Nebraska Math Standards

655 standards, Kindergarten through AP.

Kindergarten

K.A ALGEBRA: Students will solve problems and reason with algebra using multiple representations, make connections within math and across disciplines, and communicate their ideas.

K.A.1SEE NUMBER AND ALGEBRAIC RELATIONSHIPS IN NUMBER (K.N.4)

K.D DATA: Students will solve problems and reason with data/probability using multiple representations, make connections within math and across disciplines, and communicate their ideas.

K.D.1 Classification: Students will sort and classify objects using one or more attributes.

K.D.1.aIdentify, sort, and classify objects by size, shape, color, and other attributes.

K.D.1.bIdentify objects that do not belong to a particular group and explain the reasoning used.

K.G GEOMETRY: Students will solve problems and reason with geometry using multiple representations, make connections within math and across disciplines, and communicate their ideas.

K.G.1 Shapes and Their Attributes: Students will identify and represent the attributes of two-dimensional shapes and three-dimensional solids.

K.G.1.aIdentify and name two-dimensional shapes including circles, triangles, squares, and rectangles regardless of orientation or size.

K.G.1.bIdentify and name three-dimensional shapes including spheres, cubes, cylinders, and cones regardless of orientation or size.

K.G.1.cDescribe the relative positions of shapes in relation to other objects or shapes using terms such as above, below, in front of, behind, and next to.

K.G.1.dCreate shapes using given materials and describe one or more of the attributes such as number of sides/corners.

K.G.1.eCombine simple shapes to compose larger shapes.

K.G.2 Measurement: Students will describe and compare measurable attributes.

K.G.2.aDescribe measurable attributes of authentic objects including length, capacity, and weight.

K.G.2.bDirectly compare two objects with a measurable attribute in common to describe which object is longer/shorter, heavier/lighter, and has more/less-capacity.

K.G.3 Time and Money: Students will know coin names and values and tell time to the hour.

K.G.3.aIdentify the name and value of pennies, nickels, and dimes.

K.G.3.bIdentify the parts of digital and analog clocks. Tell and write time to the hour using digital clocks and analog clocks using only the hour hand.

K.N NUMBER: Students will solve problems and reason with number concepts using multiple representations, make connections within math and across disciplines, and communicate their ideas.

K.N.1 Subitizing: Students will quantify briefly shown collections and verbally label the arrangements without counting.

K.N.1.aWithout counting, recognize and verbally label arrangements for briefly shown collections up to 10 (e.g., “I saw 5.” “How did you know?” “I saw 3 and 2, that is 5.”

K.N.2 Counting and Cardinality: Students will understand the relationship between numbers and quantities.

K.N.2.aUse one-to-one correspondence when counting objects to show the relationship between numbers and quantities and understand the last number counted is a direct representation of the total objects in a given set.

K.N.2.bUnderstand that each successive number name refers to a quantity that is one larger.

K.N.2.cCount out the number of objects given a number from 1 to 20.

K.N.2.dCount up to 20 objects arranged in a line, a rectangular array, or a circle, and count up to 10 objects in a scattered configuration.

K.N.2.eCount verbally forward and backward from any given number within 20.

K.N.2.fCount verbally in sequential order by ones and by tens to 100, making accurate decade transitions (e.g., 89 to 90).

K.N.2.gWrite and name numbers 0 to 20. Represent a number of objects with a written numeral 0 to 20.

K.N.2.hCompare the number of objects in two groups, up to 20, using the words fewer than, more than, the same as.

K.N.3 Base Ten: Students will work with numbers 11 to 19 to gain a foundation for place value.

K.N.3.aCompose and decompose numbers from 11 to 19 into a group of ten ones and some more ones using a model, drawing, or equation.

K.N.4 Number and Algebraic Relationships: Students will understand and demonstrate the meaning of addition and subtraction.

K.N.4.aRepresent and explain addition and subtraction as part-whole relationships, with addition as putting together and/or adding to and subtraction as taking apart and/or taking from, using objects, drawings, numbers, and equations.

K.N.4.bCompose and decompose numbers less than or equal to 10 into pairs in more than one way using verbal explanations, objects, or drawings.

K.N.4.cFor any number from 1 to 9, find the number that makes 10 when added to the given number, sharing the answer with a model, drawing, or equation.

K.N.4.dEfficiently, flexibly, and accurately add and subtract within 5.

K.N.4.eSolve authentic problems that involve addition and subtraction within 10 (e.g., by using objects, drawings, and equations to represent the problem).

Grade 1

1.A ALGEBRA: Students will solve problems and reason with algebra using multiple representations, make connections within math and across disciplines, and communicate their ideas.

1.A.1SEE NUMBER AND ALGEBRAIC RELATIONSHIPS IN NUMBER (1.N.5)

1.D DATA: Students will solve problems and reason with data/probability using multiple representations, make connections within math and across disciplines, and communicate their ideas.

1.D.1 Data Collection: Students will formulate questions to collect, organize, and represent data.

1.D.1.aCollect, organize, and represent a data set with up to three categories using a picture graph.

1.D.2 Analyze Data and Interpret Results: Students will analyze the data and interpret the results.

1.D.2.aAsk and answer questions about the total number of data points, how many in each category, and compare categories by identifying how many more or less are in a particular category using a picture graph.

1.G GEOMETRY: Students will solve problems and reason with geometry using multiple representations, make connections within math and across disciplines, and communicate their ideas.

1.G.1 Shapes and Their Attributes: Students will represent and describe the attributes of two-dimensional shapes.

1.G.1.aDetermine geometric attributes of two-dimensional shapes regardless of orientation or size for rhombi, trapezoids, and hexagons (e.g., a hexagon is closed with six sides).

1.G.1.bDetermine geometric attributes of three-dimensional shapes including cones, cylinders, cubes, and rectangular prisms regardless of orientation or size.

1.G.1.cDescribe lines and sides of shapes as parallel or non-parallel.

1.G.1.dPartition circles and rectangles into two and four equal parts using the language halves and fourths.

1.G.2 Measurement: Students will measure and compare lengths.

1.G.2.aMeasure the length of an object as a whole number of same-size, non-standard units by placing them end to end.

1.G.2.bOrder three objects by directly comparing their lengths or indirectly by using a third object.

1.G.3 Time and Money: Students will solve problems with coins and tell time to the half hour.

1.G.3.aUnderstand the value of dimes and pennies (e.g., a dime is equal to ten pennies) relating to tens and ones and solve problems involving dimes and pennies using the ¢ symbol appropriately.

1.G.3.bCount collections of like coins (penny, nickel, and dime) relating to patterns of counting by 1s, 5s, and 10s.

1.G.3.cTell and write time to the half hour and hour using analog and digital clocks.

1.N NUMBER: Students will solve problems and reason with number concepts using multiple representations, make connections within math and across disciplines, and communicate their ideas.

1.N.1 Subitizing: Students will quantify briefly shown collections and verbally label the arrangements without counting.

1.N.1.aWithout counting, recognize and verbally label arrangements for briefly shown collections up to 20 (e.g.,” I saw 16.” “How did you know?” “I saw 10 and 6, that is 16”).

1.N.2 Counting and Cardinality: Students will understand the relationship between numbers and quantities to extend the counting sequence.

1.N.2.aCount verbally by ones and tens within 120 starting at any given number.

1.N.2.bCount verbally by ones and tens within 120 starting at any given number. Understand that the given number is a direct representation of the total objects in a given set and counting on each successive number represents adding an additional object, and counting back each proceeding number represents removing an object.

1.N.2.cWrite numerals to match a representation of a given set of objects for numbers up to 120.

1.N.2.dUnderstand patterns of skip counting by 2s, 5s, and 10s.

1.N.3 Base Ten: Students will work with numbers 11 to 19 to gain a foundation for place value.

1.N.3.aUnderstand 10 as a bundle, collection, or (more abstractly) composition of ten ones and that the two digits of a two-digit number represent a composition of some tens and some ones.

1.N.3.bCompare two, two-digit numbers using words greater than, less than, equal to, and symbols <, >, =. Justify comparisons based on the number of tens and ones.

1.N.4 Number and Operations: Students will compute using addition and subtraction.

1.N.4.aAdd and subtract within 20, using flexible strategies such as counting on or counting back, making ten, using ten, and using doubles and near doubles.

1.N.4.bEfficiently, flexibly, and accurately add and subtract within 10.

1.N.4.cFind the difference between two numbers that are multiples of 10, ranging from 10 to 90 using concrete models, drawings, or strategies, and write the corresponding equation.

1.N.4.dMentally find 10 more or 10 less than a two-digit number without having to count and explain the reasoning used.

1.N.4.eAdd within 100, including adding a two-digit number and a one-digit number, adding a two-digit number and a multiple of ten, using concrete models, drawings, and strategies that reflect an understanding of place value, the relationship between addition and subtraction, and the properties of operations. Relate the strategy to a written method and explain the reasoning used to solve.

1.N.4.fUnderstand that in adding two-digit numbers, one adds tens and tens, ones and ones; sometimes it is necessary to compose a ten.

1.N.4.gSubtract multiples of ten from two-digit numbers (positive or zero differences) using concrete models, drawings, and strategies that reflect an understanding of place value, the relationship between addition and subtraction, and the properties of operations. Relate the strategy to a written method and explain the reasoning used to solve.

1.N.5 Number and Algebraic Relationships: Students will understand and apply properties of operations and the relationship between addition and subtraction to solve problems.

1.N.5.aUse the meaning of the equal sign to determine if equations are true and give examples of equations that are true (e.g., 4 = 4, 6 = 7 – 1, 6 + 3 = 3 + 6, 7 + 2 = 5 + 4).

1.N.5.bUse the relationship of addition and subtraction to solve subtraction problems (e.g., find 12 – 9 = ___, using the addition fact 9 + 3 = 12).

1.N.5.cDetermine the unknown whole number in an addition or subtraction equation (e.g., 7 + ? = 13).

1.N.5.dUse the commutative property of addition to develop addition strategies and compose/decompose numbers to develop addition and subtraction strategies. (See other flexible strategies in 1.N.4.a49).

1.N.5.eSolve problems that call for addition of three whole numbers whose sum is less than or equal to 20 using flexible strategies with objects, drawings, and/or equations.

1.N.5.fSolve authentic problems involving addition and subtraction within 20 in situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all parts of the addition or subtraction problem by using objects, drawings, and/or equations with a symbol for the unknown number to represent the problem.

1.N.5.gCreate an authentic problem to represent a given equation involving addition and subtraction within 20.

Grade 2

2.A.1SEE NUMBER AND ALGEBRAIC RELATIONSHIPS IN NUMBER (2.N.5)

2.D.1 Data Collection: Students will formulate questions to collect, organize, and represent data.

2.D.1.aAsk authentic questions to generate data and represent the data using scaled picture graphs with up to four categories.

2.D.1.bAsk authentic questions to generate data and represent the data using bar graphs with up to four categories.

2.D.1.cCreate and represent a data set by making a line plot using whole numbers.

2.D.2 Analyze Data and Interpret Results: Students will analyze the data and interpret the results.

2.D.2.aAnalyze data using scaled picture graphs or bar graphs with up to four categories. Solve problems including one-step comparison problems, using information from the graphs.

2.G.1 Shapes and Their Attributes: Students will recognize and represent the attributes of two-dimensional shapes and three-dimensional solids.

2.G.1.aRecognize and describe all faces of three-dimensional shapes as two-dimensional shapes. Identify and count attributes of solid shapes including the edges, faces, and vertices.

2.G.1.bRecognize and draw two-dimensional shapes having a specific number of sides, angles, and vertices including triangles, quadrilaterals, pentagons, and hexagons.

2.G.1.cPartition a rectangle into rows and columns of equal-sized squares and count to find the total.

2.G.1.dDivide circles and rectangles into two, three, or four equal parts and describe the parts using the language of halves, thirds, fourths, half of, a third of, and a fourth of.

2.G.1.eRecognize that equal shares of identical wholes need not have the same shape.

2.G.2 Describe Measurable Attributes: Students will measure, estimate, and compare lengths to build meaning of the measurement process.

2.G.2.aMeasure the length of an object using two different length units and describe how the measurements relate to the size of the specific unit.

2.G.2.bCompare the difference in length of objects using inches and feet or centimeters and meters.

2.G.3 Measurement: Students will use tools to measure and estimate length using standard units.

2.G.3.aIdentify and use appropriate tools for measuring length.

2.G.3.bMeasure and estimate lengths using whole numbers with inches, feet, centimeters, and meters.

2.G.4 Relate Addition and Subtraction to Measurement: Students will add or subtract to solve length problems.

2.G.4.aRepresent whole numbers as equally spaced lengths on a number line diagram. Use number lines to find sums and differences within 100.

2.G.4.bUse addition and subtraction within 100 to solve problems using the same standard-length units.

2.G.5 Time and Money: Students will solve problems with dollar bills and coins and tell time to the nearest five-minute interval.

2.G.5.aSolve problems involving dollar bills, quarters, dimes, nickels, and pennies using $ and ¢ symbols appropriately.

2.G.5.bIdentify and write time to five-minute intervals using analog and digital clocks and both a.m. and p.m.

2.N.1 Subitizing: Students will quantify briefly shown collections and verbally label the arrangements without counting.

2.N.1.aWithout counting, recognize and verbally label structured arrangements for briefly shown collections using groups, multiplicative thinking, and place value (e.g.,” I saw 48.” “How did you know?” “I saw 4 groups of 10 and 2 groups of 4 is 8...4 tens and 8 ones...48”).

2.N.2 Counting: Students will understand the relationship between numbers and quantities to extend the counting sequence.

2.N.2.aCount within 1,000, including skip counting by 5s, 10s, and 100s starting at a variety of multiples of 5, 10, or 100.

2.N.3 Base Ten: Students will represent and compare three-digit numbers to apply concepts of place value.

2.N.3.aRead and write numbers within the range of 0 to 1,000 using standard, word, and expanded forms.

2.N.3.bUnderstand 100 as a bundle, collection, or (more abstractly) composition of ten tens and that the three digits of a three-digit number represent a composition of some hundreds, some tens, and some ones.

2.N.3.cCompare two three-digit numbers by using symbols <, >, = and justify the comparison based on the value of the hundreds, tens, and ones.

2.N.4 Number and Operations: Students will compute using addition and subtraction.

2.N.4.aFluently add and subtract within 20.

2.N.4.bAdd and subtract within 100 strategies based on place value including properties of operations, relationships between addition and subtraction, and algorithms.

2.N.4.cMentally add or subtract 10 or 100 to or from a given number 100 to 900.

2.N.4.dAdd up to three two-digit numbers using strategies based on place value and understanding of properties.

2.N.4.eAdd and subtract within 1,000 using concrete models, drawings, and strategies that reflect an understanding of place value and the properties of operations.

2.N.5 Number and Algebraic Relationships: Students will create and solve problems involving addition and subtraction and work with equal groups of objects to gain foundations for multiplication.

2.N.5.aSolve authentic problems involving addition and subtraction within 100 in situations of addition and subtraction, including adding to, subtracting from, joining and separating, and comparing situations with unknowns in all positions using objects, models, drawings, verbal explanations, expressions, and equations.

2.N.5.bCreate authentic problems to represent one-step addition and subtraction within 100 with unknowns in all positions.

2.N.5.cUse repeated addition to find the total number of objects arranged in an array no larger than five rows and five columns and write an equation to express the total.

2.N.5.dIdentify a group of objects from 0 to 20 as even or odd by counting by 2s or by showing even numbers as a sum of two equal parts.

Grade 3

3.A.1 Operations and Algebraic Thinking: Students will extend understanding of multiplication and apply operational properties to solve problems.

3.A.1.aAdd and subtract up to four-digit whole numbers with or without regrouping using strategies based on place value and algorithms.

3.A.1.bDetermine the reasonableness of whole number sums and differences using estimations and number sense.

3.A.1.cSolve and write one-step whole number equations to represent authentic problems using the four operations including equations with an unknown start, unknown change, or unknown result.

3.A.1.dInterpret and solve two-step authentic problems involving whole numbers and the four operations.

3.A.1.eApply commutative, associative, distributive, identity, and zero properties as strategies to multiply and divide.

3.A.1.fUse drawings, words, arrays, symbols, repeated addition, equal groups, and number lines to interpret and explain the meaning of multiplication and division and their relationship.

3.A.1.gFluently multiply and divide within 100 using strategies based on understanding and properties of operations.

3.A.1.hMultiply one-digit whole numbers by multiples of 10 in the range of 10 to 90 using strategies based on place value and properties of operations.

3.D.1 Data Collection: Students will formulate questions to collect, organize, and represent data.

3.D.1.aCreate scaled picture graphs and scaled bar graphs to represent a data set with more than four categories, including data collected through observations, surveys, and experiments.

3.D.1.bGenerate and represent data using line plots where the horizontal scale is marked off in halves and whole number units.

3.D.2 Analyze Data and Interpret Results: Students will analyze the data and interpret the results.

3.D.2.aAnalyze data and make simple statements using information represented in picture graphs, line plots, and bar graphs.

3.G.1 Shapes and Their Attributes: Students will recognize and represent the attributes of two-dimensional shapes.

3.G.1.aSort quadrilaterals into categories according to their attributes.

3.G.2 Area and Perimeter: Students will recognize perimeter and area as attributes of plane figures and understand concepts of area measurement.

3.G.2.aSolve authentic problems involving perimeters of polygons when given the side lengths or when given the perimeter and unknown side length(s).

3.G.2.bUse concrete and pictorial models to measure areas in square units by counting square units.

3.G.2.cFind the area of a rectangle with whole-number side lengths by modeling with unit squares; show that area can be additive and is the same as it would be found by multiplying the side lengths.

3.G.3 Measurement: Students will use tools to solve measurement problems.

3.G.3.aIdentify and use the appropriate tools and units of measurement, both customary and metric, to solve authentic problems involving length, weight, mass, liquid volume, and capacity (within the same system and unit).

3.G.3.bEstimate and measure length to the nearest half inch, fourth inch, and centimeter.

3.G.4 Time: Students will tell time to the nearest minute and find elapsed time.

3.G.4.aTell and write time to the minute using both analog and digital clocks.

3.G.4.bSolve authentic problems involving addition and subtraction of time intervals and find elapsed time.

3.N.1 Numeric Relationships: Students will demonstrate and represent multi-digit numbers using place value understanding.

3.N.1.aRead, write, and demonstrate multiple equivalent representations for numbers up to 10,000 using objects or visual representations including standard form and expanded form.

3.N.1.bRepresent and justify comparisons of whole numbers up to 10,000 using number lines and reasoning strategies.

3.N.2 Fractions: Students will develop understanding of fractions as numbers.

3.N.2.aPartition two-dimensional figures into equal areas and express the area of each part as a unit fraction of the whole.

3.N.2.bFind parts of a whole using visual fraction models.

3.N.2.cRepresent and understand a fraction as a number on a number line.

3.N.2.dShow and identify equivalent fractions using visual representations including pictures, manipulatives, and number lines.

3.N.2.eJustify whole numbers as fractions and identify fractions that are equivalent to whole numbers.

3.N.2.fCompare and order fractions having the same numerators or denominators by reasoning about their size.

Grade 4

4.A.1 Operations and Algebraic Thinking: Students will extend understanding of multiplication and division and apply operational properties to solve problems involving variables.

4.A.1.aAdd and subtract multi-digit numbers using an algorithm.

4.A.1.bMultiply up to a four-digit whole number by a one-digit whole number and multiply a two-digit whole number by a two-digit whole number, using strategies based on place value, properties of operations, and algorithms.

4.A.1.cDivide up to a four-digit whole number by a one-digit divisor with and without a remainder using strategies based on place value.

4.A.1.dDetermine the reasonableness of whole number products and quotients using estimations and number sense.

4.A.1.eCreate a simple algebraic expression or equation using a variable for an unknown number to represent an authentic mathematical situation (e.g., 3 + n = 15, 81 ÷ n = 9).

4.A.1.fSolve one- and two-step authentic problems using the four operations including interpreting remainders and the use of a letter to represent the unknown quantity.

4.D.1 Data Collection: Students will formulate questions to collect, organize, and represent data.

4.D.1.aGenerate and represent data using line plots where the horizontal scale is marked off in appropriate units—whole numbers, halves, fourths, or eighths.

4.D.2 Analyze Data and Interpret Results: Students will analyze the data and interpret the results.

4.D.2.aSolve authentic problems and analyze data involving addition or subtraction of fractions presented in line plots.

4.G.1 Shapes and Their Attributes: Students will draw and identify lines and angles and classify shapes by properties of their lines and angles.

4.G.1.aIdentify, create, and describe points, lines, line segments, rays, angles, parallel lines, perpendicular lines, and intersecting lines.

4.G.1.bJustify the classification of angles as acute, obtuse, or right.

4.G.1.cJustify the classification of two-dimensional shapes based on the presence or absence of parallel and perpendicular lines or the presence or absence of specific angles.

4.G.1.dRecognize, draw, and justify lines of symmetry in two-dimensional shapes.

4.G.2 Measurement: Students will generate simple conversions from a larger unit to a smaller unit to solve authentic problems and measure angles.

4.G.2.aIdentify and use the appropriate tools, operations, and units of measurement, both customary and metric, to solve authentic problems involving time, length, weight, mass, and capacity.

4.G.2.bDetermine the reasonableness of measurements involving time, length, weight, mass, capacity, and angles.

4.G.2.cGenerate simple conversions from a larger unit to a smaller unit within the customary and metric systems of measurement.

4.G.2.dMeasure angles in whole number degrees using a protractor and relate benchmark angle measurements to their rotation through a circle (e.g., 180º = 1/2 of a circle).

4.G.2.eRecognize angle measures as additive and solve problems involving addition and subtraction to find unknown angles on a diagram.

4.G.3 Area and Perimeter: Students will apply perimeter and area formulas for rectangles.

4.G.3.aApply perimeter and area formulas for rectangles to solve authentic problems.

4.N.1 Numeric Relationships: Students will demonstrate and represent multi-digit numbers using relationships with the base-ten number system.

4.N.1.aRead, write, and demonstrate multiple equivalent representations for whole numbers up to 1,000,000 and decimals to the hundredths using visual representations, standard form, and expanded form.

4.N.1.bRepresent and justify comparisons of whole numbers up to 1,000,000 and decimals through the hundredths place using number lines and reasoning strategies.

4.N.1.cRecognize a digit in one place represents ten times what it represents in the place to its right.

4.N.1.dUse decimal notation for fractions with denominators of 10 or 100 (e.g., 43/100 = 0.43).

4.N.2 Fractions and Decimals: Students will extend understanding of fractions by equivalence and ordering and will develop an understanding of decimals.

4.N.2.aExplain and demonstrate how a mixed number is equivalent to a fraction greater than one and how a fraction greater than one is equivalent to a mixed number using visual fraction models and reasoning strategies.

4.N.2.bExplain and demonstrate how equivalent fractions are generated by multiplying by a fraction equivalent to 1 using visual fraction models and the Identity Property of Multiplication.

4.N.2.cCompare and order fractions having unlike numerators or denominators using number lines, benchmarks, reasoning strategies, and/or equivalence.

4.N.3 Operations with Fractions: Students will understand and demonstrate fractional computation.

4.N.3.aDecompose a fraction into a sum of fractions with the same denominator in more than one way and record each decomposition with an equation and a visual representation.

4.N.3.bExplain the meaning of addition and subtraction of fractions with like denominators using visual fraction models, properties of operations, and reasoning strategies.

4.N.3.cAdd and subtract fractions and mixed numbers with like denominators.

4.N.3.dSolve authentic problems involving addition and subtraction of fractions and mixed numbers with like denominators.

4.N.3.eMultiply a fraction by a whole number using visual fraction models and properties of operations.

4.N.4 Factors and Multiples: Students will find factors and multiples and classify numbers as prime or composite.

4.N.4.aDetermine whether a given whole number up to 100 is a multiple of a given one-digit number.

4.N.4.bDetermine factors of any whole number up to 100 and classify a number up to 100 as prime or composite.

Grade 5

5.A.1 Operations and Algebraic Thinking: Students will extend understanding of division and apply operational properties to solve problems involving order of operations.

5.A.1.aMultiply multi-digit whole numbers using an algorithm.

5.A.1.bDivide four-digit whole numbers by a two-digit divisor, with and without remainders, using strategies based on place value.

5.A.1.cJustify the reasonableness of computations involving whole numbers, fractions, and decimals.

5.A.1.dSolve authentic numerical or algebraic expressions using order of operations (excluding exponents).

5.D.1 Data Collection: Students will formulate questions to collect, organize, and represent data.

5.D.1.aNo additional indicators at this level.

5.D.2 Analyze Data and Interpret Results: Students will analyze the data and interpret the results.

5.D.2.aRepresent, analyze, and solve authentic problems using information presented in one or more tables or line plots including whole numbers and fractions.

5.G.1 Shapes and Their Attributes: Students will classify two-dimensional figures into categories based on their properties.

5.G.1.aIdentify and describe faces, edges, and vertices of rectangular prisms.

5.G.1.bRecognize volume as an attribute of solid figures that is measured in cubic units.

5.G.1.cJustify the classification of two-dimensional figures in a hierarchy based on their properties.

5.G.2 Coordinate Geometry: Graph points on the coordinate plane to solve authentic problems.

5.G.2.aIdentify the origin, x axis, and y axis of the coordinate plane.

5.G.2.bGraph and name points in the first quadrant of the coordinate plane using ordered pairs of whole numbers.

5.G.2.cForm ordered pairs from authentic problems involving rules or patterns and graph the ordered pairs in the first quadrant on a coordinate plane and interpret coordinate values in the context of the situation.

5.G.3 Measurement: Generate conversions within the customary and metric systems of measurement to solve authentic problems.

5.G.3.aGenerate conversions in authentic mathematical situations from larger units to smaller units and smaller units to larger units, within the customary and metric systems of measurement.

5.G.4 Area and AreaAngleVolume: Students will extend area problems for rectangles to include fractions and build meaning for measuring volume.

5.G.4.aFind the area of a rectangle with fractional side lengths by tiling it with unit squares of the fraction side lengths and show that the area is the same as would be found by multiplying the side lengths.

5.G.4.bMultiply fractional side lengths to find areas of rectangles and represent fraction products as rectangular areas.

5.G.4.cUse concrete models to measure the volume of rectangular prisms by counting cubic units.

5.G.4.dFind the volume of a rectangular prism with whole-number side lengths by modeling with unit squares and show that the volume can be additive and is the same as would be found by multiplying the area of the base times height.

5.G.4.eSolve authentic problems by applying the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of rectangular prisms with whole number edge lengths.

5.N.1 Numeric Relationships: Students will understand the place value system.

5.N.1.aRead, write, and demonstrate multiple equivalent representations for multi-digit whole numbers and decimals through the thousandths place using standard form and expanded form.

5.N.1.bRecognize a digit in one place represents 1/10 of what it represents in the place to its left.

5.N.1.cUse whole number exponents to denote powers of 10.

5.N.2 Fractions and Decimals: Students will extend understanding of fraction and decimal equivalence and ordering.

5.N.2.aGenerate equivalent forms of commonly used fractions and decimals (e.g., halves, fourths, fifths, tenths).

5.N.2.bRepresent and justify comparisons of whole numbers, fractions, mixed numbers, and decimals through the thousandths place using number lines, reasoning strategies, and/or equivalence.

5.N.3 Operations with Fractions and Decimals: Students will apply and extend previous understandings of whole number operations to add, subtract, multiply and divide fractions and decimals.

5.N.3.aInterpret a fraction as division of the numerator by the denominator.

5.N.3.bMultiply a whole number by a fraction or a fraction by a fraction, including mixed numbers, using visual fraction models and properties of operations.

5.N.3.cDivide a unit fraction by a whole number and a whole number by a unit fraction using visual fraction models and properties of operations.

5.N.3.dSolve authentic problems involving addition, subtraction, and multiplication of fractions and mixed numbers with like and unlike denominators.

5.N.3.eAdd and subtract fractions and mixed numbers with unlike denominators without simplifying.

5.N.3.fSolve authentic problems involving division of fractions by whole numbers and division of whole numbers by unit fractions.

5.N.3.gAdd, subtract, multiply, and divide decimals to hundredths using strategies based on place value, properties of operations, and/or algorithms.

Grade 6

6.A.1 Algebraic Processes: Students will apply the operational properties when evaluating expressions and solving equations and inequalities.

6.A.1.aRecognize and generate equivalent algebraic expressions involving the distributive property and combining like terms.

6.A.1.bGiven the value of the variable, evaluate algebraic expressions with non-negative rational numbers with respect to order of operations, which may include absolute value.

6.A.1.cUse substitution to determine if a given value for a variable makes an equation or inequality true.

6.A.1.dSolve one-step equations with non-negative rational numbers using addition, subtraction, multiplication, and division.

6.A.1.eSolve one-step inequalities with whole numbers using addition, subtraction, multiplication, and division and represent solutions on a number line (e.g., graph 3x > 3).

6.A.2 Applications: Students will solve authentic problems with algebraic expressions, equations, and inequalities.

6.A.2.aCreate algebraic expressions (e.g., one operation, one variable as well as multiple operations, one variable) from word phrases.

6.A.2.bWrite equations (e.g., one operation, one variable) to represent authentic situations involving non- negative rational numbers.

6.A.2.cWrite inequalities (e.g., one operation, one variable) to represent authentic situations involving whole numbers.

6.D.1 Data Collection and Statistical Methods: Students will formulate statistical investigative questions, collect data, and organize data.

6.D.1.aNo additional indicators at this level.

6.D.2 Analyze Data and Interpret Results: Students will represent and analyze the data and interpret the results.

6.D.2.aRepresent data using dot plots, box-and-whisker plots, and histograms.

6.D.2.bSolve problems using information presented in dot plots, box-and-whisker plots, histograms, and circle graphs.

6.D.2.cFind and interpret the mean, median, mode, and range for a set of data.

6.D.2.dCompare the mean, median, mode, and range from two sets of data.

6.D.2.eCompare and interpret data sets based upon their measures of central tendency and graphical representations (e.g., center, spread, shape).

6.D.3 Probability: Students will interpret and apply concepts of probability.

6.D.3.aIdentify a list of possible outcomes for a simple event.

6.D.3.bDescribe the theoretical and experimental probability of an event using a fraction, percentage, and decimal.

6.D.3.cExpress the degree of likelihood (possible, impossible, certain, more likely, equally likely, or less likely) of simple events.

6.D.3.dCompare and contrast theoretical and experimental probabilities.

6.G.1 Attributes: Students will identify and describe geometric attributes of two- dimensional shapes.

6.G.1.aIdentify and create nets to represent two-dimensional drawings of prisms and pyramids.

6.G.2 Coordinate Geometry: Students will determine location, orientation, and relationships on the coordinate plane.

6.G.2.aSEE WORK WITH COORDINATE PLANES IN RATIOS AND PROPORTIONS (6.R.2)

6.G.3 Measurement: Students identify geometric attributes that create two- and three-dimensional shapes in order to perform measurements and apply formulas to find area and volume.

6.G.3.aDetermine the area of quadrilaterals and triangles by composition and decomposition of these shapes, as well as applications of properties and formulas. Quadrilaterals include parallelograms and trapezoids.

6.G.3.bDetermine the surface area of rectangular prisms and triangular prisms using nets as well as application of formulas.

6.G.3.cApply volume formulas for triangular prisms.

6.N.1 Numeric Relationships: Students will demonstrate, represent, and show relationships among fractions, decimals, percents, and integers within the base-ten number system.

6.N.1.aDetermine common factors and common multiples.

6.N.1.bDetermine prime factorization of numbers with and without exponents.

6.N.1.cModel integers using drawings, words, number lines, models and symbols.

6.N.1.dDetermine absolute value of rational numbers.

6.N.1.eCompare and order numbers including non-negative fractions and decimals, integers, and absolute values and locate them on the number line.

6.N.2 Operations: Students will compute with fractions and decimals accurately.

6.N.2.aDivide multi-digit whole numbers and decimals using an algorithm.

6.N.2.bDivide non-negative fractions and mixed numbers.

6.N.2.cEvaluate numerical expressions including absolute value and/or positive exponents with respect to order of operations.

6.R RATIOS AND PROPORTIONS

6.R.1 Ratios and Rates: Students will understand the concept of ratios and unit rates, use language to describe the relationship between two quantities, and use ratios and unit rates to solve authentic situations.

6.R.1.aDetermine ratios from concrete models, drawings, and/or words.

6.R.1.bExplain and determine unit rates.

6.R.1.cFind a percent of a quantity as a rate per 100 and solve problems involving finding the whole, given a part and the percent.

6.R.1.dConvert among fractions, decimals, and percents using multiple representations.

6.R.1.eSolve authentic problems using ratios, unit rates, and percents.

6.R.1.fUse ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

6.R.2 Represent: Students will represent ratios and rates on the coordinate plane.

6.R.2.aIdentify the ordered pair of a given point in the coordinate plane.

6.R.2.bPlot the location of an ordered pair in the coordinate plane.

6.R.2.cIdentify the location of a given point in the coordinate plane (e.g., axis, origin, quadrant).

6.R.2.dMake tables of equivalent ratios relating quantities with whole number measurements.

6.R.2.eUse the constant of proportionality to find the missing value in ratio tables.

6.R.2.fPlot the pair of values from a ratio table on the coordinate plane.

6.R.2.gExplain what a point (x, y) on the graph of a proportional relationship means in terms of the situation.

Grade 7

7.A.1 Algebraic Processes: Students will apply the operational properties when evaluating expressions, and solving equations and inequalities.

7.A.1.aUse factoring and properties of operations to create equivalent algebraic expressions (e.g., 2x + 6 = 2(x + 3)).

7.A.1.bGiven the value of the variable(s), evaluate algebraic expressions, which may include absolute value.

7.A.1.cSolve one- and two-step equations involving rational numbers.

7.A.1.dSolve equations using the distributive property and combining like terms.

7.A.1.eSolve one- and two-step inequalities involving integers and represent solutions on a number line.

7.A.2 Applications: Students will solve authentic problems with algebraic expressions, equations, and inequalities.

7.A.2.aWrite one- and two-step equations involving rational numbers from words, tables, and authentic situations.

7.A.2.bWrite one- and two-step inequalities to represent authentic situations involving integers.

7.D.1 Data Collection and Statistical Methods: Students will formulate statistical investigative questions, collect data, and organize data.

7.D.1.aCreate an investigative question and collect data.

7.D.1.bGenerate conclusions about a population based on a random sample.

7.D.1.cIdentify and critique biases in various data representations.

7.D.2 Analyze Data and Interpret Results: Students will represent and analyze the data and interpret the results.

7.D.2.aNo additional indicator(s) at this level.

7.D.3 Probability: Students will interpret and apply concepts of probability.

7.D.3.aFind theoretical and experimental probabilities for compound independent and dependent events.

7.D.3.bIdentify complementary events and calculate their probabilities.

7.G.1 Attributes: Students will identify angle relationships and apply properties to determine angle measures.

7.G.1.aApply properties of adjacent, complementary, supplementary, linear pair, and vertical angles to find missing angle measures.

7.G.2 Coordinate Geometry: Students will determine location, orientation, and relationships on the coordinate plane.

7.G.2.aDraw polygons in the coordinate plane given coordinates for the vertices.

7.G.2.bCalculate vertical and horizontal distances in the coordinate plane to find perimeter and area of rectangles.

7.G.3 Measurement: Students will identify geometric attributes that create two- and three-dimensional shapes in order to perform measurements and apply formulas to find area and volume.

7.G.3.aSolve authentic problems involving perimeter and area of composite shapes made from triangles and quadrilaterals.

7.G.3.bDetermine surface area and volume of composite rectangular and triangular prisms.

7.G.3.cDetermine the area and circumference of circles both on and off the coordinate plane using 3.14 for the value of Pi.

7.N.1 Numeric Relationships: Students will demonstrate, represent, and show relationships among rational numbers within the base-ten number system.

7.N.1.aNo additional indicator(s) at this level.

7.N.2 Operations: Students will compute with rational numbers accurately.

7.N.2.aAdd, subtract, multiply, and divide rational numbers (e.g., positive and negative fractions, decimals, and integers).

7.N.2.bApply properties of operations (commutative, associative, distributive, identity, inverse, zero) as strategies for problem solving with rational numbers.

7.R RATIOS AND PROPORTIONS

7.R.1 Proportional Relationships: Students will understand the concept of proportions, use language to describe the relationship between two quantities, and use proportions to solve authentic situations.

7.R.1.aDecide whether two quantities are in a proportional relationship (e.g., by testing for equivalent ratios in a table).

7.R.1.bRepresent and solve authentic problems with proportions.

7.R.1.cUse proportional relationships to solve authentic percent problems (e.g., percent change, sales tax, mark-up, discount, tip).

7.R.1.dSolve authentic problems involving scale drawings.

Grade 8

8.A.1 Algebraic Processes: Students will apply the operational properties when evaluating expressions and solving equations.

8.A.1.aDescribe single variable equations as having one solution, no solution, or infinitely many solutions.

8.A.1.bSolve multi-step equations involving rational numbers with the same variable appearing on both sides of the equation.

8.A.1.cSolve equations of the form x^2 = k(k <= 400) and x^3 = k(k <= 125), where k is a positive rational number, using square root and cube root symbols.

8.A.2 Applications: Students will solve authentic problems involving multi-step equations.

8.A.2.aWrite multi-step single variable equations from words, tables, and authentic situations.

8.A.2.bDetermine and describe the rate of change for given situations through the use of tables and graphs.

8.A.2.cGraph proportional relationships and interpret the rate of change.

8.D.1 Data Collection and Statistical Methods: Students will formulate statistical investigative questions, collect data, and organize data.

8.D.1.aNo additional indicator(s) at this level.

8.D.2 Analyze Data and Interpret Results: Students will represent and analyze the data and interpret the results.

8.D.2.aRepresent and interpret bivariate data (e.g., ordered pairs) using scatter plots.

8.D.2.bDescribe patterns such as positive or negative association, linear or nonlinear association, clustering, and outliers when bivariate data is represented on a coordinate plane.

8.D.2.cDraw an informal line of best fit based on the closeness of the data points to the line.

8.D.2.dUse a linear model to make predictions and interpret the rate of change and y-intercept in context.

8.D.3 Probability: Students will interpret and apply concepts of probability.

8.D.3.aNo additional indicator(s) at this level.

8.G.1 Attributes: Students will apply properties of angle relationships in triangles and with lines to determine angle measures.

8.G.1.aDetermine and use the relationships of the interior angles of a triangle to solve for missing measures.

8.G.1.bIdentify and apply geometric properties of parallel lines cut by a transversal and the resulting corresponding same side interior, alternate interior, and alternate exterior angles to find missing measures.

8.G.2 Coordinate Geometry: Students will determine location, orientation, and relationships on the coordinate plane.

8.G.2.aPerform and describe positions and orientations of shapes under single transformations including rotations in multiples of 90 degrees about the origin, translations, reflections, and dilations on and off the coordinate plane.

8.G.2.bDetermine if two-dimensional figures are congruent or similar.

8.G.2.cPerform and describe positions and orientations of shapes under a sequence of transformations on and off the coordinate plane.

8.G.3 Measurement: Students will reason with formulas and context to determine and compare length, area, and volume.

8.G.3.aExplain a model of the Pythagorean Theorem.

8.G.3.bApply the Pythagorean Theorem to find side lengths of triangles and to solve authentic problems.

8.G.3.cFind the distance between any two points on the coordinate plane using the Pythagorean Theorem.

8.G.3.dDetermine the volume of cones, cylinders, and spheres and solve authentic problems using volumes.

8.N.1 Numeric Relationships: Students will demonstrate, represent, and show relationships among real numbers within the base-ten number system.

8.N.1.aDetermine subsets of numbers as natural, whole, integer, rational, irrational, or real based on the definitions of these sets of numbers.

8.N.1.bRepresent numbers with positive and negative exponents and in scientific notation.

8.N.1.cDescribe the difference between a rational and irrational number.

8.N.1.dApproximate, compare, and order real numbers, both rational and irrational, and locate them on the number line.

8.N.2 Operations: Students will compute with exponents and roots.

8.N.2.aEvaluate the square roots of perfect squares less than or equal to 400 and cube roots of perfect cubes less than or equal to 125.

8.N.2.bSimplify numerical expressions involving integer exponents, square roots, and cube roots (e.g., 4-2 is the same as 1/16).

8.N.2.cEvaluate numerical expressions involving absolute value.

8.N.2.dMultiply and divide numbers using scientific notation.

High School

HS.A.1 Algebraic Relationships: Students will demonstrate and represent relationships with functions.

HS.A.1.aDemonstrate that functions are a well mapped subdomain of relations.

HS.A.1.bAnalyze a relation to determine if it is a function given mapping diagrams, function notation (e.g., f(x)=x^2), a table, or a graph.

HS.A.1.cClassify a function given its mapping diagram, function notation, table, or graph as a linear, quadratic, absolute value, exponential, or other function.

HS.A.1.dAnalyze a function’s domain and range to determine if it is one-to-one and has an inverse function both algebraically and graphically.

HS.A.1.eDefine, interpret, and analyze linear, quadratic, absolute value, and exponential functions using the points of interest of the functions and graphing technology.

HS.A.1.fIdentify, analyze, and apply transformations of existing functions (including translation and dilation).

HS.A.1.gInterpret logarithmic equations as exponential equations.

HS.A.1.hDescribe arithmetic sequences using tables of values and functions in explicit and recursive forms.

HS.A.1.iDescribe geometric sequences using tables of values and functions in explicit and recursive forms.

HS.A.2 Algebraic Processes: Students will apply the operational properties when evaluating rational expressions and solving linear and quadratic equations, and inequalities.

HS.A.2.aAnalyze and explain the properties used in solving equations, inequalities, systems of linear equations, systems of linear inequalities, and literal equations.

HS.A.2.bGenerate expressions in equivalent forms by using algebraic properties to make different characteristics or features visible.

HS.A.2.cAnalyze equations and inequalities to determine and apply efficient methods to solve and use appropriate technology as needed.

HS.A.2.dCalculate the slope (rate of change) of a line given coordinate points, a graph, or a table of values.

HS.A.2.eWrite and graph equations of functions (linear, absolute value, quadratic, and exponential) using the points of interest of the function.

HS.A.2.fGiven a line, write the equation of a line that is parallel or perpendicular to it.

HS.A.2.gPerform and explain operations such as addition, subtraction, multiplication, division, and factoring on polynomials.

HS.A.2.hExplain the connection between the factors of a polynomial and the zeros of a polynomial.

HS.A.2.iCombine functions by composition and perform operations on functions.

HS.A.3 Applications: Students will solve authentic problems using nonlinear functions.

HS.A.3.aAnalyze and model authentic situations using various representations and appropriate technology.

HS.A.3.bIdentify, interpret, relate, and graph the factors, x-intercepts, roots, and zeros of polynomial functions using algebraic and graphing methods.

HS.A.3.cIdentify and predict appropriate solutions to equations given context and domain/range (e.g., extraneous solutions, imaginary solutions, no solution, infinitely many solutions).

HS.D.1 Data Collection and Statistical Methods: Students will formulate statistical investigative questions, collect data, and organize data.

HS.D.1.aFormulate multi-variable statistical investigative questions and determine how data can be collected and analyzed to provide an answer.

HS.D.1.bApply an appropriate data collection plan when collecting primary data for the statistical investigative question of interest.

HS.D.1.cUse appropriate technology, including spreadsheet-based logic, to organize data for analysis.

HS.D.1.dDistinguish between surveys, observational studies, and experiments.

HS.D.1.eUnderstand what constitutes good practice in designing a sample survey, an experiment, and an observational study.

HS.D.1.fUnderstand issues of bias and confounding variables in a study and their implications for interpretation.

HS.D.2 Analyze Data and Interpret Results: Students will represent and analyze the data and interpret the results.

HS.D.2.aIdentify appropriate ways to summarize and then represent the distribution of univariate data and bivariate data through the construction of histograms, dot plots, stem plots, box plots, cumulative relative frequency graphs, time plots, circle graphs, stacked bar graphs, and mosaic bar graphs by hand or with technology.

HS.D.2.bDescribe the shape, identify any outliers, and determine the spread of a data set.

HS.D.2.cSelect and determine the appropriate measure of center based on the shape of a distribution and/or the presence of outliers.

HS.D.2.dRecognize when a data set can be reasonably said to be normally distributed and draw conclusions about the data from the associated normal distribution.

HS.D.2.eSummarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data and recognize possible associations and trends in the data.

HS.D.2.fRepresent data on two quantitative variables on a scatter plot and describe how the variables are related.

HS.D.2.gUse technology to develop regression models for linear and non-linear data to predict unobserved outcomes. Interpret slope and y-intercept in the context of the problem.

HS.D.2.hMeasure the strength of association using correlation coefficients for regression curves and interpret their meanings for the model.

HS.D.2.iUse residuals and residual plots to judge the quality of a regression model.

HS.D.2.jRecognize and explain when arguments based on data confuse correlation with causation.

HS.D.2.kUnderstand what constitutes statistical significance. Interpret statistical significance in the context of a situation and answer investigative questions appropriately.

HS.D.2.lUse probability as a tool for assessing risk and for informed decision making by interpreting P-values.

HS.D.3 Probability: Students will interpret and apply concepts of probability.

HS.D.3.aDescribe events as subsets of a sample space using characteristics of the outcomes or as unions, intersections, or complements of other events.

HS.D.3.bExplain independent versus dependent probability of an event.

HS.D.3.cDetermine when order in counting matters and use permutations and combinations to compute probabilities of events accordingly.

HS.D.3.dDetermine whether or not events are mutually exclusive (disjoint) and calculate their probabilities in either case.

HS.D.3.eRecognize and explain the concepts of conditional probability in everyday language and everyday situations.

HS.G.1 Attributes: Students will identify and describe geometric attributes, apply properties and theorems, and create two- dimensional shapes.

HS.G.1.aDemonstrate that two figures are similar or congruent by using a sequence of rigid motions and dilations that map a figure onto the other in problems both with and without coordinates.

HS.G.1.bDescribe symmetries of a figure in terms of rigid motions that map a figure onto itself and make inferences about symmetric figures (e.g., unknown side lengths or angle measures) in problems both with and without coordinates.

HS.G.1.cExplain how the criteria for triangle congruence and similarity (ASA, SAS, and AAS SSS congruence; AA similarity criterion) follow from the definition of congruence and similarity in terms of corresponding parts.

HS.G.1.dIdentify and apply right triangle relationships including converse of the Pythagorean Theorem.

HS.G.1.eApply side and angle relationships of special right triangles (30-60-90 and 45-45-90) to solve geometric problems.

HS.G.1.fIdentify and apply right triangle relationships including sine, cosine, and tangent.

HS.G.1.gApply interior and exterior angle formulas for n-gons and apply to authentic situations.

HS.G.1.hCompare/contrast the properties of quadrilaterals: parallelograms, rectangles, rhombi, squares, kites, trapezoids, and isosceles trapezoids.

HS.G.1.iUse slope and the distance formula to determine the type of quadrilateral.

HS.G.1.jIdentify, describe, apply, and reason through properties of central angles, inscribed angles, angles formed by intersecting chords, secants, and/or tangents to find the measures of angles related to the circle, arc lengths, and areas of sectors.

HS.G.2 Attributes: Students will identify and describe geometric attributes, apply properties and theorems and create three-dimensional shapes.

HS.G.2.aConvert between various units of volume (e.g., cubic feet to cubic yards).

HS.G.2.bApply the effect of a scale factor to determine the volume of similar three-dimensional shapes and solids.

HS.G.2.cDetermine surface area and volume of pyramids, as well as solids that are composites of pyramids, prisms, spheres, cylinders, and cones, using formulas and appropriate units.

HS.G.3 Coordinate Geometry and Transformations: Students will demonstrate and represent location, orientation, and relationships on the coordinate plane.

HS.G.3.aDerive the midpoint formula using the concept of average and apply the midpoint formula to find coordinates.

HS.G.3.bFind the images and preimages of transformations of a point, shape, or a relation on the coordinate plane. Transformations include the following and their compositions: reflections across horizontal and vertical lines and the lines y=x and y=-x, rotations about the origin of 90 degrees, dilations about the origin by any positive scale factor, and any translation.

HS.G.3.cFind the equation of a circle given the radius and the center.

HS.G.4 Logic and Proof: Students will use geometric definitions and theorems to reason abstractly and quantitatively.

HS.G.4.aKnow and use definitions to make deductions in mathematical argumentation (e.g., syllogism, detachment).

HS.G.4.bEvaluate the validity of conditional statements, including biconditional statements (e.g., conditional, converse, contrapositive, inverse).

HS.G.4.cEvaluate the validity of an argument communicated in different ways (e.g., a flow format, two- column, paragraph format).

HS.G.4.dUse coordinate geometry to prove triangles are right, acute, obtuse, isosceles, equilateral, or scalene.

HS.G.4.eProve and apply geometric properties and theorems regarding triangles, congruence, and similarity using deductive reasoning.

HS.G.4.fProve and apply geometric theorems about quadrilaterals using deductive reasoning.

HS.N.1 Estimation and Technology: Students will use estimation strategies and technology to reason, to solve problems, and to make connections within mathematics and across disciplines.

HS.N.1.aSelect, apply, and explain the method of computation when problem solving using real numbers (e.g., models, mental computation, paper-pencil, technology).

HS.N.1.bDetermine if the context of a problem calls for an approximation or an exact value.

HS.N.1.cDetermine the rounding convention to be used based on the context of a problem.

HS.N.1.dEstimate a value using the concept of betweenness by bounding above and below (e.g., since log(10) = 1 and log(1,000) = 3 we know log(500) is between 1 and 3).

HS.N.1.eDetermine the tolerance interval and percent of error in measurement.

HS.N.1.fConvert equivalent rates (e.g., miles per hour to feet per second).

HS.N.1.gDetermine whether extremely large or extremely small quantities can be reasonably represented by a calculator or graphing utility.

HS.N.1.hUse scientific notation to appropriately represent large and small quantities.

HS.N.2 Sets and Operations: Students will use number sets and operations to reason and to solve problems.

HS.N.2.aExtend the properties of exponents to rational numbers.

HS.N.2.bUse properties of rational and irrational numbers.

HS.N.2.cDemonstrate, represent, and show relationships among the subsets of real numbers and the complex number system.

HS.N.2.dCompute with subsets of the complex number system including imaginary, rational, irrational, integers, whole, and natural numbers.

HS.N.3 Interpretation and Sense Making: Students will reason abstractly and quantitatively using units to solve problems and interpret results in context.

HS.N.3.aUnderstand roundoff error and why roundoff error accumulates when rounding occurs prior to the last step in a computation.

HS.N.3.bUse estimation methods to check the reasonableness of real number computations and decide if the problem calls for an approximation (including appropriate rounding) or an exact number.

HS.N.3.cUse units to assess the validity of an answer in the context of a problem.

HS.N.3.dCommunicate the meaning of an answer in the context of a problem.

High School Advanced Topics

AT.A.1 Algebraic Relationships: Students will demonstrate and represent relationships with functions.

AT.A.1.aAnalyze and graph nonlinear functions (trigonometric, rational, higher-order polynomials, logarithmic, and piecewise) and relations (conic sections) using their points of interest and graphing technology.

AT.A.1.bUse the unit circle to define the trigonometric functions on multiples of known angles (positive and negative multiples of 30 and 45 degrees or pi/6 and pi/4).

AT.A.1.cGiven a function, list the sequence of algebraic transformations that changes a parent function to the given function.

AT.A.1.dDefine the radian unit of measure and its relationship with degrees.

AT.A.2 Algebraic Processes: Students will apply the operational properties when evaluating nonlinear expressions and solving nonlinear equations and inequalities.

AT.A.2.aExplain symmetry of functions and determine whether a function is odd, even, or neither.

AT.A.2.bRepresent, interpret, and analyze inverses of functions algebraically and graphically using domain restrictions when necessary.

AT.A.2.cWrite equations of nonlinear functions (trigonometric, rational, higher-order polynomials, logarithmic and piecewise) using points of interest of the function.

AT.A.2.dConvert between radian and degree measures of an angle.

AT.A.2.eUse limits to describe the behavior of a function near its asymptotes and removable discontinuities.

AT.A.3 Applications: Students will solve authentic problems using nonlinear functions and relations.

AT.A.3.aAnalyze and model authentic situations using various non-linear representations and relations with appropriate technology.

AT.A.3.bAnalyze and model authentic application situations using various non-linear representations and relations with appropriate technology.

AT.D.1 Data Collection and Statistical Methods: Students will formulate statistical investigative questions, collect data, and organize data.

AT.D.1.aExplain what constitutes good practice in designing a sample survey, an experiment, and an observational study.

AT.D.1.bExplain the use of randomization to reduce the influence of confounding or lurking variables.

AT.D.1.cExplain issues of bias and confounding variables in a study and their implications for interpretation.

AT.D.1.dDemonstrate knowledge of the role sampling distributions play in the estimation of an unknown population parameter through the use of appropriate sampling techniques.

AT.D.2 Analyze Data and Interpret Results: Students will represent and analyze the data and interpret the results.

AT.D.2.aDetermine when a data set can be reasonably said to be normally distributed and draw conclusions about the data from the associated normal distribution.

AT.D.2.bUse technology to develop regression models for linear and non-linear data to predict unobserved outcomes. Apply algebraic transformations to non-linear data to generate a linearized data set and employ linear regression techniques to analyze the non-linear data set.

AT.D.3 Probability: Students will interpret and apply concepts of probability.

AT.D.3.aWeigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. Interpret the expected value as the mean of a probability distribution.

AT.D.3.bCommunicate what constitutes statistical significance. Interpret statistical significance in the context of a situation and answer investigative questions appropriately.

AT.D.3.cUse data to compare two groups, describe sample variability, and decide if differences between parameters are significant based on the statistics.

AT.D.3.dUse probability as a tool for assessing risk and for informed decision making by computing and interpreting P-values.

AT.D.3.eUse confidence intervals to estimate an unknown population parameter.

AT.G.1 Attributes: Students will identify and describe geometric attributes, apply properties and theorems, and create two- dimensional shapes.

AT.G.1.aApply the Law of Sines and the Law of Cosines to find unknown measures in triangles.

AT.G.2 Attributes: Students will identify and describe geometric attributes, apply properties and theorems, and create three-dimensional shapes.

AT.G.2.aDetermine the three-dimensional object created by rotating or revolving a two-dimensional object about an axis.

AT.G.2.bDetermine the shape of a two-dimensional cross-section of a three-dimensional object.

AT.G.2.cUse Cavalieri’s Principle to determine volume of three-dimensional figures.

AT.G.3 Coordinate Geometry and Transformations: Students will demonstrate and represent location, orientation, and relationships on the coordinate plane.

AT.G.3.aIdentify symmetry properties of a function (e.g., axis of symmetry of a parabola) and know the connection between its symmetry properties and specific transformations.

AT.G.3.bRecognize that translations can be described in terms of vectors.

AT.G.3.cFind the images and preimages of transformations of a point, shape, or relation on the coordinate plane, where transformations include the following compositions: reflections about lines of any rational slope passing through the origins, delations about the origin by any positive scale factor, and translations.

AT.G.3.dExplain the focus-directrix construction of a parabola and derive the equation of a parabola from focus and directrix for a parabola whose axis of symmetry is a coordinate axis.

AT.G.4 Logic and Proof: Students will use geometric definitions and theorems to reason abstractly and quantitatively.

AT.G.4.aUse known definitions and results in informal argumentation to construct logical arguments.

AT.G.4.bDistinguish between empirical reasoning, examples, and deductive reasoning, as well as informal and formal reasoning.

AT.G.4.cEvaluate the deductive consequences of alternative definitions of known objects (e.g., whether a trapezoid is defined as a quadrilateral with exactly one pair of parallel sides or defined as at least one pair of parallel sides).

AT.N.1 Estimation and Technology: Students will use estimation strategies and technology to reason, to solve problems, and to make connections within mathematics and across disciplines.

AT.N.1.aUse domain and range restrictions to apply an appropriate viewing window while using graphing technology.

AT.N.1.bCompare and contrast radians and degrees as measures of angles and the reason graphing utilities tend to use radians as the default setting.

AT.N.2 Sets and Operations: Students will compare and contrast subsets and perform operations with subsets of the complex number system to reason and to solve problems.

AT.N.2.aPerform arithmetic operations with complex numbers.

AT.N.2.bRepresent complex numbers and their operations in the complex plane.

AT.N.2.cUse complex numbers in polynomial identities and equations.

AT.N.2.dRepresent quantities using bases other than decimal such as binary (base 2) or hexadecimal (base 16) and convert numbers to and from base 10.

AT.N.2.eExplain modular arithmetic and its role in computer programming.

AT.N.2.fRepresent and model vector quantities.

AT.N.2.gPerform operations on vectors.

AT.N.2.hPerform operations on matrices and use matrices in applications.

AT.N.3 Interpretation and Sense Making: Students will reason abstractly and quantitatively using units to solve problems and interpret results in context.

AT.N.3.aUse vectors to communicate the geometric relationships between complex numbers in the complex plane.

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.