IXL - New York algebra standards

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2011 New York State P-12 Common Core Learning Standards 2011 New York State P-12 Common Core Learning Standards
2005 New York Core Curriculum 2005 New York Core Curriculum

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A.PS Problem Solving

A.PS Students will build new mathematical knowledge through problem solving.
A.PS.1 Use a variety of problem solving strategies to understand new mathematical content
A.PS.2 Recognize and understand equivalent representations of a problem situation or a mathematical concept
A.PS Students will solve problems that arise in mathematics and in other contexts.
A.PS.3 Observe and explain patterns to formulate generalizations and conjectures
A.PS.4 Use multiple representations to represent and explain problem situations (e.g., verbally, numerically, algebraically, graphically)
A.PS Students will apply and adapt a variety of appropriate strategies to solve problems.
A.PS.5 Choose an effective approach to solve a problem from a variety of strategies (numeric, graphic, algebraic)
A.PS.6 Use a variety of strategies to extend solution methods to other problems
A.PS.7 Work in collaboration with others to propose, critique, evaluate, and value alternative approaches to problem solving
A.PS Students will monitor and reflect on the process of mathematical problem solving.
A.PS.8 Determine information required to solve a problem, choose methods for obtaining the information, and define parameters for acceptable solutions
A.PS.9 Interpret solutions within the given constraints of a problem
A.PS.10 Evaluate the relative efficiency of different representations and solution methods of a problem

A.RP Reasoning and Proof

A.RP Students will recognize reasoning and proof as fundamental aspects of mathematics.
A.RP.1 Recognize that mathematical ideas can be supported by a variety of strategies
A.RP Students will make and investigate mathematical conjectures.
A.RP.2 Use mathematical strategies to reach a conclusion and provide supportive arguments for a conjecture
- Logic: Identify hypotheses and conclusions (Algebra - HH.1)
- Logic: Counterexamples (Algebra - HH.2)
A.RP.3 Recognize when an approximation is more appropriate than an exact answer
A.RP Students will develop and evaluate mathematical arguments and proofs.
A.RP.4 Develop, verify, and explain an argument, using appropriate mathematical ideas and language
- Logic: Identify hypotheses and conclusions (Algebra - HH.1)
A.RP.5 Construct logical arguments that verify claims or counterexamples that refute them
- Logic: Counterexamples (Algebra - HH.2)
A.RP.6 Present correct mathematical arguments in a variety of forms
A.RP.7 Evaluate written arguments for validity
A.RP Students will select and use various types of reasoning and methods of proof.
A.RP.8 Support an argument by using a systematic approach to test more than one case
A.RP.9 Devise ways to verify results or use counterexamples to refute incorrect statements
- Logic: Identify hypotheses and conclusions (Algebra - HH.1)
- Logic: Counterexamples (Algebra - HH.2)
A.RP.10 Extend specific results to more general cases
A.RP.11 Use a Venn diagram to support a logical argument
- Problem solving: Use Venn diagrams to solve problems (Eighth grade - M.3)
A.RP.12 Apply inductive reasoning in making and supporting mathematical conjectures

A.CM Communication

A.CM Students will organize and consolidate their mathematical thinking through communication.
A.CM.1 Communicate verbally and in writing a correct, complete, coherent, and clear design (outline) and explanation for the steps used in solving a problem
A.CM.2 Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, Venn diagrams, and other diagrams
A.CM Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
A.CM.3 Present organized mathematical ideas with the use of appropriate standard notations, including the use of symbols and other representations when sharing an idea in verbal and written form
A.CM.4 Explain relationships among different representations of a problem
A.CM.5 Communicate logical arguments clearly, showing why a result makes sense and why the reasoning is valid
- Logic: Identify hypotheses and conclusions (Algebra - HH.1)
- Logic: Counterexamples (Algebra - HH.2)
A.CM.6 Support or reject arguments or questions raised by others about the correctness of mathematical work
A.CM Students will analyze and evaluate the mathematical thinking and strategies of others.
A.CM.7 Read and listen for logical understanding of mathematical thinking shared by other students
A.CM.8 Reflect on strategies of others in relation to one's own strategy
A.CM.9 Formulate mathematical questions that elicit, extend, or challenge strategies, solutions, and/or conjectures of others
A.CM Students will use the language of mathematics to express mathematical ideas precisely.
A.CM.10 Use correct mathematical language in developing mathematical questions that elicit, extend, or challenge other students' conjectures
A.CM.11 Represent word problems using standard mathematical notation
A.CM.12 Understand and use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale
A.CM.13 Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing

A.CN Connections

A.R Representation

A.R Students will create and use representations to organize, record, and communicate mathematical ideas.
A.R.1 Use physical objects, diagrams, charts, tables, graphs, symbols, equations, or objects created using technology as representations of mathematical concepts
A.R.2 Recognize, compare, and use an array of representational forms
A.R.3 Use representation as a tool for exploring and understanding mathematical ideas
A.R Students will select, apply, and translate among mathematical representations to solve problems.
A.R.4 Select appropriate representations to solve problem situations
A.R.5 Investigate relationships between different representations and their impact on a given problem
A.R Students will use representations to model and interpret physical, social, and mathematical phenomena.
A.R.6 Use mathematics to show and understand physical phenomena (e.g., find the height of a building if a ladder of a given length forms a given angle of elevation with the ground)
A.R.7 Use mathematics to show and understand social phenomena (e.g., determine profit from student and adult ticket sales)
A.R.8 Use mathematics to show and understand mathematical phenomena (e.g., compare the graphs of the functions represented by the equations y = x² and y = -x²)

A.N Number Sense and Operations

A.N Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
A.N Number Theory
A.N.1 Identify and apply the properties of real numbers (closure, commutative, associative, distributive, identity, inverse) Note: Students do not need to identify groups and fields, but students should be engaged in the ideas.
A.N Students will understand meanings of operations and procedures, and how they relate to one another.
A.N Operations
A.N.2 Simplify radical terms (no variable in the radicand)
- Radical expressions: Simplify radical expressions (Algebra - EE.1)
- Radical expressions: Simplify radical expressions by rationalizing the denominator (Algebra - EE.2)
A.N.3 Perform the four arithmetic operations using like and unlike radical terms and express the result in simplest form
A.N.4 Understand and use scientific notation to compute products and quotients of numbers
A.N.5 Solve algebraic problems arising from situations that involve fractions, decimals, percents (decrease/increase and discount), and proportionality/direct variation
A.N.6 Evaluate expressions involving factorial(s), absolute value(s), and exponential expression(s)
- Exponential functions: Evaluate an exponential function (Algebra - X.1)
- Absolute value functions: Complete a function table: absolute value functions (Algebra - DD.1)
A.N.7 Determine the number of possible events, using counting techniques or the Fundamental Principle of Counting
A.N.8 Determine the number of possible arrangements (permutations) of a list of items
- Probability: Permutations (Algebra - II.6)

A.A Algebra

A.A Students will represent and analyze algebraically a wide variety of problem solving situations.
A.A Variables and Expressions
A.A.1 Translate a quantitative verbal phrase into an algebraic expression
- Variable expressions and equations: Write variable expressions (Algebra - I.1)
A.A.2 Write a verbal expression that matches a given mathematical expression
A.A Equations and Inequalities
A.A.3 Distinguish the difference between an algebraic expression and an algebraic equation
- Variable expressions and equations: Write variable expressions (Algebra - I.1)
- Variable expressions and equations: Write variable equations (Algebra - I.3)
A.A.4 Translate verbal sentences into mathematical equations or inequalities
- Ratios and proportions: Solve proportions: word problems (Algebra - C.6)
- Percents: Percent word problems (Algebra - D.3)
- Percents: Percent of change: word problems (Algebra - D.5)
- Geometry: Pythagorean theorem: word problems (Algebra - F.13)
- Variable expressions and equations: Write variable equations (Algebra - I.3)
- Solve equations: Solve linear equations: word problems (Algebra - J.8)
- Problem solving: Word problems: mixed review (Algebra - O.1)
- Problem solving: Word problems with money (Algebra - O.2)
- Problem solving: Consecutive integer problems (Algebra - O.3)
- Problem solving: Rate of travel: word problems (Algebra - O.4)
- Problem solving: Weighted averages: word problems (Algebra - O.5)
- Linear functions: Linear function word problems (Algebra - S.8)
- Linear inequalities: Linear inequalities: word problems (Algebra - T.4)
A.A.5 Write algebraic equations or inequalities that represent a situation
- Variable expressions and equations: Write variable equations (Algebra - I.3)
- Single-variable inequalities: Write inequalities from graphs (Algebra - K.2)
A.A.6 Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable
- Solve equations: Solve linear equations: word problems (Algebra - J.8)
A.A.7 Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables
- Systems of linear equations: Solve a system of equations by graphing: word problems (Algebra - U.3)
- Systems of linear equations: Solve a system of equations using substitution: word problems (Algebra - U.9)
- Systems of linear equations: Solve a system of equations using elimination: word problems (Algebra - U.11)
- Systems of linear equations: Solve a system of equations using augmented matrices: word problems (Algebra - U.13)
- Systems of linear equations: Solve a system of equations using any method: word problems (Algebra - U.15)
A.A.8 Analyze and solve verbal problems that involve quadratic equations
A.A.9 Analyze and solve verbal problems that involve exponential growth and decay
- Exponential functions: Exponential growth and decay: word problems (Algebra - X.3)
A.A.10 Solve systems of two linear equations in two variables algebraically (See A.G.7)
- Systems of linear equations: Is (x, y) a solution to the system of equations? (Algebra - U.1)
- Systems of linear equations: Find the number of solutions to a system of equations (Algebra - U.5)
- Systems of linear equations: Classify a system of equations (Algebra - U.7)
- Systems of linear equations: Solve a system of equations using substitution (Algebra - U.8)
- Systems of linear equations: Solve a system of equations using elimination (Algebra - U.10)
- Systems of linear equations: Solve a system of equations using augmented matrices (Algebra - U.12)
- Systems of linear equations: Solve a system of equations using any method (Algebra - U.14)
A.A.11 Solve a system of one linear and one quadratic equation in two variables, where only factoring is required Note: The quadratic equation should represent a parabola and the solution(s) should be integers.
A.A Students will perform algebraic procedures accurately.
A.A Variables and Expressions
A.A.12 Multiply and divide monomial expressions with a common base, using the properties of exponents Note: Use integral exponents only
- Exponents: Exponents with integer bases (Algebra - V.1)
- Exponents: Exponents with decimal and fractional bases (Algebra - V.2)
- Exponents: Negative exponents (Algebra - V.3)
- Exponents: Multiplication with exponents (Algebra - V.4)
- Exponents: Division with exponents (Algebra - V.5)
- Exponents: Multiplication and division with exponents (Algebra - V.6)
- Exponents: Power rule (Algebra - V.7)
- Exponents: Simplify expressions involving exponents (Algebra - V.8)
A.A.13 Add, subtract, and multiply monomials and polynomials
- Monomials: Identify monomials (Algebra - Y.1)
- Monomials: Multiply monomials (Algebra - Y.2)
- Monomials: Divide monomials (Algebra - Y.3)
- Monomials: Multiply and divide monomials (Algebra - Y.4)
- Monomials: Powers of monomials (Algebra - Y.5)
- Polynomials: Polynomial vocabulary (Algebra - Z.1)
- Polynomials: Model polynomials with algebra tiles (Algebra - Z.2)
- Polynomials: Add and subtract polynomials using algebra tiles (Algebra - Z.3)
- Polynomials: Add and subtract polynomials (Algebra - Z.4)
- Polynomials: Add polynomials to find perimeter (Algebra - Z.5)
- Polynomials: Multiply a polynomial by a monomial (Algebra - Z.6)
- Polynomials: Multiply two polynomials using algebra tiles (Algebra - Z.7)
- Polynomials: Multiply two binomials (Algebra - Z.8)
- Polynomials: Multiply two binomials: special cases (Algebra - Z.9)
- Polynomials: Multiply polynomials (Algebra - Z.10)
A.A.14 Divide a polynomial by a monomial or binomial, where the quotient has no remainder
- Rational functions and expressions: Simplify complex fractions (Algebra - GG.2)
- Rational functions and expressions: Simplify rational expressions (Algebra - GG.3)
- Rational functions and expressions: Multiply and divide rational expressions (Algebra - GG.4)
- Rational functions and expressions: Divide polynomials (Algebra - GG.5)
A.A.15 Find values of a variable for which an algebraic fraction is undefined
- Rational functions and expressions: Rational functions: asymptotes and excluded values (Algebra - GG.1)
A.A.16 Simplify fractions with polynomials in the numerator and denominator by factoring both and renaming them to lowest terms
- Factoring: GCF of monomials (Algebra - AA.1)
- Factoring: Factor out a monomial (Algebra - AA.2)
- Factoring: Factor quadratics with leading coefficient 1 (Algebra - AA.3)
- Factoring: Factor quadratics with other leading coefficients (Algebra - AA.4)
- Factoring: Factor quadratics: special cases (Algebra - AA.5)
- Factoring: Factor by grouping (Algebra - AA.6)
- Factoring: Factor polynomials (Algebra - AA.7)
- Rational functions and expressions: Simplify complex fractions (Algebra - GG.2)
- Rational functions and expressions: Simplify rational expressions (Algebra - GG.3)
A.A.17 Add or subtract fractional expressions with monomial or like binomial denominators
- Rational functions and expressions: Add and subtract rational expressions (Algebra - GG.6)
A.A.18 Multiply and divide algebraic fractions and express the product or quotient in simplest form
- Rational functions and expressions: Simplify complex fractions (Algebra - GG.2)
- Rational functions and expressions: Simplify rational expressions (Algebra - GG.3)
- Rational functions and expressions: Multiply and divide rational expressions (Algebra - GG.4)
A.A.19 Identify and factor the difference of two perfect squares
- Quadratic equations: Solve a quadratic equation using square roots (Algebra - BB.2)
A.A.20 Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF)
- Factoring: GCF of monomials (Algebra - AA.1)
- Factoring: Factor out a monomial (Algebra - AA.2)
- Factoring: Factor quadratics with leading coefficient 1 (Algebra - AA.3)
- Factoring: Factor quadratics with other leading coefficients (Algebra - AA.4)
- Factoring: Factor quadratics: special cases (Algebra - AA.5)
- Factoring: Factor by grouping (Algebra - AA.6)
- Factoring: Factor polynomials (Algebra - AA.7)
A.A Equations and Inequalities
A.A.21 Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable
- Variable expressions and equations: Does x satisfy the equation? (Algebra - I.4)
- Single-variable inequalities: Identify solutions to inequalities (Algebra - K.3)
A.A.22 Solve all types of linear equations in one variable
- Solve equations: Model and solve equations using algebra tiles (Algebra - J.1)
- Solve equations: Write and solve equations that represent diagrams (Algebra - J.2)
- Solve equations: Solve one-step linear equations (Algebra - J.3)
- Solve equations: Solve two-step linear equations (Algebra - J.4)
- Solve equations: Solve advanced linear equations (Algebra - J.5)
- Solve equations: Solve equations with variables on both sides (Algebra - J.6)
- Solve equations: Identities and equations with no solutions (Algebra - J.7)
- Solve equations: Solve linear equations: word problems (Algebra - J.8)
- Solve equations: Solve linear equations: mixed review (Algebra - J.9)
A.A.23 Solve literal equations for a given variable
- Problem solving: Rate of travel: word problems (Algebra - O.4)
A.A.24 Solve linear inequalities in one variable
- Single-variable inequalities: Solve one-step linear inequalities: addition and subtraction (Algebra - K.4)
- Single-variable inequalities: Solve one-step linear inequalities: multiplication and division (Algebra - K.5)
- Single-variable inequalities: Solve one-step linear inequalities (Algebra - K.6)
- Single-variable inequalities: Graph solutions to one-step linear inequalities (Algebra - K.7)
- Single-variable inequalities: Solve two-step linear inequalities (Algebra - K.8)
- Single-variable inequalities: Graph solutions to two-step linear inequalities (Algebra - K.9)
- Single-variable inequalities: Solve advanced linear inequalities (Algebra - K.10)
- Single-variable inequalities: Graph solutions to advanced linear inequalities (Algebra - K.11)
- Single-variable inequalities: Graph compound inequalities (Algebra - K.12)
- Single-variable inequalities: Write compound inequalities from graphs (Algebra - K.13)
- Single-variable inequalities: Solve compound inequalities (Algebra - K.14)
- Single-variable inequalities: Graph solutions to compound inequalities (Algebra - K.15)
A.A.25 Solve equations involving fractional expressions Note: Expressions which result in linear equations in one variable.
- Solve equations: Solve two-step linear equations (Algebra - J.4)
- Solve equations: Solve advanced linear equations (Algebra - J.5)
A.A.26 Solve algebraic proportions in one variable which result in linear or quadratic equations
- Ratios and proportions: Solve proportions (Algebra - C.5)
- Ratios and proportions: Solve proportions: word problems (Algebra - C.6)
- Ratios and proportions: Scale drawings and scale factors (Algebra - C.7)
A.A.27 Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots
- Quadratic equations: Solve an equation using the zero product property (Algebra - BB.3)
A.A.28 Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expression
- Factoring: Factor quadratics with leading coefficient 1 (Algebra - AA.3)
- Factoring: Factor quadratics with other leading coefficients (Algebra - AA.4)
- Factoring: Factor quadratics: special cases (Algebra - AA.5)
- Quadratic equations: Solve a quadratic equation by factoring (Algebra - BB.4)
A.A Students will recognize, use, and represent algebraically patterns, relations, and functions.
A.A Patterns, Relations, and Functions
A.A.29 Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form
A.A.30 Find the complement of a subset of a given set, within a given universe
A.A.31 Find the intersection of sets (no more than three sets) and/or union of sets (no more than three sets)
A.A Coordinate Geometry
A.A.32 Explain slope as a rate of change between dependent and independent variables
- Linear functions: Find the slope of a graph (Algebra - S.2)
- Linear functions: Find slope from two points (Algebra - S.3)
- Linear functions: Slope-intercept form: find slope and y-intercept (Algebra - S.4)
A.A.33 Determine the slope of a line, given the coordinates of two points on the line
- Linear functions: Find slope from two points (Algebra - S.3)
A.A.34 Write the equation of a line, given its slope and the coordinates of a point on the line
- Linear functions: Slope-intercept form: find slope and y-intercept (Algebra - S.4)
- Linear functions: Slope-intercept form: write an equation from a graph (Algebra - S.6)
- Linear functions: Slope-intercept form: write an equation (Algebra - S.7)
A.A.35 Write the equation of a line, given the coordinates of two points on the line
- Linear functions: Find slope from two points (Algebra - S.3)
- Linear functions: Slope-intercept form: find slope and y-intercept (Algebra - S.4)
A.A.36 Write the equation of a line parallel to the x- or y-axis
- Linear functions: Equations of horizontal and vertical lines (Algebra - S.12)
A.A.37 Determine the slope of a line, given its equation in any form
- Linear functions: Slope-intercept form: find slope and y-intercept (Algebra - S.4)
- Linear functions: Point-slope form: write an equation (Algebra - S.16)
A.A.38 Determine if two lines are parallel, given their equations in any form
- Linear functions: Slopes of parallel and perpendicular lines (Algebra - S.17)
- Linear functions: Write an equation for a parallel or perpendicular line (Algebra - S.18)
A.A.39 Determine whether a given point is on a line, given the equation of the line
- Relations and functions: Complete a function table (Algebra - Q.6)
- Relations and functions: Find points on a function graph (Algebra - Q.11)
A.A.40 Determine whether a given point is in the solution set of a system of linear inequalities
- Linear inequalities: Is (x, y) a solution to the system of inequalities? (Algebra - T.5)
A.A.41 Determine the vertex and axis of symmetry of a parabola, given its equation (See A.G.10)
A.A Trigonometric Functions
A.A.42 Find the sine, cosine, and tangent ratios of an angle of a right triangle, given the lengths of the sides
A.A.43 Determine the measure of an angle of a right triangle, given the length of any two sides of the triangle
A.A.44 Find the measure of a side of a right triangle, given an acute angle and the length of another side
A.A.45 Determine the measure of a third side of a right triangle using the Pythagorean theorem, given the lengths of any two sides
- Geometry: Pythagorean theorem (Algebra - F.12)
- Geometry: Pythagorean theorem: word problems (Algebra - F.13)

A.G Geometry

A.G Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
A.G Shapes
A.G.1 Find the area and/or perimeter of figures composed of polygons and circles or sectors of a circle Note: Figures may include triangles, rectangles, squares, parallelograms, rhombuses, trapezoids, circles, semi-circles, quarter-circles, and regular polygons (perimeter only).
A.G.2 Use formulas to calculate volume and surface area of rectangular solids and cylinders
- Geometry: Volume (Algebra - F.3)
- Geometry: Surface area (Algebra - F.4)
A.G Students will apply coordinate geometry to analyze problem solving situations.
A.G Coordinate Geometry
A.G.3 Determine when a relation is a function, by examining ordered pairs and inspecting graphs of relations
- Relations and functions: Identify functions (Algebra - Q.4)
- Relations and functions: Identify functions: vertical line test (Algebra - Q.5)
A.G.4 Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions
A.G.5 Investigate and generalize how changing the coefficients of a function affects its graph
A.G.6 Graph linear inequalities
- Single-variable inequalities: Graph inequalities (Algebra - K.1)
A.G.7 Graph and solve systems of linear equations and inequalities with rational coefficients in two variables (See A.A.10)
A.G.8 Find the roots of a parabolic function graphically Note: Only quadratic equations with integral solutions.
- Quadratic equations: Characteristics of quadratic functions (Algebra - BB.1)
A.G.9 Solve systems of linear and quadratic equations graphically Note: Only use systems of linear and quadratic equations that lead to solutions whose coordinates are integers.
- Systems of linear equations: Solve a system of equations by graphing (Algebra - U.2)
- Systems of linear equations: Find the number of solutions to a system of equations by graphing (Algebra - U.4)
A.G.10 Determine the vertex and axis of symmetry of a parabola, given its graph (See A.A.41) Note: The vertex will have an ordered pair of integers and the axis of symmetry will have an integral value.
- Quadratic equations: Characteristics of quadratic functions (Algebra - BB.1)

A.M Measurement

A.G Students will determine what can be measured and how, using appropriate methods and formulas.
A.G Units of Measurement
A.M.1 Calculate rates using appropriate units (e.g., rate of a space ship versus the rate of a snail)
A.M.2 Solve problems involving conversions within measurement systems, given the relationship between the units
A.G Students will understand that all measurement contains error and be able to determine its significance.
A.G Error and Magnitude
A.M.3 Calculate the relative error in measuring square and cubic units, when there is an error in the linear measure

A.S Statistics and Probability

A.S Students will collect, organize, display, and analyze data.
A.S Organization and Display of Data
A.S.1 Categorize data as qualitative or quantitative
A.S.2 Determine whether the data to be analyzed is univariate or bivariate
A.S.3 Determine when collected data or display of data may be biased
- Statistics: Identifying biased samples (Algebra - JJ.3)
A.S.4 Compare and contrast the appropriateness of different measures of central tendency for a given data set
- Statistics: Mean, median, mode, and range (Algebra - JJ.1)
A.S.5 Construct a histogram, cumulative frequency histogram, and a box-and-whisker plot, given a set of data
- Charts and graphs: Create bar graphs, line graphs, and histograms (Algebra - N.2)
A.S.6 Understand how the five statistical summary (minimum, maximum, and the three quartiles) is used to construct a box-and-whisker plot
- Charts and graphs: Interpret box-and-whisker plots (Algebra - N.5)
- Statistics: Quartiles (Algebra - JJ.2)
A.S.7 Create a scatter plot of bivariate data
- Charts and graphs: Interpret a scatter plot (Algebra - N.6)
A.S.8 Construct manually a reasonable line of best fit for a scatter plot and determine the equation of that line
- Charts and graphs: Scatter plots: line of best fit (Algebra - N.7)
A.S Analysis of Data
A.S.9 Analyze and interpret a frequency distribution table or histogram, a cumulative frequency distribution table or histogram, or a box-and-whisker plot
- Charts and graphs: Interpret bar graphs, line graphs, and histograms (Algebra - N.1)
- Charts and graphs: Interpret box-and-whisker plots (Algebra - N.5)
A.S.10 Evaluate published reports and graphs that are based on data by considering: experimental design, appropriateness of the data analysis, and the soundness of the conclusions
A.S.11 Find the percentile rank of an item in a data set and identify the point values for first, second, and third quartiles
A.S.12 Identify the relationship between the independent and dependent variables from a scatter plot (positive, negative, or none)
- Charts and graphs: Interpret a scatter plot (Algebra - N.6)
A.S.13 Understand the difference between correlation and causation
A.S.14 Identify variables that might have a correlation but not a causal relationship
A.S Students will make predictions that are based upon data analysis.
A.S Predictions from Data
A.S.15 Identify and describe sources of bias and its effect, drawing conclusions from data
- Statistics: Identifying biased samples (Algebra - JJ.3)
A.S.16 Recognize how linear transformations of one-variable data affect the data's mean, median, mode, and range
A.S.17 Use a reasonable line of best fit to make a prediction involving interpolation or extrapolation
- Charts and graphs: Scatter plots: line of best fit (Algebra - N.7)
A.S Students will understand and apply concepts of probability.
A.S Probability
A.S.18 Know the definition of conditional probability and use it to solve for probabilities in finite sample spaces
A.S.19 Determine the number of elements in a sample space and the number of favorable events
- Probability: Theoretical probability (Algebra - II.1)
- Probability: Compound events: find the number of outcomes (Algebra - II.3)
A.S.20 Calculate the probability of an event and its complement
- Probability: Probability of opposite, mutually exclusive, and overlapping events (Eighth grade - AA.2)
A.S.21 Determine empirical probabilities based on specific sample data
- Probability: Experimental probability (Algebra - II.2)
A.S.22 Determine, based on calculated probability of a set of events, if:
A.S.22.a some or all are equally likely to occur
A.S.22.b one is more likely to occur than another
A.S.22.c whether or not an event is certain to happen or not to happen
A.S.23 Calculate the probability of:
A.S.23.a a series of independent events
- Probability: Probability of independent and dependent events (Algebra - II.5)
A.S.23.b a series of dependent events
- Probability: Probability of independent and dependent events (Algebra - II.5)
A.S.23.c two mutually exclusive events
- Probability: Probability of opposite, mutually exclusive, and overlapping events (Eighth grade - AA.2)
A.S.23.d two events that are not mutually exclusive
- Probability: Probability of opposite, mutually exclusive, and overlapping events (Eighth grade - AA.2)