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;

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Rational Numbers, Opposites, and Absolute Values
Unit Conversions

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;

Compound Interest
Linear Inequalities in Two Variables
Solving Equations on the Number Line

2.2: represent functional relationships using written explanations, tables, equations, and graphs, and describing the connections among these representations;

Linear Functions

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

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Exponential Functions
Linear Functions
Logarithmic Functions
Translating and Scaling Functions

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

3.2: analyze statistical claims for erroneous conclusions or distortions;

Polling: City
Polling: Neighborhood
Populations and Samples

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;

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
Zap It! Game

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);

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

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); and

Binomial Probabilities
Geometric Probability
Independent and Dependent Events
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).

Binomial Probabilities
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;

Dilations
Rotations, Reflections, and Translations
Similar Figures
Translations

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

Area of Parallelograms
Area of Triangles
Circumference and Area of Circles
Perimeter and Area of Rectangles
Prisms and Cylinders
Pyramids and Cones

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).

Sine, Cosine, and Tangent Ratios

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;

Perimeters and Areas of Similar Figures
Similar Figures
Sine, Cosine, and Tangent Ratios

5.4: demonstrate the meanings of area under a curve and length of an arc.

Riemann Sum

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;

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percent of Change
Real-Time Histogram

6.3: describe the limitations of estimation, and assess the amount of error resulting from estimation within acceptable limits.

Polling: City