1: Number Sense and Operations

1.1: Understand and apply numbers, ways of representing numbers, the relationships among numbers and different number systems.

1.1.PO 3: Distinguish between finite and infinite sets of numbers.

Arithmetic and Geometric Sequences
Geometric Sequences

2: Data Analysis, Probability, and Discrete Mathematics

2.1: Understand and apply data collection, organization and representation to analyze and sort data.

2.1.PO 2: Organize collected data into an appropriate graphical representation.

Box-and-Whisker Plots
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

2.1.PO 3: Display data as lists, tables, matrices, and plots.

Scatter Plots - Activity A

2.1.PO 4: Construct equivalent displays of the same data.

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

2.1.PO 6: Identify which of the measures of central tendency is most appropriate in a given situation.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

2.1.PO 7: Make reasonable predictions based upon linear patterns in data sets or scatter plots.

Linear Functions
Scatter Plots - Activity A

2.1.PO 10: Apply the concepts of mean, median, mode, range, and quartiles to summarize data sets.

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

2.1.PO 12: Recognize and explain the impact of interpreting data (making inferences or drawing conclusions) from a biased sample.

Correlation

2.1.PO 13: Draw a line of best fit for a scatter plot.

Correlation
Lines of Best Fit Using Least Squares - Activity A
Solving Using Trend Lines

2.1.PO 14: Determine whether a displayed data has positive, negative, or no correlation.

Correlation
Solving Using Trend Lines

2.1.PO 17: Identify differences between biased and unbiased samples.

Polling: Neighborhood

2.2: Understand and apply the basic concepts of probability.

2.2.PO 1: Find the probability that a specific event will occur, with or without replacement.

Binomial Probabilities
Geometric Probability - Activity A

2.2.PO 2: Determine simple probabilities related to geometric figures.

Geometric Probability - Activity A
Probability Simulations
Theoretical and Experimental Probability

2.2.PO 4: Record the data from performing a grade level appropriate probability experiment.

Geometric Probability - Activity A
Probability Simulations

2.2.PO 5: Compare the outcome of an experiment to predictions made prior to performing the experiment.

Populations and Samples

2.2.PO 6: Distinguish between independent and dependent events.

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

2.2.PO 7: Compare the results of two repetitions of the same grade level appropriate probability experiment.

Geometric Probability - Activity A
Populations and Samples
Probability Simulations

2.3: Understand and demonstrate the systematic listing and counting of possible outcomes.

2.3.PO 1: Determine the number of possible outcomes for a contextual event using a chart, a tree diagram, or the counting principle.

Binomial Probabilities
Histograms
Permutations
Permutations and Combinations

2.3.PO 2: Determine when to use combinations versus permutations in counting objects.

Binomial Probabilities
Permutations
Permutations and Combinations

2.3.PO 3: Use combinations or permutations to solve contextual problems.

Binomial Probabilities
Permutations
Permutations and Combinations

3: Patterns, Algebra, and Functions

3.1: Identify patterns and apply pattern recognition to reason mathematically.

3.1.PO 1: Communicate a grade level appropriate iterative or recursive pattern, using symbols or numbers.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

3.1.PO 2: Find the nth term of an iterative or recursive pattern.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

3.1.PO 3: Evaluate problems using basic recursion formulas.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

3.2: Describe and model functions and their relationships.

3.2.PO 1: Determine if a relationship is a function, given a graph, table, or set of ordered pairs.

Cosine Function
Cubic Function Activity
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
Tangent Function
Using Tables, Rules and Graphs

3.2.PO 2: Describe a contextual situation that is depicted by a given graph.

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

3.2.PO 3: Identify a graph that models a given real-world situation.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Modeling Linear Systems - Activity A

3.2.PO 4: Sketch a graph that models a given contextual situation.

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

3.2.PO 5: Determine domain and range for a function.

Functions Involving Square Roots
Introduction to Functions

3.2.PO 6: Determine the solution to a contextual maximum / minimum problem, given the graphical representation.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

3.2.PO 7: Express the relationship between two variables using tables/ matrices, equations, or graphs.

Using Algebraic Equations
Using Tables, Rules and Graphs

3.2.PO 8: Interpret the relationship between data suggested by tables/ matrices, equations, or graphs.

Using Tables, Rules and Graphs

3.2.PO 9: Determine from two linear equations whether the lines are parallel, perpendicular, coincident, or intersecting but not perpendicular.

Construct Parallel and Perpendicular Lines

3.3: Represent and analyze mathematical situations and structures using algebraic representations.

3.3.PO 1: Evaluate algebraic expressions, including absolute value and square roots.

Simplifying Radicals - Activity A
Square Roots

3.3.PO 3: Multiply and divide monomial expressions with integral exponents.

Dividing Exponential Expressions
Multiplying Exponential Expressions
Simplifying Radicals - Activity A

3.3.PO 4: Translate a written expression or sentence into a mathematical expression or sentence.

Using Algebraic Equations
Using Algebraic Expressions

3.3.PO 5: Translate a sentence written in context into an algebraic equation involving multiple operations.

Using Algebraic Equations
Using Algebraic Expressions

3.3.PO 6: Write a linear equation for a table of values.

Slope-Intercept Form of a Line - Activity A
Using Algebraic Equations
Using Algebraic Expressions
Using Tables, Rules and Graphs

3.3.PO 7: Write a linear algebraic sentence that represents a data set that models a contextual situation.

Using Algebraic Equations
Using Algebraic Expressions

3.3.PO 8: Solve linear (first degree) equations in one variable (may include absolute value).

Solving Equations By Graphing Each Side

3.3.PO 9: Solve linear inequalities in one variable.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

3.3.PO 10: Write an equation of the line given: two points on the line, the slope and a point on the line, or the graph 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

3.3.PO 11: Solve an algebraic proportion.

Estimating Population Size

3.3.PO 12: Solve systems of linear equations in two variables (integral coefficients and rational solutions).

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

3.3.PO 15: Simplify square roots and cube roots with monomial radicands (including those with variables) that are perfect squares or perfect cubes.

Simplifying Radicals - Activity A

3.3.PO 16: Solve square root radical equations involving only one radical.

Square Roots

3.3.PO 17: Solve quadratic equations.

Roots of a Quadratic

3.3.PO 18: Identify the sine, cosine, and tangent ratios of the acute angles of a right triangle.

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

3.4: Analyze change in a variable over time and in various contexts.

3.4.PO 1: Determine slope, x-, and y-intercepts of a linear equation.

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

3.4.PO 2: Solve formulas for specified variables.

Solving Formulas for any Variable

4: Geometry and Measurement

4.1: Analyze the attributes and properties of two and three dimensional shapes and develop mathematical arguments about their relationships.

4.1.PO 1: Identify the attributes of special triangles. (isosceles, equilateral, right)

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

4.1.PO 2: Identify the hierarchy of quadrilaterals.

Classifying Quadrilaterals - Activity B

4.1.PO 3: Make a net to represent a three-dimensional object.

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

4.1.PO 4: Make a three-dimensional model from a net.

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

4.1.PO 6: Solve problems related to complementary, supplementary, or congruent angle concepts.

Investigating Angle Theorems - Activity A

4.1.PO 7: Solve problems by applying the relationship between circles, angles, and intercepted arcs.

Chords and Arcs
Inscribing Angles

4.1.PO 8: Solve problems by applying the relationship between radii, diameters, chords, tangents or secants.

Chords and Arcs

4.1.PO 9: Solve problems using the triangle inequality property.

Triangle Inequalities

4.1.PO 11: Determine when triangles are congruent by applying SSS, ASA, AAS or SAS.

Congruence in Right Triangles
Proving Triangles Congruent
Triangle Angle Sum - Activity A

4.1.PO 12: Determine when triangles are similar by applying SAS, SSS, or AA similarity postulates.

Isosceles and Equilateral Triangles
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons
Triangle Angle Sum - Activity A

4.1.PO 13: Construct a triangle congruent to a given triangle.

Congruence in Right Triangles
Proving Triangles Congruent

4.1.PO 14: Solve contextual situations using angle and side length relationships.

Classifying Triangles

4.2: Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.

4.2.PO 1: Sketch the planar figure that is the result of two or more transformations.

Dilations
Reflections
Rotations, Reflections and Translations

4.2.PO 2: Identify the properties of the planar figure that is the result of two or more transformations.

Dilations
Reflections
Rotations, Reflections and Translations

4.2.PO 3: Determine the new coordinates of a point when a single transformation is performed on a planar geometric figure.

Rotations, Reflections and Translations

4.2.PO 4: Determine whether a given pair of figures on a coordinate plane represents a translation, reflection, rotation, or dilation.

Dilations
Reflections
Rotations, Reflections and Translations
Translations

4.2.PO 5: Classify transformations based on whether they produce congruent or similar figures.

Constructing Congruent Segments and Angles
Dilations
Perimeters and Areas of Similar Figures
Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
Similar Polygons

4.2.PO 6: Determine the effects of a single transformation on linear or area measurements of a planar geometric figure.

Area of Parallelograms - Activity A
Dilations
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Reflections
Rotations, Reflections and Translations

4.3: Specify and describe spatial relationships using coordinate geometry and other representational systems.

4.3.PO 1: Graph a quadratic equation with lead coefficient equal to one.

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

4.3.PO 2: Graph a linear equation in two variables.

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

4.3.PO 3: Graph a linear inequality in two variables.

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Systems of Linear Inequalities (Slope-intercept form) - Activity A

4.3.PO 4: Determine the solution to a system of equations in two variables from a given graph.

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

4.3.PO 6: Determine changes in the graph of a linear function when constants and coefficients in its equation are varied.

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

4.3.PO 7: Determine the distance between two points in the coordinate system.

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

4.4: Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.

4.4.PO 1: Calculate the area of geometric shapes composed of two or more geometric figures.

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

4.4.PO 2: Calculate the volumes of three-dimensional geometric figures.

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

4.4.PO 3: Calculate the surface areas of three-dimensional geometric figures.

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

4.4.PO 4: Compare perimeter, area, or volume of figures when dimensions are changed.

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

4.4.PO 6: Find the area of a sector of a circle.

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

4.4.PO 7: Solve for missing measures in a pyramid. (i.e., slant height, height)

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

4.4.PO 8: Find the sum of the interior and exterior angles of a polygon.

Polygon Angle Sum - Activity A
Triangle Angle Sum - Activity A

4.4.PO 9: Solve scale factor problems using ratios and proportions.

Beam to Moon (Ratios and Proportions)
Dilations
Estimating Population Size
Part:Part and Part:Whole Ratios
Perimeters and Areas of Similar Figures
Polling: Neighborhood
Similar Figures - Activity A
Similar Polygons

4.4.PO 10: Solve applied problems using similar triangles.

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

5: Structure and Logic

5.1: Use reasoning to solve mathematical problems in contextual situations.

5.1.PO 2: Determine whether a given procedure for solving an equation is valid.

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

5.1.PO 3: Determine whether a given procedure for solving a linear inequality is valid.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

5.2: Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions and recognize their applications.

5.2.PO 4: Analyze assertions related to a contextual situation by using principles of logic.

Biconditional Statement
Conditional Statement

5.2.PO 7: Create inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Biconditional Statement
Conditional Statement
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Perimeters and Areas of Similar Figures
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Similar Figures - Activity A
Similar Polygons

5.2.PO 8: Critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Biconditional Statement
Conditional Statement
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Perimeters and Areas of Similar Figures
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Similar Figures - Activity A
Similar Polygons

5.2.PO 13: Construct a simple formal or informal deductive proof.

Biconditional Statement
Conditional Statement
Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

5.2.PO 14: Verify characteristics of a given geometric figure using coordinate formulas such as distance, mid-point, and slope to confirm parallelism, perpendicularity, and congruency.

Congruence in Right Triangles
Distance Formula - Activity A
Proving Triangles Congruent
Slope - Activity B