7G: 7th Grade

7G.1: The students will acquire number sense and perform operations with rational and real numbers.

7G.1.1: Compute fluently and make reasonable estimates.

7G.1.1.1: Compute fluently with integers, positive decimals, fractions, and percents.

Adding Real Numbers
Adding and Subtracting Integers with Chips
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Percents and Proportions
Sums and Differences with Decimals

7G.1.1.2: Determine the reasonableness of a solution to a problem after computing its value.

Adding Real Numbers

7G.1.3: Identify relationships among whole numbers, fractions (rational numbers), and decimals.

7G.1.3.1: Compare and order whole numbers, fractions (rational numbers), and decimals and find their approximate locations 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

7G.1.3.2: Predict the outcome of operating among fractions, decimals, percents, and integers, e.g., when multiplying a positive number by a number between 0 and 1 the result is a smaller number.

Adding and Subtracting Integers with Chips
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Percents and Proportions
Sums and Differences with Decimals

7G.1.4: Solve problems involving rational numbers using addition, subtraction, multiplication, and division.

7G.1.4.1: Solve problems involving rational numbers using factors, multiples, prime factorization, relatively prime numbers, and common divisibility rules.

Finding Factors with Area Models

7G.1.4.2: Simplify computations using the inverse operations of addition and subtraction, multiplication and division, and squaring and finding square roots of perfect squares.

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

7G.1.4.3: Compute with percents including those greater than 100% and those less than 1%.

Adding Real Numbers
Percents and Proportions

7G.1.4.4: Simplify expressions using order of operations.

Order of Operations

7G.2: Students will use patterns, relations, and functions to represent and analyze mathematical situations using algebraic symbols.

7G.2.1: Understand patterns, relations, and functions.

7G.2.1.1: Describe a pattern using a mathematical rule or algebraic expression.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

7G.2.1.2: Create simple numerical and visual patterns.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

7G.2.1.3: Extend simple numerical and visual patterns.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

7G.2.2: Represent, solve, and analyze mathematical situations using algebraic symbols.

7G.2.2.2: Translate verbal expressions into symbolic representations, e.g., “increase by three” translates to + 3.

Using Algebraic Equations
Using Algebraic Expressions

7G.2.2.3: Translate numerical representations into verbal expressions, e.g., 5 – 3 translates to “five subtract three.”

Using Algebraic Equations
Using Algebraic Expressions

7G.2.2.4: Verify that performing the same operation to both sides of an equation will produce an equivalent equation, e.g., a + 2 = 4 is the same as a = 2 if 2 is subtracted from both sides of the equation.

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

7G.2.2.6: Solve two-step single variable equations and inequalities.

Modeling and Solving Two-Step Equations
Solving Two-Step Equations

7G.2.2.7: Use proportional reasoning to solve problems.

Similar Figures - Activity A
Similar Polygons

7G.2.3: Represent quantitative relationships using mathematical models and symbols.

7G.2.3.1: Model and solve real-world problems using various representations, such as graphs, tables, manipulatives, and pictures.

Modeling One-Step Equations - Activity A

7G.2.3.3: Use graphs and tables to identify and describe changes in related quantities.

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

7G.3: Students will use spatial and logical reasoning to recognize, describe, and identify geometric shapes and principles.

7G.3.1: Describe, identify, and analyze characteristics and properties of geometric shapes.

7G.3.1.1: Classify common two- and three-dimensional objects using information about the sides and angles.

Classifying Quadrilaterals - Activity A
Classifying Quadrilaterals - Activity B
Classifying Triangles
Parallelogram Conditions
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Special Quadrilaterals

7G.3.1.2: Identify similar and congruent figures.

Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

7G.3.1.3: Identify relationships among angles, side lengths, and perimeters of similar objects, e.g., corresponding angles of similar triangles have the same measure and the ratios of the corresponding sides are equal.

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

7G.3.1.5: Describe and draw parallel and intersecting lines, including perpendicular lines.

Construct Parallel and Perpendicular Lines

7G.3.1.6: Classify angles as acute, obtuse, or right.

Classifying Triangles

7G.3.2: Specify locations and describe spatial relationships using coordinate geometry.

7G.3.2.1: Graph ordered pairs of integers on a rectangular coordinate system.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Introduction to Functions
Points in the Coordinate Plane - Activity A

7G.3.2.2: Identify the coordinates of a point plotted on a rectangular coordinate system.

Points in the Coordinate Plane - Activity A

7G.3.3: Visualize and identify geometric shapes after applying transformations, and identify lines of symmetry.

7G.3.3.1: Identify line(s) of symmetry in plane figures.

Holiday Snowflake Designer

7G.3.3.2: Transform geometric shapes using translations (slides), rotations (turns), and reflections (flips).

Dilations
Reflections
Rotations, Reflections and Translations
Translations

7G.3.3.3: Recognize a three-dimensional figure from a net.

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

7G.3.3.4: Draw two-dimensional representations of three-dimensional objects.

3D and Orthographic Views - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

7G.4: Students will understand and apply measurement tools, formulas, and techniques.

7G.4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

7G.4.1.2: Convert from one unit of measure to another within the same system, e.g., convert miles per hour to feet per second.

Elapsed Time

7G.4.1.4: Select and use units of appropriate size and type to describe or identify measurements of angles, perimeter, area, volume, and weight.

Perimeter, Circumference, and Area - Activity B

7G.4.2: Determine measurements using appropriate tools and formulas.

7G.4.2.2: Measure length, area, volume, and angles to appropriate levels of precision.

Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

7G.4.2.3: Develop formulas for the area of parallelograms (including rectangles and squares) and triangles.

Area of Parallelograms - Activity A
Parallelogram Conditions

7G.4.2.4: Determine perimeters of polygons and circumferences of circles; areas of triangles, parallelograms, and circles; volumes of right rectangular and triangular prisms and cylinders; and surface areas of right rectangular and triangular prisms and cylinders using formulas.

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

7G.5: Students will draw conclusions using concepts of probability after collecting, organizing, and analyzing a data set.

7G.5.1: Design investigations to reach conclusions using statistical methods to analyze data.

7G.5.1.1: Identify appropriate questions for data collection and then collect, organize, and display responses to the questions.

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

7G.5.1.2: Collect, organize, and display data using frequency tables, line plots, bar graphs, circle graphs, line graphs, and stem-and-leaf plots.

Describing Data Using Statistics
Line Plots
Stem-and-Leaf Plots

7G.5.1.3: Display the same set of data utilizing two or more different types of representations.

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

7G.5.1.4: Compare two similar sets of data using the same type of graph.

Populations and Samples

7G.5.1.6: Predict basic trends illustrated in a graph.

Solving Using Trend Lines

7G.5.2: Apply basic concepts of probability.

7G.5.2.1: Conduct experiments to approximate the probability of simple events.

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

7G.5.2.2: Compare individual, small group, and large group results of an experiment.

Geometric Probability - Activity A
Populations and Samples
Probability Simulations

7G.5.2.3: Write the results of a probability experiment as a ratio, decimal, or percent.

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

7G.5.2.4: Identify the probability of an event as a number between 0 (cannot happen) and 1 (must happen).

Binomial Probabilities
Estimating Population Size
Geometric Probability - Activity A

7G.5.2.5: Compute simple probabilities using methods such as lists, tree diagrams, or area models.

Binomial Probabilities
Geometric Probability - Activity A
Permutations
Permutations and Combinations

7G.5.2.6: Recognize that the sum of the probabilities of all outcomes of an event is 1.

Binomial Probabilities
Estimating Population Size
Geometric Probability - Activity A

PA: Pre-Algebra

PA.1: Students will acquire number sense and perform operations with rational numbers.

PA.1.1: Compute fluently and make reasonable estimates.

PA.1.1.1: Compute using selected methods from among mental arithmetic, estimation, paper and pencil, and calculator.

Estimating Sums and Differences

PA.1.1.2: Add, subtract, multiply, and divide integers.

Adding Real Numbers
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Order of Operations

PA.1.2: Represent rational numbers in a variety of ways.

PA.1.2.1: Recognize and create equivalent forms of a rational number.

Improper Fractions and Mixed Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents, Fractions and Decimals

PA.1.2.2: Find an approximate location of a rational number 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.1.2.3: Find a rational number between any two rational numbers.

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

PA.1.2.4: Choose appropriate and convenient forms of rational numbers for solving problems and representing solutions.

Improper Fractions and Mixed Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents, Fractions and Decimals

PA.1.3: Identify relationships among rational numbers and operations involving these numbers.

PA.1.3.1: Compare and order rational numbers.

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

PA.1.3.2: Identify the effects of arithmetic operations among fractions, decimals, percents, and integers; e.g., multiplying or dividing by a number larger or smaller than 1.

Adding and Subtracting Integers with Chips
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Percents and Proportions
Sums and Differences with Decimals

PA.1.3.5: Recognize and use the inverse relationships of addition and subtraction, multiplication and division, and perfect square roots and squares.

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

PA.1.4: Solve problems involving rational numbers using addition, subtraction, multiplication, and division.

PA.1.4.1: Recognize absolute value of a rational number as the value of its distance from zero.

Comparing and Ordering Integers
Real Number Line - Activity A

PA.1.4.2: Evaluate numerical and algebraic expressions containing absolute value.

Comparing and Ordering Integers
Order of Operations
Real Number Line - Activity A

PA.1.4.3: Compute with percents, including those greater than 100% and less than 1%.

Adding Real Numbers
Percents and Proportions

PA.1.4.4: Solve problems using simple proportions.

Estimating Population Size

PA.2: Students will represent and analyze mathematical situations and properties using patterns, relations, functions, and algebraic symbols.

PA.2.1: Use patterns, relations, and functions to represent mathematical situations.

PA.2.1.1: Represent a variety of relations and functions using tables, graphs, manipulatives, verbal rules, or algebraic rules.

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

PA.2.1.2: Describe simple patterns using a mathematical rule or algebraic expression.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

PA.2.1.3: Create and extend simple numeric and visual patterns, including those that have a recursive nature (e.g., Fibonacci numbers, triangular and square numbers).

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

PA.2.2: Represent, solve, and analyze mathematical situations and properties using algebraic symbols.

PA.2.2.2: Identify the horizontal and vertical intercepts of a linear relation from a graph or table.

Defining a Line with Two Points
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
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

PA.2.2.3: Determine the slope of a linear relation from a graph or ordered pairs.

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

PA.2.2.4: Solve one- and two-step single-variable equations and inequalities.

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

PA.2.3: Represent quantitative relationships using mathematical models and symbols.

PA.2.3.1: Create a table, graph, or algebraic expression to represent the relationship between two variables.

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

PA.2.3.2: Graph ordered pairs of rational numbers on a rectangular coordinate system.

Points in the Coordinate Plane - Activity A

PA.2.3.3: Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Points in the Coordinate Plane - Activity A

PA.2.3.4: Model real-world problems using various representations, such as graphs, tables, equations, manipulatives, and pictures.

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

PA.3: Students will recognize, describe, and identify geometric shapes, and solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.

PA.3.1: Analyze characteristics and properties of two- and three-dimensional shapes and develop mathematical arguments about geometric relationships.

PA.3.1.1: Identify congruent and similar shapes.

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

PA.3.1.2: Find missing lengths of similar plane figures using proportions.

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

PA.3.1.3: Classify two- and three-dimensional objects according to the defining characteristics.

Classifying Quadrilaterals - Activity A
Classifying Quadrilaterals - Activity B
Classifying Triangles
Parallelogram Conditions
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Special Quadrilaterals

PA.3.1.4: Identify relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Perimeter, Circumference, and Area - Activity B
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

PA.3.3: Apply transformations and use symmetry to analyze mathematical situations.

PA.3.3.1: Reflect a geometric shape across a line in a coordinate plane and identify the coordinates of the vertices.

Reflections
Rotations, Reflections and Translations

PA.3.3.2: Translate a geometric shape a given distance on a coordinate plane and identify the vertices.

Rotations, Reflections and Translations
Translations

PA.4: Students will understand and apply measurement tools, formulas, and techniques.

PA.4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

PA.4.1.2: Convert from one unit of measure to an equivalent unit of measure using a given conversion factor, e.g., 60 miles/hour 1 hour/3600 sec 5280 ft/1 mile = 88 ft/sec.

Elapsed Time

PA.4.1.3: Measure angles, perimeter, area, and volume using the correct size and type of units.

Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Rectangle: Perimeter and Area

PA.4.2: Determine measurements using appropriate techniques, tools, and formulas.

PA.4.2.2: Solve problems involving scale factors using ratios and proportions.

Dilations
Estimating Population Size
Perimeters and Areas of Similar Figures
Proportions and Common Multipliers
Similar Figures - Activity A
Similar Polygons

PA.4.2.3: Solve problems involving rates and derived measures, e.g., miles per hour, kilometers per liter, cubic feet.

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

PA.4.2.4: Measure inaccessible heights or distances using similar triangles.

Perimeters and Areas of Similar Figures
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Similar Figures - Activity A
Similar Polygons

PA.4.2.5: Calculate surface area and volume of right prisms and cylinders using appropriate units.

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

PA.4.2.6: Develop formulas for calculating the circumference of circles and the areas of triangles, parallelograms, and trapezoids.

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

PA.4.2.7: Calculate the circumference of circles and the areas of triangles, parallelograms, and trapezoids using formulas.

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

PA.5: Students will draw conclusions using concepts of probability after collecting, organizing, and analyzing a data set.

PA.5.1: Formulate and answer questions by collecting, organizing, and analyzing data.

PA.5.1.2: Organize and display data using graphical representations such as line plots, bar graphs, stem-and-leaf plots, histograms, scatter plots, circle graphs, box plots (box-and-whisker plots), and pictographs.

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

PA.5.1.4: Calculate the mean, median, mode, and range for a data set.

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

PA.5.1.5: Choose a measure of central tendency most appropriate to analyze a particular set of data.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

PA.5.1.6: Describe how an individual data point may affect the measures of central tendency.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

PA.5.1.7: Interpret and describe the spread of a set of data, e.g., range, box plot (box-and-whisker).

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Line Plots
Solving Using Trend Lines

PA.5.2: Apply basic concepts of probability.

PA.5.2.1: Conduct experiments to approximate the probability of simple events.

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

PA.5.2.2: Recognize that results of an experiment more closely approximate the actual or theoretical probability of an event as the number of trials increases.

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

PA.5.2.3: Derive the probability of an event mathematically, e.g., building a table or tree diagram, creating an area model, making a list, or using the basic counting principle.

Binomial Probabilities
Geometric Probability - Activity A
Permutations
Permutations and Combinations

PA.5.2.4: Represent the probability of an event as a fraction, percent, ratio, or decimal.

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

EA: Elementary Algebra

EA.1: Students will acquire number sense and perform operations with real numbers.

EA.1.1: Compute fluently and make reasonable estimates.

EA.1.1.2: Compute solutions to problems.

Adding Real Numbers

EA.1.2: Represent real numbers in a variety of ways.

EA.1.2.1: Compare and order real numbers.

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

EA.1.2.2: Choose appropriate and convenient forms of real numbers for solving problems and representing answers, e.g., radical form, multiples of pi, decimal, fraction, or percent.

Improper Fractions and Mixed Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents, Fractions and Decimals

EA.1.3: Identify relationships among real numbers and operations involving these numbers.

EA.1.3.2: Relate properties and operations of rational numbers to irrational numbers.

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

EA.1.3.3: Simplify numerical expressions and solve problems using real numbers.

Operations with Radical Expressions
Order of Operations
Simplifying Radicals - Activity A

EA.2: Students will represent and analyze mathematical situations and properties using patterns, relations, functions, and algebraic symbols.

EA.2.1: Use patterns, relations, and functions to represent mathematical situations.

EA.2.1.1: Write algebraic expressions or equations to generalize visual patterns, numerical patterns, relations, data sets, or scatter plots.

Arithmetic Sequences
Introduction to Functions
Scatter Plots - Activity A
Using Algebraic Equations

EA.2.1.2: Represent linear equations in slope-intercept form, y = mx + b, or 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

EA.2.1.3: Distinguish between linear and non-linear functions or equations by examining a table, equation, or graph.

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Functions Involving Square Roots
General Form of a Rational Function
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Sine Function
Slope-Intercept Form of a Line - Activity A
Tangent Function
Unit Circle
Using Tables, Rules and Graphs

EA.2.1.4: Identify the slope of a linear function as an average rate of change in real-world situations.

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

EA.2.2: Evaluate, solve, and analyze mathematical situations using algebraic properties and symbols.

EA.2.2.1: Solve real-world problems involving constant rates of change, e.g., rates of travel, hourly wages, or rates of interest.

Direct Variation
Direct and Inverse Variation
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Modeling Linear Systems - Activity A
Simple and Compound Interest

EA.2.2.2: Solve multi-step equations and inequalities:

EA.2.2.2.a: Numerically; e.g., from a table or guess and check.

Modeling and Solving Two-Step Equations
Solving Two-Step Equations
Using Tables, Rules and Graphs

EA.2.2.2.b: Algebraically, including the use of manipulatives.

Modeling and Solving Two-Step Equations
Solving Two-Step Equations

EA.2.2.2.c: Graphically.

Defining a Line with Two Points
Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Modeling and Solving Two-Step Equations
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations
Standard Form of a Line
Systems of Linear Inequalities (Slope-intercept form) - Activity A

EA.2.2.2.d: Using technology.

Modeling and Solving Two-Step Equations
Solving Two-Step Equations

EA.2.2.3: Solve systems of two linear equations or inequalities:

EA.2.2.3.a: Numerically; e.g., from a table or guess and check.

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

EA.2.2.3.b: Algebraically.

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

EA.2.2.3.c: Graphically.

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

EA.2.2.3.d: Using technology.

Solving Linear Systems by Graphing

EA.2.2.5: Evaluate numerical expressions (including exponents and square roots), algebraic expressions, formulas, and equations.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Order of Operations
Solving Two-Step Equations
Square Roots

EA.2.2.6: Solve linear formulas and literal equations for a specified variable, e.g., solve for p in I = prt.

Solving Formulas for any Variable

EA.2.2.7: Simplify algebraic expressions, including those having integer exponents.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

EA.2.2.8: Solve proportions that include algebraic first-degree expressions.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Polling: Neighborhood
Proportions and Common Multipliers
Similar Figures - Activity A
Similar Polygons

EA.2.3: Represent quantitative relationships using mathematical models and symbols.

EA.2.3.1: Identify the slope of a line when given:

EA.2.3.1.a: A set of two ordered pairs.

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

EA.2.3.1.b: An equation of a linear function.

Linear Functions
Modeling Linear Systems - Activity A
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

EA.2.3.1.c: The graph of a linear function.

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

EA.2.3.1.d: A table of values.

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

EA.2.3.2: Write the equation of a line when given:

EA.2.3.2.a: A set of ordered pairs.

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

EA.2.3.2.b: The slope and a point on the line.

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

EA.2.3.2.c: 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

EA.2.3.3: Identify horizontal and vertical lines given the equations.

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

EA.2.3.4: Identify the domain and range of a relation or function from a graph, equation, table, or set of ordered pairs.

Cosine Function
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Functions Involving Square Roots
General Form of a Rational Function
Introduction to Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Radical Functions
Rational Functions
Sine Function
Tangent Function
Using Tables, Rules and Graphs

EA.2.3.5: Determine the effect of parameter changes on the graphs of linear relations.

Functions Involving Square Roots
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

EA.2.3.7: Determine the x- and y-intercepts from an equation or 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

EA.2.3.8: Graph linear functions:

EA.2.3.8.a: By plotting points.

Points in the Coordinate Plane - Activity A

EA.2.3.8.b: By finding x- and y-intercepts.

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

EA.2.3.8.c: Using the slope-intercept form of a line.

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

EA.2.3.8.d: Using the slope and any point on the line.

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

EA.2.3.9: Graph linear inequalities and identify the boundary line and solution area.

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

EA.2.3.10: Determine and explain the meaning of intercepts using real-world examples.

Modeling Linear Systems - Activity A
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A

EA.2.3.11: Use direct variation to model rates of change, e.g., if income = 40 hours times rate of pay, then increasing the rate of pay increases income.

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

EA.3: Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.

EA.3.2: Specify locations and describe spatial relationships using coordinate geometry.

EA.3.2.1: Find the distance between two given points and find the coordinates of the midpoint between them.

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

EA.3.2.2: Solve problems using the distance formula.

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

EA.3.2.3: Solve problems for areas, perimeters, volumes, and surface areas using formulas.

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

EA.3.3: Solve problems using visualization, spatial reasoning, and geometric modeling.

EA.3.3.1: Solve problems using the Pythagorean Theorem.

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

EA.3.3.2: Find missing parts of geometric figures using proportional reasoning and geometric relationships.

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

EA.3.3.3: Illustrate multiplication of polynomials using area models, e.g., (a + b)² , x(x + 2), or (x + a)(x + b).

Polynomials and Linear Factors

EA.3.3.4: Factor polynomials using area models:

EA.3.3.4.a: To identify the greatest common monomial factor.

Addition of Polynomials - Activity A
Factoring Special Products
Modeling and Solving Two-Step Equations

EA.3.3.4.b: Of the form ax squared + bx + c when a = 1.

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

EA.4: Students will understand and apply measurement tools, formulas, and techniques.

EA.4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

EA.4.1.2: Express the rate of change as a ratio of two different measures.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Similar Figures - Activity A
Similar Polygons

EA.4.1.3: Select appropriate units to achieve the desired precision when solving problems.

Triple Beam Balance

EA.5: Students will draw conclusions using concepts of probability after collecting, organizing, and analyzing a data set.

EA.5.1: Formulate and answer questions by collecting, organizing, and analyzing data.

EA.5.1.1: Collect, record, organize, and display a set of data.

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

EA.5.1.2: Determine whether the pattern of the data is linear or nonlinear when given in a list, table, or graph.

Arithmetic and Geometric Sequences
Linear Functions

EA.5.1.3: Interpret the correlation between two variables as being positive, negative, or having no correlation.

Correlation
Solving Using Trend Lines

EA.5.1.5: Analyze the meaning of the slope and y-intercept of a line of best fit as it relates to the data.

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

EA.5.2: Apply basic concepts of probability.

EA.5.2.1: Determine and express the probability of an event as a fraction, percent, ratio, or decimal.

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

EA.5.2.2: Identify the probability of an event as being between zero (event not possible) and one (event certain).

Binomial Probabilities
Estimating Population Size
Geometric Probability - Activity A

GE: Geometry

GE.2: Students will represent and analyze mathematical situations and properties using patterns, relations, functions, and algebraic symbols.

GE.2.1: Use patterns, relations, and functions to represent mathematical situations.

GE.2.1.1: Identify trigonometric relationships (sine, cosine, and tangent) using right triangles, expressing the relationships as fractions or decimals.

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

GE.2.1.2: Analyze geometric patterns to develop formulas and communicate how the formulas were derived, e.g., angle measure and number of sides of a polygon, interior and exterior angles, diagonals, and vertices.

Finding Patterns
Triangle Angle Sum - Activity A

GE.2.1.4: Identify the effect on area or volume when changing linear dimensions.

Circle: Circumference and Area
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

GE.2.2: Evaluate, solve, and analyze mathematical situations using algebraic properties and symbols.

GE.2.2.1: Find the angle measure in degrees given the trigonometric ratio using a calculator.

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

GE.2.2.2: 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

GE.2.2.3: Find the missing measures of right triangles.

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

GE.2.2.5: Write an equation of a line perpendicular or parallel to a line through a given point.

Point-Slope Form of a Line - Activity A

GE.2.2.6: Model and solve geometric situations using algebraic properties.

Ellipse - Activity A
Hyperbola - Activity A

GE.3: Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.

GE.3.1: Analyze characteristics and properties of two- and three-dimensional shapes and develop mathematical arguments about geometric relationships.

GE.3.1.1: Use accepted geometric notations, e.g., congruencies, transformations, similarities.

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

GE.3.1.2: Write conditional statements, converses, and inverses and determine the truth value of the statements.

Conditional Statement

GE.3.1.4: Identify angle pairs as adjacent, complementary, supplementary, a linear pair, or vertical angles.

Investigating Angle Theorems - Activity A

GE.3.1.5: Differentiate between parallel, perpendicular, skew, and intersecting lines.

Construct Parallel and Perpendicular Lines
Investigating Parallel Lines and Planes

GE.3.1.6: Classify angle pairs formed by two lines and a transversal, e.g., corresponding, alternate interior, and supplementary angles.

Investigating Angle Theorems - Activity A
Triangle Angle Sum - Activity A

GE.3.1.7: Prove lines parallel or perpendicular using slope or angle relationships.

Construct Parallel and Perpendicular Lines
Slope - Activity B

GE.3.1.8: Prove congruency and similarity of geometric figures.

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

GE.3.1.9: Identify medians, altitudes, and angle bisectors of a triangle, and the perpendicular bisectors of the sides of a triangle.

Concurrent Lines, Medians, and Altitudes

GE.3.1.10: Classify a quadrilateral as a parallelogram, trapezoid, rectangle, square, rhombus, kite, or none of the above.

Area of Parallelograms - Activity A
Classifying Quadrilaterals - Activity A
Classifying Quadrilaterals - Activity B
Parallelogram Conditions
Special Quadrilaterals

GE.3.1.11: Identify radii, diameters, chords, secants, arcs, sectors, central angles, inscribed angles, and tangents for circles.

Chords and Arcs
Inscribing Angles

GE.3.1.12: Classify and use the properties of acute, right, scalene, oblique, isosceles, equilateral, or equiangular triangles.

Classifying Triangles
Isosceles and Equilateral Triangles
Pythagorean Theorem - Activity B
Triangle Angle Sum - Activity A

GE.3.1.13: Classify polyhedrons and other three-dimensional figures according to their properties.

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

GE.3.2: Specify locations and describe spatial relationships using coordinate geometry.

GE.3.2.1: Graph a circle given the equation in the form (x - h)² + (y - k)² = r².

Circles

GE.3.2.2: Write the equation of a circle given its graph.

Circles

GE.3.2.3: Verify the classifications of geometric figures using coordinate geometry to find lengths and slopes, e.g., verify or prove the diagonals of a rectangle are congruent using the distance formula.

Classifying Quadrilaterals - Activity A
Classifying Quadrilaterals - Activity B
Classifying Triangles
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Parallelogram Conditions
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Slope - Activity B
Special Quadrilaterals

GE.3.2.4: Perform and analyze transformations (translations, rotations, reflections, and dilations) using coordinate geometry.

Dilations
Reflections
Rotations, Reflections and Translations
Translations

GE.3.3: Use visualization, spatial reasoning, and geometric modeling to solve problems.

GE.3.3.1: Construct/copy angles and segments, bisect angles and segments, and create perpendicular lines and parallel lines using a compass and straight edge, technology, or other manipulatives.

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

GE.3.3.2: Define p as the ratio of the circumference to the diameter of a circle.

Circle: Circumference and Area

GE.3.3.3: Identify the relationships between the measures of intercepted arcs and inscribed or central angles.

Chords and Arcs
Inscribing Angles

GE.3.3.4: Solve real-world problems using trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

Congruence in Right Triangles
Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

GE.3.3.5: Sketch cross-sections of geometric solids.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

GE.4: Students will understand and apply measurement tools, formulas, and techniques.

GE.4.2: Determine measurements using appropriate techniques, tools, and formulas.

GE.4.2.1: Find the area of a regular polygon.

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

GE.4.2.3: Find the surface area and volume for prisms, cylinders, pyramids, cones, and spheres given the formula.

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

GE.5: Students will draw conclusions using concepts of probability after collecting, organizing, and analyzing a data set.

GE.5.2: Apply basic concepts of probability.

GE.5.2.1: Identify geometric probabilities by performing simulations involving length or area.

Geometric Probability - Activity A
Probability Simulations

GE.5.2.2: Calculate geometric probability.

Geometric Probability - Activity A

IA: Intermediate Algebra

IA.1: Students will acquire number sense and perform operations with real and complex numbers.

IA.1.2: Represent complex numbers in a variety of ways.

IA.1.2.1: Extend the number system to include complex numbers in the form a + bi.

Points in the Complex Plane - Activity A

IA.1.2.3: Simplify expressions involving radical expressions including square roots of negative numbers.

Operations with Radical Expressions
Simplifying Radicals - Activity A

IA.2: Students will represent and analyze mathematical situations and properties using patterns, relations, functions, and algebraic symbols.

IA.2.1: Use patterns, relations, and functions to represent mathematical situations.

IA.2.1.1: Compare and contrast relations and functions.

Introduction to Functions
Linear Functions

IA.2.1.2: Identify the domain and range of 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, Cosine and Tangent
Translating and Scaling Functions
Unit Circle

IA.2.1.5: Find the inverse of a function by interchanging the values of domain and range, reflecting across the line y = x, or by using algebra.

Absolute Value with Linear Functions - Activity B

IA.2.1.6: Relate the sine, cosine, tangent, cosecant, secant, and cotangent to the unit circle.

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

IA.2.1.7: Express angle measure in degrees or radians when given the trigonometric value.

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

IA.2.2: Evaluate, solve, and analyze mathematical situations using algebraic properties and symbols.

IA.2.2.1: Solve quadratic equations.

Roots of a Quadratic

IA.2.2.4: Solve single-variable quadratic and absolute value inequalities.

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

IA.2.2.5: Write a quadratic equation when given the rational roots or zeroes of the function.

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

IA.2.2.6: Solve systems of equations with no more than three variables using technology.

Solving Linear Systems by Graphing

IA.2.2.7: Solve and graph systems of linear inequalities.

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

IA.2.2.9: Recognize that a to the -nth power is defined as the reciprocal of a to the nth power, i.e., a to the -nth power = 1 over a to the nth power if a is not equal 0.

Dividing Exponential Expressions
Exponents and Power Rules

IA.2.3: Represent quantitative relationships using mathematical models and symbols.

IA.2.3.1: Interpret rates of change by analyzing graphical and numerical data for quadratic and radical functions.

Direct Variation
Direct and Inverse Variation
Functions Involving Square Roots
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Roots of a Quadratic

IA.2.3.2: Find the vertex, maximum or minimum values, intercepts, and axis of symmetry of a quadratic or absolute value function, algebraically, graphically, and numerically.

Holiday Snowflake Designer
Inequalities Involving Absolute Values
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

IA.2.3.3: Write the equation of a parabola in the form y = a(x - h)² + k and a circle in the form y = a(x - h)² + (y - k)² = r² by completing the square.

Parabolas - Activity A

IA.3: Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.

IA.3.2: Specify locations and describe spatial relationships using coordinate geometry.

IA.3.2.1: Sketch the graph of a quadratic and absolute value function.

Comparing and Ordering Integers
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Real Number Line - Activity A
Roots of a Quadratic

IA.3.2.2: Sketch the solutions of absolute value and quadratic inequalities of one variable on a number line.

Comparing and Ordering Integers
Compound Inequalities
Quadratic Inequalities - Activity A
Real Number Line - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

IA.3.2.3: Sketch the solutions of absolute value and quadratic inequalities of two variables on a Cartesian coordinate system.

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

IA.3.2.4: Sketch the graph of a square root function.

Functions Involving Square Roots
Radical Functions

IA.3.2.5: Write an equation of a parabola in the form y = a(x -h)² + k when given a graph.

Parabolas - Activity A

IA.3.2.6: Graph sine and cosine functions.

Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
Unit Circle

IA.3.2.7: Perform the transformations of stretching, shifting, and reflecting the graphs of linear, absolute value, quadratic, and radical functions.

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

IA.3.2.8: Perform transformation on the sine and cosine functions involving amplitude, period, phase shift, vertical shift, and reflections.

Absolute Value with Linear Functions - Activity B
Cosine Function
Reflections of a Linear Function
Reflections of a Quadratic Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

IA.3.3: Solve problems using visualization, spatial reasoning, and geometric modeling.

IA.3.3.1: Solve problems involving absolute value and quadratic functions algebraically and graphically.

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

IA.3.3.2: Solve problems using graphs of sine and cosine functions.

Cosine Function
Point-Slope Form of a Line - Activity A
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Slope-Intercept Form of a Line - Activity A
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
Unit Circle

IA.4: Students will understand and apply measurement tools, formulas, and techniques.

IA.4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

IA.4.1.2: Calculate the exact values of the sine, cosine, and tangent functions for the special angles of the unit circle.

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

IA.4.2: Determine measurements using appropriate techniques, tools, and formulas.

IA.4.2.2: Find the area of a sector in a circle using radian measure.

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

IA.5: Students will draw conclusions using concepts of probability after collecting, organizing, and analyzing a data set.

IA.5.2: Apply basic concepts of probability.

IA.5.2.1: Identify the difference between a permutation and a combination.

Binomial Probabilities
Permutations
Permutations and Combinations

IA.5.2.2: Calculate a probability using the Fundamental Counting Principle.

Binomial Probabilities
Geometric Probability - Activity A

IA.5.2.3: Calculate simple combinations and permutations of n objects taken r at a time.

Binomial Probabilities
Permutations
Permutations and Combinations

PC: Pre-Calculus

PC.1: Students will acquire number sense and perform operations with real and complex numbers.

PC.1.1: Compute fluently and make reasonable estimates.

PC.1.1.1: Add, subtract, multiply, and find the absolute value using complex numbers.

Real Number Line - Activity A

PC.1.1.2: Add, subtract and perform scalar multiplication on vectors using a variety of techniques with or without the use of technology.

Vectors

PC.1.2: Represent complex numbers and vectors in a variety of ways.

PC.1.2.1: Represent vectors graphically and symbolically.

Vectors

PC.1.2.2: Represent complex numbers in rectangular and polar form and convert between rectangular and polar form.

Complex Numbers in Polar Form

PC.1.3: Identify relationships among complex numbers and vectors and operations involving these items.

PC.1.3.1: Analyze properties of vectors and their effects on vector operations.

Vectors

PC.1.3.2: Analyze properties of complex numbers and their effects on operations in rectangular and polar form.

Complex Numbers in Polar Form

PC.2: Students will represent and analyze mathematical situations and properties using patterns, relations, functions, and algebraic symbols.

PC.2.1: Use patterns, relations, and functions to represent mathematical situations.

PC.2.1.1: Identify the domain, range, and other attributes of families of functions and their inverses, i.e., exponential, polynomial, rational, logarithmic, piece-wise, and trigonometric.

Cosine Function
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Rational Functions
Sine Function
Tangent Function

PC.2.1.3: Write functions and relations in parametric form.

Introduction to Functions

PC.2.1.4: Identify vector-valued functions using a variety of approaches, e.g., algebraically or graphically.

Roots of a Quadratic
Translating and Scaling Functions

PC.2.1.5: Identify and generate arithmetic and geometric sequences and series recursively and explicitly using correct notation.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

PC.2.1.6: Identify a geometric series as convergent or divergent.

Arithmetic and Geometric Sequences
Geometric Sequences

PC.2.2: Evaluate, solve, and analyze mathematical situations using algebraic properties and symbols.

PC.2.2.1: Solve equations and inequalities involving exponential, logarithmic, power, polynomial, rational, and trigonometric functions, including real-world situations.

Cosine Function
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Rational Functions
Sine Function
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Tangent Function

PC.2.2.2: Compare logarithmic and exponential functions.

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

PC.2.2.3: Combine and compose functions using algebraic methods or by using technology when appropriate.

Addition and Subtraction of Polynomials

PC.2.2.6: Solve systems of non-linear equations and inequalities.

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

PC.2.2.7: Find the x- and y-intercepts, zeros (roots), maxima, and minima of functions.

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

PC.2.2.8: Approximate instantaneous rates of change and find average rates of change using graphical and numerical data.

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

PC.2.3: Represent quantitative relationships using mathematical models and symbols.

PC.2.3.1: Represent quantitative, real-world situations using exponential, logarithmic, power, polynomial, rational, and trigonometric functions, vector and parametric equations, and sequences and series.

Arithmetic and Geometric Sequences
Cosine Function
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Geometric Sequences
Half-life
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Rational Functions
Sine Function
Tangent Function

PC.2.3.2: Identify and analyze graphical features of functions such as asymptotes, holes, local, global, and end behavior.

General Form of a Rational Function
Rational Functions
Tangent Function
Unit Circle

PC.2.3.3: Recognize symmetric properties of even and odd functions.

Cosine Function
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Sine Function
Tangent Function

PC.2.3.4: Relate the graphical representation of discontinuities and end-behavior to the concept of limit.

Functions Involving Square Roots

PC.2.3.5: Identify the effects of changing the parameters in transformations of functions.

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

PC.2.3.6: Identify a family or families of functions that model real-world relationships.

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
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.3: Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.

PC.3.1: Analyze characteristics and properties of two- and three-dimensional shapes and develop mathematical arguments about geometric relationships.

PC.3.1.1: Determine and analyze the characteristics of graphs and the related equations of conic sections.

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

PC.3.1.2: Analyze problems and solutions involving vectors using algebraic and graphical techniques.

Vectors

PC.3.2: Specify locations and describe spatial relationships using coordinate geometry.

PC.3.2.1: Perform transformations on exponential, power, polynomial, rational, logarithmic, and trigonometric functions.

Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Rational Functions
Sine Function
Tangent Function
Translating and Scaling Functions

PC.4: Students will understand and apply measurement tools, formulas, and techniques.

PC.4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

PC.4.1.1: Select appropriate units and scales for situations involving measurement.

Dilations
Similar Figures - Activity A
Similar Polygons

PC.4.1.2: Recognize the changes in magnitude with various measurement scales, e.g., Richter, pH, decibel.

Dilations
Similar Figures - Activity A
Similar Polygons

PC.5: Students will draw conclusions using concepts of probability after collecting, organizing, and analyzing a data set.

PC.5.1: Formulate and answer questions by collecting, organizing, and analyzing data.

PC.5.1.1: Find regression equation for bivariate data including power, exponential, logarithmic, polynomial, and sinusoidal curves using technology.

Sine, Cosine and Tangent

PC.5.2: Apply basic concepts of probability.

PC.5.2.1: Find sample spaces and probability distributions in simple cases.

Binomial Probabilities

PC.5.2.2: Differentiate between independent and dependent events and calculate the probability of each.

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

PC.5.2.4: Calculate the probability of a compound event.

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

PC.5.2.5: Calculate and interpret the expected value (weighted average) of random variables in simple cases.

Mean, Median and Mode

AM1.1: Students will acquire number sense and perform operations with real numbers.

AM1.1.1: Compute fluently and make reasonable estimates.

AM1.1.1.1: Add, subtract, multiply, and divide real numbers using the order of operations.

Adding Real Numbers
Order of Operations

AM1.1.1.2: Approximate radical expressions.

Operations with Radical Expressions
Simplifying Radicals - Activity A
Square Roots

AM1.1.2: Represent real numbers in a variety of ways.

AM1.1.2.1: Compare and order real numbers.

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

AM1.1.3: Identify relationships among real numbers and operations involving these numbers.

AM1.1.3.1: Simplify numerical expressions and solve problems using real numbers.

Order of Operations

AM1.2: Students will represent and analyze mathematical situations and properties using patterns, relations, functions, and algebraic symbols.

AM1.2.1: Use patterns, relations, and functions to represent mathematical situations.

AM1.2.1.1: Distinguish between linear and non-linear functions when given a table, equation, or graph.

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Functions Involving Square Roots
General Form of a Rational Function
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Sine Function
Slope-Intercept Form of a Line - Activity A
Tangent Function
Unit Circle
Using Tables, Rules and Graphs

AM1.2.1.2: Represent linear equations in slope-intercept form, y = mx + b, or 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

AM1.2.1.3: Write algebraic expressions describing numerical patterns or relations; e.g., triangular numbers, square numbers, arithmetic sequences, and recursive sequences.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
Introduction to Functions

AM1.2.1.4: Determine whether a relation is a function when given a graph or set of ordered pairs.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions - Activity A
Introduction to Functions
Linear Functions
Logarithmic Functions: Translating and Scaling

AM1.2.2: Evaluate, solve, and analyze mathematical situations using algebraic properties and symbols.

AM1.2.2.1: Evaluate numerical and algebraic expressions, formulas, and equations.

Using Algebraic Equations

AM1.2.2.2: Solve multi-step linear equations and inequalities algebraically and graphically.

Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
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

AM1.2.2.3: Solve systems of two linear equations and inequalities that have two variables algebraically and graphically.

Inequalities Involving Absolute Values
Linear Programming - Activity A
Modeling Linear Systems - Activity A
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

AM1.2.2.5: Solve proportions that include algebraic first-degree expressions.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Polling: Neighborhood
Proportions and Common Multipliers
Similar Figures - Activity A
Similar Polygons

AM1.2.2.6: Solve linear formulas and literal equations for a specified variable, e.g., solve for p in I = prt.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Formulas for any Variable
Solving Two-Step Equations

AM1.2.2.7: Solve real-world problems involving constant rates of change, e.g., distance, rate and time, hourly wages, rates of interest.

Modeling Linear Systems - Activity A
Simple and Compound Interest

AM1.2.3: Represent quantitative relationships using mathematical models and symbols.

AM1.2.3.1: Write the equation of a line given:

AM1.2.3.1.a: Ordered pairs.

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Points in the Coordinate Plane - Activity A
Standard Form of a Line

AM1.2.3.1.b: The slope and a point on the line.

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

AM1.2.3.1.c: 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

AM1.2.3.2: Graph linear functions:

AM1.2.3.2.a: By plotting points.

Points in the Coordinate Plane - Activity A

AM1.2.3.2.b: By finding x- and y-intercepts.

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

AM1.2.3.2.c: Using the slope-intercept form of a line.

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

AM1.2.3.2.d: Using the slope and any point on the line.

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

AM1.2.3.3: Identify the domain and range of a relation or function when given a graph, equation, table, or ordered pairs.

Cosine Function
Functions Involving Square Roots
General Form of a Rational Function
Introduction to Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Radical Functions
Rational Functions
Sine Function
Tangent Function
Using Tables, Rules and Graphs

AM1.2.3.4: Identify horizontal and vertical lines given their equations.

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

AM1.2.3.5: Determine the effect of parameter changes on the graphs of linear relations using appropriate technology.

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

AM1.2.3.6: Identify the x- and y-intercepts when given the equation 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

AM1.2.3.7: Determine the slope of a line when given a set of ordered pairs, the graph, or the equation of the line.

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

AM1.2.3.8: Graph linear inequalities and identify the boundary line and solution area.

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

AM1.2.3.9: Determine and explain the meaning of intercepts using real-world examples.

Modeling Linear Systems - Activity A
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A

AM1.2.3.10: Use direct variation to model rates of change, e.g., if income = 40 hours times rate of pay, then increasing the rate of pay increases income.

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

AM1.3: Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.

AM1.3.1: Analyze characteristics and properties of two- and three-dimensional shapes and develop mathematical arguments about geometric relationships.

AM1.3.1.1: Draw geometric objects when given specified properties, e.g., side lengths or angle measures.

Classifying Quadrilaterals - Activity A
Classifying Quadrilaterals - Activity B
Classifying Triangles
Parallelogram Conditions
Special Quadrilaterals

AM1.3.3: Solve problems using visualization, spatial reasoning, and geometric modeling.

AM1.3.3.2: Solve problems involving right triangles using the ratios for the sine, cosine, and tangent.

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

AM1.3.3.3: Solve problems using the Pythagorean Theorem.

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

AM1.3.3.4: Find missing parts of geometric figures using proportional reasoning and geometric relationships.

Classifying Quadrilaterals - Activity A
Classifying Quadrilaterals - Activity B
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

AM1.3.3.5: Solve problems using similar triangles.

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

AM1.3.3.6: Illustrate multiplication and factoring of polynomials using area models, e.g., (a + b)² or (x + b)(x + a).

Factoring Special Products
Modeling and Solving Two-Step Equations
Modeling the Factorization of x²+bx+c
Polynomials and Linear Factors

AM1.3.3.7: Factor polynomials using area models:

AM1.3.3.7.a: To identify the greatest common monomial factor.

Factoring Special Products

AM1.3.3.7.b: Of the form ax squared + bx + c when a = 1.

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

AM1.4: Students will understand and apply measurement tools, formulas, and techniques.

AM1.4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

AM1.4.1.1: Measure lengths of designated sides and calculate area and volume using the correct units.

Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

AM1.4.1.3: Express the rate of change as a ratio of two different measures.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Geometric Probability - Activity A
Part:Part and Part:Whole Ratios
Polling: Neighborhood
Similar Figures - Activity A
Similar Polygons

AM1.4.2: Determine measurements using appropriate techniques, tools, and formulas.

AM1.4.2.1: Calculate derived measures using formulas, e.g., areas and velocities.

Perimeter, Circumference, and Area - Activity B

AM1.4.2.3: Select and use an appropriate tool to measure a given attribute.

Triple Beam Balance

AM1.5: Students will draw conclusions using concepts of probability, after collecting, organizing, and analyzing a data set.

AM1.5.1: Formulate and answer questions by collecting, organizing, and analyzing data.

AM1.5.1.1: Collect, record, organize, and display a set of data.

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

AM1.5.1.2: Make predictions using a box plot, scatter plot, or histogram for a given set of data.

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

AM1.5.1.4: Interpret the correlation between two variables as positive, negative, or having no correlation.

Correlation
Solving Using Trend Lines

AM1.5.1.5: Find mean, median, mode, and range for a data set.

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

AM1.5.2: Apply basic concepts of probability.

AM1.5.2.1: Determine and express the probability of an event as a fraction, percent, ratio, or decimal.

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

AM1.5.2.2: Determine the odds of an event when given the probability, and determine the probability of an event when given the odds.

Geometric Probability - Activity A

AM1.5.2.4: Compute simple probabilities using the Fundamental Counting Principle or a tree diagram.

Binomial Probabilities
Compound Independent Events
Compound Independent and Dependent Events
Estimating Population Size
Geometric Probability - Activity A
Independent and Dependent Events
Permutations
Permutations and Combinations
Probability Simulations
Theoretical and Experimental Probability

AM1.5.2.5: Identify the probability of an event as being between zero (event not possible) and one (event certain).

Binomial Probabilities
Estimating Population Size
Geometric Probability - Activity A

2: Students will represent and analyze mathematical situations and properties using patterns, relations, functions, and algebraic symbols.

2.1: Use patterns, relations, and functions to represent mathematical situations.

2.1.1: Identify the trigonometric relationships (sine, cosine, tangent) using right triangles and express them as fractions or decimals.

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

2.1.4: Recognize the relationship between the length of a side of a triangle and the size of the angle opposite the side.

Classifying Triangles
Isosceles and Equilateral Triangles
Triangle Angle Sum - Activity A

2.1.5: Identify the effect on area or volume when changing linear dimensions.

Area of Parallelograms - Activity A
Circle: Circumference and Area
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

2.2: Evaluate, solve, and analyze mathematical situations using algebraic properties and symbols.

2.2.1: Find the angle measure in degrees given the trigonometric ratio using a calculator.

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

2.2.2: 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

2.2.3: Find missing parts of right triangles using the Pythagorean Theorem.

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

2.2.4: Find missing parts of right triangles using sine, cosine, and tangent functions and their inverses.

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

2.2.5: Solve for corresponding sides of similar figures using proportions.

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

2.2.7: Develop and graph equations using two variables to represent real-world situations, e.g., the volume of an open box made by cutting the corners from a rectangular sheet.

Modeling Linear Systems - Activity A
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

3: Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.

3.1: Analyze characteristics and properties of two- and three-dimensional shapes and develop mathematical arguments about geometric relationships.

3.1.1: Write a conditional statement and its converse, then determine the truth value of each statement.

Conditional Statement

3.1.3: Identify angle pairs as adjacent, complementary, supplementary, a linear pair, or vertical angles.

Investigating Angle Theorems - Activity A

3.1.4: Identify the medians, altitudes, and angle bisectors of a triangle and the perpendicular bisectors of the sides of a triangle.

Concurrent Lines, Medians, and Altitudes

3.1.5: Identify radius, diameter, chord, secant, arc, sector, central angle, inscribed angle, and tangent for a circle.

Chords and Arcs
Inscribing Angles

3.1.6: Differentiate between skew and parallel lines.

Investigating Parallel Lines and Planes

3.1.7: Prove lines parallel or perpendicular using slope or angle relationships.

Construct Parallel and Perpendicular Lines
Slope - Activity B

3.1.8: Prove congruency and similarity of triangles.

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

3.1.9: Identify the geometric mean formed by the altitude to the hypotenuse.

Similarity in Right Triangles

3.1.10: Classify polygons by their distinguishing characteristics.

Classifying Quadrilaterals - Activity A
Classifying Quadrilaterals - Activity B
Classifying Triangles
Parallelogram Conditions
Special Quadrilaterals

3.1.12: Draw three-dimensional objects from different perspectives using nets, cross-sections, and two-dimensional views.

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

3.2: Specify locations and describe spatial relationships using coordinate geometry.

3.2.2: Solve problems using the distance formula.

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

3.2.3: Write an equation of a line perpendicular or parallel to a line through a given point.

Point-Slope Form of a Line - Activity A

3.2.4: Verify the classifications of geometric figures using coordinate geometry to find lengths and slopes.

Classifying Quadrilaterals - Activity A
Classifying Quadrilaterals - Activity B
Classifying Triangles
Parallelogram Conditions
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Pythagorean Theorem - Activity B
Slope - Activity B
Special Quadrilaterals

3.3: Use visualization, spatial reasoning, and geometric modeling to solve problems.

3.3.2: Determine whether coplanar lines are parallel or perpendicular.

Construct Parallel and Perpendicular Lines

3.3.3: Construct/copy angles and segments, bisect angles and segments, and create perpendicular lines and parallel lines using a compass and straight edge, technology, or other manipulatives.

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

3.3.4: Identify and perform transformations, i.e., translations, rotations, reflections, and dilations, on geometric objects.

Dilations
Reflections
Rotations, Reflections and Translations
Translations

3.3.5: Tessellate a plane using reflections, translations, and rotations.

Reflections
Rotations, Reflections and Translations
Translations

3.3.6: Solve problems using geometric modeling, e.g., similar figures, diagrams, and symbolic notation.

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

3.3.: Sketch cross-sections of geometric solids.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

4: Students will understand and apply measurement tools, formulas, and techniques.

4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

4.1.1: Represent vector quantities with correct notation.

Vectors

4.1.2: Define sums and differences of vector quantities.

Vectors

4.2: Determine measurements using appropriate techniques, tools, and formulas.

4.2.2: Determine perimeter, area, surface area, lateral area, and volume for a variety of geometric shapes and objects.

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

4.2.3: Find the length of an arc and the area of a sector.

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

5: Students will draw conclusions using concepts of probability, after collecting, organizing, and analyzing a data set.

5.1: Formulate and answer questions by collecting, organizing, and analyzing data.

5.1.1: Collect, organize, and display a data set using technology or other methods.

Describing Data Using Statistics

5.1.2: Display data using a box plot, circle graph, or scatter plot.

Box-and-Whisker Plots
Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

5.2: Apply basic concepts of probability.

5.2.1: Identify geometric probabilities by performing simulations involving length or area.

Geometric Probability - Activity A
Probability Simulations

5.2.2: Solve problems using geometric probabilities.

Geometric Probability - Activity A