1: Students will understand numerical concepts and mathematical operations.

1.A: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

1.A.1: Sort numbers by their properties (e.g., prime, composite, square, square root).

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Square Roots

1.B: Understand the meaning of operations and how they relate to one another.

1.B.1: Use real number properties (e.g., commutative, associative, distributive) to perform various computational procedures.

Adding Real Numbers

1.B.2: Perform arithmetic operations and their inverses (e.g., addition/subtraction, multiplication/division, square roots of perfect squares, cube roots of perfect cubes) on real numbers.

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

1.B.3: Find roots of real numbers using calculators.

Operations with Radical Expressions

1.C: Compute fluently and make reasonable estimates.

1.C.1: Formulate algebraic expressions that include real numbers to describe and solve real-world problems.

Using Algebraic Equations
Using Algebraic Expressions

1.C.2: Use a variety of computational methods to estimate quantities involving real numbers.

Estimating Population Size
Estimating Sums and Differences

1.C.4: Use real number properties to perform various computational procedures and explain how they were used.

Adding Real Numbers

1.C.5: Perform and explain computations with rational numbers, pi, and first-degree algebraic expressions in one variable in a variety of situations.

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

1.C.6: Select and use appropriate forms of rational numbers to solve real-world problems including those involving proportional relationships.

Estimating Population Size
Improper Fractions and Mixed Numbers

1.C.9: Estimate answers and use formulas to solve application problems involving surface area and volume.

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

2: Students will understand algebraic concepts and applications.

2.A: Understand patterns, relations, and functions.

2.A.1: Move between numerical, tabular, and graphical representations of linear relationships.

Introduction to Functions
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Algebraic Equations
Using Tables, Rules and Graphs

2.A.2: Use variables to generalize patterns and information presented in tables, charts, and graphs:

2.A.2.a: graph linear functions noting that the vertical change per unit of horizontal change (the slope of the graph) is always the same

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

2.A.2.b: plot the values of quantities whose ratios are always the same, fit a line to the plot, and understand that the slope of the line equals the quantities

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

2.B: Represent and analyze mathematical situations and structures using algebraic symbols.

2.B.1: Demonstrate the difference between an equation and an expression.

Using Algebraic Equations

2.B.2: Solve two-step linear equations and inequalities in one variable with rational solutions.

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

2.B.4: Demonstrate understanding of the relationships between ratios, proportions, and percents and solve for a missing term in a proportion.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part:Part and Part:Whole Ratios
Polling: Neighborhood
Proportions and Common Multipliers

2.B.5: Graph solution sets of linear equations in two variables on the coordinate plane.

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

2.B.6: Formulate and solve problems involving simple linear relationships, find percents of a given number, variable situations, and unknown quantities.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations
Using Algebraic Equations

2.B.7: Use symbols, variables, expressions, inequalities, equations, and simple systems of equations to represent problem situations that involve variables or unknown quantities.

Using Algebraic Equations
Using Algebraic Expressions

2.C: Use mathematical models to represent and understand quantitative relationships.

2.C.1: Generate different representations to model a specific numerical relationship given one representation of data (e.g., a table, a graph, an equation, a verbal description).

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

2.D: Analyze changes in various contexts.

2.D.1: Use graphs, tables, and algebraic representations to make predictions and solve problems that involve change.

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

2.D.2: Estimate, find, and justify solutions to problems that involve change using tables, graphs, and algebraic expressions.

Estimating Population Size
Estimating Sums and Differences

2.D.4: Solve multi-step problems that involve changes in rate, average speed, distance, and time.

Distance Formula - Activity A
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A

2.D.5: Analyze problems that involve change by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing, and observing patterns.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Finding Patterns

2.D.6: Generalize a pattern of change using algebra and show the relationship among the equation, graph, and table of values.

Linear Functions
Using Tables, Rules and Graphs

3: Students will understand geometric concepts and applications.

3.A: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematics arguments about geometric relationships.

3.A.1: Recognize, classify, and discuss properties of all geometric figures including point, line, and plane.

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

3.A.2: Identify arc, chord, and semicircle and explain their attributes.

Chords and Arcs

3.A.3: Use the Pythagorean theorem and its converse to find the missing side of a right triangle and the lengths of the other line segments.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Sine and Cosine Ratios - Activity A

3.B: Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

3.B.1: Represent, formulate, and solve distance and geometry problems using the language and symbols of algebra and the coordinate plane and space (e.g., ordered triplets).

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

3.C: Apply transformations and use symmetry to analyze mathematical situations.

3.C.1: Describe the symmetry of three-dimensional figures.

Holiday Snowflake Designer

3.C.2: Describe and perform single and multiple transformations that include rotation, reflection, translation, and dilation (i.e., shrink or magnify) to two-dimensional figures.

Dilations
Reflections
Rotations, Reflections and Translations
Translations

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

3.D.1: Understand angle relationships formed by parallel lines cut by a transversal.

Investigating Angle Theorems - Activity A

3.D.2: Recognize and apply properties of corresponding parts of similar and congruent triangles and quadrilaterals.

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

3.D.3: Represent and solve problems relating to size, shape, area, and volume using geometric models.

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

3.D.4: Develop and use formulas for area, perimeter, circumference, and volume.

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

3.D.5: Construct two-dimensional patterns for three-dimensional models (e.g., cylinders, prisms, cones).

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

4: Students will understand measurement systems and applications.

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

4.A.1: Understand the concept of volume and use the appropriate units in common measuring systems (e.g., cubic centimeter, cubic inch, cubic yard) to compute the volume of rectangular solids.

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

4.B: Apply appropriate techniques, tools, and formulas to determine measurements.

4.B.1: Use ratios and proportions to measure hard-to-measure objects.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Proportions and Common Multipliers

4.B.3: Use proportional relationships in similar shapes to find missing measurements.

Perimeters and Areas of Similar Figures

4.B.4: Apply strategies to determine the surface area and volume of prisms, pyramids, and cylinders.

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

4.B.6: Estimate volume in cubic units.

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

4.B.7: Solve simple problems involving rates and derived measurements for such properties as velocity and density.

Density Laboratory
Determining Density via Water Displacement
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

5: Students will understand how to formulate questions, analyze data, and determine probabilities.

5.A: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

5.A.1: Represent two numerical variables on a plot, describe how the data points are distributed, and identify relationships that exist between the two variables.

Solving Using Trend Lines

5.A.3: Organize, analyze, and display appropriate quantitative and qualitative data to address specific questions including:

5.A.3.a: frequency distributions

Describing Data Using Statistics
Histograms
Line Plots
Mean, Median and Mode
Populations and Samples
Scatter Plots - Activity A
Stem-and-Leaf Plots

5.A.3.b: plots

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

5.A.3.c: histograms

Describing Data Using Statistics
Histograms

5.A.3.d: bar, line, and pie graphs

Describing Data Using Statistics

5.A.3.e: diagram and pictorial displays

Describing Data Using Statistics

5.A.3.f: charts and tables

Describing Data Using Statistics
Histograms

5.A.4: Select the appropriate measure of central tendency to describe a set of data for a particular problem situation.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

5.A.5: Simulate an event selecting and using different models.

Probability Simulations

5.B: Select and use appropriate statistical methods to analyze data.

5.B.3: Analyze data to make decisions and to develop convincing arguments from data displayed in a variety of formats that include:

5.B.3.d: scatter plots

Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

5.B.4: Interpret and analyze data from graphical representations and draw simple conclusions (e.g., line of best fit).

Correlation
Solving Using Trend Lines

5.B.6: Use appropriate central tendency and spread as a means for effective decision-making in analyzing data and outliers.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

5.B.7: Identify simple graphic misrepresentations and distortions of sets of data (e.g., unequal interval sizes, omission of parts of axis range, scaling).

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

5.B.8: Use appropriate technology to display data as lists, tables, matrices, graphs, and plots and to analyze the relationships of variables in the data displayed.

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

5.C: Develop and evaluate inferences and predictions that are based on data.

5.C.1: Describe how changes in scale, intervals, or categories influence arguments for a particular interpretation of the data.

Correlation

5.C.2: Describe how reader bias, measurement errors, and display distortion can affect the interpretation of data, predictions, and inferences based on data.

Box-and-Whisker Plots
Histograms
Polling: Neighborhood
Scatter Plots - Activity A

5.C.3: Conduct simple experiments and/or simulations, record results in charts, tables, or graphs, and use the results to draw conclusions and make predictions.

Histograms
Probability Simulations

5.C.4: Compare expected results with experimental results and information used in predictions and inferences.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
Polling: City
Probability Simulations
Theoretical and Experimental Probability

5.D: Understand and apply basic concepts of probability.

5.D.2: Design and use an appropriate simulation to estimate the probability of a real-world event (e.g., disk toss, cube toss).

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
Probability Simulations

5.D.3: Explain the relationship between probability and odds and calculate the odds of a desired outcome in a simple experiment.

Geometric Probability - Activity A

5.D.4: Use theoretical or experimental probability to make predictions about real-world events.

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

5.D.5: Use probability to generate convincing arguments, draw conclusions, and make decisions in a variety of situations.

Geometric Probability - Activity A

5.D.6: Understand that the probability of two unrelated events occurring is the sum of the two individual possibilities and that the probability of one event following another, in independent trials, is the product of the two probabilities.

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