Minnesota Math Standards

557 standards, Kindergarten through AP.

Kindergarten

K.1 Number & Operation
K.1.1 Understand the relationship between quantities and whole numbers up to 31.
K.1.1.1Recognize that a number can be used to represent how many objects are in a set or to represent the position of an object in a sequence.
K.1.1.2Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes.
K.1.1.3Count, with and without objects, forward and backward to at least 20.
K.1.1.4Find a number that is 1 more or 1 less than a given number.
K.1.1.5Compare and order whole numbers, with and without objects, from 0 to 20.
K.1.2 Use objects and pictures to represent situations involving combining and separating.
K.1.2.1Use objects and draw pictures to find the sums and differences of numbers between 0 and 10.
K.1.2.2Compose and decompose numbers up to 10 with objects and pictures.
K.2 Algebra
K.2.1 Recognize, create, complete, and extend patterns.
K.2.1.1Identify, create, complete, and extend simple patterns using shape, color, size, number, sounds and movements. Patterns may be repeating, growing or shrinking such as ABB, ABB, ABB or o, oo, ooo.
K.3 Geometry & Measurement
K.3.1 Recognize and sort basic two and three dimensional shapes; use them to model real world objects.
K.3.1.1Recognize basic two- and three-dimensional shapes such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, cones, cylinders and spheres.
K.3.1.2Sort objects using characteristics such as shape, size, color and thickness.
K.3.1.3Use basic shapes and spatial reasoning to model objects in the real-world.
K.3.2 Compare and order objects according to location and measurable attributes.
K.3.2.1Use words to compare objects according to length, size, weight and position.
K.3.2.2Order 2 or 3 objects using measurable attributes, such as length and weight.

Grade 1

1.1 Number & Operation
1.1.1 Count, compare and represent whole numbers up to 120, with an emphasis on groups of tens and ones.
1.1.1.1Use place value to describe whole numbers between 10 and 100 in terms of tens and ones.
1.1.1.2Read, write and represent whole numbers up to 120. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks.
1.1.1.3Count, with and without objects, forward and backward from any given number up to 120.
1.1.1.4Find a number that is 10 more or 10 less than a given number.
1.1.1.5Compare and order whole numbers up to 120.
1.1.1.6Use words to describe the relative size of numbers.
1.1.1.7Use counting and comparison skills to create and analyze bar graphs and tally charts.
1.1.2 Use a variety of models and strategies to solve addition and subtraction problems in real world and mathematical contexts.
1.1.2.1Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations.
1.1.2.2Compose and decompose numbers up to 12 with an emphasis on making ten.
1.1.2.3Recognize the relationship between counting and addition and subtraction. Skip count by 2s, 5s, and 10s.
1.2 Algebra
1.2.1 Recognize and create patterns; use rules to describe patterns.
1.2.1.1Create simple patterns using objects, pictures, numbers and rules. Identify possible rules to complete or extend patterns. Patterns may be repeating, growing or shrinking. Calculators can be used to create and explore patterns.
1.2.2 Use number Sentences involving addition and subtraction basic facts to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.
1.2.2.1Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences.
1.2.2.2Determine if equations involving addition and subtraction are true.
1.2.2.3Use number sense and models of addition and subtraction, such as objects and number lines, to identify the missing number in an equation such as: 2 + 4 = x, 3 + x= 7 , 5 = x - 3.
1.2.2.4Use addition or subtraction basic facts to represent a given problem situation using a number sentence.
1.3 Geometry & Measurement
1.3.1 Describe characteristics of basic shapes. Use basic shapes to compose and decompose other objects in various contexts.
1.3.1.1Describe characteristics of two- and three-dimensional objects, such as triangles, squares, rectangles, circles, rectangular prisms, cylinders, cones and spheres.
1.3.1.2Compose (combine) and decompose (take apart) two- and three-dimensional figures such as triangles, squares, rectangles, circles, rectangular prisms and cylinders.
1.3.2 Use basic concepts of measurement in real-world and mathematical situations involving length, time and money.
1.3.2.1Measure the length of an object in terms of multiple copies of another object.
1.3.2.2Tell time to the hour and half-hour.
1.3.2.3Identify pennies, nickels and dimes; find the value of a group of these coins, up to one dollar.

Grade 2

2.1 Number & Operation
2.1.1 Compare and represent whole numbers up to 1000 with an emphasis on place value and equality.
2.1.1.1Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks.
2.1.1.2Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds.
2.1.1.3Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number.
2.1.1.4Round numbers up to the nearest 10 and 100 and round numbers down to the nearest 10 and 100.
2.1.1.5Compare and order whole numbers up to 1000.
2.1.2 Demonstrate mastery of addition and subtraction basic facts; add and subtract one- and two-digit numbers in real-world and mathematical problems.
2.1.2.1Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtraction to generate basic facts.
2.1.2.2Demonstrate fluency with basic addition facts and related subtraction facts.
2.1.2.3Estimate sums and differences up to 100.
2.1.2.4Use mental strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences.
2.1.2.5Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits.
2.1.2.6Use addition and subtraction to create and obtain information from tables, bar graphs and tally charts.
2.2 Algebra
2.2.1 Recognize, create, describe, and use patterns and rules to solve real world and mathematical problems.
2.2.1.1Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts.
2.2.2 Use number Sentences involving addition, subtraction and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.
2.2.2.1Understand how to interpret number sentences involving addition, subtraction and unknowns represented by letters. Use objects and number lines and create real-world situations to represent number sentences.
2.2.2.2Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true.
2.3 Geometry & Measurement
2.3.1 Identify, describe, and compare basic shapes according to their geometric attributes.
2.3.1.1Describe, compare, and classify two- and three-dimensional figures according to number and shape of faces, and the number of sides, edges and vertices (corners)
2.3.1.2Identify and name basic two- and three-dimensional shapes, such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, rectangular prisms, cones, cylinders and spheres.
2.3.2 Understand length as a measurable attribute; use tools to measure length.
2.3.2.1Understand the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object.
2.3.2.2Demonstrate an understanding of the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest centimeter or inch.
2.3.3 Use time and money in real world and mathematical situations.
2.3.3.1Tell time to the quarter-hour and distinguish between a.m. and p.m.
2.3.3.2Identify pennies, nickels, dimes and quarters. Find the value of a group of coins and determine combinations of coins that equal a given amount.

Grade 3

3.1 Number & Operation
3.1.1 Compare and represent whole numbers up to 100,000 with an emphasis on place value and equality.
3.1.1.1Read, write and represent whole numbers up to 100,000. Representations may include numerals, expressions with operations, words, pictures, number lines, and manipulatives such as bundles of sticks and base 10 blocks.
3.1.1.2Use place value to describe whole numbers between 1000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones.
3.1.1.3Find 10,000 more or 10,000 less than a given five-digit number. Find 1000 more or 1000 less than a given four- or five-digit. Find 100 more or 100 less than a given four- or five-digit number.
3.1.1.4Round numbers to the nearest 10,000, 1000, 100 and 10. Round up and round down to estimate sums and differences.
3.1.1.5Compare and order whole numbers up to 100,000.
3.1.2 Add and subtract multi-digit whole numbers; represent multiplication and division in various ways; solve real world and mathematical problems using arithmetic.
3.1.2.1Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms.
3.1.2.2Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results.
3.1.2.3Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division.
3.1.2.4Solve real-world and mathematical problems involving multiplication and division, including both ''how many in each group'' and ''how many groups'' division problems.
3.1.2.5Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties.
3.1.3 Understand meanings and uses of fractions in real-world and mathematical situations.
3.1.3.1Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line.
3.1.3.2Understand that the size of a fractional part is relative to the size of the whole.
3.1.3.3Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator.
3.2 Algebra
3.2.1 Use single operation Input output rules to represent patterns and relationships and to solve real world and mathematical problems.
3.2.1.1Create, describe, and apply single-operation input-output rules involving addition, subtraction and multiplication to solve problems in various contexts.
3.2.2 Use number Sentences involving multiplication and division basic facts and unknowns to represent and solve real-world and mathematical problems; create real-world Situations corresponding to number sentences.
3.2.2.1Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences.
3.2.2.2Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true.
3.3 Geometry & Measurement
3.3.1 Use geometric attributes to describe and create shapes in various contexts.
3.3.1.1Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms and trapezoids.
3.3.1.2Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons and octagons.
3.3.2 Understand perimeter as a measurable attribute of real world and mathematical objects. Use various tools to measure distances.
3.3.2.1Use half units when measuring distances.
3.3.2.2Find the perimeter of a polygon by adding the lengths of the sides.
3.3.2.3Measure distances around objects.
3.3.3 Use time, money and temperature to solve real world and mathematical problems.
3.3.3.1Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute.
3.3.3.2Know relationships among units of time.
3.3.3.3Make change up to one dollar in several different ways, including with as few coins as possible.
3.3.3.4Use an analog thermometer to determine temperature to the nearest degree in Fahrenheit and Celsius.
3.4 Data Analysis
3.4.1 Collect, organize, display, and interpret data. Use labels and a variety of scales and units in displays.
3.4.1.1Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units.

Grade 4

4.1 Number & Operation
4.1.1 Demonstrate mastery of multiplication and division basic facts; multiply multi-digit numbers; solve real-world and mathematical problems using arithmetic.
4.1.1.1Demonstrate fluency with multiplication and division facts.
4.1.1.2Use an understanding of place value to multiply a number by 10, 100 and 1000.
4.1.1.3Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.
4.1.1.4Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results.
4.1.1.5Solve multi-step real-world and mathematical 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 technology, and the context of the problem to assess the reasonableness of results.
4.1.1.6Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction.
4.1.2 Represent and compare fractions and decimals in real-world and mathematical situations; use place value to understand how decimals represent quantities.
4.1.2.1Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions.
4.1.2.2Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions.
4.1.2.3Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators.
4.1.2.4Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths.
4.1.2.5Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks.
4.1.2.6Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths.
4.1.2.7Round decimals to the nearest tenth.
4.2 Algebra
4.2.1 Use input-output rules, tables and charts to represent patterns and relationships and to solve real world and mathematical problems.
4.2.1.1Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table.
4.2.2 Use number Sentences involving multiplication, division and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.
4.2.2.1Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences.
4.2.2.2Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true.
4.3 Geometry & Measurement
4.3.1 Name, describe, classify and sketch polygons.
4.3.1.1Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Name, describe, classify and sketch polygons.
4.3.1.2Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts.
4.3.2 Understand angle and area as measurable attributes of real world and mathematical objects. Use various tools to measure angles and areas.
4.3.2.1Measure angles in geometric figures and real-world objects with a protractor or angle ruler.
4.3.2.2Compare angles according to size. Classify angles as acute, right and obtuse.
4.3.2.3Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns.
4.3.2.4Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements.
4.3.3 Use translations, reflections and rotations to establish congruency and understand symmetries.
4.3.3.1Apply translations (slides) to figures.
4.3.3.2Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry.
4.3.3.3Apply rotations (turns) of 90 degrees clockwise or counterclockwise.
4.3.3.4Recognize that translations, reflections and rotations preserve congruency and use them to show that two figures are 4 congruent.
4.4 Data Analysis
4.4.1 Collect, organize, display and interpret data, including data collected over a period of time and data represented by fractions and decimals.
4.4.1.1Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data.

Grade 5

5.1 Numbers & Operation
5.1.1 Divide multi-digit numbers; solve real-world and mathematical problems using arithmetic.
5.1.1.1Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal.
5.1.1.2Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately.
5.1.1.3Estimate solutions to arithmetic problems in order to assess the reasonableness of results.
5.1.1.4Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.
5.1.2 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.
5.1.2.1Read and write decimals using place value to describe decimals in terms of groups from millionths to millions.
5.1.2.2Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number.
5.1.2.3Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
5.1.2.4Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts.
5.1.2.5Round numbers to the nearest 0.1, 0.01 and 0.001.
5.1.3 Add and subtract fractions, mixed numbers and decimals to solve real-world and mathematical problems.
5.1.3.1Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms.
5.1.3.2Model addition and subtraction of fractions and decimals using a variety of representations.
5.1.3.3Estimate sums and differences of decimals and fractions to assess the reasonableness of results.
5.1.3.4Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data.
5.2 Algebra
5.2.1 Recognize and represent patterns of change; use patterns, tables, graphs and rules to solve real world and mathematical problems.
5.2.1.1Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems.
5.2.1.2Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system.
5.2.2 Use properties of arithmetic to generate equivalent numerical expressions and evaluate expressions involving whole numbers.
5.2.2.1Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers.
5.2.3 Understand and interpret equations and inequalities involving variables and whole numbers, and use them to represent and solve real-world and mathematical problems.
5.2.3.1Determine whether an equation or inequality involving a variable is true or false for a given value of the variable.
5.2.3.2Represent real-world situations using equations and inequalities involving variables. Create real-world situations corresponding to equations and inequalities.
5.2.3.3Evaluate expressions and solve equations involving variables when values for the variables are given.
5.3 Geometry & Measurement
5.3.1 Describe, classify, and draw representations of three-dimensional figures.
5.3.1.1Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces.
5.3.1.2Recognize and draw a net for a three-dimensional figure.
5.3.2 Determine the area of triangles and quadrilaterals; determine the surface area and volume of rectangular prisms in various contexts.
5.3.2.1Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles.
5.3.2.2Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms.
5.3.2.3Understand that the volume of a three-dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements.
5.3.2.4Develop and use the formulas V = lwh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a rectangular prism by breaking the prism into layers of unit cubes.
5.4 Data Analysis
5.4.1 Display and interpret data; determine mean, median and range.
5.4.1.1Know and use the definitions of the mean, median and range of a set of data. Know how to use a spreadsheet to find the mean, median and range of a data set. Understand that the mean is a ''leveling out'' of data.
5.4.1.2Create and analyze double-bar graphs and line graphs by applying understanding of whole numbers, fractions and decimals. Know how to create spreadsheet tables and graphs to display data.

Grade 6

6.1 Number & Operation
6.1.1 Read, write, represent and compare positive rational numbers expressed as fractions, decimals, percents and ratios; write positive integers as products of factors; use these representations in real-world and mathematical situations.
6.1.1.1Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid.
6.1.1.2Compare positive rational numbers represented in various forms. Use the symbols <, = and >.
6.1.1.3Understand that percent represents parts out of 100 and ratios to 100.
6.1.1.4Determine equivalences among fractions, decimals and percents; select among these representations to solve problems.
6.1.1.5Factor whole numbers; express a whole number as a product of prime factors with exponents.
6.1.1.6Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions.
6.1.1.7Convert between equivalent representations of positive rational numbers.
6.1.2 Understand the concept of ratio and its relationship to fractions and to the multiplication and division of whole numbers. Use ratios to solve real-world and mathematical problems.
6.1.2.1Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction.
6.1.2.2Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations.
6.1.2.3Determine the rate for ratios of quantities with different units.
6.1.2.4Use reasoning about multiplication and division to solve ratio and rate problems.
6.1.3 Multiply and divide decimals, fractions and mixed numbers; solve real-world and mathematical problems using arithmetic with positive rational numbers.
6.1.3.1Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms.
6.1.3.2Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions.
6.1.3.3Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts.
6.1.3.4Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers.
6.1.3.5Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem.
6.2 Algebra
6.2.1 Recognize and Represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs and rules to solve real world and mathematical problems.
6.2.1.1Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts.
6.2.1.2Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations.
6.2.2 Use properties of arithmetic to generate equivalent numerical expressions and evaluate expressions involving positive rational numbers.
6.2.2.1Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers.
6.2.3 Understand and interpret equations and inequalities involving variables and positive rational numbers. Use equations and inequalities to represent real world and mathematical problems; use the idea of maintaining equality to solve equations. Interpret solutions in the original context.
6.2.3.1Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers.
6.2.3.2Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results.
6.3 Geometry & Measurement
6.3.1 Calculate perimeter, area, surface area and volume of two and three dimensional figures to solve real-world and mathematical problems.
6.3.1.1Calculate the surface area and volume of prisms and use appropriate units, such as cm2 and cm3. Justify the formulas used. Justification may involve decomposition, nets or other models.
6.3.1.2Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid.
6.3.1.3Estimate the perimeter and area of irregular figures on a grid when they cannot be decomposed into common figures and use correct units, such as cm and cm2.
6.3.2 Understand and use relationships between angles in geometric figures.
6.3.2.1Solve problems using the relationships between the angles formed by intersecting lines.
6.3.2.2Determine missing angle measures in a triangle using the fact that the sum of the interior angles of a triangle is 180 degrees. Use models of triangles to illustrate this fact.
6.3.2.3Develop and use formulas for the sums of the interior angles of polygons by decomposing them into triangles.
6.3.3 Choose appropriate units of measurement and use ratios to convert within measurement systems to solve real-world and mathematical problems.
6.3.3.1Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units.
6.3.3.2Estimate weights, capacities and geometric measurements using benchmarks in measurement systems with appropriate units.
6.4 Data Analysis & Probability
6.4.1 Use probabilities to solve real-world and mathematical problems; represent probabilities using fractions, decimals and percents.
6.4.1.1Determine the sample space (set of possible outcomes) 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.
6.4.1.2Determine the 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 inclusive. Understand that probabilities measure likelihood.
6.4.1.3Perform experiments for situations in which the probabilities are known, compare the resulting relative frequencies with the known probabilities; know that there may be differences.
6.4.1.4Calculate experimental probabilities from experiments; represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown.

Grade 7

7.1 Number & Operation
7.1.1 Read, write, represent and compare positive and negative rational numbers, expressed as integers, fractions and decimals.
7.1.1.1Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that pi is not rational, but that it can be approximated by rational numbers such as 22/7 and 3.14.
7.1.1.2Understand that division of two integers will always result in a rational number. Use this information to interpret the decimal result of a division problem when using a calculator.
7.1.1.3Locate positive and negative rational numbers on a number line, understand the concept of opposites, and plot pairs of positive and negative rational numbers on a coordinate grid.
7.1.1.4Compare positive and negative rational numbers expressed in various forms using the symbols <, >, =, less than or equal to, greater than or equal to
7.1.1.5Recognize and generate equivalent representations of positive and negative rational numbers, including equivalent fractions.
7.1.2 Calculate with positive and negative rational numbers, and rational numbers with whole number exponents, to solve real-world and mathematical problems.
7.1.2.1Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents.
7.1.2.2Use real-world contexts and the inverse relationship between addition and subtraction to explain why the procedures of arithmetic with negative rational numbers make sense.
7.1.2.3Understand that calculators and other computing technologies often truncate or round numbers.
7.1.2.4Solve problems in various contexts involving calculations with positive and negative rational numbers and positive integer exponents, including computing simple and compound interest.
7.1.2.5Use proportional reasoning to solve problems involving ratios in various contexts.
7.1.2.6Demonstrate an understanding of the relationship between the absolute value of a rational number and distance on a number line. Use the symbol for absolute value.
7.1.7 7.1.7
7.1.7.2 7.1.7.2
7.1.7.2.1Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships.
7.2 Algebra
7.2.1 7.2.1
7.2.1.1Understand that a relationship between two variables, x and y, is proportional if it can be expressed in the form y/x = k or y = kx. Distinguish proportional relationships from other relationships, including inversely proportional relationships (xy = k or y = k/x).
7.2.1.2Understand that the graph of a proportional relationship is a line through the origin whose slope is the unit rate (constant of proportionality). Know how to use graphing technology to examine what happens to a line when the unit rate is changed.
7.2.2 7.2.2
7.2.2.1Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations.
7.2.2.2Solve multi-step problems involving proportional relationships in numerous contexts.
7.2.2.3Use knowledge of proportions to assess the reasonableness of solutions.
7.2.2.4Represent real-world or mathematical situations using equations and inequalities involving variables and positive and negative rational numbers.
7.2.3 Apply understanding of order of operations and algebraic properties to generate equivalent numerical and algebraic expressions containing positive and negative rational numbers and grouping symbols; evaluate such expressions.
7.2.3.1Use properties of algebra to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. Properties of algebra include associative, commutative and distributive laws.
7.2.3.2Evaluate algebraic expressions containing rational numbers and whole number exponents at specified values of their variables.
7.2.3.3Apply understanding of order of operations and grouping symbols when using calculators and other technologies.
7.2.4 Represent real world And mathematical situations using equations with variables. Solve equations symbolically, using the properties of equality. Also solve equations graphically and numerically. Interpret solutions in the original context.
7.2.4.1Represent relationships in various contexts with equations involving variables and positive and negative rational numbers. Use the properties of equality to solve for the value of a variable. Interpret the solution in the original context.
7.2.4.2Solve equations resulting from proportional relationships in various contexts.
7.2.7 7.2.7
7.2.7.2 7.2.7.2
7.2.7.2.1Recognize Proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols and graphs; solve problems involving proportional relationships and explain results in the original context.
7.3 Geometry & Measurement
7.3.1 Use reasoning with proportions and ratios to determine measurements, justify formulas and solve real world and mathematical problems involving circles and related geometric figures.
7.3.1.1Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is pi. Calculate the circumference and area of circles and sectors of circles to solve problems in various contexts.
7.3.1.2Calculate the volume and surface area of cylinders and justify the formulas used.
7.3.2 Analyze the effect of change of scale, translations and reflections on the attributes of two-dimensional figures.
7.3.2.1Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors.
7.3.2.2Apply scale factors, length ratios and area ratios to determine side lengths and areas of similar geometric figures.
7.3.2.3Use proportions and ratios to solve problems involving scale drawings and conversions of measurement units.
7.3.2.4Graph and describe translations and reflections of figures on a coordinate grid and determine the coordinates of the vertices of the figure after the transformation.
7.4 Data Analysis & Probability
7.4.1 Use mean, median and range to draw conclusions about data and make predictions.
7.4.1.1Design simple experiments and collect data. Determine mean, median and range for quantitative data and from data represented in a display. Use these quantities to draw conclusions about the data, compare different data sets, and make predictions.
7.4.1.2Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet to examine this impact.
7.4.2 Display and interpret data in a variety of ways, including circle graphs and histograms.
7.4.2.1Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology.
7.4.3 Calculate probabilities and reason about probabilities using proportions to solve real-world and mathematical problems.
7.4.3.1Use random numbers generated by a calculator or a spreadsheet or taken from a table to simulate situations involving randomness, make a histogram to display the results, and compare the results to known probabilities.
7.4.3.2Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as percents, decimals and fractions.
7.4.3.3Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on probabilities.

Grade 8

8.1 Number & Operation
8.1.1 Read, write, compare, classify and represent real numbers, and use them to solve problems in various contexts.
8.1.1.1Classify real numbers as rational or irrational. Know that when a square root of a positive integer is not an integer, then it is irrational. Know that the sum of a rational number and an irrational number is irrational, and the product of a non-zero rational number and an irrational number is irrational.
8.1.1.2Compare real numbers; locate real numbers on a number line. Identify the square root of a positive integer as an integer, or if it is not an integer, locate it as a real number between two consecutive positive integers.
8.1.1.3Determine rational approximations for solutions to problems involving real numbers.
8.1.1.4Know and apply the properties of positive and negative integer exponents to generate equivalent numerical expressions.
8.1.1.5Express approximations of very large and very small numbers using scientific notation; understand how calculators display numbers in scientific notation. Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation, using the correct number of significant digits when physical measurements are involved.
8.2 Algebra
8.2.1 Understand the concept of function in real world and mathematical situations, and distinguish between linear and nonlinear functions.
8.2.1.1Understand 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. Use functional notation, such as f(x), to represent such relationships.
8.2.1.2Use linear functions to represent relationships in which changing the input variable by some amount leads to a change in the output variable that is a constant times that amount.
8.2.1.3Understand that a function is linear if it can be expressed in the form f (x)= mx+b or if its graph is a straight line.
8.2.1.4Understand that an arithmetic sequence is a linear function that can be expressed in the form f (x)= mx+b , where x = 0, 1, 2, 3,....
8.2.1.5Understand that a geometric sequence is a non-linear function that can be expressed in the form f (x)= ab^x , where x = 0, 1, 2, 3,....
8.2.2 Recognize linear functions in real world and mathematical situations; represent linear functions and other functions with tables, verbal descriptions, symbols and graphs; solve problems involving these functions and explain results in the original context.
8.2.2.1Represent linear functions with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another.
8.2.2.2Identify graphical properties of linear functions including slopes 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.
8.2.2.3Identify how coefficient changes in the equation f (x) = mx + b affect the graphs of linear functions. Know how to use graphing technology to examine these effects.
8.2.2.4Represent arithmetic sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems.
8.2.2.5Represent geometric sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems.
8.2.3 Generate Equivalent numerical and algebraic expressions and use algebraic properties to evaluate expressions.
8.2.3.1Evaluate algebraic expressions, including expressions containing radicals and absolute values, at specified values of their variables.
8.2.3.2Justify steps in generating equivalent expressions by identifying the properties used, including the properties of algebra. Properties include the associative, commutative and distributive laws, and the order of operations, including grouping symbols.
8.2.4 Represent real world and mathematical situations using equations and inequalities involving linear expressions. Solve equations and inequalities symbolically and graphically. Interpret solutions in the original context.
8.2.4.1Use linear equations to represent situations involving a constant rate of change, including proportional and non-proportional relationships.
8.2.4.2Solve multi-step equations in one variable. Solve for one variable in a multi-variable equation in terms of the other variables. Justify the steps by identifying the properties of equalities used.
8.2.4.3Express linear equations in slope-intercept, point-slope and standard forms, and convert between these forms. Given sufficient information, find an equation of a line.
8.2.4.4Use linear inequalities to represent relationships in various contexts.
8.2.4.5Solve linear inequalities using properties of inequalities. Graph the solutions on a number line.
8.2.4.6Represent relationships in various contexts with equations and inequalities involving the absolute value of a linear expression. Solve such equations and inequalities and graph the solutions on a number line.
8.2.4.7Represent relationships in various contexts using systems of linear equations. Solve systems of linear equations in two variables symbolically, graphically and numerically.
8.2.4.8Understand that a system of linear equations may have no solution, one solution, or an infinite number of solutions. Relate the number of solutions to pairs of lines that are intersecting, parallel or identical. Check whether a pair of numbers satisfies a system of two linear equations in two unknowns by substituting the numbers into both equations.
8.2.4.9Use the relationship between square roots and squares of a number to solve problems.
8.3 Geometry & Measurement
8.3.1 Solve problems involving right triangles using the Pythagorean Theorem and its converse.
8.3.1.1Use the Pythagorean Theorem to solve problems involving right triangles.
8.3.1.2Determine the distance between two points on a horizontal or vertical line in a coordinate system. Use the Pythagorean Theorem to find the distance between any two points in a coordinate system.
8.3.1.3Informally justify the Pythagorean Theorem by using measurements, diagrams and computer software.
8.3.2 Solve problems involving parallel and perpendicular lines on a coordinate system.
8.3.2.1Understand and apply the relationships between the slopes of parallel lines and between the slopes of perpendicular lines. Dynamic graphing software may be used to examine these relationships.
8.3.2.2Analyze polygons on a coordinate system by determining the slopes of their sides.
8.3.2.3Given a line on a coordinate system and the coordinates of a point not on the line, find lines through that point that are parallel and perpendicular to the given line, symbolically and graphically.
8.4 Data Analysis & Probability
8.4.1 Interpret data using scatterplots and approximate lines of best fit. Use lines of best fit to draw conclusions about data.
8.4.1.1Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit and determine an equation for the line. Use appropriate titles, labels and units. Know how to use graphing technology to display scatterplots and corresponding lines of best fit.
8.4.1.2Use a line of best fit to make statements about approximate rate of change and to make predictions about values not in the original data set.
8.4.1.3Assess the reasonableness of predictions using scatterplots by interpreting them in the original context.

9

9.2 Algebra
9.2.1 Understand the concept of function, and identify important features of functions and other relations using symbolic and graphical methods where appropriate.
9.2.1.1Understand the definition of a function. Use functional notation and evaluate a function at a given point in its domain.
9.2.1.2Distinguish between functions and other relations defined symbolically, graphically or in tabular form.
9.2.1.3Find the domain of a function defined symbolically, graphically or in a real-world context.
9.2.1.4Obtain information and draw conclusions from graphs of functions and other relations.
9.2.1.5Identify the vertex, line of symmetry and intercepts of the parabola corresponding to a quadratic function, using symbolic and graphical methods, when the function is expressed in the form f (x) = ax^2 + bx + c, in the form f (x) = a(x - h)^2 + k , or in factored form.
9.2.1.6Identify intercepts, zeros, maxima, minima and intervals of increase and decrease from the graph of a function.
9.2.1.7Understand the concept of an asymptote and identify asymptotes for exponential functions and reciprocals of linear functions, using symbolic and graphical methods.
9.2.1.8Make qualitative statements about the rate of change of a function, based on its graph or table of values.
9.2.1.9Determine how translations affect the symbolic and graphical forms of a function. Know how to use graphing technology to examine translations.
9.2.2 Recognize linear, quadratic, exponential and other common functions in real world and mathematical situations; represent these functions with tables, verbal descriptions, symbols and graphs; solve problems involving these functions, and explain results in the original context.
9.2.2.1Represent and solve problems in various contexts using linear and quadratic functions.
9.2.2.2Represent and solve problems in various contexts using exponential functions, such as investment growth, depreciation and population growth.
9.2.2.3Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions.
9.2.2.4Express the terms in a geometric sequence recursively and by giving an explicit (closed form) formula, and express the partial sums of a geometric series recursively.
9.2.2.5Recognize and solve problems that can be modeled using finite geometric sequences and series, such as home mortgage and other compound interest examples. Know how to use spreadsheets and calculators to explore geometric sequences and series in various contexts.
9.2.2.6Sketch the graphs of common non-linear functions such as f(x) = square root of x, f(x)= |x|, f(x) = 1/x, f(x) = x^3, and translations of these functions, such as f(x)= square root of (x-2) + 4. Know how to use graphing technology to graph these functions.
9.2.3 Generate equivalent algebraic expressions involving polynomials and radicals; use algebraic properties to evaluate expressions.
9.2.3.1Evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified points in their domains.
9.2.3.2Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree.
9.2.3.3Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares.
9.2.3.4Add, subtract, multiply, divide and simplify algebraic fractions.
9.2.3.5Check whether a given complex number is a solution of a quadratic equation by substituting it for the variable and evaluating the expression, using arithmetic with complex numbers.
9.2.3.6Apply the properties of positive and negative rational exponents to generate equivalent algebraic expressions, including those involving nth roots.
9.2.3.7Justify steps in generating equivalent expressions by identifying the properties used. Use substitution to check the equality of expressions for some particular values of the variables; recognize that checking with substitution does not guarantee equality of expressions for all values of the variables.
9.2.4 Represent real world and mathematical situations using equations and inequalities involving linear, quadratic, exponential and nth root functions. Solve equations and inequalities symbolically and graphically. Interpret solutions in the original context.
9.2.4.1Represent relationships in various contexts using quadratic equations and inequalities. Solve quadratic equations and inequalities by appropriate methods including factoring, completing the square, graphing and the quadratic formula. Find non-real complex roots when they exist. Recognize that a particular solution may not be applicable in the original context. Know how to use calculators, graphing utilities or other technology to solve quadratic equations and inequalities.
9.2.4.2Represent relationships in various contexts using equations involving exponential functions; solve these equations graphically or numerically. Know how to use calculators, graphing utilities or other technology to solve these equations.
9.2.4.3Recognize that to solve certain equations, number systems need to be extended from whole numbers to integers, from integers to rational numbers, from rational numbers to real numbers, and from real numbers to complex numbers. In particular, non-real complex numbers are needed to solve some quadratic equations with real coefficients.
9.2.4.4Represent relationships in various contexts using systems of linear inequalities; solve them graphically. Indicate which parts of the boundary are included in and excluded from the solution set using solid and dotted lines.
9.2.4.5Solve linear programming problems in two variables using graphical methods.
9.2.4.6Represent relationships in various contexts using absolute value inequalities in two variables; solve them graphically.
9.2.4.7Solve equations that contain radical expressions. Recognize that extraneous solutions may arise when using symbolic methods.
9.2.4.8Assess the reasonableness of a solution in its given context and compare the solution to appropriate graphical or numerical estimates; interpret a solution in the original context.
9.3 Geometry & Measurement
9.3.1 Calculate measurements of plane and solid geometric figures; know that physical measurements depend on the choice of a unit and that they are approximations.
9.3.1.1Determine the surface area and volume of pyramids, cones and spheres. Use measuring devices or formulas as appropriate.
9.3.1.2Compose and decompose two- and three-dimensional figures; use decomposition to determine the perimeter, area, surface area and volume of various figures.
9.3.1.3Understand that quantities associated with physical measurements must be assigned units; apply such units correctly in expressions, equations and problem solutions that involve measurements; and convert between measurement systems.
9.3.1.4Understand and apply the fact that the effect of a scale factor k on length, area and volume is to multiply each by k, k^2 and k^3, respectively.
9.3.1.5Make reasonable estimates and judgments about the accuracy of values resulting from calculations involving measurements.
9.3.2 Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry.
9.3.2.1Understand the roles of axioms, definitions, undefined terms and theorems in logical arguments.
9.3.2.2Accurately interpret and use words and phrases such as ''if...then,'' ''if and only if,'' ''all,'' and ''not.'' Recognize the logical relationships between an ''if...then'' statement and its inverse, converse and contra positive.
9.3.2.3Assess the validity of a logical argument and give counterexamples to disprove a statement.
9.3.2.4Construct logical arguments and write proofs of theorems and other results in geometry, including proofs by contradiction. Express proofs in a form that clearly justifies the reasoning, such as two-column proofs, paragraph proofs, flow charts or illustrations.
9.3.2.5Use technology tools to examine theorems, make and test conjectures, perform constructions and develop mathematical reasoning skills in multi-step problems. The tools may include compass and straight edge, dynamic geometry software, design software or Internet applets.
9.3.3 Know and apply properties of geometric figures to solve real world and mathematical problems and to logically justify results in geometry.
9.3.3.1Know and apply properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve problems and logically justify results.
9.3.3.2Know and apply properties of angles, including corresponding, exterior, interior, vertical, complementary and supplementary angles, to solve problems and logically justify results.
9.3.3.3Know and apply properties of equilateral, isosceles and scalene triangles to solve problems and logically justify results.
9.3.3.4Apply the Pythagorean Theorem and its converse to solve problems and logically justify results.
9.3.3.5Know and apply properties of right triangles, including properties of 45-45-90 and 30-60-90 triangles, to solve problems and logically justify results.
9.3.3.6Know and apply properties of congruent and similar figures to solve problems and logically justify results.
9.3.3.7Use properties of polygons--including quadrilaterals and regular polygons--to define them, classify them, solve problems and logically justify results.
9.3.3.8Know and apply properties of a circle to solve problems and logically justify results.
9.3.4 Solve real-world and mathematical geometric problems using algebraic methods.
9.3.4.1Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine and tangent of an acute angle in a right triangle.
9.3.4.2Apply the trigonometric ratios sine, cosine and tangent to solve problems, such as determining lengths and areas in right triangles and in figures that can be decomposed into right triangles. Know how to use calculators, tables or other technology to evaluate trigonometric ratios.
9.3.4.3Use calculators, tables or other technologies in connection with the trigonometric ratios to find angle measures in right triangles in various contexts.
9.3.4.4Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints and slopes of line segments.
9.3.4.5Know the equation for the graph of a circle with radius r and center (h, k), (x - h)^2 + (y - k)^2 = r^2, and justify this equation using the Pythagorean Theorem and properties of translations.
9.3.4.6Use numeric, graphic and symbolic representations of transformations in two dimensions, such as reflections, translations, scale changes and rotations about the origin by multiples of 90 degrees, to solve problems involving figures on a coordinate grid.
9.3.4.7Use algebra to solve geometric problems unrelated to coordinate geometry, such as solving for an unknown length in a figure involving similar triangles, or using the Pythagorean Theorem to obtain a quadratic equation for a length in a geometric figure.
9.4 Data Analysis & Probability
9.4.1 Display and analyze data; use various measures associated with data to draw conclusions, identify trends and describe relationships.
9.4.1.1Describe a data set using data displays, including box-and whisker plots; describe and compare data sets using summary statistics, including measures of center, location and spread. Measures of center and location include mean, median, quartile and percentile. Measures of spread include standard deviation, range and inter-quartile range. Know how to use calculators, spreadsheets or other technology to display data and calculate summary statistics.
9.4.1.2Analyze the effects on summary statistics of changes in data sets.
9.4.1.3Use scatterplots to analyze patterns and describe relationships between two variables. Using technology, determine regression lines (line of best fit) and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions.
9.4.1.4Use the mean and standard deviation of a data set to fit it to a normal distribution (bell-shaped curve) and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets and tables to estimate areas under the normal curve.
9.4.2 Explain the uses of data and statistical thinking to draw inferences, make predictions and justify conclusions.
9.4.2.1Evaluate reports based on data published in the media by identifying the source of the data, the design of the study, and the way the data are analyzed and displayed. Show how graphs and data can be distorted to support different points of view. Know how to use spreadsheet tables and graphs or graphing technology to recognize and analyze distortions in data displays.
9.4.2.2Identify and explain misleading uses of data; recognize when arguments based on data confuse correlation and causation.
9.4.2.3Design simple experiments and explain the impact of sampling methods, bias and the phrasing of questions asked during data collection.
9.4.3 Calculate probabilities and apply probability concepts to solve real-world and mathematical problems.
9.4.3.1Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities.
9.4.3.2Calculate experimental probabilities by performing simulations or experiments involving a probability model and using relative frequencies of outcomes.
9.4.3.3Understand that the Law of Large Numbers expresses a relationship between the probabilities in a probability model and the experimental probabilities found by performing simulations or experiments involving the model.
9.4.3.4Use random numbers generated by a calculator or a spreadsheet, or taken from a table, to perform probability simulations and to introduce fairness into decision making.
9.4.3.5Apply probability concepts such as intersections, unions and complements of events, and conditional probability and independence, to calculate probabilities and solve problems.
9.4.3.6Describe the concepts of intersections, unions and complements using Venn diagrams. Understand the relationships between these concepts and the words AND, OR, NOT, as used in computerized searches and spreadsheets.
9.4.3.7Understand and use simple probability formulas involving intersections, unions and complements of events.
9.4.3.8Apply probability concepts to real-world situations to make informed decisions.
9.4.3.9Use the relationship between conditional probabilities and relative frequencies in contingency tables.

AP Calculus Learning Objectives

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

AP Statistics Learning Objectives

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

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