1: Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.

1.1: Demonstrate meanings for real numbers, absolute value, and scientific notation using physical materials and technology in problem-solving situations.

1.1.a: Compare and order sets of real numbers.

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

1.2: Develop, test, and conjectures about the properties of number systems and sets of numbers.

1.2.b: Verify and apply the properties of the operation “to the power of”.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

2: Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems.

2.1: Model real world phenomena (for example, distance-versus-time relationships, compound interest, amortization tables, mortality rates) using functions, equations, inequalities, and matrices.

2.1.a: Model real world phenomena involving linear, quadratic and exponential relationships using multiple representations of rules that can take the form of a recursive process, a function, an equation, or an inequality.

Exponential Functions - Activity A
Linear Functions
Quadratic Inequalities - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Using Algebraic Equations

2.2: Represent functional relationships using written explanations, tables, equations, and graphs and describe the connections among these representations.

2.2.a: Represent functional relationships using written explanations, tables, equations, and graphs, and describe the connections among these representations.

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
Polynomials and Linear Factors
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Sine Function
Slope-Intercept Form of a Line - Activity A
Tangent Function
Using Algebraic Equations
Using Tables, Rules and Graphs

2.2.b: Convert from one functional representation to another.

Introduction to Functions
Linear Functions
Using Algebraic Equations
Using Tables, Rules and Graphs

2.3: Solve problems involving functional relationships using graphing calculators and/or computers as well as appropriate paper-and-pencil techniques.

2.3.a: Solve problems involving functions and relations using calculators, graphs, tables, and algebraic methods.

Introduction to Functions
Linear Functions

2.3.b: Solve simple systems of equations using algebraic, graphical or numeric methods.

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

2.3.c: Solve equations with more than one variable for a given variable (for example, solve for p in 1= prt or for r in C=2 pi r).

Solving Formulas for any Variable

2.4: Analyze and explain the behaviors, transformations, and general properties of types of equations and functions (for example, linear, quadratic, exponential).

2.4.a: Identify and interpret x- and y- intercepts in the context of a problem.

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

2.4.b: Using a graph, identify the maximum and minimum value within a given domain.

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

2.4.c: Demonstrate horizontal and vertical translations on graphs of functions and their meanings in the context of a problem.

Circles
Ellipse - Activity A
Hyperbola - Activity A
Logarithmic Functions: Translating and Scaling
Quadratics in Factored Form
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

2.4.d: Recognize when a relation is a function.

Introduction to Functions
Linear Functions

2.5: Interpret algebraic equations and inequalities geometrically and describe geometric relationships algebraically.

2.5.a: Graph solutions to equations and inequalities in one-and two-dimensions.

Defining a Line with Two Points
Ellipse - Activity A
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
Standard Form of a Line
Systems of Linear Inequalities (Slope-intercept form) - Activity A

2.5.b: Express the perimeter, area and volume relationships of geometric figures algebraically.

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

2.5.c: Describe geometric relationships algebraically.

Ellipse - Activity A
Hyperbola - Activity A

3: Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning used in solving these problems.

3.1: Design and conduct a statistical experiment to study a problem, and interpret and communicate the results using the appropriate technology (for example, graphing calculators, computer software).

3.1.c: Select and use an appropriate display to represent and describe a set of data (for example, scatter plot, line graph and histogram).

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

3.2: Analyze statistical claims for erroneous conclusions or distortions.

3.2.c: Describe how data can be interpreted in more than one way or be used to support more than one position in a debate.

Correlation

3.3: Fit curves to scatter plots using informal methods or appropriate technology to determine the strength of the relationship between two data sets and to make predictions.

3.3.a: Graph data sets, create a scatter plot, and identify the control (independent) variable and dependent variable.

Correlation
Introduction to Functions
Scatter Plots - Activity A
Solving Using Trend Lines

3.3.b: Determine a line of best fit from a scatter plot using visual techniques.

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

3.4: Draw conclusions about distributions of data based on analysis of statistical summaries (for example, the combination of mean and standard deviation, and differences between the mean and median).

3.4.a: Differentiate between mean, median, and mode and demonstrate the appropriate use of each.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

3.4.d: Demonstrate how outliers might affect various representations of data and measures of central tendency*.

Describing Data Using Statistics
Mean, Median and Mode

3.5: Use experimental and theoretical probability to represent and solve problems involving uncertainty (for example, the chance of playing professional sports if a student is a successful high school athlete).

3.5.a: Determine the probability of an identified event using the sample space.

Geometric Probability - Activity A

3.5.b: Distinguish between experimental and theoretical probability and use each appropriately.

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

3.5.c: Differentiate between independent and dependent events to calculate the probability in real-world situations.

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

3.5.d: Calculate the probability of event A and B occurring and the probability of event A or B occurring.

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

3.5.e: Use area models to determine probability (for example, the probability of hitting the bull’s eye region in a target).

Geometric Probability - Activity A

3.6: Solve real-world problems with informal use of combinations and permutations for example, determining the number of possible meals at a restaurant featuring a given number of side dishes).

3.6.a: Apply organized counting techniques to determine combinations and permutations in problem-solving situations.

Binomial Probabilities
Permutations
Permutations and Combinations

4: Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems.

4.1: Find and analyze relationships among geometric figures using transformations (for example, reflections, translations, rotations, dilations) in coordinate systems.

4.1.a: Describe and apply the properties of similar and congruent figures.

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

4.1.b: Solve problems involving symmetry and transformations.

Dilations
Holiday Snowflake Designer
Reflections
Rotations, Reflections and Translations

4.1.d: Describe cylinders, cones and spheres that result from the rotation of rectangles, triangles and semicircles about a line.

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

4.2: Derive and use methods to measure perimeter, area, and volume of regular and irregular geometric figures.

4.2.a: Use the Pythagorean Theorem and its converse to solve real-world problems.

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

4.2.c: Use properties of geometric solids to find volumes and surface areas of regular and irregular geometric solids.

Classifying Triangles
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

4.3: Make and test conjectures about geometric shapes and their properties, incorporating technology where appropriate.

4.3.a: Make and test conjectures about geometric shapes and their properties to include parallelism and perpendicularity, numerical relationships on a triangle, relationships between triangles, and properties of quadrilaterals and regular polygons.

Parallelogram Conditions
Triangle Inequalities

4.3.b: Apply geometric relationships such as parallelism and perpendicularity, numerical relationships on a triangle, relationships between triangles, and properties of quadrilaterals and regular polygons to solve problems.

Area of Parallelograms - Activity A
Parallelogram Conditions

4.4: Use trigonometric ratios in problem-solving situations (for example, finding the height of a building from a given point, if the distance to the building and the angle of elevation are known).

4.4.a: Use right triangle trigonometry to solve real-world problems.

Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent

5: Students use a variety of tools and techniques to measure, apply the results in problem-solving situations, and communicate the reasoning used in solving these problems.

5.1: Measure quantities indirectly using techniques of algebra, geometry, or trigonometry.

5.1.a: Use appropriate measurements to solve problems indirectly (for example, find the height of a flagpole using similar triangles.

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

5.1.b: Use measurement to solve real-world problems involving rate of change (for example, distance traveled using rate and time).

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

5.1.c: Given the rate of change, model real-world problems algebraically or graphically.

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

5.1.d: Describe how changing the measure of one attribute of a geometric figure affects the other measurements.

Prisms and Cylinders - Activity A

5.2: Select and use appropriate tools and techniques to measure quantities in order to achieve specified degrees of precision, accuracy and error (or tolerance) of measurements.

5.2.a: Select and use appropriate tools and techniques to measure quantities in order to achieve specified degrees of precision, accuracy, and error of measurements.

Triple Beam Balance

6: Students link concepts and procedures as they develop and use computational techniques, including estimation, mental arithmetic, paper-and-pencil, calculators, and computers, in problem-solving situations and communicate the reasoning used in solving these problems.

6.1: Use ratios, proportions, and percents in problem-solving situations.

6.1.a: Use ratios, proportions, and percents in problem-solving situations that involve rational numbers.

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

6.1.c: Apply direct variation to problem-solving situations.

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation