1: The student will describe functional relationships in a variety of ways.

1.A.1: The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways.

1.A.1.A: describe independent and dependent quantities in functional relationships;

Introduction to Functions
Linear Functions

1.A.1.C: describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations;

Linear Functions
Linear Inequalities in Two Variables - Activity A

1.A.1.D: represent relationships among quantities using [concrete] models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities; and

Introduction to Functions
Linear Functions
Using Algebraic Equations
Using Algebraic Expressions
Using Tables, Rules and Graphs

1.A.1.E: interpret and make decisions, predictions, and critical judgments from functional relationships.

Linear Functions

2: The student will demonstrate an understanding of the properties and attributes of functions.

2.A.2: The student uses the properties and attributes of functions.

2.A.2.A: identify [and sketch] the general forms of linear (y = x) and quadratic (y = x 2) parent functions;

Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

2.A.2.B: identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete;

Introduction to Functions

2.A.2.C: interpret situations in terms of given graphs [or create situations that fit given graphs]; and

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

2.A.2.D: [collect and] organize data, [make and] interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.

Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

2.A.3: The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations.

2.A.3.B: look for patterns and represent generalizations algebraically.

Arithmetic and Geometric Sequences
Linear Functions

2.A.4: The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.

2.A.4.A: find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations;

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

2.A.4.B: use the commutative, associative, and distributive properties to simplify algebraic expressions; and

Solving Equations By Graphing Each Side

3: The student will demonstrate an understanding of linear functions.

3.A.5: The student understands that linear functions can be represented in different ways and translates among their various representations.

3.A.5.A: determine whether or not given situations can be represented by linear functions; and

Introduction to Functions
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

3.A.5.C: use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions.

Introduction to Functions
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

3.A.6: The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations.

3.A.6.A: develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations;

Direct Variation
Direct and Inverse Variation
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Linear Functions
Modeling Linear Systems - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A

3.A.6.B: interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs;

Defining a Line with Two Points
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

3.A.6.C: investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b;

Cosine Function
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Sine Function
Tangent Function
Translating and Scaling Functions

3.A.6.D: graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept;

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

3.A.6.E: determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations;

Arithmetic Sequences
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Linear Functions
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

3.A.6.F: interpret and predict the effects of changing slope and y-intercept in applied situations; and

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line
Translating and Scaling Functions

3.A.6.G: relate direct variation to linear functions and solve problems involving proportional change.

Direct Variation
Direct and Inverse Variation
Linear Functions
Polling: Neighborhood

4: The student will formulate and use linear equations and inequalities.

4.A.7: The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

4.A.7.A: analyze situations involving linear functions and formulate linear equations or inequalities to solve problems;

Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Using Tables, Rules and Graphs

4.A.7.B: investigate methods for solving linear equations and inequalities using [concrete] models, graphs, and the properties of equality, select a method, and solve the equations and inequalities; and

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Formulas for any Variable
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations

4.A.7.C: interpret and determine the reasonableness of solutions to linear equations and inequalities.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

4.A.8: The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

4.A.8.B: solve systems of linear equations using [concrete] models, graphs, tables, and algebraic methods; and

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

5: The student will demonstrate an understanding of quadratic and other nonlinear functions.

5.A.9: The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions.

5.A.9.B: investigate, describe, and predict the effects of changes in a on the graph of y = ax 2 + c;

Cosine Function
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Functions Involving Square Roots
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Sine Function
Tangent Function
Translating and Scaling Functions

5.A.9.C: investigate, describe, and predict the effects of changes in c on the graph of y = ax 2 + c; and

Cosine Function
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Functions Involving Square Roots
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Sine Function
Tangent Function
Translating and Scaling Functions

5.A.9.D: analyze graphs of quadratic functions and draw conclusions.

Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

5.A.10: The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods.

5.A.10.B: make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function.

Polynomials and Linear Factors
Roots of a Quadratic

5.A.11: The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations.

5.A.11.A: use [patterns to generate] the laws of exponents and apply them in problem-solving situations.

Arithmetic and Geometric Sequences
Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

6: The student will demonstrate an understanding of geometric relationships and spatial reasoning.

6.8.6: The student uses transformational geometry to develop spatial sense.

6.8.6.A: generate similar figures using dilations including enlargements and reductions; and

Dilations
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

6.8.6.B: graph dilations, reflections, and translations on a coordinate plane.

Circles
Dilations
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Reflections
Rotations, Reflections and Translations
Translations

7: The student will demonstrate an understanding of two- and three-dimensional representations of geometric relationships and shapes.

7.8.7: The student uses geometry to model and describe the physical world.

7.8.7.A: draw three-dimensional figures from different perspectives;

Prisms and Cylinders - Activity A

7.8.7.B: use geometric concepts and properties to solve problems in fields such as art and architecture; and

Classifying Triangles

7.8.7.C: use pictures or models to demonstrate the Pythagorean Theorem.

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

8: The student will demonstrate an understanding of the concepts and uses of measurement and similarity.

8.8.8: The student uses procedures to determine measures of three-dimensional figures.

8.8.8.A: find lateral and total surface area of prisms, pyramids, and cylinders using [concrete] models and nets (two-dimensional models);

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

8.8.8.B: connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects; and

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

8.8.8.C: estimate measurements and use formulas to solve application problems involving lateral and total surface area and volume.

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

8.8.9: The student uses indirect measurement to solve problems.

8.8.9.A: use the Pythagorean Theorem to solve real-life problems; and

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

8.8.9.B: use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements.

Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

8.8.10: The student describes how changes in dimensions affect linear, area, and volume measures.

8.8.10.A: describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally; and

Area of Parallelograms - Activity A
Circle: Circumference and Area
Minimize Perimeter
Polling: Neighborhood
Prisms and Cylinders - Activity A
Rectangle: Perimeter and Area

8.8.10.B: describe the resulting effect on volume when dimensions of a solid are changed proportionally.

Polling: Neighborhood
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

9: The student will demonstrate an understanding of percents, proportional relationships, probability, and statistics in application problems.

9.8.11: The student applies concepts of theoretical and experimental probability to make predictions.

9.8.11.A: find the probabilities of dependent and independent events; and

Compound Independent Events
Compound Independent and Dependent Events

9.8.11.B: use theoretical probabilities and experimental results to make predictions and decisions.

Geometric Probability - Activity A
Probability Simulations
Theoretical and Experimental Probability

9.8.12: The student uses statistical procedures to describe data.

9.8.12.A: select the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation; and

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

9.8.12.C: select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, [stem and leaf plots,] circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, with and without the use of technology.

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