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 rational numbers and common irrational numbers (square root of 2, square root of 5 and pi.)

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

1.1.b: Recognize and use equivalent representations of rational numbers and common irrational numbers (square root of 2, square root of 5, pi), including scientific notation.

Square Roots

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 and non-linear relationships using multiple representations of rules that can take the form of recursive processes, functions, equations, or inequalities.

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Introduction to Functions
Linear Functions
Logarithmic Functions - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Sine Function
Using Algebraic Equations
Using Tables, Rules and Graphs

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
Exponential Growth and Decay - Activity B
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Introduction to Functions
Linear Functions
Logarithmic Functions - Activity A
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
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

2.2.c: Interpret a graphical representation of a real-world situation.

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

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
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Sine Function

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

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).

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

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.

Polynomials and Linear Factors
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: Analyze the effects of change in the leading coefficient and/or the vertical translation (for example, given y = kx + c and y = kx² + c, how do changes in k and/or c affect the graphs?

Circles
Ellipse - Activity A
Hyperbola - Activity A
Quadratics in Factored Form
Translating and Scaling 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 and determine solutions.

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
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
Solving Two-Step Equations
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

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

3.4: 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: Determine, analyze, and use measure of central tendency (such as mean, median, and mode) and measures of variability (such as range and quartiles) in problem-solving situations.

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

3.4.b: Use averages (including averages per trial, expected value) to draw conclusions about distributions of data (for example, if there are 10 people with one five dollar bill and one dollar bill in their wallets and they each randomly place one of the bills in a donation box, what will be the average amount of money donated per person?).

Line Plots
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: Make predictions using theoretical probability in real-world problems.

Probability Simulations
Theoretical and Experimental Probability

3.5.c: Use a model (list, tree diagram, area model) to determine theoretical probabilities* to solve problems involving uncertainty.

Binomial Probabilities
Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
Permutations
Permutations and Combinations
Probability Simulations
Theoretical and Experimental Probability

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: 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).

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: Find and analyze relationships among geometric figures using transformation (for example, reflections, translation, rotations, dilation) in coordinate systems.

Dilations
Reflections
Rotations, Reflections and Translations
Translations

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

4.2.a: Solve problems involving perimeter, area, and volumeof regular and irregular geometric figures.

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

4.2.b: Use the Pythagorean theorem to solve real-world problems.

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

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 (for example, parallelism, perpendicularity, similarity, congruence, symmetry).

Holiday Snowflake Designer
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

4.3.b: Use coordinate geometry* to solve problems involving shapes and their properties.

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

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: Describe how changing one attribute of a shape affects its angle measure, perimeter, circumference, area, surface 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

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 (or tolerance) 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