2.1.8: Numbers, Number Systems and Number Relationships

2.1.8.A: Represent and use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, exponents, scientific notation, square roots).

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

2.1.8.B: Simplify numerical expressions involving exponents, scientific notation and using order of operations.

Order of Operations

2.1.8.C: Distinguish between and order rational and irrational numbers.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers

2.1.8.D: Apply ratio and proportion to mathematical problem situations involving distance, rate, time and similar triangles.

Beam to Moon (Ratios and Proportions)
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Estimating Population Size
Part:Part and Part:Whole Ratios
Polling: Neighborhood
Proportions and Common Multipliers

2.1.8.E: Simplify and expand algebraic expressions using exponential forms.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

2.1.8.F: Use the number line model to demonstrate integers and their applications.

Comparing and Ordering Integers
Real Number Line - Activity A

2.1.8.G: Use the inverse relationships between addition, subtraction, multiplication, division, exponentiation and root extraction to determine unknown quantities in equations.

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

2.2.8: Computation and Estimation

2.2.8.A: Complete calculations by applying the order of operations.

Order of Operations

2.2.8.B: Add, subtract, multiply and divide different kinds and forms of rational numbers including integers, decimal fractions, percents and proper and improper fractions.

Adding Real Numbers
Adding and Subtracting Integers
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Order of Operations
Sums and Differences with Decimals

2.3.8: Measurement and Estimation

2.3.8.A: Develop formulas and procedures for determining measurements (e.g., area, volume, distance).

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

2.3.8.: B. Solve rate problems (e.g., rate X time = distance, principal X interest rate = interest).

Simple and Compound Interest

2.3.8.D: Estimate, use and describe measures of distance, rate, perimeter, area, volume, weight, mass and angles.

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

2.3.8.E: Describe how a change in linear dimension of an object affects its perimeter, area and volume.

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

2.3.8.F: Use scale measurements to interpret maps or drawings.

Dilations
Similar Figures - Activity A
Similar Polygons

2.3.8.G: Create and use scale models.

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

2.6.8: Statistics and Data Analysis

2.6.8.A: Compare and contrast different plots of data using values of mean, median, mode, quartiles and range.

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

2.6.8.C: Fit a line to the scatter plot of two quantities and describe any correlation of the variables.

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

2.6.8.D: Design and carry out a random sampling procedure.

Polling: Neighborhood

2.6.8.E: Analyze and display data in stem-and- leaf and box-and-whisker plots.

Box-and-Whisker Plots
Stem-and-Leaf Plots

2.7.8: Probability and Predictions

2.7.8.A: Determine the number of combinations and permutations for an event.

Permutations
Permutations and Combinations

2.7.8.B: Present the results of an experiment using visual representations (e.g., tables, charts, graphs).

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

2.7.8.D: Compare and contrast results from observations and mathematical models.

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

2.7.8.E: Make valid inferences, predictions and arguments based on probability.

Estimating Population Size
Geometric Probability - Activity A

2.8.8: Algebra and Functions

2.8.8.A: Apply simple algebraic patterns to basic number theory and to spatial relations

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

2.8.8.B: Discover, describe and generalize patterns, including linear, exponential and simple quadratic relationships.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Exponential Functions - Activity A
Finding Patterns
Geometric Sequences
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

2.8.8.C: Create and interpret expressions, equations or inequalities that model problem situations.

Using Algebraic Equations

2.8.8.E: Select and use a strategy to solve an equation or inequality, explain the solution and check the solution for accuracy.

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

2.8.8.F: Solve and graph equations and inequalities using scientific and graphing calculators and computer spreadsheets.

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - 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

2.8.8.G: Represent relationships with tables or graphs in the coordinate plane and verbal or symbolic rules.

Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Introduction to Functions
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 Algebraic Equations
Using Tables, Rules and Graphs

2.8.8.H: Graph a linear function from a rule or table.

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

2.8.8.I: Generate a table or graph from a function and use graphing calculators and computer spreadsheets to graph and analyze functions.

Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Introduction to Functions
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

2.8.8.J: Show that an equality relationship between two quantities remains the same as long as the same change is made to both quantities; explain how a change in one quantity determines another quantity in a functional relationship.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Formulas for any Variable
Solving Two-Step Equations

2.9.8: Geometry

2.9.8.A: Construct figures incorporating perpendicular and parallel lines, the perpendicular bisector of a line segment and an angle bisector using computer software.

Construct Parallel and Perpendicular Lines

2.9.8.B: Draw, label, measure and list the properties of complementary, supplementary and vertical angles.

Investigating Angle Theorems - Activity A

2.9.8.C: Classify familiar polygons as regular or irregular up to a decagon.

Parallelogram Conditions
Special Quadrilaterals

2.9.8.D: Identify, name, draw and list all properties of squares, cubes, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, spheres, triangles, prisms and cylinders.

Area of Parallelograms - Activity A
Parallelogram Conditions
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Special Quadrilaterals
Surface and Lateral Area of Prisms and Cylinders

2.9.8.E: Construct parallel lines, draw a transversal and measure and compare angles formed (e.g., alternate interior and exterior angles).

Construct Parallel and Perpendicular Lines
Investigating Angle Theorems - Activity A
Triangle Angle Sum - Activity A

2.9.8.F: Distinguish between similar and congruent polygons.

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

2.9.8.H: Use simple geometric figures (e.g., triangles, squares) to create, through rotation, transformational figures in three dimensions.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Rotations, Reflections and Translations

2.9.8.I: Generate transformations using computer software.

Dilations
Reflections
Rotations, Reflections and Translations

2.9.8.J: Analyze geometric patterns (e.g., tessellations, sequences of shapes) and develop descriptions of the patterns.

Finding Patterns

2.9.8.K: Analyze objects to determine whether they illustrate tessellations, symmetry, congruence, similarity and scale.

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

2.10.8: Trigonometry

2.10.8.A: Compute measures of sides and angles using proportions, the Pythagorean Theorem and right triangle relationships.

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

2.10.8.B: Solve problems requiring indirect measurement for lengths of sides of triangles.

Perimeters and Areas of Similar Figures

2.11.8: Concepts of Calculus

2.11.8.A: Analyze graphs of related quantities for minimum and maximum values and justify the findings.

Roots of a Quadratic

2.11.8.C: Continue a pattern of numbers or objects that could be extended infinitely.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences