Math Standard 3 Algebra

New York State Learning Standards

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Problem Solving
Reasoning and Proof
Communication
Connections
Representation
Number Sense and Operations
Algebra
Geometry
Measurement
Statistics and Probability

MST Standard Three: Mathematics: Algebra Students will: · understand the concepts of and become proficient with the skills of mathematics; · communicate and reason mathematically; · become problem solvers by using appropriate tools and strategies; through the integrated study of number sense and operations, algebra, geometry, measurement, and statistics and probability.
*Problem Solving* 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
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*Problem Solving* 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)
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*Problem Solving* 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
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*Problem Solving* 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
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*Reasoning and Proof* 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
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*Reasoning and Proof* Students will make and investigate mathematical conjectures.

	A.RP.2	Use mathematical strategies to reach a conclusion and provide supportive arguments for a conjecture
	A.RP.3	Recognize when an approximation is more appropriate than an exact answer
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*Reasoning and Proof* Students will develop and evaluate mathematical arguments and proofs.

	A.RP.4	Develop, verify, and explain an argument, using appropriate mathematical ideas and language
	A.RP.5	Construct logical arguments that verify claims or counterexamples that refute them
	A.RP.6	Present correct mathematical arguments in a variety of forms
	A.RP.7	Evaluate written arguments for validity
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*Reasoning and Proof* 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
	A.RP.10	Extend specific results to more general cases
	A.RP.11	Use a Venn diagram to support a logical argument
	A.RP.12	Apply inductive reasoning in making and supporting mathematical conjectures
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*Communication* 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
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*Communication* 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
	A.CM.6	Support or reject arguments or questions raised by others about the correctness of mathematical work
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*Communication* 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
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*Communication* 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
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*Connections* Students will recognize and use connections among mathematical ideas.

	A.CN.1	Understand and make connections among multiple representations of the same mathematical idea
	A.CN.2	Understand the corresponding procedures for similar problems or mathematical concepts
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*Connections* Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

	A.CN.3	Model situations mathematically, using representations to draw conclusions and formulate new situations
	A.CN.4	Understand how concepts, procedures, and mathematical results in one area of mathematics can be used to solve problems in other areas of mathematics
	A.CN.5	Understand how quantitative models connect to various physical models and representations
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*Connections* Students will recognize and apply mathematics in contexts outside of mathematics.

	A.CN.6	Recognize and apply mathematics to situations in the outside world
	A.CN.7	Recognize and apply mathematical ideas to problem situations that develop outside of mathematics
	A.CN.8	Develop an appreciation for the historical development of mathematics
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*Representation* 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	Gather Data
	A.R.3	Use representation as a tool for exploring and understanding mathematical ideas
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*Representation* Students will select, apply, and translate among mathematical representations to solve problems.

	A.R.4	Select appropriate representations to solve problem situations	Building Connections Among Classes of Polynomial Functions Gather Data
	A.R.5	Investigate relationships between different representations and their impact on a given problem	Building Connections Among Classes of Polynomial Functions Reflect on Your Work
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*Representation* 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)	Reflect on Your Work
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*Number Sense and Operations* Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
*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.
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*Number Sense and Operations* Students will understand meanings of operations and procedures, and how they relate to one another.
*Operations*
	A.N.2	Simplify radical terms (no variable in the radicand)
	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	The Devil and Daniel Webster Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond: Understanding the Problem Iterating to Find the Square Root of 2
	A.N.5	Solve algebraic problems arising from situations that involve fractions, decimals, percents (decrease/increase and discount), and proportionality/direct variation	Be All You Can Be'...For Minimum Wage? Stock Market Price History The Devil and Daniel Webster Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond: Understanding the Problem Iterating to Find the Square Root of 2
	A.N.6	Evaluate expressions involving factorial(s), absolute value(s), and exponential expression(s)	The Devil and Daniel Webster Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond: Understanding the Problem Iterating to Find the Square Root of 2
	A.N.7	Determine the number of possible events, using counting techniques or the Fundamental Principle of Counting	Will the Best Candidate Win?
	A.N.8	Determine the number of possible arrangements (permutations) of a list of items	Will the Best Candidate Win?
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*Algebra* Students will represent and analyze algebraically a wide variety of problem solving situations.
*Variables and Expressions*
	A.A.1	Translate a quantitative verbal phrase into an algebraic expression
	A.A.2	Write a verbal expression that matches a given mathematical expression	The Regression Line The Effects of Outliers Correlation and the Regression Line The Centroid and the Regression Line
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*Algebra* Students will represent and analyze algebraically a wide variety of problem solving situations.
*Equations and Inequalities*
	A.A.3	Distinguish the difference between an algebraic expression and an algebraic equation	The Regression Line The Effects of Outliers Correlation and the Regression Line The Centroid and the Regression Line
	A.A.4	Translate verbal sentences into mathematical equations or inequalities
	A.A.5	Write algebraic equations or inequalities that represent a situation	The Regression Line The Effects of Outliers Correlation and the Regression Line The Centroid and the Regression Line
	A.A.6	Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable	Numerical Analysis Smokey the Bear Takes Algebra Modeling Orbital Debris Problems Orbiting Satellites
	A.A.7	Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables	Supply and Demand - An Application of Linear Equations Modeling Orbital Debris Problems
	A.A.8	Analyze and solve verbal problems that involve quadratic equations	Smokey the Bear Takes Algebra Modeling Orbital Debris Problems
	A.A.9	Analyze and solve verbal problems that involve exponential growth and decay	Time Value of Money The Devil and Daniel Webster Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond: Understanding the Problem Iterating to Find the Square Root of 2 Smokey the Bear Takes Algebra Modeling Orbital Debris Problems Make a Conjecture
	A.A.10	Solve systems of two linear equations in two variables algebraically (See A.G.7)	Supply and Demand - An Application of Linear Equations
	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.	Building Connections Among Classes of Polynomial Functions
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*Algebra* Students will perform algebraic procedures accurately.
*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.
	A.A.13	Add, subtract, and multiply monomials and polynomials
	A.A.14	Divide a polynomial by a monomial or binomial, where the quotient has no remainder
	A.A.15	Find values of a variable for which an algebraic fraction is undefined
	A.A.16	Simplify fractions with polynomials in the numerator and denominator by factoring both and renaming them to lowest terms
	A.A.17	Add or subtract fractional expressions with monomial or like binomial denominators
	A.A.18	Multiply and divide algebraic fractions and express the product or quotient in simplest form
	A.A.19	Identify and factor the difference of two perfect squares
	A.A.20	Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF)
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*Algebra* Students will perform algebraic procedures accurately.
*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	Numerical Analysis
	A.A.22	Solve all types of linear equations in one variable	Numerical Analysis Smokey the Bear Takes Algebra
	A.A.23	Solve literal equations for a given variable
	A.A.24	Solve linear inequalities in one variable
	A.A.25	Solve equations involving fractional expressions Note: Expressions which result in linear equations in one variable.
	A.A.26	Solve algebraic proportions in one variable which result in linear or quadratic equations
	A.A.27	Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots
	A.A.28	Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expression
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*Algebra* Students will recognize, use, and represent algebraically patterns, relations, and functions.
*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)
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*Algebra* Students will recognize, use, and represent algebraically patterns, relations, and functions.
*Coordinate Geometry*
	A.A.32	Explain slope as a rate of change between dependent and independent variables	Bouncing Tennis Balls Supply and Demand - An Application of Linear Equations Numerical Analysis
	A.A.33	Determine the slope of a line, given the coordinates of two points on the line	Exploring Linear Data Supply and Demand - An Application of Linear Equations Graphical Analysis Symbolic Analysis Rates and Taxes Taking Its Toll: Examining the Relationship Between Tolls and Distance
	A.A.34	Write the equation of a line, given its slope and the coordinates of a point on the line	Exploring Linear Data Supply and Demand - An Application of Linear Equations Graphical Analysis Symbolic Analysis Rates and Taxes Taking Its Toll: Examining the Relationship Between Tolls and Distance
	A.A.35	Write the equation of a line, given the coordinates of two points on the line	Exploring Linear Data Supply and Demand - An Application of Linear Equations Graphical Analysis Symbolic Analysis Rates and Taxes Taking Its Toll: Examining the Relationship Between Tolls and Distance
	A.A.36	Write the equation of a line parallel to the x- or y-axis
	A.A.37	Determine the slope of a line, given its equation in any form
	A.A.38	Determine if two lines are parallel, given their equations in any form
	A.A.39	Determine whether a given point is on a line, given the equation of the line	Taking Its Toll: Examining the Relationship Between Tolls and Distance
	A.A.40	Determine whether a given point is in the solution set of a system of linear inequalities
	A.A.41	Determine the vertex and axis of symmetry of a parabola, given its equation (See A.G.10 )
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*Algebra* Students will recognize, use, and represent algebraically patterns, relations, and functions.
*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	Trigonometry Drills
	A.A.43	Determine the measure of an angle of a right triangle, given the length of any two sides of the triangle	Trigonometry Drills
	A.A.44	Find the measure of a side of a right triangle, given an acute angle and the length of another side	Trigonometry Drills
	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	Trigonometry Drills Mathematical Proofs
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*Geometry* Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
*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).	Fill'r Up Purple Prisms Building A Box: Using Nets and Three-Dimensional Visualization Discovering the Area Formula for Triangles: Lesson 1 of 4 Finding the Area of Irregular Figures
	A.G.2	Use formulas to calculate volume and surface area of rectangular solids and cylinders	Fill'r Up Purple Prisms Building A Box: Using Nets and Three-Dimensional Visualization Discovering the Area Formula for Triangles: Lesson 1 of 4 Finding the Area of Irregular Figures
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*Geometry* Students will apply coordinate geometry to analyze problem solving situations.
*Coordinate Geometry*
	A.G.3	Determine when a relation is a function, by examining ordered pairs and inspecting graphs of relations
	A.G.4	Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions	Smokey the Bear Takes Algebra Make a Conjecture Analyzing the Data
	A.G.5	Investigate and generalize how changing the coefficients of a function affects its graph	Smokey the Bear Takes Algebra Make a Conjecture Analyzing the Data
	A.G.6	Graph linear inequalities
	A.G.7	Graph and solve systems of linear equations and inequalities with rational coefficients in two variables (See A.A.10)	Supply and Demand - An Application of Linear Equations
	A.G.8	Find the roots of a parabolic function graphically Note: Only quadratic equations with integral solutions.
	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.
	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.
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*Measurement* Students will determine what can be measured and how, using appropriate methods and formulas.
*Units of Measurement*
	A.M.1	Calculate rates using appropriate units (e.g., rate of a spaceship versus the rate of a snail)	Be All You Can Be'...For Minimum Wage? The Golden Ratio
	A.M.2	Solve problems involving conversions within measurement systems, given the relationship between the units	The Golden Ratio
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*Measurement* Students will understand that all measurement contains error and be able to determine its significance.
*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
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*Statistics and Probability* Students will collect, organize, display, and analyze data.
*Organization and Display of Data*
	A.S.1	Categorize data as qualitative or quantitative	Will the Best Candidate Win? Gather Data Frosty the Snowman Meets His Demise: An Analogy to Carbon Dating
	A.S.2	Determine whether the data to be analyzed is univariate or bivariate	Exploring Linear Data Generating and Analyzing Data Sound Wave Traveling Distances Bathtub Water Levels My Graph Is... Gallery Walk Automobile Mileage: Year vs. Mileage Automobile Mileage: Age vs. Mileage Automobile Mileage: Years Since 1990 vs. Mileage Automobile Mileage: Comparing and Contrasting The Regression Line The Effects of Outliers Correlation and the Regression Line The Centroid and the Regression Line Analyze the Data Will the Best Candidate Win? Make a Conjecture Conduct an Experiment Work to a Conclusion Frosty the Snowman Meets His Demise: An Analogy to Carbon Dating
	A.S.3	Determine when collected data or display of data may be biased	Traveling Distances Bathtub Water Levels My Graph Is... Gallery Walk Automobile Mileage: Year vs. Mileage Automobile Mileage: Age vs. Mileage Automobile Mileage: Years Since 1990 vs. Mileage Automobile Mileage: Comparing and Contrasting Will the Best Candidate Win?
	A.S.4	Compare and contrast the appropriateness of different measures of central tendency for a given data set	Generating and Analyzing Data Students as Researchers: An Inclined Plane Activity Traveling Distances Bathtub Water Levels My Graph Is... Gallery Walk Automobile Mileage: Year vs. Mileage Automobile Mileage: Age vs. Mileage Automobile Mileage: Years Since 1990 vs. Mileage Automobile Mileage: Comparing and Contrasting Will the Best Candidate Win? Shops at the Mall Analyze the Data Work to a Conclusion
	A.S.5	Construct a histogram, cumulative frequency histogram, and a box-and-whisker plot, given a set of data	Who Knows What Inefficiencies Lurk in the Hearts of Rent Controlled Housing Markets? The Shadow Market Knows! Look for Patterns Skin Weight Exploring Histograms Exploring Linear Data Five's a Crowd: A Game of Population Density The Pizza Palace Sorting Activities for Polygons Students as Researchers: An Inclined Plane Activity History of Populations Traveling Distances Bathtub Water Levels My Graph Is... Gallery Walk Automobile Mileage: Year vs. Mileage Automobile Mileage: Age vs. Mileage Automobile Mileage: Years Since 1990 vs. Mileage Automobile Mileage: Comparing and Contrasting In Your Shadow Home Is Where the Heart Is Mathematics as Communication: Graphing Information Collected Over Time Shops at the Mall Make a Conjecture Conduct an Experiment Heartifacts Comparing Averages State Names: Investigating Real-World Data
	A.S.6	Understand how the five statistical summary (minimum, maximum, and the three quartiles) is used to construct a box-and-whisker plot	Exploring Histograms Five's a Crowd: A Game of Population Density The Pizza Palace Generating and Analyzing Data Students as Researchers: An Inclined Plane Activity History of Populations Traveling Distances Bathtub Water Levels My Graph Is... Gallery Walk Automobile Mileage: Year vs. Mileage Automobile Mileage: Age vs. Mileage Automobile Mileage: Years Since 1990 vs. Mileage Automobile Mileage: Comparing and Contrasting In Your Shadow Mathematics as Communication: Graphing Information Collected Over Time Shops at the Mall Work to a Conclusion Comparing Averages State Names: Investigating Real-World Data
	A.S.7	Create a scatter plot of bivariate data	Look for Patterns Skin Weight Exploring Linear Data The Pizza Palace Generating and Analyzing Data Sorting Activities for Polygons Students as Researchers: An Inclined Plane Activity Traveling Distances Bathtub Water Levels My Graph Is... Gallery Walk Automobile Mileage: Year vs. Mileage Automobile Mileage: Age vs. Mileage Automobile Mileage: Years Since 1990 vs. Mileage Automobile Mileage: Comparing and Contrasting The Regression Line The Effects of Outliers Correlation and the Regression Line The Centroid and the Regression Line Mathematics as Communication: Graphing Information Collected Over Time Shops at the Mall Make a Conjecture Conduct an Experiment Taking Its Toll: Examining the Relationship Between Tolls and Distance State Names: Investigating Real-World Data Frosty the Snowman Meets His Demise: An Analogy to Carbon Dating How Old Are the Stars?
	A.S.8	Construct manually a reasonable line of best fit for a scatter plot and determine the equation of that line	Look for Patterns Exploring Linear Data Students as Researchers: An Inclined Plane Activity Traveling Distances Bathtub Water Levels My Graph Is... Gallery Walk Automobile Mileage: Year vs. Mileage Automobile Mileage: Age vs. Mileage Automobile Mileage: Years Since 1990 vs. Mileage Automobile Mileage: Comparing and Contrasting The Regression Line The Effects of Outliers Correlation and the Regression Line The Centroid and the Regression Line Smokey the Bear Takes Algebra Mathematics as Communication: Graphing Information Collected Over Time Make a Conjecture Conduct an Experiment Taking Its Toll: Examining the Relationship Between Tolls and Distance Frosty the Snowman Meets His Demise: An Analogy to Carbon Dating How Old Are the Stars?
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*Statistics and Probability* Students will collect, organize, display, and analyze data.
*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	Look for Patterns Five's a Crowd: A Game of Population Density History of Populations Traveling Distances Bathtub Water Levels My Graph Is... Gallery Walk Automobile Mileage: Year vs. Mileage Automobile Mileage: Age vs. Mileage Automobile Mileage: Years Since 1990 vs. Mileage Automobile Mileage: Comparing and Contrasting In Your Shadow Will the Best Candidate Win? Mathematics as Communication: Graphing Information Collected Over Time Make a Conjecture Work to a Conclusion Comparing Averages State Names: Investigating Real-World Data
	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	Economic Forecasting: An Internet WebQuest The Pizza Palace Traveling Distances Bathtub Water Levels My Graph Is... Gallery Walk Automobile Mileage: Year vs. Mileage Automobile Mileage: Age vs. Mileage Automobile Mileage: Years Since 1990 vs. Mileage Automobile Mileage: Comparing and Contrasting Analyze the Data Analyze the Data Work to a Conclusion
	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	Five's a Crowd: A Game of Population Density The Pizza Palace In Your Shadow
	A.S.12	Identify the relationship between the independent and dependent variables from a scatter plot (positive, negative, or none)	Exploring Linear Data Generating and Analyzing Data Traveling Distances Bathtub Water Levels My Graph Is... Gallery Walk Automobile Mileage: Year vs. Mileage Automobile Mileage: Age vs. Mileage Automobile Mileage: Years Since 1990 vs. Mileage Automobile Mileage: Comparing and Contrasting The Regression Line The Effects of Outliers Correlation and the Regression Line The Centroid and the Regression Line Analyze the Data Make a Conjecture Conduct an Experiment Taking Its Toll: Examining the Relationship Between Tolls and Distance Frosty the Snowman Meets His Demise: An Analogy to Carbon Dating
	A.S.13	Understand the difference between correlation and causation	Analyze the Data
	A.S.14	Identify variables that might have a correlation but not a causal relationship	Analyze the Data
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*Statistics and Probability* Students will make predictions that are based upon data analysis.
*Predictions from Data*
	A.S.15	Identify and describe sources of bias and its effect, drawing conclusions from data	Will the Best Candidate Win?
	A.S.16	Recognize how linear transformations of one-variable data affect the data’s mean, median, mode, and range	Exploring Histograms Traveling Distances Bathtub Water Levels My Graph Is... Gallery Walk Automobile Mileage: Year vs. Mileage Automobile Mileage: Age vs. Mileage Automobile Mileage: Years Since 1990 vs. Mileage Automobile Mileage: Comparing and Contrasting Will the Best Candidate Win? Gather Data Conduct an Experiment Work to a Conclusion
	A.S.17	Use a reasonable line of best fit to make a prediction involving interpolation or extrapolation	Frosty the Snowman Meets His Demise: An Analogy to Carbon Dating
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*Statistics and Probability* Students will understand and apply concepts of probability.
*Probability*
	A.S.18	Know the definition of conditional probability and use it to solve for probabilities in finite sample spaces	Explorations with Chance Exploring the Birthday Paradox Using a Monte Carlo Simulation Simulating Probability Situations Using Box Models Monty's Dilemma: Should You Stick or Switch? Analyze the Data
	A.S.19	Determine the number of elements in a sample space and the number of favorable events	Simulating Probability Situations Using Box Models Monty's Dilemma: Should You Stick or Switch? Analyze the Data
	A.S.20	Calculate the probability of an event and its complement	Simulating Probability Situations Using Box Models Monty's Dilemma: Should You Stick or Switch?
	A.S.21	Determine empirical probabilities based on specific sample data	Explorations with Chance Exploring the Birthday Paradox Using a Monte Carlo Simulation Simulating Probability Situations Using Box Models Monty's Dilemma: Should You Stick or Switch? Work to a Conclusion
	A.S.22	Determine, based on calculated probability of a set of events, if:o some or all are equally likely to occuro one is more likely to occur than anothero whether or not an event is certain to happen or not to happen	Simulating Probability Situations Using Box Models Monty's Dilemma: Should You Stick or Switch?
	A.S.23	Calculate the probability of:o a series of independent eventso a series of dependent eventso two mutually exclusive eventso two events that are not mutually exclusive	Explorations with Chance Exploring the Birthday Paradox Using a Monte Carlo Simulation Simulating Probability Situations Using Box Models Monty's Dilemma: Should You Stick or Switch?
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