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 1: Locate rational numbers on a number line.

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

1.2: Understand and apply numerical operations and their relationship to one another.

1.2.PO 4: Determine the square root of an integer.

Square Roots

1.2.PO 6: Apply grade level appropriate properties to assist in computation.

Adding Real Numbers

1.2.PO 7: Apply the symbols "square root of" to represent square root, "±" to represent roots, "{}" as grouping symbols.

Square Roots

1.2.PO 9: Calculate the missing value in a percentage problem.

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents and Proportions

1.2.PO 11: Simplify numerical expressions using the order of operations with grade appropriate operations on number sets.

Order of Operations

1.3: Use estimation strategies reasonably and fluently.

1.3.PO 2: Use estimation to verify the reasonableness of a calculation. (e.g., Is 32 the square root of 64?)

Square Roots

1.3.PO 3: Express answers to the appropriate place or degree of precision. (e.g., time and money)

Triple Beam Balance

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: Construct box and whisker plots.

Box-and-Whisker Plots

2.1.PO 3: Determine the appropriate type of graphical display for a given data set.

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

2.1.PO 4: Interpret box-and-whisker plots, circle graphs and scatter plots.

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

2.1.PO 5: Answer questions based on box-and-whisker plots, circle graphs and scatter plots.

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

2.1.PO 6: Solve problems in contextual situations using the mean, median, mode, and range of a given data set.

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

2.1.PO 8: Compare trends in data related to the same investigation.

Populations and Samples
Solving Using Trend Lines

2.1.PO 9: Solve contextual problems using scatter plots, box-and-whiskers plots, and double line graphs of continuous data.

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

2.1.PO 11: Identify 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 12: Distinguish between causation and correlation.

Correlation
Solving Using Trend Lines

2.2: Understand and apply the basic concepts of probability.

2.2.PO 1: Determine the probability that a specific event will occur in a 2-stage probability experiment.

Geometric Probability - Activity A

2.2.PO 2: Solve contextual situations using probability. (e.g., If the probability of Michelle making a free throw is 0.25, what is the probability that she will make three free throws in a row?)

Geometric Probability - Activity A

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 all possible outcomes involving the combination of two or more sets of objects. (e.g. If you roll a 6 sided number cube 4 times how many possible outcomes are possible?)

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: Extend a grade level appropriate iterative or recursive pattern.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

3.1.PO 3: Solve grade level appropriate iterative or recursive pattern problems.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

3.2: Describe and model functions and their relationships.

3.2.PO 1: Describe the rule used in a simple grade level appropriate function. (e.g., T-chart, input/output model)

Introduction to Functions
Linear Functions
Using Tables, Rules and Graphs

3.2.PO 2: Distinguish between linear and nonlinear functions, given graphic examples.

Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Linear Functions
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
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

3.2.PO 3: Determine whether a graph or table are related to a given an equation of the form y=ax² where ‘a’ is a natural number.

Linear Functions
Parabolas - Activity A
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

3.2.PO 4: Identify independent and dependent variables for a contextual situation.

Introduction to Functions

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

3.3.PO 2: Use variables in contextual situations.

Using Algebraic Equations

3.3.PO 3: Translate a written sentence or phrase into an algebraic equation or expression and vice versa. (e.g., Three less than twice a number is 2n-3.)

Using Algebraic Equations
Using Algebraic Expressions

3.3.PO 4: Translate a sentence written in context into an algebraic equation involving two operations.

Using Algebraic Equations
Using Algebraic Expressions

3.3.PO 5: Translate a contextual situation into an algebraic inequality. (e.g., Joe earns more than $5.00 an hour; therefore, x > 5)

Using Algebraic Equations
Using Algebraic Expressions

3.3.PO 6: Identify an equation or inequality that represents a contextual situation.

Using Algebraic Equations
Using Algebraic Expressions

3.3.PO 7: Solve one-step equations with rational numbers as coefficients or as solutions.

Modeling One-Step Equations - Activity A

3.3.PO 8: Solve one-step equations that model contextual situations.

Modeling One-Step Equations - Activity A

3.3.PO 9: Solve two-step equations with rational coefficients and integer solutions. (e.g., 3x + 5 = 11, 4x – 20 = 8)

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

3.3.PO 10: Graph an inequality on a number line.

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

3.3.PO 11: Solve a simple algebraic proportion.

Estimating Population Size

3.3.PO 12: Solve applied problems using the Pythagorean theorem.

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

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

3.4.PO 1: Identify the slope of a line as the rate of change. (the ratio of rise over run)

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

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: Draw a model that demonstrates basic geometric relationships such as parallelism, perpendicularity, similarity/ proportionality, and congruence.

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

4.1.PO 2: Draw three-dimensional figures by applying properties of each. (e.g., parallelism, perpendicularity and congruency)

Classifying Triangles

4.1.PO 3: Recognize the three-dimensional figure represented by a net.

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

4.1.PO 4: Represent the surface area of rectangular prisms and cylinders as the area of their net.

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

4.1.PO 6: Identify the properties of angles created by a transversal intersecting two parallel lines (e.g., corresponding angles are congruent).

Investigating Angle Theorems - Activity A

4.1.PO 7: Recognize the relationship between inscribed angles and intercepted arcs.

Chords and Arcs
Inscribing Angles

4.1.PO 10: Identify corresponding angles of similar polygons as congruent and sides as proportional.

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

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

4.2.PO 1: Identify the planar geometric figure that is the result of a given rigid transformation.

Dilations
Reflections
Rotations, Reflections and Translations

4.2.PO 2: Model a simple transformation on a coordinate grid. (e.g. translate right four units and down two units)

Rotations, Reflections and Translations
Translations

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

4.3.PO 1: Use a table of values to graph a linear equation.

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

4.3.PO 2: Determine the midpoint given two points on a number line.

Real Number Line - Activity A

4.3.PO 3: Determine the distance between two points on a number line.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Real Number Line - Activity A

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

4.4.PO 1: Solve problems for the area of a trapezoid.

Perimeter, Circumference, and Area - Activity B

4.4.PO 2: Solve problems involving the volume of rectangular prisms and cylinders.

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

4.4.PO 3: Calculate the surface area of rectangular prisms or cylinders.

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

4.4.PO 4: Identify rectangular prisms and cylinders having the same volume.

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

4.4.PO 5: Find the measure of a missing interior angle in a triangle or quadrilateral.

Area of Parallelograms - Activity A
Triangle Angle Sum - Activity A

4.4.PO 6: Solve problems using ratios and proportions, given the scale factor.

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

4.4.PO 7: Calculate the length of a side given two similar triangles.

Estimating Population Size
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 1: Describe how to use a proportion to solve a problem in context.

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

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

5.2.PO 1: Solve a logic problem given the necessary information.

Biconditional Statement
Conditional Statement

5.2.PO 2: Identify simple valid arguments using if...then statements. (e.g., All squares are rectangles. If quadrilateral ABCD is a rectangle, is it a square?)

Special Quadrilaterals

5.2.PO 4: Verify the Pythagorean theorem using an area dissection argument.

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