and division.
3.N.2.7Apply the relationship between multiplication and division to represent and solve problems.
3.N.2.8Use various strategies (e.g., base ten blocks, area models, arrays, repeated addition, algorithms) based on knowledge of place value, equality, and properties of addition and multiplication to multiply a two-digit factor by a one-digit factor.
3.N.3 Use and justify fractional representations in real-world and mathematical problems.
3.N.3.1Read and write fractions with words and symbols using appropriate terminology (i.e., numerator and denominator).
3.N.3.2Model fractions using length, set, and area for halves, thirds, fourths, sixths, and eighths.
3.N.3.3Apply understanding of unit fractions and use this understanding to compose and decompose fractions related to the same whole.
3.N.3.4Use models and number lines to order and compare fractions that are related to the same whole.
3.N.4 Determine the value of a set of coins and determine the value of a set of bills in monetary transactions.
3.N.4.1Use addition and subtraction to determine the value of a collection of coins up to one dollar using the cent symbol and in monetary transactions.
3.N.4.2Add and subtract a collection of bills up to twenty dollars using whole dollars in monetary transactions.

Fourth Grade (4)

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4.A Algebraic Reasoning & Algebra (A)
4.A.1 Describe, create, and analyze multiple representations of patterns to solve real-world and mathematical problems.
4.A.1.1Create an input/output chart or table to represent or extend a numerical pattern.
4.A.1.2Describe the single operation rule for a pattern from an input/output table or function machine involving any operation of a whole number.
4.A.1.3Construct models to show growth patterns involving geometric shapes and define the single operation rule of the pattern.
4.A.2 Use multiplication and division with variables to create number sentences representing a given mathematical situation.
4.A.2.1Use the relationships between multiplication and division with the properties of multiplication to solve problems and find values for variables that make number sentences true.
4.A.2.2Solve for a variable in an equation involving addition, subtraction, multiplication, or division with whole numbers. Analyze models to represent number sentences and vice versa.
4.A.2.3Determine the unknown addend or factor in equivalent and non-equivalent expressions (e.g., 5 + 6 = 4 + □, 3 ∙ 8 < 3 ∙ □).
4.D Data & Probability (D)
4.D.1 Summarize, construct, and analyze data.
4.D.1.1Create and organize data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units.
4.D.1.2Organize data sets to create tables, bar graphs, timelines, and Venn diagrams. The data may include benchmark fractions or decimals (1/4, 1/3, 1/2, 2/3, 3/4, 0.25, 0.50, 0.75).
4.D.1.3Solve one- and two-step problems by analyzing data in whole number, decimal, or fraction form in a frequency table and line plot.
4.GM Geometry & Measurement (GM)
4.GM.1 Name, describe, classify, and construct polygons and three-dimensional figures based on their attributes; recognize polygons and three-dimensional figures in real-life and mathematical situations.
4.GM.1.1Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various models.
4.GM.1.2Describe, classify, and construct quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various models.
4.GM.1.3Given two three-dimensional shapes, identify each shape. Compare and contrast their similarities and differences based on their attributes.
4.GM.2 Recognize and measure attributes in real-world and mathematical situations using various tools.
4.GM.2.1Measure angles in geometric figures and real-world objects with a protractor or angle ruler.
4.GM.2.2Find the area of polygons by determining if they can be decomposed into rectangles.
4.GM.2.3Develop the concept that the volume of rectangular prisms with whole-number edge lengths can be found by counting the total number of same-sized unit cubes that fill a shape without gaps or overlaps. Use a variety of tools and create models to determine the volume using appropriate measurements (e.g., cm3).
4.GM.2.4Choose an appropriate instrument to measure the length of an object to the nearest whole centimeter or quarter inch.
4.GM.2.5Recognize and use the relationship between inches, feet, and yards to measure and compare objects.
4.GM.2.6Recognize and use the relationship between millimeters, centimeters, and meters to measure and compare objects.
4.GM.2.7Determine and justify the best use of customary and metric measurements in a variety of situations (liquid volumes, mass vs. weight, temperatures above 0 (zero) degrees, and length).
4.GM.3 Determine elapsed time and convert between units of time.
4.GM.3.1Determine elapsed time.
4.GM.3.2Convert one measure of time to another including seconds to minutes, minutes to hours, hours to days, and vice versa, using various models.
4.N Numbers & Operations (N)
4.N.1 Compare and represent whole numbers up to 1,000,000 with an emphasis on place value and equality.
4.N.1.1Read, write, discuss, and represent whole numbers up to 1,000,000. Representations may include numerals, words, pictures, number lines, and manipulatives.
4.N.1.2Use place value to describe whole numbers between 1,000 and 1,000,000 in terms of millions, hundred thousands, ten thousands, thousands, hundreds, tens, and ones with written, standard, and expanded forms.
4.N.1.3Applying knowledge of place value, use mental strategies (no written computations) to multiply or divide a number by 10, 100 and 1,000.
4.N.1.4Use place value to compare and order whole numbers up to 1,000,000, using comparative language, numbers, and symbols.
4.N.2 Solve real-world and mathematical problems using multiplication and division.
4.N.2.1Demonstrate fluency with multiplication and division facts with factors up to 12.
4.N.2.2Multiply 3-digit by 1-digit and 2-digit by 2-digit whole numbers, using various strategies, including but not limited to standard algorithms.
4.N.2.3Estimate products of 3-digit by 1-digit and 2-digit by 2-digit whole number factors using a variety of strategies (e.g., rounding, front end estimation, adjusting, compatible numbers) to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns.
4.N.2.4Apply and analyze models to solve multi-step problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results.
4.N.2.5Use strategies and algorithms (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties) based on knowledge of place value, equality, and properties of operations to divide a 3-digit dividend by a 1-digit whole number divisor, with and without remainders.
4.N.3 Represent and compare fractions and decimals in real-world and mathematical situations; use place value to understand decimal quantities.
4.N.3.1Represent and rename equivalent fractions using fraction models (e.g., parts of a set, area models, fraction strips, number lines).
4.N.3.2Use benchmark fractions (0, 1/4, 1/3, 1/2, 2/3, 3/4, 1) to locate additional fractions with denominators up to twelfths on a number line.
4.N.3.3Use models to order and compare whole numbers and fractions less than and greater than one, using comparative language and symbols.
4.N.3.4Decompose a fraction into a sum of fractions with the same denominator in more than one way, using concrete and pictorial models and recording results with numerical representations (e.g., 3/4 = 1/4+1/4+1/4 and 3/4 = 2/4+1/4).
4.N.3.5Use models to add and subtract fractions with like denominators.
4.N.3.6Represent tenths and hundredths with concrete and pictorial models, making connections between fractions and decimals.
4.N.3.7Read and write decimals in standard, word, and expanded form up to at least the hundredths place in a variety of contexts, including money.
4.N.3.8Compare and order decimals and whole numbers using place value and various models including but not limited to grids, number lines, and base 10 blocks.
4.N.3.9Compare and order benchmark fractions (0, 1/4, 1/3, 2/3, 3/4, 1) and decimals (0, 0.25, 0.50, 0.75, 1.00) in a variety of representations.
4.N.4 Determine the value of bills and coins in order to solve monetary transactions.
4.N.4.1Select the fewest number of coins for a given amount of money up to one dollar.
4.N.4.2Given a total cost (dollars and coins up to twenty dollars) and amount paid (dollars and coins up to twenty dollars), find the change required in a variety of ways.

Fifth Grade (5)

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5.A Algebraic Reasoning & Algebra (A)
5.A.1 Describe and graph patterns of change created through numerical patterns.
5.A.1.1Use tables and rules with up to two operations to describe patterns of change and make predictions and generalizations about various mathematical situations.
5.A.1.2Use a rule or table to represent ordered pairs of whole numbers and graph these ordered pairs on a coordinate plane, identifying the origin and axes in relation to the coordinates.
5.A.2 Understand and interpret expressions, equations, and inequalities involving variables and whole numbers, and use them to represent and evaluate real-world and mathematical problems.
5.A.2.1Generate equivalent numerical expressions and solve problems using number sense involving whole numbers by applying the commutative property, associative property, distributive property, and order of operations (excluding exponents).
5.A.2.2Determine whether an equation or inequality involving a variable is true or false for a given value of the variable.
5.A.2.3Evaluate expressions involving variables when values for the variables are given.
5.D Data & Probability (D)
5.D.1 Create and analyze data to find the range and measures of central tendency (mean, median, mode).
5.D.1.1Find the measures of central tendency (i.e., mean, median, mode) and range of a set of data. Understand that the mean is a “leveling out” or central balance point of the data.
5.D.1.2Create and analyze line and double-bar graphs with increments of whole numbers, fractions, and decimals.
5.GM Geometry & Measurement (GM)
5.GM.1 Describe, identify, classify, and construct two- and three-dimensional figures using their geometric attributes.
5.GM.1.1Describe, identify, classify, and construct triangles (equilateral, right, scalene, isosceles) by their attributes using various mathematical models.
5.GM.1.2Describe, identify, and classify three-dimensional figures (cubes, rectangular prisms, and pyramids) and their attributes (number of edges, faces, vertices, shapes of faces), given various mathematical models.
5.GM.1.3Recognize and draw a net for a three-dimensional figure (cube, rectangular prism, pyramid).
5.GM.2 Determine volume using the object’s dimensions. Compare and analyze rectangular prisms with equivalent volume to recognize their different dimensions.
5.GM.2.1Determine the volume of rectangular prisms by the number of unit cubes (n) used to construct the shape and by the product of the dimensions of the prism 𝑎 ⋅ 𝑏 ⋅ 𝑐 = 𝑛. Understand rectangular prisms of different dimensions (p, q, and r) can have the same volume if 𝑎 ⋅ 𝑏 ⋅ 𝑐 = 𝑝 ⋅ 𝑞 ⋅ 𝑟 = 𝑛.
5.GM.2.2Estimate the perimeter of polygons and create arguments for reasonable perimeter values of shapes that may include curves.
5.GM.3 Understand angle, length, weight, and capacity as measurable attributes of real-world and mathematical objects, using various tools to measure them. Solve real-world problems of length.
5.GM.3.1Measure and compare angles according to size using various tools.
5.GM.3.2Measure the length of an object to the nearest whole centimeter or up to 1/16 inch using an appropriate instrument.
5.GM.3.3Apply the relationship between inches, feet, and yards to measure, convert, and compare objects to solve problems.
5.GM.3.4Apply the relationship between millimeters, centimeters, and meters to measure, convert, and compare objects to solve problems.
5.GM.3.5Estimate lengths and geometric measurements to the nearest whole unit, using benchmarks in customary and metric measurement systems.
5.N Numbers & Operations (N)
5.N.1 Read, write, represent, and compare fractions and decimals; recognize and write equivalent fractions; convert between fractions and decimals; use fractions and decimals in real-world and mathematical situations.
5.N.1.1Represent decimal fractions using a variety of models (e.g., 10 by 10 grids, base-ten blocks, meter stick) and show the rational number relationships among fractions, decimals and whole numbers.
5.N.1.2Read, write, and represent decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers up to seven digits.
5.N.1.3Compare and order decimals and fractions, including mixed numbers and fractions less than one, and locate on a number line.
5.N.1.4Recognize and generate equivalent terminating decimals, fractions, mixed numbers, and fractions in various models.
5.N.2 Divide multi-digit numbers and solve real-world and mathematical problems using arithmetic.
5.N.2.1Estimate solutions to division problems to assess the reasonableness of results.
5.N.2.2Divide multi-digit numbers, by one- and two-digit divisors, based on knowledge of place value, including but not limited to standard algorithms.
5.N.2.3Recognize that remainders can be represented in a variety of ways, including a whole number, fraction, or decimal. Determine the most meaningful form of a remainder based on the context of the problem.
5.N.2.4Construct models to solve multi-digit whole number problems requiring addition, subtraction, multiplication, and division using various representations, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.
5.N.3 Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals to solve real-world and mathematical problems.
5.N.3.1Estimate sums and differences of fractions with like and unlike denominators, mixed numbers, and decimals to assess the reasonableness of the results.
5.N.3.2Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of mathematical models (e.g., fraction strips, area models, number lines, fraction rods).
5.N.3.3Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, involving money, measurement, geometry, and data. Use various models and efficient strategies, including but not limited to standard algorithms.
5.N.3.4Apply mental math and knowledge of place value (no written computations) to find 0.1 more or 0.1 less than a number, 0.01 more or 0.01 less than a number, and 0.001 more or 0.001 less than a number.

Sixth Grade (6)

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6.A Algebraic Reasoning & Algebra (A)
6.A.1 Recognize and represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs, and rules to model and solve mathematical problems.
6.A.1.1Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs.
6.A.1.2Represent relationships between two varying positive quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.
6.A.1.3Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.
6.A.2 Use properties of arithmetic to generate equivalent numerical expressions and evaluate expressions involving positive rational numbers.
6.A.2.1Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to model and solve mathematical problems.
6.A.3 Use equations and inequalities to model and solve mathematical problems and use the idea of maintaining equality to solve equations. Interpret solutions in the original context.
6.A.3.1Model mathematical situations using expressions, equations and inequalities involving variables and rational numbers.
6.A.3.2Use number sense and properties of operations and equality to model and solve mathematical problems involving equations in the form 𝑥 + 𝑝 = 𝑞 and 𝑝𝑥 = 𝑞, where p and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.
6.D Data & Probability (D)
6.D.1 Interpret and analyze data.
6.D.1.1Interpret the mean, median, and mode for a set of data.
6.D.1.2Explain and justify which measure of center (mean, median, or mode) would provide the most descriptive information for a given set of data.
6.D.2 Use probability to model and solve mathematical problems; represent probabilities using fractions and decimals.
6.D.2.1Represent possible outcomes using a probability continuum from impossible to certain.
6.D.2.2Determine the sample space for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial representations.
6.D.2.3Demonstrate simple experiments in which the probabilities are known and compare the resulting relative frequencies with the known probabilities, recognizing that there may be differences between the two results.
6.GM Geometry & Measurement (GM)
6.GM.1 Use translations, reflections, and rotations to establish congruence and understand symmetry (not on a coordinate plane).
6.GM.1.1Predict, describe, and apply translations (slides), reflections (flips), and rotations (turns) to a two-dimensional figure.
6.GM.1.2Recognize that translations, reflections, and rotations preserve congruence and use them to show that two figures are congruent.
6.GM.1.3Identify and describe the line(s) of symmetry in two-dimensional shapes.
6.GM.2 Use mathematical modeling to calculate the area of squares, parallelograms, and triangles to solve problems.
6.GM.2.1Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithms and finding unknown measures.
6.GM.2.2Develop and use formulas to determine the area of triangles and find unknown measures.
6.GM.2.3Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes.
6.GM.3 Understand and use relationships between angles in geometric figures.
6.GM.3.1Solve problems using the relationships between the angles (vertical, complementary, and supplementary) formed by intersecting lines.
6.GM.3.2Develop and use the fact that the sum of the interior angles of a triangle is 180° to determine missing angle measures in a triangle.
6.GM.4 Choose appropriate units of measurement and use ratios to convert within measurement systems to model and solve real-world and mathematical problems.
6.GM.4.1Estimate weights and capacities using benchmarks in customary and metric measurement systems with appropriate units.
6.GM.4.2Solve problems that require the conversion of lengths within the same measurement systems using appropriate units.
6.N Numbers & Operations (N)
6.N.1 Read, write, and represent rational numbers expressed as integers, fractions, decimals, percents, and ratios; use these representations in real-world and mathematical situations.
6.N.1.1Use manipulatives and models (e.g., number lines) to determine positive and negative numbers and their contexts, identify opposites, and explain the meaning of 0 (zero) in a variety of situations.
6.N.1.2Compare and order positive rational numbers, represented in various forms, or integers using the symbols "<", ">", and "=".
6.N.1.3Explain that a percent represents parts “out of 100” and ratios “to 100.”
6.N.1.4Determine equivalencies among fractions, mixed numbers, decimals, and percents.
6.N.2 Read, write, and model whole-number and integer operations to solve problems.
6.N.2.1Estimate solutions for integer addition and subtraction of problems in order to assess the reasonableness of results.
6.N.2.2Illustrate addition and subtraction of integers using a variety of representations.
6.N.2.3Add and subtract integers in a variety of situations; use efficient and generalizable procedures including but not limited to standard algorithms.
6.N.2.4Identify and represent patterns with whole-number exponents and perfect squares. Evaluate powers with whole-number bases and exponents.
6.N.2.5Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents.
6.N.2.6Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.
6.N.3 Explain and use the concept of ratio and its relationship to other rational numbers and to the multiplication and division of whole numbers. Use ratios to solve problems.
6.N.3.1Identify and use ratios to compare and relate quantities in multiple ways. Recognize that multiplicative comparison and additive comparison are different.
6.N.3.2Determine the unit rate for ratios.
6.N.3.3Apply the relationship between ratios, equivalent fractions, unit rates, and percents to solve problems in various contexts.
6.N.4 Multiply and divide decimals, fractions, and mixed numbers; solve real-world and mathematical problems with rational numbers.
6.N.4.1Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers, and use the estimates to assess the reasonableness of results in the context of the problem.
6.N.4.2Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.
6.N.4.3Multiply and divide fractions and decimals using efficient and generalizable procedures.
6.N.4.4Use mathematical modeling to solve and interpret problems including money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.

Seventh Grade (7)

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7.A Algebraic Reasoning & Algebra (A)
7.A.1 Explain the concept of proportionality in mathematical models and situations and distinguish between proportional and non-proportional relationships.
7.A.1.1Identify a relationship between two varying quantities, x and y, as proportional if it can be expressed in the form y/x = 𝑘 or y=kx; distinguish proportional relationships from non-proportional relationships.
7.A.1.2Recognize that the graph of a proportional relationship is a line through the origin and the coordinate (1, r), where r is the slope and the unit rate (constant of proportionality, k).
7.A.2 Identify and justify proportional relationships using mathematical models and situations; solve problems involving proportional relationships and interpret results in the original context.
7.A.2.1Represent proportional relationships with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. Determine and compare the unit rate (constant of proportionality, slope, or rate of change) given any of these representations.
7.A.2.2Solve multi-step problems with proportional relationships (e.g., distance-time, percent increase or decrease, discounts, tips, unit pricing, mixtures and concentrations, similar figures, other mathematical situations).
7.A.2.3Use proportional reasoning to solve problems involving ratios.
7.A.2.4Use proportional reasoning to assess the reasonableness of solutions.
7.A.3 Represent mathematical situations using equations and inequalities involving variables and rational numbers.
7.A.3.1Write and solve problems leading to linear equations with one variable in the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers.
7.A.3.2Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form 𝑥 + 𝑝 > 𝑞 and 𝑥 + 𝑝 < 𝑞, where 𝑝, and 𝑞 are nonnegative rational numbers.
7.A.4 Use order of operations and properties of operations to generate and evaluate equivalent numerical and algebraic expressions.
7.A.4.1Use properties of operations (associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents.
7.A.4.2Evaluate numerical expressions using calculators and other technologies and justify solutions using order of operations and grouping symbols.
7.D Data & Probability (D)
7.D.1 Interpret and analyze data, creating the most appropriate display, using a variety of tools.
7.D.1.1Design simple experiments, collect data, and calculate measures of center (mean, median, and mode) and spread (range and interquartile range). Use these quantities to draw conclusions about the data collected and make predictions.
7.D.1.2Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms.
7.D.1.3Use technology to create and analyze box plots.
7.D.2 Calculate and use proportional reasoning with probabilities to model and solve mathematical problems.
7.D.2.1Determine the theoretical probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions and decimals between 0 and 1.
7.D.2.2Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as percents, decimals and fractions.
7.D.2.3Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on theoretical probabilities.
7.GM Geometry & Measurement (GM)
7.GM.1 Develop and understand the concept of surface area and volume of rectangular prisms with rational-valued edge lengths.
7.GM.1.1Recognize that the surface area of a rectangular prism can be found by finding the area of each component of the net of that figure. Know that rectangular prisms of different dimensions can have the same surface area.
7.GM.1.2Using a variety of tools and strategies, develop the concept that surface area of a rectangular prism can be found by wrapping the figure with same-sized square units without gaps or overlap. Use appropriate measurements (e.g., cm^2).
7.GM.1.3Using a variety of tools and strategies, develop the concept that the volume of rectangular prisms can be found by counting the total number of same-sized unit cubes that fill a shape without gaps or overlaps. Use appropriate measurements (e.g., cm^3).
7.GM.2 Use mathematical models and problems to calculate and justify the area of trapezoids and the area and perimeter of composite figures with rational measurements.
7.GM.2.1Develop and use the formula to determine the area of a trapezoid.
7.GM.2.2Find the area and perimeter of composite figures.
7.GM.3 Use mathematical models and reasoning with proportions and ratios to determine measurements, justify formulas, and solve problems.
7.GM.3.1Solve problems that require the conversion of weights and capacities within the same measurement systems using appropriate units.
7.GM.3.2Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is pi (𝜋) and can be approximated by rational numbers such as 22/7 and 3.14.
7.GM.3.3Calculate the circumference and area of circles to solve problems in various contexts, in terms of pi (𝜋) and using approximations for pi (𝜋).
7.GM.4 Analyze the effect of translations, reflections, rotations, and dilations on the attributes of two-dimensional figures on and off the coordinate plane.
7.GM.4.1Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors resulting from dilations.
7.GM.4.2Apply proportions, ratios, and scale factors to solve problems involving scale drawings and to determine side lengths and areas of similar triangles and rectangles.
7.GM.4.3Graph and describe translations (with directional and algebraic instructions), reflections across the x- and y-axes, and rotations in 90° increments about the origin of figures on a coordinate plane, and determine the coordinates of the vertices of a figure after a transformation.
7.N Numbers & Operations (N)
7.N.1 Read, write, represent, and compare rational numbers, expressed as integers, fractions, and decimals. Explain and apply the concept of absolute value.
7.N.1.1Compare and order rational numbers expressed in various forms using the symbols "<", ">", and "=".
7.N.1.2Recognize and generate equivalent representations of rational numbers, including equivalent fractions.
7.N.1.3Explain the relationship between the absolute value of a rational number and the distance of that number from zero on a number line. Use the symbol for absolute value. Apply the concept of absolute value to model and solve problems.
7.N.2 Calculate with rational numbers, with and without positive integer exponents, to model and solve mathematical problems.
7.N.2.1Estimate solutions to multiplication and division of integers in order to assess the reasonableness of results.
7.N.2.2Illustrate multiplication and division of integers using a variety of representations.
7.N.2.3Multiply and divide integers in a variety of situations; use efficient and generalizable procedures, including standard algorithms.
7.N.2.4Raise rational numbers (integers, fractions, and decimals) to positive integer exponents.
7.N.2.5Model and solve problems using rational numbers involving addition, subtraction, multiplication, division, and positive integer exponents.

Algebra 1 (A1)

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A1.A Algebraic Reasoning & Algebra (A)
A1.A.1 Represent and solve mathematical and real-world problems using linear equations, absolute value equations, and systems of equations; interpret solutions in the original context.
A1.A.1.1Use knowledge of solving equations with rational values to represent, use and apply mathematical models (e.g., angle measures, geometric formulas, dimensional analysis, Pythagorean theorem, science, statistics) and interpret the solutions in the original context.
A1.A.1.2Solve absolute value equations and interpret the solutions in the original context.
A1.A.1.3Analyze, use and apply mathematical models to solve problems involving systems of linear equations with a maximum of two variables by graphing, substitution, and elimination. Graphing calculators or other appropriate technology may be utilized. Interpret the solutions in the original context.
A1.A.2 Represent and solve real-world and mathematical problems using linear inequalities and compound inequalities; interpret solutions in the original context.
A1.A.2.1Represent relationships using mathematical models with linear inequalities; solve the resulting inequalities, graph on a coordinate plane, and interpret the solutions.
A1.A.2.2Represent relationships using mathematical models with compound and absolute value inequalities and solve the resulting inequalities by graphing and interpreting the solutions on a number line.
A1.A.3 Create and evaluate equivalent algebraic expressions and equations using algebraic properties.
A1.A.3.1Solve equations involving several variables for one variable in terms of the others.
A1.A.3.2Simplify polynomial expressions by adding, subtracting, or multiplying.
A1.A.3.3Factor common monomial factors from polynomial expressions and factor quadratic expressions with a leading coefficient of 1.
A1.A.3.4Evaluate linear, absolute value, rational, and radical expressions. Include applying a nonstandard operation such as x ⨀ y=2x+y
A1.A.4 Analyze real-world and mathematical problems involving linear equations.
A1.A.4.1Analyze, use and apply mathematical models and other data sets (e.g., graphs, equations, two points, a set of data points) to calculate and interpret slope and the x- and y-intercepts of a line.
A1.A.4.2Analyze and interpret mathematical models involving lines that are parallel, perpendicular, horizontal, and vertical.
A1.A.4.3Write the equation of the line given its slope and y-intercept, slope and one point, two points, x- and y-intercepts, or a set of data points.
A1.A.4.4Express linear equations in slope-intercept, point-slope, and standard forms. Convert between these forms.
A1.A.4.5Analyze and interpret associations between graphical representations and written scenarios.
A1.D Data & Probability (D)
A1.D.1 Display, describe, and compare data. For linear relationships, make predictions, and assess the reliability of those predictions.
A1.D.1.1Display, describe, and compare data sets using summary statistics (central tendency and spread (range)). Utilize technology (e.g., spreadsheets, calculators) to display data and calculate summary statistics.
A1.D.1.2Collect data and analyze scatter plots for patterns, linearity, and outliers.
A1.D.1.3Make predictions based upon the linear regression, and use the correlation coefficient to assess the reliability of those predictions using graphing technology.
A1.D.2 Calculate probabilities, and apply probability concepts.
A1.D.2.1Apply simple counting procedures (factorials, permutations, combinations, and tree diagrams) to determine sample size, sample space, and calculate probabilities.
A1.D.2.2Given a Venn diagram, determine the probability of the union of events, the intersection of events, and the complement of an event. Understand the relationships between these concepts and the words “AND,” “OR,” and “NOT.”
A1.D.2.3Use simulations and experiments to calculate experimental probabilities.
A1.D.2.4Apply probability concepts to real-world situations to make informed decisions.
A1.F Functions (F)
A1.F.1 Understand functions as descriptions of covariation (how related quantities vary together) in real-world and mathematical problems.
A1.F.1.1Distinguish between relations and functions.
A1.F.1.2Identify the dependent variable, independent variable, domain and range given a function, equation, or graph. Identify restrictions on the domain and range in mathematical models.
A1.F.1.3Write linear functions, using function notation, to represent mathematical models.
A1.F.1.4Read and interpret the linear piecewise function, given a graph modeling a situation.
A1.F.1.5Interpret graphs as being discrete or continuous.
A1.F.2 Recognize and understand that families of functions are defined by their characteristics.
A1.F.2.1Distinguish between linear and nonlinear (including exponential) functions. Understand that linear functions grow by equal intervals (arithmetic) and that exponential functions grow by equal factors over equal intervals (geometric).
A1.F.2.2Recognize the parent functions 𝑓(𝑥) = 𝑥 and 𝑓(𝑥) = |𝑥|. Predict the effects of vertical and horizontal transformations 𝑓(𝑥 + 𝑐) and 𝑓(𝑥) + 𝑐, algebraically and graphically.
A1.F.3 Represent functions in multiple ways and use the representation to interpret real-world and mathematical problems.
A1.F.3.1Identify and generate equivalent representations of linear functions, graphs, tables, and real-world situations.
A1.F.3.2Use function notation; evaluate a function, including nonlinear, at a given point in its domain algebraically and graphically. Interpret the results in terms of the original context.
A1.F.3.3Add, subtract, and multiply functions using function notation.
A1.N Numbers & Operations (N)
A1.N.1 Extend the understanding of exponents to include square roots and cube roots.
A1.N.1.1Write square roots and cube roots of constants and monomial algebraic expressions in simplest radical form.
A1.N.1.2Add, subtract, multiply, divide, and simplify square roots of constants, rationalizing the denominator when necessary.

Algebra 2 (A2)

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A2.A Algebraic Reasoning & Algebra (A)
A2.A.1 Represent and solve mathematical and real-world problems using nonlinear equations, systems of linear equations, and systems of linear inequalities; interpret the solutions in the original context.
A2.A.1.1Use mathematical models to represent quadratic relationships and solve using factoring, completing the square, the quadratic formula, and various methods (including graphing calculator or other appropriate technology). Find non-real roots when they exist.
A2.A.1.2Use mathematical models to represent exponential relationships, such as compound interest, depreciation, and population growth. Solve these equations algebraically or graphically (including graphing calculator or other appropriate technology).
A2.A.1.3Solve one-variable rational equations and check for extraneous solutions.
A2.A.1.4Solve polynomial equations with real roots using various methods (e.g., polynomial division, synthetic division, using graphing calculators or other appropriate technology).
A2.A.1.5Solve square and cube root equations with one variable, and check for extraneous solutions.
A2.A.1.6Solve common and natural logarithmic equations using the properties of logarithms.
A2.A.1.7Represent and evaluate mathematical models using systems of linear equations with a maximum of three variables. Graphing calculators or other appropriate technology may be used.
A2.A.1.8Use tools to solve systems of equations containing one linear equation and one quadratic equation. Graphing calculators or other appropriate technology may be used.
A2.A.1.9Solve systems of linear inequalities in two variables, with a maximum of three inequalities; graph and interpret the solutions on a coordinate plane. Graphing calculators or other appropriate technology may be used.
A2.A.2 Generate and evaluate equivalent algebraic expressions and equations using various strategies.
A2.A.2.1Factor polynomial expressions including, but not limited to, trinomials, differences of squares, sum and difference of cubes, and factoring by grouping, using a variety of tools and strategies.
A2.A.2.2Add, subtract, multiply, divide, and simplify polynomial expressions.
A2.A.2.3Add, subtract, multiply, divide, and simplify rational expressions.
A2.A.2.4Recognize that a quadratic function has different equivalent representations [𝑓(𝑥) = 𝑎𝑥^2 + 𝑏𝑥 + 𝑐, 𝑓(𝑥) = 𝑎(𝑥 − ℎ)^2 + 𝑘, 𝑎𝑛𝑑 𝑓(𝑥) = 𝑎(𝑥 − 𝑝)(𝑥 − 𝑞)]. Identify and use the mathematical model that is most appropriate to solve problems.
A2.A.2.5Rewrite algebraic expressions involving radicals and rational exponents using the properties of exponents.
A2.A.3 Represent and solve mathematical and real-world problems involving arithmetic and geometric sequences and series.
A2.A.3.1Recognize that arithmetic sequences are linear using equations, tables, graphs, and verbal descriptions. Using the pattern, find the next term.
A2.A.3.2Recognize that geometric sequences are exponential using equations, tables, graphs, and verbal descriptions. Given the formula 𝑓(𝑥) = 𝑎(𝑟)^x, find the next term and define the meaning of 𝑎 and 𝑟 within the context of the problem.
A2.A.3.3Solve problems that can be modeled using arithmetic sequences or series given the 𝑛th terms and sum formulas. Graphing calculators or other appropriate technology may be used.
A2.A.3.4Solve problems that can be modeled using finite geometric sequences and series given the 𝑛th terms and sum formulas. Graphing calculators or other appropriate technology may be used.
A2.D Data & Probability (D)
A2.D.1 Display, describe, and compare data. For linear and nonlinear relationships, make predictions and assess the reliability of those predictions.
A2.D.1.1Use the mean and standard deviation of a data set to create a normal distribution (bell-shaped curve).
A2.D.1.2Collect data and use scatter plots to analyze patterns and describe linear, exponential, or quadratic relationships between two variables.
A2.D.1.3Make predictions based upon the regression equation (linear, exponential, or quadratic), and use the correlation coefficient to assess the reliability of those predictions using graphing technology.
A2.D.2 Analyze statistical thinking to draw inferences, make predictions, and justify conclusions.
A2.D.2.1Evaluate reports by making inferences, justifying conclusions, and determining appropriateness of data collection methods. Show how graphs and data can be distorted to support different points of view.
A2.D.2.2Identify and explain misleading conclusions and graphical representations of data sets.
A2.D.2.3Differentiate between correlation and causation when describing the relationship between two variables.
A2.F Functions (F)
A2.F.1 Understand functions as descriptions of covariation (how related quantities vary together).
A2.F.1.1Use algebraic, interval, and set notations to specify the domain and range of various types of functions, and evaluate a function at a given point in its domain.
A2.F.1.2Identify the parent forms of exponential, radical (square root and cube root only), quadratic, and logarithmic functions. Predict the effects of transformations [𝑓(𝑥 + 𝑐), 𝑓(𝑥) + 𝑐, 𝑓(𝑐𝑥), 𝑎𝑛𝑑 𝑐𝑓(𝑥)] algebraically and graphically.
A2.F.1.3Graph a quadratic function. Identify the domain, range, x- and y-intercepts, maximum or minimum value, axis of symmetry, and vertex using various methods and tools that may include a graphing calculator or appropriate technology.
A2.F.1.4Graph exponential and logarithmic functions. Identify the domain, range, asymptotes, and x- and y-intercepts using various methods and tools that may include calculators or other appropriate technology. Recognize exponential decay and growth graphically and algebraically.
A2.F.1.5Analyze the graph of a polynomial function by identifying the domain, range, intercepts, zeros, relative maxima, relative minima, and intervals of increase and decrease.
A2.F.1.6Graph a rational function and identify the domain (including holes), range, x- and y-intercepts, vertical and horizontal asymptotes, using various methods and tools that may include a graphing calculator or other appropriate technology (excluding slant or oblique asymptotes).
A2.F.1.7Graph a radical function (square root and cube root only). Identify the domain, range, and x- and y-intercepts using various methods and tools that may include a graphing calculator or other appropriate technology.
A2.F.1.8Graph piecewise functions with no more than three branches (linear, quadratic, or exponential). Analyze the function by identifying the domain, range, intercepts, and intervals for which it is increasing, decreasing, and constant using various methods and tools (e.g., graphing calculator, other appropriate technology).
A2.F.1.9Recognize whether a discrete or continuous graphical representation is appropriate to create a graph based upon a mathematical model.
A2.F.2 Analyze functions through algebraic combinations, compositions, and inverses if they exist.
A2.F.2.1Add, subtract, multiply, and divide functions using function notation and recognize domain restrictions.
A2.F.2.2Combine functions by com position and recognize that 𝑔(𝑥) = 𝑓^-1(𝑥), the inverse function of 𝑓(𝑥), if and only if 𝑓(𝑔(𝑥)) = 𝑔(𝑓(𝑥)) = 𝑥.
A2.F.2.3Find and graph the inverse of a function, if it exists, in mathematical models. Know that the domain of a function f is the range of the inverse function 𝑓(! and the range of the function 𝑓 is the dom ain of the inverse function 𝑓(!
A2.F.2.4Apply the inverse relationship between exponential and logarithmic functions to convert from one form to another.
A2.N Numbers & Operations (N)
A2.N.1 Extend the understanding of numbers and operations to include complex numbers, radical expressions, and expressions written with rational exponents.
A2.N.1.1Find the value of 𝑖^n for any whole number 𝑛.
A2.N.1.2Simplify, add, subtract, multiply, and divide complex numbers.
A2.N.1.3Understand and apply the relationship between rational exponents to integer exponents and radicals to solve problems.
A2.N.2 Extend the understanding of numbers and operations to matrices.
A2.N.2.1Use matrices to organize and represent data. Identify the order (dimension) of a matrix.
A2.N.2.2Use addition, subtraction, and scalar multiplication of matrices to solve problems.

Geometry (G)

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G.2D Geometry: Two-Dimensional Shapes (G.2D)
G.2D.1 Discover, evaluate, and analyze the relationships between lines, angles, and polygons to solve real-world and mathematical problems; express proofs in a form that clearly justifies the reasoning (e.g., two-column proofs, paragraph proofs, flowcharts).
G.2D.1.1Use properties of parallel lines cut by a transversal to determine angle relationships and solve problems.
G.2D.1.10Construct logical arguments to prove triangle similarity (AA, SSS, SAS).
G.2D.1.11Use numeric, graphic, and algebraic representations of transformations in two dimensions (e.g., reflections, translations, dilations, rotations about the origin by multiples of 90') to solve problems involving figures on a coordinate plane and identify types of symmetry.
G.2D.1.2Use the angle relationships formed by lines cut by a transversal to determine if the lines are parallel and verify, using algebraic and deductive proofs.
G.2D.1.3Apply the properties of angles (corresponding, exterior, interior, vertical, complementary, supplementary) to solve problems using mathematical models, algebraic reasoning, and proofs.
G.2D.1.4Apply theorems involving the interior and exterior angle sums of polygons to solve problems using mathematical models, algebraic reasoning, and proofs.
G.2D.1.5Apply the properties of special quadrilaterals (square, rectangle, trapezoid, isosceles trapezoid, rhombus, kite, parallelogram) to solve problems involving angle measures and segment lengths using mathematical models, algebraic reasoning, and proofs.
G.2D.1.6Use coordinate geometry and algebraic reasoning to represent and analyze line segments and polygons, including determining lengths, midpoints, and slopes of line segments.
G.2D.1.7Apply the properties of polygons, and use them to represent and apply mathematical models involving perimeter and area (e.g., triangles, special quadrilaterals, regular polygons up to 12 sides, composite figures).
G.2D.1.8Apply the properties of congruent or similar polygons to solve problems using mathematical models and algebraic and logical reasoning.
G.2D.1.9Construct logical arguments to prove triangle congruence (SSS, SAS, ASA, AAS and HL).
G.3D Geometry: Three-Dimensional Shapes (G.3D)
G.3D.1 Solve real-world and mathematical problems involving three-dimensional figures.
G.3D.1.1Represent, use, and apply mathematical models and other tools (e.g., nets, measuring devices, formulas) to solve problems involving surface area and volume of three-dimensional figures (prisms, cylinders, pyramids, cones, spheres, composites of these figures).
G.3D.1.2Use ratios derived from similar three-dimensional figures to make conjectures, generalize, and to solve for unknown values such as angles, side lengths, perimeter, and circumference of a face, area of a face, and volume.
G.C Geometry: Circles (G.C)
G.C.1 Solve real-world and mathematical problems using the properties of circles.
G.C.1.1Apply the properties of circles to solve problems involving circumference and area, using approximate values and in terms of pi, using algebraic and logical reasoning.
G.C.1.2Use the distance and midpoint formula, where appropriate, to recognize and write the radius r, center (h,k), and standard form of the equation of a circle (x − ℎ)^2 + (y − k)^2 = r^2 with and without graphs.
G.C.1.3Apply the properties of circles and relationships among angles; arcs; and distances in a circle among radii, chords, secants, and tangents to solve problems using algebraic and logical reasoning.
G.RL Geometry: Reasoning & Logic (G.RL)
G.RL.1 Use appropriate tools and logic, including algebraic methods, to evaluate mathematical arguments.
G.RL.1.1Use undefined terms, definitions, postulates, and theorems in logical arguments/proofs.
G.RL.1.2Analyze and draw conclusions based on a set of conditions using inductive and deductive reasoning. Recognize the logical relationships between a conditional statement and its inverse, converse, and contrapositive.
G.RL.1.3Assess the validity of a logical argument and give counterexamples to disprove a statement.
G.RT Geometry: Right Triangle Trigonometry (G.RT)
G.RT.1 Apply mathematical relationships of right triangles and trigonometric ratios to solve real-world and mathematical problems.
G.RT.1.1Apply the distance formula, the Pythagorean theorem, and the Pythagorean theorem converse (approximate and exact values, including Pythagorean triples) to solve problems, using algebraic and logical reasoning and mathematical models.
G.RT.1.2Verify and apply properties of right triangles, including properties of 45-45-90 and 30-60-90 triangles, to solve problems using algebraic and logical reasoning.
G.RT.1.3Use the definition of the trigonometric functions to determine the sine, cosine, and tangent ratio of an acute angle in a right triangle. Apply the inverse trigonometric functions to find the measure of an acute angle in right triangles.
G.RT.1.4Apply the trigonometric functions as ratios (sine, cosine, tangent) to find side lengths in right triangles in mathematical models, including the coordinate plane.

Pre-Algebra (PA)

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PA.A Algebraic Reasoning & Algebra (A)
PA.A.1 Explain the concept of function in mathematical situations and distinguish between the concepts of linear and nonlinear functions.
PA.A.1.1Recognize that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable.
PA.A.1.2Use linear functions to represent and model mathematical situations.
PA.A.1.3Identify a function as linear if it can be expressed in the form y=mx + b or if its graph is a non-vertical straight line.
PA.A.2 Identify and justify linear functions using mathematical models and situations; solve problems involving linear functions and interpret results in the original context.
PA.A.2.1Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another.
PA.A.2.2Identify, describe, and analyze linear relationships between two variables.
PA.A.2.3Identify graphical properties of linear functions, including slope and intercepts. Know that the slope equals the rate of change, and that the y-intercept is zero when the function represents a proportional relationship.
PA.A.2.4Predict the effect on the graph of a linear function when the slope or y-intercept changes. Use appropriate tools to examine these effects.
PA.A.2.5Solve problems involving linear functions and interpret results in the original context.
PA.A.3 Generate equivalent numerical and algebraic expressions and use algebraic properties to evaluate expressions.
PA.A.3.1Use substitution to simplify and evaluate algebraic expressions.
PA.A.3.2Justify steps in generating equivalent expressions by combining like terms and using order of operations (to include grouping symbols). Identify the properties used, including the properties of operations (associative, commutative, and distributive).
PA.A.4 Represent and solve problems using mathematical models and situations with equations and inequalities involving linear expressions.
PA.A.4.1Solve mathematical problems using linear equations with one variable where there could be one, infinitely many, or no solutions. Represent situations using linear equations and interpret solutions in the original context.
PA.A.4.2Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form 𝑝𝑥 + 𝑞 > 𝑟 and 𝑝𝑥 + 𝑞 < 𝑟, where p, q, and r are rational numbers.
PA.A.4.3Represent real-world situations using equations and inequalities involving one variable.
PA.D Data & Probability (D)
PA.D.1 Display and interpret data in a variety of ways, including using scatter plots and approximate lines of best fit. Use the line of best fit and average rate of change to make predictions and draw conclusions about data.
PA.D.1.1Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Create data displays using technology to examine this impact.
PA.D.1.2Explain how outliers affect measures of center and spread.
PA.D.1.3Collect, display, and interpret data using scatter plots. Use the shape of the scatter plot to find the informal line of best fit, make statements about the average rate of change, and make predictions about values not in the original data set. Use appropriate titles, labels, and units.
PA.D.2 Calculate experimental probabilities and reason about probabilities to model and solve problems.
PA.D.2.1Calculate experimental probabilities and represent them as percents, fractions, and decimals between 0 and 1. Use experimental probabilities to predict relative frequencies when actual probabilities are unknown.
PA.D.2.2Determine how samples are chosen (randomness) to draw and support conclusions about generalizing a sample to a population, including identifying limitations and biases.
PA.D.2.3Define, compare, and contrast the probabilities of dependent and independent events.
PA.GM Geometry & Measurement (GM)
PA.GM.1 Apply the Pythagorean theorem to solve problems involving triangles.
PA.GM.1.1Justify the Pythagorean theorem using measurements, diagrams, or dynamic software to solve problems in two dimensions involving right triangles.
PA.GM.1.2Use the Pythagorean theorem to find the distance between any two points in a coordinate plane.
PA.GM.2 Justify and use formulas to calculate surface area and volume of three-dimensional figures.
PA.GM.2.1Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate units (e.g., cm^2).
PA.GM.2.2Calculate the surface area of a cylinder, in terms of pi (π) and using approximations for pi (π), using decomposition or nets. Use appropriate units (e.g., cm^2).
PA.GM.2.3Justify why base area (B) and height (h) in the formula V=Bh are multiplied to find the volume of a rectangular prism. Use appropriate units (e.g., cm^3).
PA.GM.2.4Develop and use the formulas 𝑉 = (𝜋𝑟)^$ℎ and 𝑉 = 𝐵ℎ to determine the volume of right cylinders, in terms of π and using approximations for pi (Τ). Justify why base area (B) and height (h) are multiplied to find the volume of a right cylinder. Use appropriate units (e.g., cm^3).
PA.N Numbers & Operations (N)
PA.N.1 Read, write, compare, classify, and represent real numbers, and use them to solve problems in various contexts.
PA.N.1.1Develop and apply the properties of integer exponents, including a^0 = 1 (with a ≠ 0), to generate equivalent numerical and algebraic expressions.
PA.N.1.2Express and compare approximations of very large and very small numbers using scientific notation.
PA.N.1.3Multiply and divide numbers expressed in scientific notation and express the answer in scientific notation.
PA.N.1.4Compare and order real numbers; locate real numbers on a number line. Identify the square roots of perfect squares to 400 or, if it is not a perfect square root, locate it as an irrational number between two consecutive positive integers.

Precalculus (PC)

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PC.CS Conic Sections (CS)
PC.CS.1 Investigate conic sections.
PC.CS.1.1Model real-world situations which involve conic sections.
PC.CS.1.2Identify key features of conic sections (foci, directrix, radii, axes, asymptotes, center) graphically and algebraically.
PC.CS.1.3Sketch a graph of a conic section using its key features.
PC.CS.1.4Write the equation of a conic section given its key features.
PC.CS.1.5Given the equation 𝑎𝑥^2 + 𝑏𝑦^2 + 𝑐𝑥 + 𝑑𝑦 + 𝑒 = 0, determine if the equation represents a circle, ellipse, parabola, or hyperbola.
PC.F Functions (F)
PC.F.1 Analyze functions and relations.
PC.F.1.1Interpret characteristics of a function defined by an expression in the context of the situation.
PC.F.1.2Sketch the graph of a function that models a relationship between two quantities, identifying key features.
PC.F.1.3Interpret characteristics of graphs and tables for a function that models a relationship between two quantities in terms of the quantities.
PC.F.1.4Describe end behavior, asymptotic behavior, and points of discontinuity.
PC.F.1.5Determine if a function has an inverse. Algebraically and graphically find the inverse or define any restrictions on the domain that meet the requirement for invertibility, and find the inverse on the restricted domain.
PC.F.2 Build functions to model and validate relationships among functions.
PC.F.2.1Model relationships through composition, and attend to the restrictions of the domain.
PC.F.2.2Rewrite a function as a composition of functions.
PC.F.2.3Interpret the meanings of quantities involving functions and their inverses.
PC.F.2.4Verify by analytical methods that one function is the inverse of another.
PC.F.3 Predict and verify solutions involving functions.
PC.F.3.1Predict solutions involving functions that are quadratic, polynomial of higher order, rational, exponential, and logarithmic.
PC.F.3.2Graphically verify solutions involving functions that are quadratic, polynomial of higher order, rational, exponential, and logarithmic.
PC.F.3.3Algebraically verify solutions involving functions that are quadratic, polynomial of higher order, rational, exponential, and logarithmic.
PC.T Trigonometry (T)
PC.T.1 Make sense of the unit circle and its relationship to the graphs of trigonometric functions.
PC.T.1.1Draw and recognize angles in standard position using radian measure, and determine the quadrant of the terminal side.
PC.T.1.2Convert radian measure to degree measure and vice-versa.
PC.T.1.3Find the length of an arc and the area of a sector on a circle.
PC.T.1.4Use special triangles to determine geometrically the values of sine, cosine, tangent for , and use the unit circle to express the values of sine, cosine, and tangent for 𝜋 − 𝑥, 𝜋 + 𝑥, and 2𝜋 − 𝑥 in terms of their values for x, where x is any real number.
PC.T.1.5Use reference angles to determine the terminal point P(x, y) on the unit circle for a given angle.
PC.T.1.6Estimate trigonometric values of any angle.
PC.T.1.7Apply the properties of a unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
PC.T.1.8Graph of all six trigonometric functions, identifying key features.
PC.T.1.9Describe and analyze the relationships of the properties of a unit circle.
PC.T.2 Apply trigonometric concepts beyond the right triangle.
PC.T.2.1Create models for situations involving trigonometry.
PC.T.2.2Apply the Law of Sines and Law of Cosines to solve problems.
PC.T.2.3Use trigonometry to find the area of triangles.
PC.T.2.4Use inverse functions to solve trigonometric equations; evaluate the solution and interpret them in terms of context.
PC.T.3 Verify trigonometric identities and solve equations.
PC.T.3.1Algebraically manipulate the structure of a trigonometric expression to identify ways to rewrite it.
PC.T.3.2Choose and produce an equivalent form of an expression to explain the properties of the quantity represented by the expression.
PC.T.3.3Graphically and algebraically verify solutions to trigonometric equations.
PC.T.4 Explore complex numbers.
PC.T.4.1Use the relation 𝑖^2 = −1 and the mathematical properties to add, subtract, and multiply complex numbers.
PC.T.4.2Find the conjugate of a complex number in rectangular forms and quotients of complex numbers.
PC.T.4.3Solve quadratic equations in one variable that have complex solutions.

Statistics & Probability (S)

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S.DA Data Analysis (DA)
S.DA.1 Use distributions of quantitative and categorical data to identify the key features of the data collected in context.
S.DA.1.1Summarize and represent the distribution for univariate quantitative data by describing and analyzing the shape of the distribution, the measures of center for the distribution, the patterns in variability for the distribution, and any outliers, gaps, or other unusual features in the distribution.
S.DA.1.2Select and create an appropriate display (e.g., dot plots, histograms, box plots) for univariate data.
S.DA.1.3Use statistics appropriate to the shape of the data distribution to compare center and variability of two or more different data sets.
S.DA.1.4Describe and analyze the distribution of univariate categorical data.
S.DA.2 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages.
S.DA.2.1Use calculators, computers, or tables to estimate areas under the normal curve. Recognize that there are data sets for which such a procedure is not appropriate.
S.DA.3 Compare two or more groups by analyzing distributions.
S.DA.3.1Construct appropriate parallel graphical displays of distributions.
S.DA.3.2Use numerical attributes of distributions to make comparisons between distributions.
S.DA.4 Analyze associations between two variables.
S.DA.4.1Create two-way tables for bivariate categorical data and analyze for possible associations between the two categories using marginal, joint, and conditional frequencies.
S.DA.4.2Make predictions and draw conclusions from regression models (linear, exponential, quadratic) from two-variable quantitative data.
S.DA.4.3Analyze scatter plots for patterns, linearity, outliers, and influential points.
S.DA.4.4Using technology, compute and interpret the correlation coefficient.
S.DA.4.5Understand the implications of extrapolating data to make predictions.
S.DA.5 Make statistical inferences and evaluate claims from studies.
S.DA.5.1Construct and interpret confidence intervals for the mean of a normally distributed population and for a population proportion.
S.DA.5.2Explain how a sample statistic and a confidence level are used in the construction of a confidence interval.
S.DA.5.3Explain how changes in the sample size, confidence level, and standard error affect the margin of error of a confidence interval.
S.DA.5.4Construct a confidence interval for the mean of a normally distributed population (with a known standard deviation) and for a population proportion. Use confidence intervals to evaluate claims.
S.DA.5.5Use confidence intervals to evaluate claims for a single population parameter.
S.DC Data Collection (DC)
S.DC.1 Distinguish among different types of study designs for collecting data, and know the scope of inference for each design type.
S.DC.1.1Distinguish among sample surveys, experiments, and observational studies.
S.DC.1.2Compare and contrast the benefits of different sampling techniques.
S.DC.1.3Determine the appropriate scope of inference for generalizing results.
S.DC.1.4Explain how sample size impacts the precision with which generalizations can be made.
S.DC.1.5Determine when a cause-and-effect inference can be drawn from an association, based on how the data were collected.
S.DC.2 Identify common sources of bias and the role of randomization in study design.
S.DC.2.1Explain how randomization and sources of bias impact the results of a study.
S.DC.2.2Understand the different roles of random selection and random assignment in study design.
S.IR Interpretation of Results (IR)
S.IR.1 Interpret and communicate the results of a statistical analysis in context.
S.IR.1.1Recognize when the difference between two sample proportions or two sample means is due to random variation or if the difference is statistically significant.
S.IR.1.2Understand the concept of a confidence interval, including the interpretation of confidence level, margin of error, and statistical significance.
S.IR.1.3Develop inferences or predictions to construct resulting decisions or recommendations.
S.IR.1.4Create and evaluate recommendations for areas of future research.
S.IR.2 Evaluate practical implications of statistical significance or lack thereof.
S.IR.2.1Develop and critique arguments for practical implications based on statistical significance.
S.IR.2.2Identify potential lurking variables which may explain an association between two variables.
S.IR.3 Evaluate real-world claims and conclusions.
S.IR.3.1Evaluate strengths and weaknesses in the studies or methods used to generate data.
S.IR.3.2Evaluate the statistical validity of claims made.
S.P Probability (P)
S.P.1 Connect basic probability concepts to statistical analysis.
S.P.1.1Describe events as subsets of a sample space.
S.P.1.2Describe the relationship between theoretical and empirical probabilities using the Law of Large Numbers.
S.P.1.3Use counting techniques (e.g., permutations and combinations) to solve mathematical and real-world problems, including determining probabilities of compound events.
S.P.2 Determine probabilities, including joint probabilities, conditional probabilities, probabilities of independent events, and probabilities of dependent events. Interpret the results.
S.P.2.1Understand that two events, A and B, are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if two events are independent.
S.P.2.2Understand and calculate the conditional probability of A given B as P(A and B)/P(B).
S.P.2.3Interpret independence of A and B as saying that the conditional probability of A, given B, is the same as the probability of A.
S.P.3 Use probability to make decisions.
S.P.3.1Analyze decisions and strategies using probability concepts and expected values.
S.P.3.2Analyze decisions about statistical significance based on reported p-values.
S.Q Statistical Questions (Q)
S.Q.1 Understand the distinction between mathematical models and statistical models.
S.Q.1.1Distinguish among different sources of variability, including measurement, natural, induced, and sampling variability.
S.Q.1.2Formulate meaningful statistical questions to clarify the problem at hand.
S.Q.2 Distinguish between the distribution of a population, a distribution of sample data, and a sampling distribution.
S.Q.2.1Distinguish between sample statistics and population parameters.
S.Q.2.2Recognize a population distribution has fixed values of its parameters and that these parameter values are typically unknown.
S.Q.2.3Recognize that a sample data distribution is taken from a population distribution, and the data distribution is what is seen in practice.
S.Q.2.4Recognize a sampling distribution is the distribution of a sample statistic (e.g., sample mean, sample proportion) obtained from repeated samples.
S.Q.3 Identify differences between categorical and quantitative data.
S.Q.3.1Determine whether categorical or quantitative data is appropriate to answer a statistical question.
S.Q.3.2Compare and contrast different potential graphical or visual representations given the same data set.

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.

Standards on this page are sourced from published state frameworks. Goblins aligns tutoring to these standards.