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.B: [gather and record data and] use data sets to determine functional relationships between quantities;

Linear Functions

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

Absolute Value Equations and Inequalities
Exponential Functions
Introduction to Exponential Functions
Linear Functions
Linear Inequalities in Two Variables
Quadratics in Factored Form
Quadratics in Polynomial Form
Radical 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;

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Arithmetic Sequences
Compound Interest
Exponential Functions
Linear Functions
Point-Slope Form of a Line
Quadratics in Factored Form
Quadratics in Polynomial Form
Roots of a Quadratic
Slope-Intercept Form of a Line
Standard Form of a Line
Translating and Scaling Functions
Zap It! Game

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

Logarithmic Functions
Radical Functions

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

Absolute Value with Linear Functions
Determining a Spring Constant
Exponential Functions
Introduction to Exponential Functions
Point-Slope Form of a Line
Quadratics in Factored Form
Quadratics in Polynomial Form
Radical Functions
Standard Form of a Line

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
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

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.A: use symbols to represent unknowns and variables; and

Solving Algebraic Equations I
Square Roots
Using Algebraic Expressions

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

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

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
Simplifying Algebraic Expressions II

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

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

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

Compound Interest
Linear Functions
Slope-Intercept Form of a Line

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

Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Exponential Functions
Geometric Sequences
Linear Functions
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

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;

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Distance-Time and Velocity-Time Graphs
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line
Standard Form of a Line

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

Cat and Mouse (Modeling with Linear Systems)
Slope-Intercept 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;

Absolute Value with Linear Functions
Slope-Intercept Form of a Line

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;

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Slope-Intercept Form of a Line
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;

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Exponential Functions
Linear Functions
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

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

Introduction to Exponential Functions
Slope-Intercept Form of a Line
Translating and Scaling Functions
Zap It! Game

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

Direct and Inverse Variation

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;

Exploring Linear Inequalities in One Variable
Linear Functions
Linear Inequalities in Two Variables
Modeling and Solving Two-Step Equations
Point-Slope Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line
Systems of Linear Inequalities (Slope-intercept form)

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

Compound Inequalities

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

Compound Inequalities
Linear Inequalities in Two Variables
Point-Slope Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line

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.A: analyze situations and formulate systems of linear equations in two unknowns to solve problems;

Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

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

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

4.A.8.C: interpret and determine the reasonableness of solutions to systems of linear equations.

Solving Linear Systems (Standard Form)

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;

Parabolas
Translating and Scaling Functions
Zap It! Game

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

Parabolas
Translating and Scaling Functions
Zap It! Game

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.A: solve quadratic equations using [concrete] models, tables, graphs, and algebraic methods; and

Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Quadratics in Polynomial Form
Roots of a Quadratic

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.

Quadratics in Factored Form
Quadratics in Polynomial Form
Roots of a Quadratic

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

6.G.5: The student uses a variety of representations to describe geometric relationships and solve problems.

6.G.5.C: use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations; and

Circles
Rotations, Reflections, and Translations
Translations

6.G.10: The student applies the concept of congruence to justify properties of figures and solve problems.

6.G.10.A: use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane.

Dilations

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

7.G.6: The student analyzes the relationship between three-dimensional geometric figures and related two-dimensional representations and uses these representations to solve problems.

7.G.6.B: use nets to represent [and construct] three-dimensional geometric figures; and

Surface and Lateral Areas of Prisms and Cylinders

7.G.6.C: use orthographic and isometric views of three-dimensional geometric figures to represent [and construct] three-dimensional geometric figures and solve problems.

3D and Orthographic Views

7.G.7: The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly.

7.G.7.A: use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures;

Linear Functions
Points in the Coordinate Plane
Slope

7.G.7.C: derive and use formulas involving length, slope, and midpoint.

Circles
Distance Formula
Slope

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

8.G.8: The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations.

8.G.8.A: find areas of regular polygons, circles, and composite figures;

Area of Triangles
Circumference and Area of Circles

8.G.8.C: [derive,] extend, and use the Pythagorean Theorem; and

Circles
Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Surface and Lateral Areas of Pyramids and Cones
Tangent Function

8.G.8.D: find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations.

Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

8.G.11: The student applies the concepts of similarity to justify properties of figures and solve problems.

8.G.11.A: use and extend similarity properties and transformations to explore and justify conjectures about geometric figures;

Dilations

8.G.11.B: use ratios to solve problems involving similar figures;

Beam to Moon (Ratios and Proportions)
Perimeters and Areas of Similar Figures
Similar Figures

8.G.11.C: [develop,] apply, and justify triangle similarity relationships, such as right triangle ratios, [trigonometric ratios,] and Pythagorean triples using a variety of methods; and

Perimeters and Areas of Similar Figures
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Similar Figures
Similarity in Right Triangles
Sine, Cosine, and Tangent Ratios

8.G.11.D: describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems.

Perimeter and Area of Rectangles

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

9.8.3: The student identifies proportional or non-proportional linear relationships in problem situations and solves problems.

9.8.3.B: estimate and find solutions to application problems involving percents and other proportional relationships, such as similarity and rates.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percent of Change

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

Independent and Dependent Events
Theoretical and Experimental Probability

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

Geometric Probability
Independent and Dependent Events
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
Mean, Median, and Mode
Stem-and-Leaf Plots

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
Compound Inequalities
Correlation
Histograms
Mean, Median, and Mode
Real-Time Histogram
Stem-and-Leaf Plots

10: The student will demonstrate an understanding of the mathematical processes and tools used in problem solving.

10.8.14: The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school.

10.8.14.A: identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;

Estimating Population Size

10.8.15: The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models.

10.8.15.A: communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.

Using Algebraic Expressions

10.8.16: The student uses logical reasoning to make conjectures and verify conclusions.

10.8.16.A: make conjectures from patterns or sets of examples and nonexamples; and

Biconditional Statements

10.8.16.B: validate his/her conclusions using mathematical properties and relationships.

Biconditional Statements