1: Calculations and Estimations

1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

1.1.2: Apply proportions to solve problems

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

1.1.3: Locate 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

1.1.4: Apply equivalent forms of rational number (including percents) to solve problems

Improper Fractions and Mixed Numbers
Percents, Fractions and Decimals

1.2: Compute fluently and make reasonable estimates

1.2.1: Develop and analyze algorithms and compute with rational numbers

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

1.2.2: Use order of operation rules, including exponents

Order of Operations

1.2.3: Develop and use strategies to estimate the results of rational number computations and judge the reasonableness of results

Estimating Population Size
Estimating Sums and Differences

1.2.4: Estimate square roots of whole numbers less than 100 and cube roots of whole numbers less than 1000 between two whole numbers

Square Roots

1.3: Understand meanings of operations and how they relate to one another

1.3.1: Demonstrate the meaning of square roots as lengths of the sides of squares and cube roots as lengths of edges of cubes

Square Roots

1.3.2: Use the inverse operations of squares and square roots to solve problems and check solutions

Square Roots

1.3.3: Apply the associative, commutative, and distributive properties to simplify computations with rational numbers

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

2: Statistics and Probability

2.1: Select and use appropriate statistical methods to analyze data

2.1.1: Choose appropriate measures of central tendencies to describe given or derived data

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

2.1.2: Estimate a line of best fit on a scatter plot and informally explain the meaning of the line and use the line to make predictions

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

2.2: Understand and apply basic concepts of probability

2.2.2: Apply theoretical probability to determine if an event or game is fair or unfair and pose and evaluate modifications to change the fairness

Geometric Probability - Activity A
Probability Simulations
Theoretical and Experimental Probability

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

2.3.2: Represent bivariate data in a scatter plot and identify relationships in the plot

Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

3: Algebraic Relationships

3.1: Understand patterns, relations, and functions

3.1.1: Represent, analyze and determine rules for finding patterns relating to linear functions, non-linear functions and arithmetic sequences with tables, graphs, and symbolic rules

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

3.1.2: Identify functions as linear or nonlinear from tables, graphs, or equations and contrast their properties

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

3.1.3: Interpret the meaning of the rate of change and y-intercept of a linear relationship in a problem setting

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-Intercept Form of a Line - Activity A

3.2: Represent and analyze mathematical situations and structures using algebraic symbols

3.2.1: Represent and solve equations of the form ax+b=c or k(ax+ b) = c

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

3.2.2: Approximate solutions of systems of linear equations from a graph

Modeling Linear Systems - Activity A

3.2.3: Recognize and generate equivalent symbolic forms for algebraic expressions with an emphasis on linear relationships

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

3.2.4: Evaluate algebraic expressions and formulas, including expressions involving exponents and parentheses, by substituting rational numbers

Order of Operations

3.2.5: Translate between and interpret linear relationships represented by words, symbols, tables, and graphs

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Algebraic Equations
Using Algebraic Expressions
Using Tables, Rules and Graphs

3.2.6: Determine the slope and x- and y-intercepts given the graph of a linear equation

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

3.2.7: Graph a linear equation given the slope and an initial value (y-intercept)

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

3.2.8: Recognize and graph the solutions of linear inequalities on a coordinate plane

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

3.2.9: Graph simple quadratic equations (y=kx² or y=kx²+b) by generating a table of values for a given equation

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

3.2.10: Identify and describe the effects of changing the slope or y-intercept on the graph of a linear relationship of the form y=kx or y=kx+b

Defining a Line with Two Points
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

3.3: Use mathematical models to represent and understand quantitative relationships

3.3.1: Model situations, make predictions and inferences, and solve problems using linear equations and inequalities

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

3.3.2: Recognize and represent direct variation using tables, graphs, and equations

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

3.3.3: Determine when data represented in a table or graph represents a linear or non-linear relationship

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

3.4: Analyze change in various contexts

3.4.1: Understand that the rate of change in a linear function is constant and is equal to the slope of its graphed line

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

3.4.3: Analyze the nature of change in quantities in linear relationships represented by graphs, tables, or formulas

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

4: Measurement

4.2: Apply appropriate techniques, tools, and formulas to determine measurements

4.2.1: Calculate and analyze changes in area and volume in relation to changes in linear measures of figures

Area of Parallelograms - Activity A
Prisms and Cylinders - Activity A

4.2.2: Analyze how changes in surface area and volume of a solid affect the dimensions of the solid

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

4.2.3: Solve problems involving rates and derived measurements for such attributes as speed, velocity, and density

Density Experiment: Slice and Dice
Density Laboratory
Determining Density via Water Displacement

4.2.4: Determine actual distances from scale drawings, blueprints, and maps and solve problems involving scale factors

Dilations
Similar Figures - Activity A
Similar Polygons

5: Geometry

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

5.1.1: Determine defining properties that characterize classes of triangles including side and angle measurements and their component parts (e.g., angle bisectors, altitudes, medians)

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

5.1.2: Use proportional reasoning, drawings, models or technology to demonstrate similarity and congruence of polygons with an emphasis on triangles

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

5.1.3: Determine the measures of corresponding sides and angles of congruent and similar triangles and their component parts

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

5.1.4: Use similar triangles to measure distances indirectly (e.g., flagpole and shadow)

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

5.1.5: Use the Pythagorean theorem to determine if triangles are right triangles and determine the lengths of missing sides in right triangles

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

5.1.6: Investigate triangles and their components parts and draw conclusion about their properties

Classifying Triangles

5.1.7: Create and critique inductive and deductive arguments to verify the pythagorean theorem

Biconditional Statement
Conditional Statement
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

5.1.8: Justify conclusions that two triangles are or are not congruent and are or are not similar

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

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

5.2.1: Draw to scale two-dimensional representations of rectangular prisms and triangles with specified side lengths or angle measures

Classifying Triangles
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders

5.2.2: Construct and read drawings and models made to scale

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

5.3: Specify locations and describe spatial relationships using coordinate geometry and other representational systems

5.3.1: On a coordinate plane, determine the relative placement (e.g., intersecting, parallel, perpendicular) of two lines

Construct Parallel and Perpendicular Lines
Points in the Coordinate Plane - Activity A

5.3.2: Determine the distance between two points on a coordinate graph using right triangles and the Pythagorean theorem

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

5.4: Apply transformations and use symmetry to analyze mathematical situations

5.4.1: Classify transformations based on whether they produce congruent or similar non-congruent figures (e.g., compare pairs of shapes (where the image has been transformed, identify the type of translation and use angles, diagonals and lines of symmetry to determine congruence)

Classifying Quadrilaterals - Activity A
Constructing Congruent Segments and Angles
Dilations
Holiday Snowflake Designer
Parallelogram Conditions
Perimeters and Areas of Similar Figures
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
Similar Polygons
Special Quadrilaterals

5.4.2: Identify and sketch the figure that is the result of a given rotation, translation, reflection or dilation or a combination of two transformations

Dilations
Reflections
Rotations, Reflections and Translations
Translations

5.4.3: Know properties of dilated images

Dilations

5.4.4: Determine the effects of a transformation on linear and area measurements of the original figure

Dilations
Perimeter, Circumference, and Area - Activity B
Reflections
Rotations, Reflections and Translations