### 1: Number, Number Sense and Operations

#### 1.I: Estimate, compute and solve problems involving scientific notation, square roots and numbers with integer exponents.

1.I.3: Use factorial notation and computations to represent and solve problem situations involving arrangements.

### 2: Measurement

#### 2.D: Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates.

2.D.5: Determine the measures of central and inscribed angles and their associated major and minor arcs.

### 3: Geometry and Spatial Sense

#### 3.A: Formally define geometric figures.

3.A.1: Formally define and explain key aspects of geometric figures, including:

3.A.1.a: interior and exterior angles of polygons;

3.A.1.b: segments related to triangles (median, altitude, midsegment);

3.A.1.c: points of concurrency related to triangles (centroid, incenter, orthocenter, and circumcenter);

3.A.1.d: circles (radius, diameter, chord, circumference, major arc, minor arc, sector, segment, inscribed angle).

3.A.2: Recognize and explain the necessity for certain terms to remain undefined, such as point, line and plane.

3.A.6: Identify the reflection and rotation symmetries of two- and three-dimensional figures.

3.A.10: Solve problems involving chords, radii, and arcs within the same circle.

#### 3.H: Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.

3.H.3: Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including:

3.H.3.a: prove the Pythagorean Theorem;

3.H.10: Solve problems involving chords, radii, and arcs within the same circle.

### 4: Patterns, Functions and Algebra

#### 4.B: Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs or equations.

4.B.2: Describe and compare characteristics of the following families of functions: square root, cubic, absolute value and basic trigonometric functions; e.g., general shape, possible number of roots, domain and range.

#### 4.D: Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.

4.D.3: Solve equations and formulas for a specified variable; e.g., express the base of a triangle in terms of the area and height.

4.D.5: Solve simple linear and nonlinear equations and inequalities having square roots as coefficients and solutions.

#### 4.F: Solve and graph linear equations and inequalities.

4.F.10: Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.

#### 4.G: Solve quadratic equations with real roots by graphing, formula and factoring.

4.G.8: Graph the quadratic relationship that defines circles.

4.G.10: Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.

#### 4.H: Solve systems of linear equations involving two variables graphically and symbolically.

4.H.7: Solve systems of linear inequalities.

4.H.11: Solve real-world problems that can be modeled, using systems of linear equations and inequalities.

#### 4.J: Describe and interpret rates of change from graphical and numerical data.

4.J.9: Recognize and explain that the slopes of parallel lines are equal and the slopes of perpendicular lines are negative reciprocals.

4.J.12: Describe the relationship between slope of a line through the origin and the tangent function of the angle created by the line and the positive x-axis.

### 5: Data Analysis and Probability

#### 5.A: Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatterplots, measures of center and variability.

5.A.2: Represent and analyze bivariate data using appropriate graphical displays (scatterplots, parallel box-and-whisker plots, histograms with more than one set of data, tables, charts, spreadsheets) with and without technology.

5.A.4: Identify outliers on a data display; e.g., use the interquartile range to identify outliers on a box-and-whisker plot.

5.A.6: Interpret the relationship between two variables using multiple graphical displays and statistical measures; e.g., scatterplots, parallel box-and-whisker plots, and measures of center and spread.

#### 5.C: Compare the characteristics of the mean, median and mode for a given set of data, and explain which measure of center best represents the data.

5.C.1: Describe measures of center and the range verbally, graphically and algebraically.

#### 5.D: Find, use and interpret measures of center and spread, such as mean and quartiles, and use those measures to compare and draw conclusions about sets of data.

5.D.6: Interpret the relationship between two variables using multiple graphical displays and statistical measures; e.g., scatterplots, parallel box-and-whisker plots, and measures of center and spread.

#### 5.G: Describe sampling methods and analyze the effects of method chosen on how well the resulting sample represents the population.

5.G.5: Provide examples and explain how a statistic may or may not be an attribute of the entire population; e.g., intentional or unintentional bias may be present.

### 6: Mathematical Processes

#### 6.F: Use precise mathematical language and notations to represent problem situations and mathematical ideas.

Correlation last revised: 8/29/2016

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.