### 1: Number and Operations

#### 1.1: Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.In

1.1.1: Justify with examples the relation between the number system being used (natural numbers, whole numbers, integers, rational numbers and irrational numbers) and the question of whether or not an equation has a solution in that number system.

1.1.3: Express that the distance between two numbers is the absolute value of their difference.

#### 1.2: Understand and apply numerical operations and their relationship to one another.

1.2.2: Summarize the properties of and connections between real number operations; justify manipulations of expressions using the properties of real number operations.

1.2.3: Calculate powers and roots of rational and irrational numbers.

1.2.4: Compute using scientific notation.

### 2: Data Analysis, Probability, and Discrete Mathematics

#### 2.1: Understand and apply data collection, organization, and representation to analyze and sort data.

2.1.2: Organize collected data into an appropriate graphical representation with or without technology.

2.1.3: Display data, including paired data, as lists, tables, matrices, and plots with or without technology; make predictions and observations about patterns or departures from patterns.

2.1.5: Determine which measure of center is most appropriate in a given situation and explain why.

2.1.6: Evaluate the reasonableness of conclusions drawn from data analysis.

2.1.7: Identify misrepresentations and distortions in displays of data and explain why they are misrepresentations or distortions.

2.1.8: Design simple experiments or investigations and collect data to answer questions.

#### 2.2: Understand and apply the basic concepts of probability.

2.2.1: Make predictions and solve problems based on theoretical probability models.

2.2.2: Determine the theoretical probability of events, estimate probabilities using experiments, and compare the two.

2.2.3: Use simulations to model situations involving independent and dependent events.

2.2.4: Explain and use the law of large numbers (that experimental results tend to approach theoretical probabilities after a large number of trials).

2.2.5: Use concepts and formulas of area to calculate geometric probabilities.

#### 2.3: Understand and demonstrate the systematic listing and counting of possible outcomes.

2.3.1: Apply the addition and multiplication principles of counting, representing these principles algebraically using factorial notation.

2.3.2: Apply appropriate means of computing the number of possible arrangements of items using permutations where order matters, and combinations where order does not matter.

2.3.3: Determine the number of possible outcomes of an event.

### 3: Patterns, Algebra, and Functions

#### 3.1: Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.

3.1.1: Recognize, describe, and analyze sequences using tables, graphs, words, or symbols; use sequences in modeling.

3.1.2: Determine a specific term of a sequence.

3.1.3: Create sequences using explicit and recursive formulas involving both subscripts and function notation.

#### 3.2: Describe and model functions and their relationships.

3.2.2: Determine if a relationship represented by an equation, graph, table, description, or set of ordered pairs is a function.

3.2.4: Use equations, graphs, tables, descriptions, or sets of ordered pairs to express a relationship between two variables.

3.2.5: Recognize and solve problems that can be modeled using a system of two equations in two variables.

3.2.6: Recognize and solve problems that can be modeled using a quadratic function.

3.2.7: Determine domain and range of a function from an equation, graph, table, description, or set of ordered pairs.

#### 3.3: Represent and analyze mathematical situations and structures using algebraic representations.

3.3.2: Solve formulas for specified variables.

3.3.3: Write an equation given a table of values, two points on the line, the slope and a point on the line, or the graph of the line.

3.3.5: Solve linear equations and equations involving absolute value, with one variable.

3.3.6: Solve linear inequalities in one variable.

3.3.7: Solve systems of two linear equations in two variables.

3.3.8: Simplify and evaluate polynomials, rational expressions, expressions containing absolute value, and radicals.

3.3.9: Multiply and divide monomial expressions with integer exponents.

3.3.10: Add, subtract, and multiply polynomial and rational expressions.

3.3.11: Solve square root equations involving only one radical.

3.3.12: Factor quadratic polynomials in the form of ax² + bx + c where a, b, and c are integers.

3.3.14: Factor higher order polynomials.

#### 3.4: Analyze how changing the values of one quantity corresponds to change in the values of another quantity.

3.4.2: Solve problems involving rate of change.

3.4.3: Solve interest problems.

### 4: Geometry and Measurement

#### 4.1: Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.

4.1.1: Use the basic properties of a circle (relationships between angles, radii, intercepted arcs, chords, tangents, and secants) to prove basic theorems and solve problems.

4.1.2: Visualize solids and surfaces in 3-dimensional space when given 2-dimensional representations and create 2-dimensional representations for the surfaces of 3-dimensional objects.

4.1.4: Apply properties, theorems, and constructions about parallel lines, perpendicular lines, and angles to prove theorems.

4.1.7: Use the hierarchy of quadrilaterals in deductive reasoning.

4.1.8: Prove similarity and congruence of triangles.

4.1.9: Solve problems using the triangle inequality property.

4.1.10: Solve problems using right triangles, including special triangles.

4.1.11: Solve problems using the sine, cosine, and tangent ratios of the acute angles of a right triangle.

#### 4.2: Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.

4.2.1: Determine whether a transformation of a 2-dimensional figure on a coordinate plane represents a translation, reflection, rotation, or dilation and whether congruence is preserved.

4.2.2: Determine the new coordinates of a point when a single transformation is performed on a 2-dimensional figure.

4.2.4: Determine the effects of a single transformation on linear or area measurements of a 2-dimensional figure.

#### 4.3: Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands.

4.3.2: Illustrate the connection between the distance formula and the Pythagorean Theorem.

4.3.3: Determine the distance between two points in the coordinate plane.

4.3.5: Graph a linear equation or linear inequality in two variables.

4.3.6: Describe how changing the parameters of a linear function affect the shape and position of its graph.

4.3.7: Determine the solution to a system of linear equations in two variables from the graphs of the equations.

#### 4.4: Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.

4.4.1: Use dimensional analysis to keep track of units of measure when converting.

4.4.2: Find the length of a circular arc; find the area of a sector of a circle.

4.4.3: Determine the effect that changing dimensions has on the perimeter, area, or volume of a figure.

4.4.4: Solve problems involving similar figures using ratios and proportions.

4.4.5: Calculate the surface area and volume of 3-dimensional figures and solve for missing measures.

Correlation last revised: 1/20/2017

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