9.2: Algebra

9.2.1: Understand the concept of function, and identify important features of functions and other relations using symbolic and graphical methods where appropriate.

9.2.1.1: Understand the definition of a function. Use functional notation and evaluate a function at a given point in its domain.

Logarithmic Functions

9.2.1.2: Distinguish between functions and other relations defined symbolically, graphically or in tabular form.

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions

9.2.1.3: Find the domain of a function defined symbolically, graphically or in a real-world context.

Exponential Functions
Introduction to Functions
Logarithmic Functions
Radical Functions

9.2.1.5: Identify the vertex, line of symmetry and intercepts of the parabola corresponding to a quadratic function, using symbolic and graphical methods, when the function is expressed in the form f(x) = ax² + bx + c, in the form f(x) = a(x ? h)² + k , or in factored form.

Parabolas
Roots of a Quadratic
Zap It! Game

9.2.1.6: Identify intercepts, zeros, maxima, minima and intervals of increase and decrease from the graph of a function.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Slope-Intercept Form of a Line
Standard Form of a Line

9.2.1.7: Understand the concept of an asymptote and identify asymptotes for exponential functions and reciprocals of linear functions, using symbolic and graphical methods.

Exponential Functions
Logarithmic Functions

9.2.1.8: Make qualitative statements about the rate of change of a function, based on its graph or table of values.

Cat and Mouse (Modeling with Linear Systems)
Slope

9.2.1.9: Determine how translations affect the symbolic and graphical forms of a function. Know how to use graphing technology to examine translations.

Absolute Value with Linear Functions
Introduction to Exponential Functions
Quadratics in Vertex Form
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations

9.2.2: Recognize linear, quadratic, exponential and other common functions in real-world and mathematical situations; represent these functions with tables, verbal descriptions, symbols and graphs; solve problems involving these functions, and explain results in the original context.

9.2.2.1: Represent and solve problems in various contexts using linear and quadratic functions.

Absolute Value with Linear Functions
Compound Interest
Quadratics in Polynomial Form
Slope-Intercept Form of a Line

9.2.2.2: Represent and solve problems in various contexts using exponential functions, such as investment growth, depreciation and population growth.

Compound Interest
Introduction to Exponential Functions

9.2.2.3: Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions.

Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line

9.2.2.4: Express the terms in a geometric sequence recursively and by giving an explicit (closed form) formula, and express the partial sums of a geometric series recursively.

Arithmetic and Geometric Sequences
Geometric Sequences

9.2.2.5: Recognize and solve problems that can be modeled using finite geometric sequences and series, such as home mortgage and other compound interest examples. Know how to use spreadsheets and calculators to explore geometric sequences and series in various contexts.

Compound Interest

9.2.2.6: Sketch the graphs of common non-linear functions such as f(x)= the square root of x, f(x) = |x|, f(x)= 1/x, f(x) = x³, and translations of these functions, such as f(x) = the square root of (x-2) + 4. Know how to use graphing technology to graph these functions.

Absolute Value with Linear Functions
General Form of a Rational Function
Linear Functions
Quadratics in Vertex Form
Radical Functions
Rational Functions
Translating and Scaling Functions

9.2.3: Generate equivalent algebraic expressions involving polynomials and radicals; use algebraic properties to evaluate expressions.

9.2.3.2: Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree.

Addition and Subtraction of Functions
Addition of Polynomials
Dividing Polynomials Using Synthetic Division
Modeling the Factorization of x²+bx+c

9.2.3.3: Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares.

Factoring Special Products

9.2.3.7: Justify steps in generating equivalent expressions by identifying the properties used. Use substitution to check the equality of expressions for some particular values of the variables; recognize that checking with substitution does not guarantee equality of expressions for all values of the variables.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II

9.2.4: Represent real-world and mathematical situations using equations and inequalities involving linear, quadratic, exponential, and nth root functions. Solve equations and inequalities symbolically and graphically. Interpret solutions in the original context.

9.2.4.1: Represent relationships in various contexts using quadratic equations and inequalities. Solve quadratic equations and inequalities by appropriate methods including factoring, completing the square, graphing and the quadratic formula. Find non-real complex roots when they exist. Recognize that a particular solution may not be applicable in the original context. Know how to use calculators, graphing utilities or other technology to solve quadratic equations and inequalities.

Addition and Subtraction of Functions
Modeling the Factorization of x²+bx+c
Quadratic Inequalities
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

9.2.4.2: Represent relationships in various contexts using equations involving exponential functions; solve these equations graphically or numerically. Know how to use calculators, graphing utilities or other technology to solve these equations.

Compound Interest
Exponential Functions
Introduction to Exponential Functions

9.2.4.3: Recognize that to solve certain equations, number systems need to be extended from whole numbers to integers, from integers to rational numbers, from rational numbers to real numbers, and from real numbers to complex numbers. In particular, non-real complex numbers are needed to solve some quadratic equations with real coefficients.

Points in the Complex Plane
Roots of a Quadratic
Solving Algebraic Equations II
Solving Equations on the Number Line

9.2.4.4: Represent relationships in various contexts using systems of linear inequalities; solve them graphically. Indicate which parts of the boundary are included in and excluded from the solution set using solid and dotted lines.

Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

9.2.4.5: Solve linear programming problems in two variables using graphical methods.

Linear Programming

9.2.4.6: Represent relationships in various contexts using absolute value inequalities in two variables; solve them graphically.

Compound Inequalities

9.2.4.8: Assess the reasonableness of a solution in its given context and compare the solution to appropriate graphical or numerical estimates; interpret a solution in the original context.

Compound Interest

9.3: Geometry & Measurement

9.3.1: Calculate measurements of plane and solid geometric figures; know that physical measurements depend on the choice of a unit and that they are approximations.

9.3.1.1: Determine the surface area and volume of pyramids, cones and spheres. Use measuring devices or formulas as appropriate.

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

9.3.1.2: Compose and decompose two- and three-dimensional figures; use decomposition to determine the perimeter, area, surface area and volume of various figures.

Surface and Lateral Areas of Prisms and Cylinders

9.3.1.3: Understand that quantities associated with physical measurements must be assigned units; apply such units correctly in expressions, equations and problem solutions that involve measurements; and convert between measurement systems.

Unit Conversions

9.3.2: Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry.

9.3.2.1: Understand the roles of axioms, definitions, undefined terms and theorems in logical arguments.

Biconditional Statements

9.3.2.2: Accurately interpret and use words and phrases in geometric proofs such as "if?then," "if and only if," "all," and "not." Recognize the logical relationships between an "if?then" statement and its inverse, converse and contrapositive.

Biconditional Statements
Conditional Statements

9.3.2.3: Assess the validity of a logical argument and give counterexamples to disprove a statement.

Biconditional Statements

9.3.3: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.

9.3.3.1: Know and apply properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve problems and logically justify results.

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Triangle Angle Sum

9.3.3.2: Know and apply properties of angles, including corresponding, exterior, interior, vertical, complementary and supplementary angles, to solve problems and logically justify results.

Congruence in Right Triangles
Investigating Angle Theorems
Proving Triangles Congruent
Similar Figures
Similarity in Right Triangles
Triangle Angle Sum

9.3.3.3: Know and apply properties of equilateral, isosceles and scalene triangles to solve problems and logically justify results.

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Isosceles and Equilateral Triangles
Triangle Inequalities

9.3.3.4: Apply the Pythagorean Theorem and its converse to solve problems and logically justify results.

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

9.3.3.5: Know and apply properties of right triangles, including properties of 45-45-90 and 30-60-90 triangles, to solve problems and logically justify results.

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Cosine Function
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Similarity in Right Triangles
Sine Function
Tangent Function

9.3.3.6: Know and apply properties of congruent and similar figures to solve problems and logically justify results.

Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Similar Figures
Similarity in Right Triangles

9.3.3.7: Use properties of polygons?including quadrilaterals and regular polygons?to define them, classify them, solve problems and logically justify results.

Classifying Quadrilaterals
Classifying Triangles
Parallelogram Conditions
Special Parallelograms

9.3.3.8: Know and apply properties of a circle to solve problems and logically justify results.

Chords and Arcs
Circles
Inscribed Angles

9.3.4: Solve real-world and mathematical geometric problems using algebraic methods.

9.3.4.1: Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine and tangent of an acute angle in a right triangle.

Sine, Cosine, and Tangent Ratios

9.3.4.2: Apply the trigonometric ratios sine, cosine and tangent to solve problems, such as determining lengths and areas in right triangles and in figures that can be decomposed into right triangles. Know how to use calculators, tables or other technology to evaluate trigonometric ratios.

Sine, Cosine, and Tangent Ratios

9.3.4.3: Use calculators, tables or other technologies in connection with the trigonometric ratios to find angle measures in right triangles in various contexts.

Sine, Cosine, and Tangent Ratios

9.3.4.5: Know the equation for the graph of a circle with radius r and center (h,k), (x ? h)² + (y ? k)² = r², and justify this equation using the Pythagorean Theorem and properties of translations.

Circles

9.3.4.6: Use numeric, graphic and symbolic representations of transformations in two dimensions, such as reflections, translations, scale changes and rotations about the origin by multiples of 90°, to solve problems involving figures on a coordinate grid.

Dilations
Rotations, Reflections, and Translations
Translations

9.3.4.7: Use algebra to solve geometric problems unrelated to coordinate geometry, such as solving for an unknown length in a figure involving similar triangles, or using the Pythagorean Theorem to obtain a quadratic equation for a length in a geometric figure.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Similar Figures

9.4: Data Analysis & Probability

9.4.1: Display and analyze data; use various measures associated with data to draw conclusions, identify trends and describe relationships.

9.4.1.1: Describe a data set using data displays, such as box-and-whisker plots; describe and compare data sets using summary statistics, including measures of center, location and spread. Measures of center and location include mean, median, quartile and percentile. Measures of spread include standard deviation, range and inter-quartile range. Know how to use calculators, spreadsheets or other technology to display data and calculate summary statistics.

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

9.4.1.3: Use scatterplots to analyze patterns and describe relationships between two variables. Using technology, determine regression lines (line of best fit) and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions.

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

9.4.1.4: Use the mean and standard deviation of a data set to fit it to a normal distribution (bell-shaped curve) and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets and tables to estimate areas under the normal curve.

Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

9.4.2: Explain the uses of data and statistical thinking to draw inferences, make predictions and justify conclusions

9.4.2.1: Evaluate reports based on data published in the media by identifying the source of the data, the design of the study, and the way the data are analyzed and displayed. Show how graphs and data can be distorted to support different points of view. Know how to use spreadsheet tables and graphs or graphing technology to recognize and analyze distortions in data displays.

Polling: City
Polling: Neighborhood
Populations and Samples

9.4.2.3: Explain the impact of sampling methods, bias and the phrasing of questions asked during data collection.

Describing Data Using Statistics
Polling: City
Real-Time Histogram

9.4.3: Calculate probabilities and apply probability concepts to solve real-world and mathematical problems.

9.4.3.1: Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities.

Binomial Probabilities
Independent and Dependent Events
Permutations and Combinations
Polling: City

9.4.3.3: Understand that the Law of Large Numbers expresses a relationship between the probabilities in a probability model and the experimental probabilities found by performing simulations or experiments involving the model.

Theoretical and Experimental Probability

9.4.3.5: Apply probability concepts such as intersections, unions and complements of events, and conditional probability and independence, to calculate probabilities and solve problems.

Binomial Probabilities
Estimating Population Size
Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

9.4.3.6: Describe the concepts of intersections, unions and complements using Venn diagrams. Understand the relationships between these concepts and the words AND, OR, NOT, as used in computerized searches and spreadsheets.

Compound Inequalities

9.4.3.8: Apply probability concepts to real-world situations to make informed decisions.

Estimating Population Size
Probability Simulations
Theoretical and Experimental Probability