### 1: The Number System

#### 1.1: Explore the real number system and its appropriate usage in real-world situations.

1.1.2: Understand that all real numbers have a decimal expansion.

### 2: Functions

#### 2.1: Explore the concept of functions.

2.1.1: Understand that a function assigns to each input exactly one output.

2.1.3: Translate among the multiple representations of a function, including mappings, tables, graphs, equations, and verbal descriptions.

2.1.4: Determine if a relation is a function using multiple representations, including mappings, tables, graphs, equations, and verbal descriptions.

2.1.5: Graph a function from a table of values. Understand that the graph and table both represent a set of ordered pairs of that function.

#### 2.3: Investigate the differences between linear and nonlinear functions using multiple representations (i.e. tables, graphs, equations, and verbal descriptions).

2.3.1: Define an equation in slope-intercept form (y = mx + b) as being a linear function.

2.3.2: Recognize that the graph of a linear function has a constant rate of change.

2.3.3: Provide examples of nonlinear functions.

#### 2.4: Apply the concepts of linear functions to real-world and mathematical situations.

2.4.1: Understand that the slope is the constant rate of change and the y- intercept is the point where x = 0.

2.4.2: Determine the slope and the 𝑦-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and verbal descriptions.

2.4.3: Construct a function in slope-intercept form that models a linear relationship between two quantities.

2.4.4: Interpret the meaning of the slope and the y - intercept of a linear function in the context of the situation.

2.4.5: Explore the relationship between linear functions and arithmetic sequences.

#### 2.5: Apply the concepts of linear and nonlinear functions to graphs in real-world and mathematical situations.

2.5.1: Analyze and describe attributes of graphs of functions (e.g., constant, increasing/decreasing, linear/nonlinear, maximum/minimum, discrete/continuous).

2.5.2: Sketch the graph of a function from a verbal description.

2.5.3: Write a verbal description from the graph of a function with and without scales.

### 3: Expressions, Equations, and Inequalities

#### 3.2: Investigate concepts of square and cube roots.

3.2.2: Evaluate square roots of perfect squares.

3.2.4: Recognize that square roots of non-perfect squares are irrational.

#### 3.3: Explore the relationship between quantities in decimal and scientific notation.

3.3.1: Express very large and very small quantities in scientific notation in the form a x 10 to the b power = p where 1 ≤ a < 10 and b is an integer.

3.3.2: Translate between decimal notation and scientific notation.

3.3.3: Estimate and compare the relative size of two quantities in scientific notation.

#### 3.4: Apply the concepts of decimal and scientific notation to solve real-world and mathematical problems.

3.4.1: Multiply and divide numbers expressed in both decimal and scientific notation.

3.4.2: Select appropriate units of measure when representing answers in scientific notation.

3.4.3: Translate how different technological devices display numbers in scientific notation.

#### 3.5: Apply concepts of proportional relationships to real-world and mathematical situations.

3.5.1: Graph proportional relationships.

#### 3.6: Apply concepts of slope and y - intercept to graphs, equations, and proportional relationships.

3.6.1: Explain why the slope, m, is the same between any two distinct points on a non-vertical line using similar triangles.

3.6.2: Derive the slope-intercept form (y = mx + b) for a non-vertical line.

#### 3.7: Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations.

3.7.1: Solve linear equations and inequalities with rational number coefficients that include the use of the distributive property, combining like terms, and variables on both sides.

3.7.2: Recognize the three types of solutions to linear equations: one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b).

3.7.3: Generate linear equations with the three types of solutions.

3.7.4: Justify why linear equations have a specific type of solution.

#### 3.8: Investigate and solve real-world and mathematical problems involving systems of linear equations in two variables with integer coefficients and solutions.

3.8.1: Graph systems of linear equations and estimate their point of intersection.

3.8.2: Understand and verify that a solution to a system of linear equations is represented on a graph as the point of intersection of the two lines.

3.8.3: Solve systems of linear equations algebraically, including methods of substitution and elimination, or through inspection.

3.8.4: Understand that systems of linear equations can have one solution, no solution, or infinitely many solutions.

### 4: Geometry and Measurement

#### 4.1: Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology).

4.1.1: Verify that lines are mapped to lines, including parallel lines.

4.1.2: Verify that corresponding angles are congruent.

4.1.3: Verify that corresponding line segments are congruent.

#### 4.2: Apply the properties of rigid transformations (rotations, reflections, translations).

4.2.1: Rotate geometric figures 90, 180, and 270 degrees, both clockwise and counterclockwise, about the origin.

4.2.2: Reflect geometric figures with respect to the x - axis and/or y - axis.

4.2.3: Translate geometric figures vertically and/or horizontally.

4.2.4: Recognize that two-dimensional figures are only congruent if a series of rigid transformations can be performed to map the pre-image to the image.

4.2.5: Given two congruent figures, describe the series of rigid transformations that justifies this congruence.

#### 4.3: Investigate the properties of transformations (rotations, reflections, translations, dilations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, dynamic software).

4.3.1: Use coordinate geometry to describe the effect of transformations on two-dimensional figures.

4.3.2: Relate scale drawings to dilations of geometric figures.

#### 4.4: Apply the properties of transformations (rotations, reflections, translations, dilations).

4.4.2: Recognize that two-dimensional figures are only similar if a series of transformations can be performed to map the pre-image to the image.

4.4.3: Given two similar figures, describe the series of transformations that justifies this similarity.

4.4.4: Use proportional reasoning to find the missing side lengths of two similar figures.

#### 4.5: Extend and apply previous knowledge of angles to properties of triangles, similar figures, and parallel lines cut by a transversal.

4.5.1: Discover that the sum of the three angles in a triangle is 180 degrees.

4.5.2: Discover and use the relationship between interior and exterior angles of a triangle.

4.5.3: Identify congruent and supplementary pairs of angles when two parallel lines are cut by a transversal.

4.5.4: Recognize that two similar figures have congruent corresponding angles.

### 5: Data Analysis, Statistics, and Probability

#### 5.1: Investigate bivariate data.

5.1.1: Collect bivariate data.

5.1.2: Graph the bivariate data on a scatter plot.

5.1.3: Describe patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, no correlation, linear, nonlinear).

#### 5.3: Apply concepts of an approximate line of best fit in real-world situations.

5.3.1: Find an approximate equation for the line of best fit using two appropriate data points.

5.3.2: Interpret the slope and intercept.

5.3.3: Solve problems using the equation.

#### 5.4: Investigate bivariate categorical data in two-way tables.

5.4.1: Organize bivariate categorical data in a two-way table.

5.4.2: Interpret data in two-way tables using relative frequencies.

#### 5.5: Organize data in matrices with rational numbers and apply to real-world and mathematical situations.

5.5.3: Add and subtract matrices of the same size.

Correlation last revised: 1/5/2017

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