1: The student understands and applies the concepts and procedures of mathematics.

1.1: Understand and apply concepts and procedures from number sense.

1.1.1: Understand the concept and symbolic representation of real numbers, including rational exponents.

1.1.1.a: Explain the meaning of the square root of a number, including why negative numbers have no real square roots.

Square Roots

1.1.5: Understand the concept and symbolic representation of rational numbers including absolute values.

1.1.5.d: Perform arithmetic operations with expressions involving absolute value.

Exponents and Power Rules
Operations with Radical Expressions

1.1.6: Complete multi-step computations of real numbers in all forms, including rational exponents and scientific notation, using order of operations and properties of operations.

1.1.6.a: Compute using rational numbers.

Fractions with Unlike Denominators

1.2: Understand and apply concepts and procedures from measurement.

1.2.2: Understand and apply rate and other derived units of measure.

1.2.2.a: Use vectors to represent velocity and direction: multiply a vector by a scalar and adds vectors both algebraically and graphically.

Vectors

1.2.2.b: Solve problems involving rates such as speed, density, population density, or flow rates.

Density Experiment: Slice and Dice
Density Laboratory
Determining Density via Water Displacement
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

1.2.5: Recognize and apply the basic right triangle trigonometric relationships of sine, cosine, and tangent to solve problems.

1.2.5.a: Use sine, cosine or tangent to find unknown distances and angles.

Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio
Unit Circle

1.2.5.c: Recognize the dependence of definitions of the trigonometric relations (sine, cosine and tangent) on the properties of similar triangles.

Cosine Function
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons
Sine Function
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle

1.2.5.d: Use sine, cosine or tangent in a right triangle to solve problems about measure of angles.

Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio
Unit Circle

1.2.5.e: Interpret and use the identity sin_(theta)+ cos_(theta) = 1 for angles between 0¡ and 90¡; recognize this identity as a special representation of the Pythagorean Theorem.

Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity B
Simplifying Trigonometric Expressions

1.3: Understand and apply concepts and procedures from geometric sense.

1.3.1: Make and test conjectures about 2-D figures (polygons and circles) and 3-D figures (spheres, right prisms and pyramids, right circular cylinders and cones), or figures constructed from these shapes.

1.3.1.b: Recall and interpret definitions and basic properties of congruent and similar triangles, circles, quadrilaterals, polygons, parallel, perpendicular, and intersecting lines, and associated angle relationships.

Chords and Arcs
Congruence in Right Triangles
Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles
Inscribing Angles
Parallelogram Conditions
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons
Special Quadrilaterals

1.3.1.c: Analyze properties of circles and spheres.

Chords and Arcs
Classifying Triangles
Inscribing Angles

1.3.2: Use properties of and relationships between 2-D or 3-D figures to draw and justify conclusions about a situation represented with such figures with or without a coordinate system.

1.3.2.a: Inductively generate a conjecture and deductively support it.

Biconditional Statement
Conditional Statement

1.3.2.b: Apply and justify the applicability of transformations, congruence, similarity, ratios, and proportions in problem-solving situations.

Dilations
Perimeters and Areas of Similar Figures
Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
Similar Polygons

1.3.2.c: Distinguish between area and perimeter of 2-D figures, surface area, and volume of 3-D figures.

Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Rectangle: Perimeter and Area
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

1.3.2.d: Calculate the area and perimeter of circles, triangles, quadrilaterals, and regular polygons.

Area of Parallelograms - Activity A
Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

1.3.2.e: Use the Pythagorean Theorem (or distance formula) in 2-D and 3-D situations when appropriate to compute unknown distances.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

1.3.2.f: Calculate the volume and surface area of spheres, right rectangular prisms, and right circular cylinders.

Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders

1.3.3: Represent the relevant features of a physical situation using 2-D figures with and without a coordinate system.

1.3.3.a: Use basic 2-D figures such as circles or polygons to represent objects essential to a situation.

Classifying Triangles

1.3.3.d: Solve problems involving the coordinate plane such as the distance between two points, the midpoint of a segment, or slopes of perpendicular or parallel lines.

Construct Parallel and Perpendicular Lines
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Slope - Activity B

1.4: Understand and apply concepts and procedures from probability and statistics.

1.4.2: Use empirical/ experimental and theoretical probability to investigate, represent, solve, and interpret the solutions to problems involving uncertainty (probability) or counting techniques.

1.4.2.a: Describe and apply the concepts of complementary, mutually exclusive, independent, and compound events.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

1.4.2.b: Describe and apply procedures for computing and comparing theoretical probabilities and empirical/experimental results.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
Polling: City
Probability Simulations
Theoretical and Experimental Probability

1.4.2.c: Describe and apply procedures for counting techniques such as the Fundamental Counting Principle, permutations, and combinations.

Permutations
Permutations and Combinations

1.4.3: Understand and apply the key characteristics of a normal distribution.

1.4.3.a: Know and interpret the key characteristics of a normal distribution such as shape, center (mean), and spread (standard deviation).

Line Plots

1.4.4: Develop and evaluate inferences and predictions that are based on data.

1.4.4.a: Use measures of central tendency (mean, median, mode) and spread (range, quartiles) to summarize data, draw inferences, make predictions, and justify conclusions.

Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.4.b: Develop and conduct an investigation drawing appropriate conclusions through the use of statistical measures of center, frequency, and spread, combined with graphical displays.

Box-and-Whisker Plots
Line Plots
Mean, Median and Mode

1.4.5: Create and evaluate the suitability of linear models for a data set.

1.4.5.c: Recognize when arguments based on data confuse correlation with causation.

Correlation
Solving Using Trend Lines

1.4.5.d: Recognize that the correlation coefficient is a number between -1 and +1 that measures the strength of the linear relationship between two variables: usually estimate the correlation coefficient (e.g., positive or negative, closer to 0, 0.5, or 1.0) of a scatter plot.

Correlation
Scatter Plots - Activity A

1.4.6: Develop informative tables, plots, and graphic displays to accurately represent and study data.

1.4.6.a: Use and interprets circle graphs, bar graphs, histograms, box-and-whisker plots, scatter plots, stem and leaf, and line graphs.

Box-and-Whisker Plots
Correlation
Histograms
Populations and Samples
Scatter Plots - Activity A
Solving Using Trend Lines
Stem-and-Leaf Plots

1.4.6.b: Analyze data displays to evaluate the reasonableness of claims, reports, studies, and conclusions.

Box-and-Whisker Plots
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

1.4.6.c: Justify the use of appropriate graphical displays to accurately represent and study data.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

1.4.6.d: Determine trends, predicted values and possible causes of skewed and clustered distributions.

Solving Using Trend Lines

1.5: Understand and apply concepts and procedures from algebraic sense.

1.5.1: Represent, analyze, and interpret basic functions (linear, quadratic, cubic, exponential, and reciprocal) and piecewise-defined functions (varying over subintervals of the domain) using and translating among words, tables, graphs, and symbols.

1.5.1.a: Evaluate functions to generate a graph.

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Introduction to Functions
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Sine Function
Tangent Function
Using Tables, Rules and Graphs

1.5.1.b: Describe relationships between the algebraic features of a function and the features of its graph and/or its tabular representation.

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Introduction to Functions
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Polynomials and Linear Factors
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Sine Function
Slope-Intercept Form of a Line - Activity A
Tangent Function
Using Algebraic Equations
Using Tables, Rules and Graphs

1.5.1.c: Use simple transformations (horizontal and vertical shifts, reflections about axes, shrinks and stretches to create the graphs of new functions using linear, quadratic, and/ or absolute value functions.

Absolute Value with Linear Functions - Activity B
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Reflections of a Linear Function
Reflections of a Quadratic Function
Roots of a Quadratic
Translating and Scaling Functions

1.5.1.d: Algebraically construct new functions using addition and subtraction (e.g., profit function).

Addition and Subtraction of Polynomials

1.5.1.e: Describe whether a relation, given verbal, symbolic, tabular, or graphical form is a function.

Introduction to Functions
Linear Functions

1.5.1.f: Identify and analyze the general forms of linear, quadratic, reciprocal (y=k/x), exponential, or trigonometric functions.

Cosine Function
Direct and Inverse Variation
Exponential Functions - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Sine Function
Tangent Function

1.5.1.g: Identify patterns in the function's rate of change, identifying intervals of increase, decrease, constancy, and, if possible, relate them to the function's description in words or graphically (using graphing calculator).

Arithmetic Sequences
Arithmetic and Geometric Sequences
Direct Variation
Direct and Inverse Variation
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Finding Patterns
Geometric Sequences
Modeling Linear Systems - Activity A

1.5.1.h: Identify y-intercepts and zeros using symbols, graphs, and tables.

Point-Slope Form of a Line - Activity A
Polynomials and Linear Factors
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

1.5.1.i: Identify extrema and trends using graphs and tables.

Linear Functions
Solving Using Trend Lines
Using Tables, Rules and Graphs

1.5.2: Determine an equation or rule for linear and non-linear functions represented in a patterns, tables, graphs, or models.

1.5.2.a: Determine an equation from a set of ordered pairs.

Using Algebraic Equations

1.5.2.c: Write an equation or rule to describe a sequence.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
Using Algebraic Equations

1.5.2.d: Write an equation for a line given a graph of the line.

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

1.5.2.e: Write a rule for a recursive geometric pattern.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

1.5.2.f: Write an expression, equation, or inequality with two variables representing a linear and/or non-linear model of a real-world problem.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Using Algebraic Equations
Using Algebraic Expressions

1.5.2.g: Write an equation for a reasonable line to describe a set of bivariate data from a table or scatter plot.

Point-Slope Form of a Line - Activity A

1.5.3: Recognize functional relationships presented in words, tables, graphs and symbols.

1.5.3.a: Recognize whether a relationship given in a symbolic, graphical, or tabular form is a function.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Introduction to Functions
Linear Functions
Using Tables, Rules and Graphs

1.5.3.b: Determine the domain of the function.

Functions Involving Square Roots

1.5.3.c: Understand and interpret function notation, particularly as it relates of graphic displays of data.

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

1.5.4: Recognize and use appropriate concepts, procedures, definitions, and properties to simplify expressions and solve equations.

1.5.4.b: Explain the distinction between expression and equation.

Using Algebraic Equations

1.5.4.d: Know what it means to have a solution to an equation.

Using Algebraic Equations

1.5.4.e: Use properties of equality to solve an equation through a series of equivalent equations.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Formulas for any Variable
Solving Two-Step Equations

1.5.4.h: Find an equation of a circle given its center and radius and, given an equation of a circle, finds its center and radius.

Circles

1.5.5: Combine and simplify algebraic expressions that contain polynomials, rational expressions, radicals, or rational exponents.

1.5.5.a: Find the sum, difference, or product of two polynomials, then simplifies the result.

Addition of Polynomials - Activity A

1.5.5.b: Factor out the greatest common factor from polynomials of any degree.

Factoring Special Products

1.5.5.c: Factor quadratic polynomials with integer coefficients into a product of linear terms.

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

1.5.5.d: Simplify quotients of polynomials given in factored form, or in a form which can be factored.

Addition of Polynomials - Activity A
Dividing Polynomials Using Synthetic Division
Modeling the Factorization of x²+bx+c

1.5.6: Solve various types of equations and inequalities numerically, graphically, and algebraically; interpret solutions algebraically and in the context of the problem; distinguish between exact and approximate answers.

1.5.6.a: Solve linear equations in one variable.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

1.5.6.b: Solve linear inequalities in one variable, including those involving "and" and "or."

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

1.5.6.c: Solve systems of linear equations in two variables.

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

1.5.6.d: Solve linear inequalities in two variables (graphically only).

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Linear Programming - 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

1.5.6.f: Use a variety of strategies to solve quadratic equations including those with irrational solutions and recognize when solutions are non-real.

Roots of a Quadratic

1.5.6.i: Solve rational equations in one variable that can be transformed into an equivalent linear or quadratic equation (limited to monomial or binomial denominators).

Roots of a Quadratic
Solving Equations By Graphing Each Side

1.5.6.j: Solve literal equations (formulas) for a particular variable.

Solving Formulas for any Variable

2: The student uses mathematics to define and solve problems.

2.2: Construct solutions.

2.2.4: Use logical reasoning and mathematical knowledge to obtain and justify mathematically correct solutions.

2.2.4.f: Use a variety of approaches - inductive and deductive, estimations, generalizations, formal, and/or informal methods of proof - to justify solutions.

Biconditional Statement
Conditional Statement
Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

3: The student uses mathematical reasoning.

3.1: Analyze information.

3.1.1: Model situations and relationships using a variety of basic functions (linear, quadratic, logarithmic, cubic, exponential, and reciprocal) and piecewise-defined functions.

3.1.1.b: Determine and interprets the meaning of rates of change, intercepts, zeros, extrema, and trends.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Polynomials and Linear Factors
Solving Using Trend Lines

3.3: Verify results.

Proving Triangles Congruent

4: The student communicates knowledge and understanding in both everyday and mathematical language.

4.2: Organize, represent, and share information.

4.2.2: Summarize and interpret mathematical information which may be in oral or written formats.

4.2.2.a: Summarize and interprets many different types of graphs.

Linear Programming - Activity A

5: The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-world situations.

5.1: Relate concepts and procedures within mathematics.

5.1.1: Understand the importance of mathematics as a language. (aligns with CRS 3.2) Make connections by using multiple representations--analytic, numeric, and geometric.

5.1.1.b: Use multiple representations to demonstrate understanding of links between math and other disciplines, and real world situations.

Estimating Population Size

5.1.1.d: Transfer mathematical vocabulary, concepts, and procedures to other disciplinary contexts and the real world.

Estimating Population Size

5.1.2: Abstract mathematical models from word problems, geometric problems, and applications.

5.1.2.b: Describe geometric objects and shapes algebraically.

Hyperbola - Activity A

5.3: Relate mathematical concepts and procedures to real-world situations.

5.3.1: Use mathematical ideas and strategies to analyze relationships within mathematics and in other disciplines and real life situations.

5.3.1.b: Recognize patterns and apply mathematical concepts and procedures in other subject areas and real world situations.

Estimating Population Size
Finding Patterns