PA: Pre Algebra

PA.I: Students will expand number sense to understand, perform operations, and solve problems with rational numbers.

PA.I.1: Compute fluently with understanding and make reasonable estimates with rational numbers.

PA.I.1.a: Compute fluently using all four operations with integers, and explain why the corresponding algorithms work.

Adding and Subtracting Integers with Chips

PA.I.1.b: Compute fluently using all four operations with rational numbers, including negative fractions and decimals, and explain why the corresponding algorithms work.

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Real Number Line - Activity A
Sums and Differences with Decimals

PA.I.2: Analyze relationships among rational numbers, including negative rational numbers, and operations involving these numbers.

PA.I.2.a: Order rational numbers in various forms, including scientific notation (positive and negative exponents), and place numbers on a number line.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Real Number Line - Activity A

PA.I.2.b: Predict the effect of operating with fractions, decimals, percents, and integers as an increase or a decrease of the original value.

Adding and Subtracting Integers with Chips
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Percent of Change
Sums and Differences with Decimals

PA.I.2.d: Recognize and use the inverse operations of adding and subtracting a fixed number, multiplying and dividing by a fixed number, and computing squares of whole numbers and taking square roots of perfect squares.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

PA.I.3: Solve problems involving rational numbers using addition, subtraction, multiplication, and division.

PA.I.3.a: Recognize the absolute value of a rational number as its distance from zero.

Comparing and Ordering Integers
Real Number Line - Activity A

PA.I.3.b: Simplify numerical expressions, including those with whole number exponents and absolute values, using the order of operations.

Order of Operations
Real Number Line - Activity A

PA.I.3.c: Solve problems involving rational numbers, percents, and proportions.

Estimating Population Size
Percents and Proportions
Polling: Neighborhood

PA.II: Students will use proportion and similarity to solve problems.

PA.II.1: Model and illustrate meanings of ratios, percents, and decimals.

PA.II.1.a: Compare ratios to determine if they are equivalent.

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents, Fractions and Decimals
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

PA.II.1.b: Compare ratios using the unit rate.

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

PA.II.1.c: Represent percents as ratios based on 100 and decimals as ratios based on powers of ten.

Perimeters and Areas of Similar Figures
Polling: Neighborhood
Similar Figures - Activity A
Similar Polygons

PA.II.1.d: Graph proportional relationships and identify the unit rate as the slope of the related line.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Perimeters and Areas of Similar Figures
Polling: Neighborhood
Similar Figures - Activity A
Similar Polygons
Slope - Activity B

PA.II.2: Solve a wide variety of problems using ratios and proportional reasoning.

PA.II.2.a: Set up and solve problems involving proportional reasoning using variables.

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

PA.II.2.b: Solve percent problems, including problems involving discounts, interest, taxes, tips, and percent increase or decrease.

Percent of Change
Simple and Compound Interest

PA.II.2.c: Solve ratio and rate problems using informal methods.

Estimating Population Size
Geometric Probability - Activity A
Part:Part and Part:Whole Ratios
Perimeters and Areas of Similar Figures
Polling: Neighborhood
Similar Figures - Activity A
Similar Polygons

PA.II.3: Recognize similar polygons and use properties of similar triangles to solve problems and define the slope of a line.

PA.II.3.a: Define similar polygons as polygons with corresponding angles congruent and corresponding sides that are proportional.

Investigating Angle Theorems - Activity A
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

PA.II.3.b: Identify pairs of similar triangles using two pairs of congruent angles, or two pairs of proportional sides with congruent included angles.

Investigating Angle Theorems - Activity A
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons
Triangle Angle Sum - Activity A

PA.II.3.c: Find missing lengths of similar triangles, including inaccessible lengths, using proportions.

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

PA.II.3.d: Define the slope of a line as the ratio of the vertical change to the horizontal change between two points, and show that the slope is constant using similarity of right triangles.

Part:Part and Part:Whole Ratios
Perimeters and Areas of Similar Figures
Point-Slope Form of a Line - Activity A
Points in the Coordinate Plane - Activity A
Similar Figures - Activity A
Similar Polygons
Slope - Activity B
Slope-Intercept Form of a Line - Activity A

PA.III: Students will develop fluency with the language and operations of algebra to analyze and represent relationships.

PA.III.1: Generalize and express patterns using algebraic expressions.

PA.III.1.a: Compare representations of a relation using tables, graphs, algebraic symbols, and mathematical rules.

Cubic Function Activity
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Introduction to Functions
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

PA.III.1.b: Describe simple patterns using a mathematical rule or algebraic expression.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

PA.III.1.c: Create and extend simple numerical and visual patterns.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

PA.III.2: Evaluate, simplify, and solve algebraic expressions, equations, and inequalities.

PA.III.2.a: Evaluate algebraic expressions, including those with whole number exponents, when given values for the variable(s).

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Using Algebraic Equations

PA.III.2.b: Simplify algebraic expressions using the order of operations, algebraic properties, and exponent rules.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Order of Operations

PA.III.2.c: Solve single-variable linear equations and inequalities, including those that must be simplified on one side or those with variables on both sides of an equation.

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

PA.III.3: Represent relationships using graphs, tables, and other models.

PA.III.3.a: Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system.

Points in the Coordinate Plane - Activity A

PA.III.3.b: Graph ordered pairs of rational numbers on a rectangular coordinate system.

Points in the Coordinate Plane - Activity A

PA.III.3.c: Graph linear equations using ordered pairs or tables.

Defining a Line with Two Points
Linear Functions
Point-Slope Form of a Line - Activity A
Points in the Coordinate Plane - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Standard Form of a Line
Using Tables, Rules and Graphs

PA.III.3.d: Recognize that all first order equations produce linear graphs.

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Standard Form of a Line
Using Algebraic Equations

PA.III.3.e: Model real-world problems using graphs, tables, equations, manipulatives, and pictures, and identify extraneous information.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Using Algebraic Equations

PA.IV: Students will use algebraic, spatial, and logical reasoning to solve geometry and measurement problems.

PA.IV.1: Apply the properties of proportionality of different units of measure.

PA.IV.1.b: Create and interpret scale drawings and approximate distance on maps using scale factors.

Dilations
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Similar Figures - Activity A
Similar Polygons

PA.IV.1.c: Solve problems using scale factors.

Dilations
Similar Figures - Activity A
Similar Polygons

PA.IV.2: Derive formulas for surface areas and volume of three-dimensional figures.

PA.IV.2.a: Derive formulas for and calculate surface area and volume of right prisms and cylinders using appropriate units.

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

PA.IV.2.b: Explain that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related and the cube of the scale factor describes how corresponding volumes are related.

Dilations
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Similar Figures - Activity A
Similar Polygons

PA.IV.2.c: Find lengths, areas, and volumes of similar figures, using the scale factor.

Dilations
Perimeter, Circumference, and Area - Activity B
Perimeters and Areas of Similar Figures
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Similar Figures - Activity A
Similar Polygons

PA.IV.2.d: Select appropriate two- and three-dimensional figures to model real-world objects, and solve a variety of problems involving surface areas and volumes of cylinders and prisms.

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

PA.V: Students will understand concepts from probability and statistics and apply statistical methods to solve problems.

PA.V.1: Calculate probabilities of events and compare theoretical and experimental probability.

PA.V.1.b: Calculate the probability of an event or sequence of events with and without replacement using models.

Geometric Probability - Activity A

PA.V.1.d: Make approximate predictions using theoretical probability and proportions.

Compound Independent Events
Compound Independent and Dependent Events
Estimating Population Size
Geometric Probability - Activity A
Independent and Dependent Events
Polling: Neighborhood
Probability Simulations
Similar Figures - Activity A
Similar Polygons
Theoretical and Experimental Probability

PA.V.1.e: Collect and interpret data to show that as the number of trials increases, experimental probability approaches the theoretical probability.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Polling: City
Probability Simulations
Theoretical and Experimental Probability

PA.V.2: Formulate questions and answer the questions by organizing and analyzing data.

PA.V.2.a: Formulate questions that can be answered through data collection and analysis.

Determining a Spring Constant

PA.V.2.b: Determine the 25th and 75th percentiles (first and third quartiles) to obtain information about the spread of data.

Box-and-Whisker Plots
Line Plots

PA.V.2.c: Graphically summarize data of a single variable using histograms and box-andwhisker plots.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Populations and Samples
Scatter Plots - Activity A

PA.V.2.d: Compute the mean and median of a numerical characteristic and relate these values to the histogram of the data.

Describing Data Using Statistics
Histograms
Line Plots
Mean, Median and Mode
Populations and Samples

PA.V.2.e: Use graphical representations and numerical summaries to answer questions and interpret data.

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

A1: Algebra 1

A1.I: Students will expand number sense to understand, perform operations, and solve problems with real numbers.

A1.I.1: Represent real numbers as points on the number line and distinguish rational numbers from irrational numbers.

A1.I.1.a: Define a rational number as a point on the number line that can be expressed as the ratio of two integers, and points that cannot be so expressed as irrational.

Comparing and Ordering Integers
Part:Part and Part:Whole Ratios
Polling: Neighborhood
Real Number Line - Activity A

A1.I.1.c: Classify pi and square roots of non-perfect square numbers as irrational.

Square Roots

A1.I.1.d: Place rational and irrational numbers on a number line between two integers.

Comparing and Ordering Integers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Real Number Line - Activity A

A1.I.2: Compute fluently and make reasonable estimates with rational and irrational numbers.

A1.I.2.a: Simplify, add, subtract, multiply, and divide expressions with square roots.

Simplifying Radicals - Activity A
Square Roots

A1.I.2.b: Evaluate and simplify numerical expressions containing rational numbers and square roots using the order of operations.

Order of Operations
Square Roots

A1.I.2.d: Calculate the measures of the sides of a right triangle using the Pythagorean Theorem.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Triangle Angle Sum - Activity A

A1.II: Students will extend concepts of proportion to represent and analyze linear relations.

A1.II.1: Represent and analyze the slope of a line.

A1.II.1.a: Identify the slope of a line when given points, a graph, or an equation.

Point-Slope Form of a Line - Activity A
Points in the Coordinate Plane - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A

A1.II.1.b: Identify horizontal and vertical lines given the equations or slopes.

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

A1.II.1.c: Determine the effect of changes in slope or y-intercept in y = mx + b.

Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A

A1.II.1.d: Determine and explain the meaning of slopes and intercepts using real-world examples.

Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A

A1.II.2: Model and interpret problems having a constant rate of change using linear functions.

A1.II.2.a: Write algebraic expressions or equations to generalize visual patterns, numerical patterns, relations, data sets, or scatter plots.

Arithmetic and Geometric Sequences
Geometric Sequences
Introduction to Functions
Scatter Plots - Activity A
Solving Using Trend Lines

A1.II.2.b: Represent linear equations in slope-intercept form, y = mx + b, and standard form, Ax+ By =C.

Defining a Line with Two Points
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line
Using Tables, Rules and Graphs

A1.II.2.c: Distinguish between linear and non-linear functions by examining a table, equation, or graph.

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

A1.II.2.d: Interpret the slope of a linear function as a rate of change in real-world situations.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Linear Functions
Slope - Activity B

A1.II.3: Represent and analyze linear relationships using algebraic equations, expressions, and graphs.

A1.II.3.a: Write the equation of a line when given two points or the slope and a point on the line.

Point-Slope Form of a Line - Activity A
Points in the Coordinate Plane - Activity A
Slope - Activity B

A1.II.3.b: Approximate the equation of a line given the graph of a 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

A1.II.3.c: Identify the x- and y-intercepts from an equation or graph of a line or a table of values.

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
Using Tables, Rules and Graphs

A1.II.3.d: Graph linear relations and inequalities by plotting points, by finding x- and y-intercepts, or by using the slope and any point on the line.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Introduction to Functions
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Point-Slope Form of a Line - Activity A
Points in the Coordinate Plane - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

A1.III: Students will develop fluency with the language and operations of algebra to analyze and represent relationships.

A1.III.1: Simplify polynomials and the quotient of monomials.

A1.III.1.a: Simplify and evaluate monomial expressions and formulas.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Order of Operations

A1.III.1.b: Add and subtract polynomials.

Addition of Polynomials - Activity A

A1.III.1.c: Multiply monomials by a polynomial.

Multiplying Exponential Expressions
Polynomials and Linear Factors

A1.III.1.d: Multiply binomials.

Polynomials and Linear Factors

A1.III.1.e: Simplify the quotient of monomials using positive exponents.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

A1.III.2: Solve and interpret linear equations and inequalities in various situations including real-world problems.

A1.III.2.a: Solve single-variable linear equations and inequalities algebraically and graphically.

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

A1.III.2.b: Solve real-world problems involving constant rates of change.

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

A1.III.2.c: Solve equations for a specified variable.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations
Using Algebraic Equations

A1.III.2.d: Solve proportions that include algebraic first-degree expressions.

Estimating Population Size

A1.III.3: Solve and interpret pairs of linear equations and inequalities.

A1.III.3.a: Solve systems of two linear equations graphically and algebraically with and without technology.

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

A1.III.3.b: Determine the number of possible solutions for a system of two linear equations.

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

A1.III.3.c: Graph a system of linear inequalities and identify the solution.

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

A1.III.4: Factor polynomials with common monomial factors and factor simple quadratic expressions.

A1.III.4.a: Find the greatest common monomial factor of a polynomial.

Factoring Special Products

A1.III.4.b: Factor trinomials with integer coefficients of the form x2 + bx + c.

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

A1.III.4.c: Factor the difference of two squares and perfect square trinomials.

Factoring Special Products

A1.III.5: Solve quadratic equations using factoring or by taking square roots.

A1.III.5.a: Solve quadratic equations that can be simplified to the form x2 = a where a ¡Ý 0 by taking square roots.

Roots of a Quadratic
Square Roots

A1.III.5.b: Solve quadratic equations using factoring.

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

A1.III.5.c: Write a quadratic equation when given the solutions.

Roots of a Quadratic

A1.IV: Students will understand concepts from statistics and apply statistical methods to solve problems.

A1.IV.1: Summarize, display, and analyze bivariate data.

A1.IV.1.a: Collect, record, organize, and display a set of data with at least two variables.

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

A1.IV.1.b: Determine whether the relationship between two variables is approximately linear or non-linear by examination of a scatter plot.

Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

A1.IV.1.c: Characterize the relationship between two linear related variables as having positive, negative, or approximately zero correlation.

Correlation
Solving Using Trend Lines

A1.IV.2: Estimate, interpret, and use lines fit to bivariate data.

A1.IV.2.a: Estimate the equation of a line of best fit to make and test conjectures.

Point-Slope Form of a Line - Activity A

A1.IV.2.b: Interpret the slope and y-intercept of a line through data.

Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A

G: Geometry

G.I: Students will use algebraic, spatial, and logical reasoning to solve geometry problems.

G.I.1: Use inductive and deductive reasoning to develop mathematical arguments.

G.I.1.a: Write conditional statements, converses, and inverses, and determine the truth value of these statements.

Conditional Statement

G.I.2: Analyze characteristics and properties of angles.

G.I.2.a: Use accepted geometric notation for lines, segments, rays, angles, similarity, and congruence.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

G.I.2.b: Identify and determine relationships in adjacent, complementary, supplementary, or vertical angles and linear pairs.

Investigating Angle Theorems - Activity A

G.I.2.c: Classify angle pairs formed by two lines and a transversal.

Investigating Angle Theorems - Activity A

G.I.2.e: Prove lines parallel or perpendicular using slope or angle relationships.

Construct Parallel and Perpendicular Lines
Slope - Activity B

G.I.3: Analyze characteristics and properties of triangles.

G.I.3.a: Prove congruency and similarity of triangles using postulates and theorems.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

G.I.3.b: Prove the Pythagorean Theorem in multiple ways, find missing sides of right triangles using the Pythagorean Theorem, and determine whether a triangle is a right triangle using the converse of the Pythagorean Theorem.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Triangle Angle Sum - Activity A

G.I.3.c: Prove and apply theorems involving isosceles triangles.

Classifying Triangles
Isosceles and Equilateral Triangles

G.I.3.d: Apply triangle inequality theorems.

Triangle Inequalities

G.I.3.e: Identify medians, altitudes, and angle bisectors of a triangle, and the perpendicular bisectors of the sides of a triangle, and justify the concurrency theorems.

Concurrent Lines, Medians, and Altitudes

G.I.4: Analyze characteristics and properties of polygons and circles.

G.I.4.a: Use examples and counterexamples to classify subsets of quadrilaterals.

Classifying Quadrilaterals - Activity A
Classifying Quadrilaterals - Activity B

G.I.4.b: Prove properties of quadrilaterals using triangle congruence relationships, postulates, and theorems.

Congruence in Right Triangles
Parallelogram Conditions
Proving Triangles Congruent

G.I.4.c: Derive, justify, and use formulas for the number of diagonals, lines of symmetry, angle measures, perimeter, and area of regular polygons.

Holiday Snowflake Designer
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

G.I.4.d: Define radius, diameter, chord, secant, arc, sector, central angle, inscribed angle, and tangent of a circle, and solve problems using their properties.

Chords and Arcs
Inscribing Angles

G.I.4.e: Show the relationship between intercepted arcs and inscribed or central angles, and find their measures.

Chords and Arcs
Inscribing Angles

G.I.5: Perform basic geometric constructions, describing and justifying the procedures used.

G.I.5.a: Investigate geometric relationships using constructions.

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

G.I.5.c: Construct perpendicular and parallel lines.

Construct Parallel and Perpendicular Lines

G.I.5.d: Justify procedures used to construct geometric figures.

Classifying Quadrilaterals - Activity A
Classifying Quadrilaterals - Activity B
Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

G.I.5.e: Discover and investigate conjectures about geometric properties using constructions.

Classifying Triangles
Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

G.I.6: Analyze characteristics and properties of three-dimensional figures.

G.I.6.a: Identify and classify prisms, pyramids, cylinders and cones based on the shape of their base(s).

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

G.I.6.b: Identify three-dimensional objects from different perspectives using nets, crosssections, and two-dimensional views.

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

G.I.6.c: Describe the symmetries of three-dimensional figures.

Holiday Snowflake Designer
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

G.II: Students will use the language and operations of algebra to explore geometric relationships with coordinate geometry.

G.II.1: Describe the properties and attributes of lines and line segments using coordinate geometry.

G.II.1.a: Verify the classifications of geometric figures using coordinate geometry to find lengths and slopes.

Slope - Activity B

G.II.1.b: Find the distance between two given points and find the coordinates of the midpoint.

Points in the Coordinate Plane - Activity A

G.II.1.c: Write an equation of a line perpendicular or a line parallel to a line through a given point.

Point-Slope Form of a Line - Activity A
Points in the Coordinate Plane - Activity A

G.II.a: Graph a circle given the equation in the form(x − h)2 + (y − k)2 = r 2 , and write the equation when given the graph.

Circles

G.III: Students will extend concepts of proportion and similarity to trigonometric ratios.

G.III.1: Use triangle relationships to solve problems.

G.III.1.b: Identify the trigonometric relationships of sine, cosine, and tangent with the appropriate ratio of sides of a right triangle.

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

G.III.1.c: Express trigonometric relationships using exact values and approximations.

Cosine Function
Sine Function
Tangent Function
Unit Circle

G.III.2: Use the trigonometric ratios of sine, cosine, and tangent to represent and solve for missing parts of triangles.

G.III.2.a: Find the angle measure in degrees when given the trigonometric ratio.

Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

G.III.2.b: Find the trigonometric ratio given the angle measure in degrees, using a calculator.

Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

G.III.2.c: Find unknown measures of right triangles using sine, cosine, and tangent functions and inverse trigonometric functions.

Cosine Function
Sine Function
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle

G.IV: Students will use algebraic, spatial, and logical reasoning to solve measurement problems.

G.IV.1: Find measurements of plane and solid figures.

G.IV.1.b: Develop surface area and volume formulas for polyhedra, cones, and cylinders.

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

G.IV.1.c: Determine perimeter, area, surface area, lateral area, and volume for prisms, cylinders, pyramids, cones, and spheres when given the formulas.

Area of Parallelograms - Activity A
Minimize Perimeter
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

G.IV.2: Solve real-world problems using visualization and spatial reasoning.

G.IV.2.a: Solve problems using the Pythagorean Theorem and its converse.

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

G.IV.2.b: Solve problems using the distance formula.

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

G.IV.2.c: Solve problems involving trigonometric ratios.

Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

G.IV.2.d: Solve problems involving geometric probability.

Geometric Probability - Activity A

AII: Algebra 2

AII.I: Students will use the language and operations of algebra to evaluate, analyze and solve problems.

AII.I.1: Evaluate, analyze, and solve mathematical situations using algebraic properties and symbols.

AII.I.1.a: Solve and graph first-degree absolute value equations of a single variable.

Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A

AII.I.1.c: Solve absolute value and compound inequalities of a single variable.

Compound Inequalities
Inequalities Involving Absolute Values
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

AII.I.2: Solve systems of equations and inequalities.

AII.I.2.a: Solve systems of linear, absolute value, and quadratic equations algebraically and graphically.

Modeling Linear Systems - Activity A
Solving Linear Systems by Graphing
Systems of Linear Equations - Activity A

AII.I.2.b: Graph the solutions of systems of linear, absolute value, and quadratic inequalities on the coordinate plane.

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Quadratic Inequalities - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

AII.I.2.c: Solve application problems involving systems of equations and inequalities.

Linear Programming - Activity A
Modeling Linear Systems - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

AII.I.3: Represent and compute fluently with complex numbers.

AII.I.3.b: Simplify expressions involving complex numbers and express them in standard form, a + bi.

Points in the Complex Plane - Activity A

AII.I.4: Model and solve quadratic equations and inequalities.

AII.I.4.b: Approximate the real solutions of quadratic equations graphically.

Roots of a Quadratic

AII.I.4.c: Solve quadratic equations of a single variable over the set of complex numbers by factoring, completing the square, and using the quadratic formula.

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

AII.I.4.d: Solve quadratic inequalities of a single variable.

Quadratic Inequalities - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Using Algebraic Equations

AII.I.4.e: Write a quadratic equation when given the solutions of the equation.

Roots of a Quadratic

AII.II: Students will understand and represent functions and analyze function behavior.

AII.II.1: Represent mathematical situations using relations.

AII.II.1.b: Describe a pattern using function notation.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

AII.II.1.c: Determine when a relation is a function.

Introduction to Functions
Linear Functions

AII.II.1.d: Determine the domain and range of relations.

Introduction to Functions

AII.II.2: Evaluate and analyze functions.

AII.II.2.a: Find the value of a function at a given point.

Linear Functions

AII.II.2.c: Add, subtract, multiply, and divide functions.

Addition and Subtraction of Polynomials
Linear Functions

AII.II.2.d: Determine whether or not a function has an inverse, and find the inverse when it exists.

Logarithmic Functions - Activity A

AII.II.2.e: Identify the domain and range of a function resulting from the combination or composition of functions.

Introduction to Functions

AII.II.3: Define and graph exponential functions and use them to model problems in mathematical and real-world contexts.

AII.II.3.a: Define exponential functions as functions of the form y = abx ,b > 0,b ?? 1.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B

AII.II.3.b: Model problems of growth and decay using exponential functions.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life
Simple and Compound Interest

AII.II.3.c: Graph exponential functions.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B

AII.II.4: Define and graph logarithmic functions and use them to solve problems in mathematics and real-world contexts.

AII.II.4.a: Relate logarithmic and exponential functions.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

AII.II.4.e: Graph logarithmic functions.

Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

AII.II.4.f: Solve problems involving growth and decay.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life

AII.III: Students will use algebraic, spatial, and logical reasoning to solve geometry and measurement problems.

AII.III.1: Examine the behavior of functions using coordinate geometry.

AII.III.1.a: Identify the domain and range of the absolute value, quadratic, radical, sine, and cosine functions.

Functions Involving Square Roots
Inequalities Involving Absolute Values
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Roots of a Quadratic
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Translating and Scaling Functions
Unit Circle

AII.III.1.b: Graph the absolute value, quadratic, radical, sine, and cosine functions.

Functions Involving Square Roots
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Roots of a Quadratic
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Translating and Scaling Functions
Unit Circle

AII.III.1.c: Graph functions using transformations of parent functions.

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

AII.III.1.d: Write an equation of a parabola in the form y = a(x − h)2 + k when given a graph or an equation..

Parabolas - Activity A

AII.III.3: Determine trigonometric measurements using appropriate techniques, tools, and formulas.

AII.III.3.a: Define the sine, cosine, and tangent functions using the unit circle.

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

AII.III.3.b: Determine the exact values of the sine, cosine, and tangent functions for the special angles of the unit circle using reference angles.

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

AII.III.3.c: Find the length of an arc using radian measure.

Unit Circle

AII.III.3.d: Find the area of a sector in a circle using radian measure.

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B
Unit Circle

AII.IV: Students will understand concepts from probability and statistics and apply statistical methods to solve problems.

AII.IV.1: Apply basic concepts of probability.

AII.IV.1.a: Distinguish between permutations and combinations and identify situations in which each is appropriate.

Binomial Probabilities
Permutations
Permutations and Combinations

AII.IV.1.b: Calculate probabilities using permutations and combinations to count events.

Binomial Probabilities
Estimating Population Size
Permutations
Permutations and Combinations

AII.IV.1.c: Compute conditional and unconditional probabilities in various ways, including by definitions, the general multiplication rule, and probability trees.

Binomial Probabilities
Permutations
Permutations and Combinations

AII.IV.2: Use percentiles and measures of variability to analyze data.

AII.IV.2.a: Compute different measures of spread, including the range, standard deviation, and interquartile range.

Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots

AII.IV.2.b: Compare the effectiveness of different measures of spread, including the range, standard deviation, and interquartile range in specific situations.

Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots

AII.IV.2.d: Use histograms to obtain percentiles.

Histograms
Populations and Samples

PC: Pre-Calculus

PC.I: Students will use the language and operations of algebra to evaluate, analyze and solve problems.

PC.I.1: Compute with matrices and use matrices to solve problems.

PC.I.1.e: Solve systems of linear equations with up to three variables using matrices.

Systems of Linear Equations - Activity A

PC.I.2: Analyze the behavior of sequences and series.

PC.I.2.a: Describe a sequence as a function where the domain is the set of natural numbers.

Arithmetic Sequences
Arithmetic and Geometric Sequences
General Form of a Rational Function
Geometric Sequences
Introduction to Functions
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Radical Functions
Rational Functions
Tangent Function

PC.I.2.b: Represent sequences and series using various notations.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

PC.I.2.c: Identify arithmetic and geometric sequences and series.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

PC.I.2.d: Discover and justify the formula for a finite arithmetic series.

Arithmetic Sequences
Arithmetic and Geometric Sequences

PC.I.2.e: Discover and justify the formulas for finite and infinite geometric series.

Arithmetic and Geometric Sequences
Geometric Sequences

PC.II: Students will understand and represent functions and analyze function behavior.

PC.II.1: Analyze and solve problems using polynomial functions.

PC.II.1.a: Raise a binomial to a power using the Binomial Theorem and Pascal?s Triangle.

Addition of Polynomials - Activity A
Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

PC.II.1.b: Determine the number and nature of solutions to polynomial equations with real coefficients over the complex numbers.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Points in the Complex Plane - Activity A
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A

PC.II.1.c: Factor polynomials to solve equations and real-world applications.

Factoring Special Products
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Modeling the Factorization of x²+bx+c
Solving Two-Step Equations

PC.II.1.d: Understand the relationships among the solutions of a polynomial equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial.

Modeling the Factorization of x²+bx+c
Point-Slope Form of a Line - Activity A
Polynomials and Linear Factors
Slope-Intercept Form of a Line - Activity A

PC.II.1.e: Write an equation with given solutions.

Using Algebraic Equations

PC.II.2: Model and graph functions and transformations of functions.

PC.II.2.b: Graph rational, piece-wise, power, exponential, and logarithmic functions.

Exponential Functions - Activity A
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Rational Functions

PC.II.2.c: Identify the effects of changing the parameter a in y = af (x), y = f (ax), y = f (x − a) , and y = f (x) + a , given the graph of y = f (x).

Functions Involving Square Roots
Logarithmic Functions: Translating and Scaling
Parabolas - Activity A
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

PC.II.3: Analyze the behavior of functions.

PC.II.3.a: Identify the domain, range, and other attributes of families of functions and their inverses.

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Fourth-Degree Polynomials - Activity A
Functions Involving Square Roots
General Form of a Rational Function
Introduction to 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

PC.II.3.b: Approximate instantaneous rates of change and find average rates of change using graphs and numerical data.

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

PC.II.3.c: Identify and analyze continuity, end behavior, asymptotes, symmetry (odd and even functions), and limits, and connect these concepts to graphs of functions.

Functions Involving Square Roots
Introduction to Functions
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
Unit Circle
Using Tables, Rules and Graphs

PC.II.3.e: Relate the graphical representation of discontinuities and end behavior to the concept of limit.

Functions Involving Square Roots

PC.III: Students will use algebraic, spatial, and logical reasoning to solve geometry and measurement problems.

PC.III.1: Solve problems using trigonometry.

PC.III.1.a: Define the six trigonometric functions using the unit circle.

Cosine Function
Sine Function
Tangent Function
Unit Circle

PC.III.1.b: Prove trigonometric identities using definitions, the Pythagorean Theorem, or other relationships.

Simplifying Trigonometric Expressions

PC.III.1.c: Simplify trigonometric expressions and solve trigonometric equations using identities.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

PC.III.1.e: Construct the graphs of the trigonometric functions and their inverses, and describe their behavior, including periodicity and amplitude.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Functions

PC.III.2: Graph curves using polar and parametric equations.

PC.III.2.a: Define and use polar coordinates and relate them to Cartesian coordinates.

Points in Polar Coordinates

PC.III.2.b: Represent complex numbers in rectangular and polar form, and convert between rectangular and polar form.

Complex Numbers in Polar Form
Points in the Complex Plane - Activity A

PC.III.2.c: Translate equations in Cartesian coordinates into polar coordinates and graph them in the polar coordinate plane.

Points in Polar Coordinates

PC.III.3: Solve problems involving the geometric properties of conic sections.

PC.III.3.a: Write equations of conic sections in standard form.

Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A

PC.III.3.b: Identify the geometric properties of conic sections (i.e., vertex, foci, lines of symmetry, directrix, major and minor axes, and asymptotes).

Holiday Snowflake Designer
Hyperbola - Activity A
Parabolas - Activity A

PC.III.3.c: Solve real-world applications of conic sections.

Hyperbola - Activity A

PC.IV: Students will understand concepts from probability and statistics and apply statistical methods to solve problems.

PC.IV.1: Compute probabilities for discrete distributions and use sampling distributions to calculate approximate probabilities.

PC.IV.1.a: Obtain sample spaces and probability distributions for simple discrete random variables.

Binomial Probabilities

PC.IV.1.b: Compute binomial probabilities using Pascal?s Triangle and the Binomial Theorem.

Binomial Probabilities
Geometric Probability - Activity A

PC.IV.1.c: Compute means and variances of discrete random variables.

Mean, Median and Mode

PC.IV.1.d: Compute probabilities using areas under the Normal Curve.

Binomial Probabilities
Geometric Probability - Activity A

PC.IV.1.e: Calculate parameters of sampling distributions for the sample average, sum, and proportion.

Estimating Population Size
Mean, Median and Mode
Polling: Neighborhood
Populations and Samples
Similar Figures - Activity A
Similar Polygons

PC.IV.1.f: Calculate probabilities in real problems using sampling distributions.

Binomial Probabilities
Geometric Probability - Activity A
Populations and Samples

PC.IV.2: Analyze bivariate data using linear regression methods.

PC.IV.2.a: Fit regression lines to pairs of numeric variables and calculate the means and standard deviations of the two variables and the correlation coefficient, using technology.

Correlation
Solving Using Trend Lines