1: The student will demonstrate the ability to investigate, interpret, and communicate solutions to mathematical and real-world problems using patterns, functions and algebra.

1.1: The student will analyze a wide variety of patterns and functional relationships using the language of mathematics and appropriate technology.

1.1.1: The student will recognize, describe and/or extend patterns and functional relationships that are expressed numerically, algebraically, and/or geometrically.

1.1.1.A: The given pattern must represent a relationship of the form y = mx + b (linear), y = x² + c (simple quadratic), y = x³ + c (simple cubic), simple arithmetic progression, or simple geometric progression with all exponents being positive.

Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

1.1.1.B: The student will not be asked to draw three-dimensional figures.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences
Linear Functions
Quadratics in Factored Form
Roots of a Quadratic

1.1.1.C: Algebraic description of patterns is in indicator 1.1.2

Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

1.1.1.a: Given a narrative, numeric, algebraic, or geometric representation description of a pattern or functional relationship, the student will give a verbal description, or predict the next term or a specific term in a pattern or functional relationship.

Using Algebraic Equations
Using Algebraic Expressions

1.1.1.b: Given a numerical or graphical representation of a relation, the student will identify if the relation is a function and/or describe it.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Introduction to Functions
Linear Functions

1.1.1.1: The student will define and interpret relations and functions numerically, graphically, and algebraically.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions

1.1.1.2: The student will use patterns of change in function tables to develop the concept of rate of change.

Arithmetic and Geometric Sequences
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Using Tables, Rules and Graphs

1.1.1.5: The student will compare, order and describe rational numbers.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Rational Numbers

1.1.1.7: The student will identify and extend an exponential pattern in a table of values.

Arithmetic and Geometric Sequences
Exponential Growth and Decay - Activity B
Finding Patterns
Using Tables, Rules and Graphs

1.1.2: The student will represent patterns and/or functional relationships in a table, as a graph, and/or by mathematical expression.

1.1.2.A: The given pattern must represent a relationship of the form mx + b (linear), x² (simple quadratic), simple arithmetic progression, or simple geometric progression with all exponents being positive.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Dividing Exponential Expressions
Exponents and Power Rules
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

1.1.2.1: The student will be able to graph an exponential function given as a table of values or as an equation of the form y= a(b to the x power), where a is a positive integer, b>0 and b is not equal to 1.

Exponential Functions - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Using Tables, Rules and Graphs

1.1.3: The student will apply addition, subtraction, multiplication, and/or division of algebraic expressions to mathematical and real-world problems.

1.1.3.A: The algebraic expression is a polynomial in one variable.

Addition of Polynomials - Activity A
Dividing Polynomials Using Synthetic Division

1.1.3.B: The polynomial is not simplified.

Addition of Polynomials - Activity A
Dividing Polynomials Using Synthetic Division

1.1.3.a: The student will represent a situation as a sum, difference, product, and/or quotient in one variable.

Addition of Polynomials - Activity A
Dividing Polynomials Using Synthetic Division

1.1.3.1: The student will locate the position of a number on the number line, know its distance from the origin is its absolute value and know that the distance between two numbers on the number line is the absolute value of their difference.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

1.1.3.3: The student will add, subtract, and multiply polynomials.

Addition of Polynomials - Activity A

1.1.3.4: The student will divide a polynomial by a monomial.

Dividing Exponential Expressions
Dividing Polynomials Using Synthetic Division

1.1.3.5: The student will factor polynomials:

1.1.3.5.a: Using greatest common factor

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

1.1.3.5.b: Using the form ax² + bx + c

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

1.1.3.5.c: Using special product patterns

1.1.3.5.c.1: Difference of squares a² + b² = (a - b)(a + b)

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

1.1.3.5.c.2: Perfect square trinomial a² + 2ab + b² = (a + b)²; a² - 2ab + b² = (a - b)²

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

1.1.3.6: The student will use the laws of exponents, including negative exponents, to simplify expressions.

Dividing Exponential Expressions
Exponents and Power Rules

1.1.3.7: The student will simplify radical expressions with or without variables.

Simplifying Radicals - Activity A

1.1.4: The student will describe the graph of a non-linear function and discuss its appearance in terms of the basic concepts of maxima and minima, zeros (roots), rate of change, domain and range, and continuity.

1.1.4.A: A coordinate graph will be given with easily read coordinates.

Function Machines 2 (Functions, Tables, and Graphs)
Functions Involving Square Roots
Polynomials and Linear Factors

1.1.4.B: ?Zeros? refers to the x-intercepts of a graph, ?roots? refers to the solution of an equation in the form p(x) = 0.

Function Machines 2 (Functions, Tables, and Graphs)
Functions Involving Square Roots
Polynomials and Linear Factors

1.1.4.C: Problems will not involve a real-world context.

Function Machines 2 (Functions, Tables, and Graphs)
Functions Involving Square Roots
Polynomials and Linear Factors

1.1.4.a: Given the graph of a non-linear function, the student will identify maxima/minima, zeros, rate of change over a given interval (increasing/decreasing), domain and range, or continuity.

Function Machines 2 (Functions, Tables, and Graphs)
Functions Involving Square Roots

1.1.4.1: The student will describe the graph of the quadratic, exponential, absolute value, piece-wise, and step functions.

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Roots of a Quadratic

1.1.4.2: The student will solve quadratic equations by factoring and graphing.

Factoring Special Products

1.2: The student will model and interpret real-world situations using the language of mathematics and appropriate technology.

1.2.1: The student will determine the equation for a line, solve linear equations, and/or describe the solutions using numbers, symbols, and/or graphs.

1.2.1.A: Functions are to have no more than two variables with rational coefficients.

Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

1.2.1.B: Linear equations will be given in the form: Ax + By = C, Ax + By + C = 0, or y = mx + b.

Modeling and Solving Two-Step Equations
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Solving Two-Step Equations
Standard Form of a Line
Using Tables, Rules and Graphs

1.2.1.C: Vertical lines are included.

Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

1.2.1.D: The majority of these items should be in real-world context.

Modeling and Solving Two-Step Equations
Road Trip (Problem Solving)
Solving Equations By Graphing Each Side
Solving Two-Step Equations

1.2.1.a: Given one or more of the following:

1.2.1.a.a: the graph of a line

Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

1.2.1.a.b: written description of a situation that can be modeled by a linear function

Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

1.2.1.a.c: two or more collinear points

Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

1.2.1.a.d: a point and slope

Modeling and Solving Two-Step Equations
Point-Slope Form of a Line - Activity A
Slope - Activity B
Solving Equations By Graphing Each Side
Solving Two-Step Equations

1.2.1.b: the student will do one or more of the following:

1.2.1.b.a: write the equation

Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

1.2.1.b.b: solve a one-variable equation for the unknown

Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

1.2.1.b.c: solve a two-variable equation for one of the variables

Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Formulas for any Variable
Solving Two-Step Equations

1.2.1.b.d: graph the resulting equation

Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

1.2.1.b.e: interpret the solution in light of the context

Modeling and Solving Two-Step Equations
Road Trip (Problem Solving)
Solving Equations By Graphing Each Side
Solving Two-Step Equations

1.2.1.b.g: create a table of values

Introduction to Functions
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

1.2.1.b.h: find and/or interpret the slope (rate of change) and/or intercepts in relation to the context.

Road Trip (Problem Solving)
Slope - Activity B
Solving Equations By Graphing Each Side

1.2.1.c: Any correct form of a linear equation will be acceptable as a response.

Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

1.2.2: The student will solve linear inequalities and describe the solutions using numbers, symbols, and/or graphs.

1.2.2.A: Inequalities will have no more than two variables with rational coefficients.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

1.2.2.B: Acceptable forms of the problem or solution are the following: Ax + By < C, Ax + By is less than or equal to C, Ax + By > C, Ax + By is greater than or equal to C, Ax + By + C < 0, Ax + By + C is less than or equal to 0, Ax + By + C > 0, Ax + By + C is greater than or equal to 0, y < mx + b, y is less than or equal to mx + b, y is greater than or equal to mx + b, y > mx + b, y < b, y is less than or equal to b, y > b, y is greater than or equal to b, x < b, x is less than or equal to b, x > b, x is greater than or equal to b, a is less than or equal to x is less than or equal to b, a < x < b, a is less than or equal to x < b, a < x is less than or equal to b, a is less than or equal to x + c is less than or equal to b, a < x + c < b, a is less than or equal to x + c < b, a < x + c is less than or equal to b.

Linear Inequalities in Two Variables - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Standard Form of a Line
Using Tables, Rules and Graphs

1.2.2.C: The majority of these items should be in real-world context.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

1.2.2.D: Systems of linear inequalities will not be included.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

1.2.2.E: Compound inequalities will be included.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

1.2.2.F: Disjoint inequalities will not be included.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

1.2.2.G: Absolute value inequalities will not be included.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

1.2.2.a: Given a linear inequality in narrative, algebraic, or graphical form, the student will graph the inequality, write an inequality and/or solve it, or interpret an inequality in the context of the problem.

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Systems of Linear Inequalities (Slope-intercept form) - Activity A

1.2.2.b: Any correct form of a linear inequality will be an acceptable response.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

1.2.2.1: The student will graph systems of linear inequalities and apply their solution to real-world applications.

Inequalities Involving Absolute Values
Linear Programming - Activity A
Modeling Linear Systems - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Special Types of Solutions to Linear Systems
Systems of Linear Inequalities (Slope-intercept form) - Activity A

1.2.3: The student will solve and describe using numbers, symbols, and/or graphs if and where two straight lines intersect.

1.2.3.A: Functions will be of the form: Ax + By = C, Ax + By + C = 0, or y = mx + b.

Slope-Intercept Form of a Line - Activity A
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Standard Form of a Line
Systems of Linear Equations - Activity A
Using Tables, Rules and Graphs

1.2.3.B: All coefficients will be rational.

Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

1.2.3.C: Vertical lines will be included.

Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

1.2.3.D: Systems of linear functions will include coincident, parallel, or intersecting lines.

Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

1.2.3.E: The majority of these items should be in real-world context.

Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

1.2.3.a: Given one or more of the following:

1.2.3.a.a: a narrative description

Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

1.2.3.a.b: the graph of two lines

Modeling Linear Systems - Activity A
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

1.2.3.a.c: equations for two lines

Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

1.2.3.b: the student will do one or more of the following:

1.2.3.b.a: determine the system of equations and/or its solution

Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

1.2.3.b.b: describe the relationship of the points on one line with points on the other line

Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

1.2.3.b.c: give the meaning of the point of intersection in the context of the problem

Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

1.2.3.b.d: graph the system, determine the solution and interpret the solution in the context of the problem

Modeling Linear Systems - Activity A
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

1.2.3.b.e: use slope to recognize the relationship between parallel lines.

Slope - Activity B
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

1.2.3.c: Any correct form of a linear equation will be an acceptable response.

Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

1.2.3.1: The student will determine if two lines in a plane are parallel, perpendicular, or neither.

Construct Parallel and Perpendicular Lines

1.2.4: The student will describe how the graphical model of a non-linear function represents a given problem and will estimate the solution.

1.2.4.A: The problem is to be in a real-world context.

Estimating Population Size

1.2.4.D: The features of the graph may include maxima/minima, zeros (roots), rate of change over a given interval (increasing/decreasing), continuity, or domain and range.

Functions Involving Square Roots

1.2.4.E: ?Zeros? refers to the x-intercepts of a graph, ?roots? refers to the solution of an equation in the form p(x) = 0.

Polynomials and Linear Factors

1.2.4.F: Functions may include step, absolute value, or piece-wise functions.

Quadratic and Absolute Value Functions

1.2.4.a: Given a graph which represents a real-world situation, the student will describe the graph and/or explain how the graph represents the problem or solution and/or estimate a solution.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

1.2.4.1: The student will describe the graph of the quadratic and exponential functions.

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

1.2.4.2: The student will identify horizontal and vertical asymptotes given the graph of a non-linear function.

Exponential Functions - Activity A
Functions Involving Square Roots
General Form of a Rational Function
Rational Functions
Unit Circle

1.2.4.3: The student will solve, by factoring or graphing, real-world problems that can be modeled using a quadratic equation.

Factoring Special Products

1.2.5: The student will apply formulas and/or use matrices (arrays of numbers) to solve real-world problems.

1.2.5.B: Formulas may express linear or non-linear relationships.

Linear Functions

1.2.5.1: The student will solve literal equations for a specified variable.

Modeling and Solving Two-Step Equations
Solving Formulas for any Variable
Solving Two-Step Equations

3: The student will demonstrate the ability to apply probability and statistical methods for representing and interpreting data and communicating results, using technology when needed.

3.1: The student will collect, organize, analyze, and present data.

3.1.1: The student will design and/or conduct an investigation that uses statistical methods to analyze data and communicate results.

3.1.1.B: Types of investigations may include: simple random sampling, representative sampling, and probability simulations.

Polling: Neighborhood
Probability Simulations

3.1.1.C: Probability simulations may include the use of spinners, number cubes, or random number generators.

Probability Simulations

3.1.1.D: In simple random sampling each member of the population is equally likely to be chosen and the members of the sample are chosen independently of each other. Sample size will be given for these investigations.

Compound Independent Events
Compound Independent and Dependent Events
Polling: City
Polling: Neighborhood

3.1.1.c: The student will demonstrate an understanding of the concepts of bias, sample size, randomness, representative samples, and simple random sampling techniques.

Polling: Neighborhood

3.1.1.1: The student will organize and display data to detect patterns and departures from patterns. One example of an appropriate method for displaying data is a spreadsheet.

Arithmetic and Geometric Sequences
Describing Data Using Statistics
Finding Patterns
Geometric Sequences

3.1.1.2: The student will communicate the differences between randomized experiments and observational studies.

Polling: Neighborhood

3.1.2: The student will use the measures of central tendency and/or variability to make informed conclusions.

3.1.2.A: Measures of central tendency include mean, median, and mode.

Describing Data Using Statistics
Mean, Median and Mode
Populations and Samples

3.1.2.B: Measures of variability include range, interquartile range, and quartiles.

Box-and-Whisker Plots
Describing Data Using Statistics

3.1.2.C: Data may be displayed in a variety of representations, which may include: frequency tables, box and whisker plots, and other displays.

Box-and-Whisker Plots
Mean, Median and Mode

3.1.2.a: The student uses measures of central tendency and variability to solve problems, make informed conclusions and/or display data.

Mean, Median and Mode

3.1.2.b: The student will recognize and apply the effect of the distribution of the data on the measures of central tendency and variability.

Describing Data Using Statistics
Mean, Median and Mode

3.1.2.1: The student will identify an outlier and describe its effect on a measure of central tendency.

Describing Data Using Statistics
Mean, Median and Mode

3.1.3: The student will calculate theoretical probability or use simulations or statistical inferences from data to estimate the probability of an event.

3.1.3.A: This indicator does not include finding probabilities of dependent events.

Compound Independent Events
Compound Independent and Dependent Events
Theoretical and Experimental Probability

3.1.3.a: Using given data, the student determines the experimental probability of an event.

Geometric Probability - Activity A
Probability Simulations
Theoretical and Experimental Probability

3.1.3.b: Given a situation involving chance, the student will determine the theoretical probability of an event.

Geometric Probability - Activity A
Probability Simulations
Theoretical and Experimental Probability

3.1.3.1: The student will determine the probability of a dependent event (conditional probability).

Binomial Probabilities
Compound Independent and Dependent Events

3.2: The student will apply the basic concepts of statistics and probability to predict possible outcomes of real-world situations

3.2.1: The student will make informed decisions and predictions based upon the results of simulations and data from research.

3.2.1.a: Given data from a simulation or research, the student makes informed decisions and predictions.

Probability Simulations

3.2.3: The student will communicate the use and misuse of statistics.

3.2.3.A: Examples of ?misuse of statistics? include the following:

3.2.3.A.b: misuse of measures of central tendency and variability to represent data,

Mean, Median and Mode

3.2.3.A.f: using data from simulations incorrectly

Probability Simulations