### 1: Number Sense and Operations

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

1.1.PO 3: Distinguish between finite and infinite sets of numbers.

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

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

2.1.PO 2: Organize collected data into an appropriate graphical representation.

2.1.PO 3: Display data as lists, tables, matrices, and plots.

2.1.PO 4: Construct equivalent displays of the same data.

2.1.PO 6: Identify which of the measures of central tendency is most appropriate in a given situation.

2.1.PO 7: Make reasonable predictions based upon linear patterns in data sets or scatter plots.

2.1.PO 10: Apply the concepts of mean, median, mode, range, and quartiles to summarize data sets.

2.1.PO 12: Recognize and explain the impact of interpreting data (making inferences or drawing conclusions) from a biased sample.

2.1.PO 13: Draw a line of best fit for a scatter plot.

2.1.PO 14: Determine whether a displayed data has positive, negative, or no correlation.

2.1.PO 17: Identify differences between biased and unbiased samples.

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

2.2.PO 1: Find the probability that a specific event will occur, with or without replacement.

2.2.PO 2: Determine simple probabilities related to geometric figures.

2.2.PO 4: Record the data from performing a grade level appropriate probability experiment.

2.2.PO 5: Compare the outcome of an experiment to predictions made prior to performing the experiment.

2.2.PO 6: Distinguish between independent and dependent events.

2.2.PO 7: Compare the results of two repetitions of the same grade level appropriate probability experiment.

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

2.3.PO 1: Determine the number of possible outcomes for a contextual event using a chart, a tree diagram, or the counting principle.

2.3.PO 2: Determine when to use combinations versus permutations in counting objects.

2.3.PO 3: Use combinations or permutations to solve contextual problems.

### 3: Patterns, Algebra, and Functions

#### 3.1: Identify patterns and apply pattern recognition to reason mathematically.

3.1.PO 1: Communicate a grade level appropriate iterative or recursive pattern, using symbols or numbers.

3.1.PO 2: Find the nth term of an iterative or recursive pattern.

3.1.PO 3: Evaluate problems using basic recursion formulas.

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

3.2.PO 1: Determine if a relationship is a function, given a graph, table, or set of ordered pairs.

3.2.PO 2: Describe a contextual situation that is depicted by a given graph.

3.2.PO 3: Identify a graph that models a given real-world situation.

3.2.PO 4: Sketch a graph that models a given contextual situation.

3.2.PO 5: Determine domain and range for a function.

3.2.PO 6: Determine the solution to a contextual maximum / minimum problem, given the graphical representation.

3.2.PO 7: Express the relationship between two variables using tables/ matrices, equations, or graphs.

3.2.PO 8: Interpret the relationship between data suggested by tables/ matrices, equations, or graphs.

3.2.PO 9: Determine from two linear equations whether the lines are parallel, perpendicular, coincident, or intersecting but not perpendicular.

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

3.3.PO 1: Evaluate algebraic expressions, including absolute value and square roots.

3.3.PO 3: Multiply and divide monomial expressions with integral exponents.

3.3.PO 4: Translate a written expression or sentence into a mathematical expression or sentence.

3.3.PO 5: Translate a sentence written in context into an algebraic equation involving multiple operations.

3.3.PO 6: Write a linear equation for a table of values.

3.3.PO 7: Write a linear algebraic sentence that represents a data set that models a contextual situation.

3.3.PO 8: Solve linear (first degree) equations in one variable (may include absolute value).

3.3.PO 9: Solve linear inequalities in one variable.

3.3.PO 10: Write an equation of the line given: two points on the line, the slope and a point on the line, or the graph of the line.

3.3.PO 11: Solve an algebraic proportion.

3.3.PO 12: Solve systems of linear equations in two variables (integral coefficients and rational solutions).

3.3.PO 15: Simplify square roots and cube roots with monomial radicands (including those with variables) that are perfect squares or perfect cubes.

3.3.PO 16: Solve square root radical equations involving only one radical.

3.3.PO 17: Solve quadratic equations.

3.3.PO 18: Identify the sine, cosine, and tangent ratios of the acute angles of a right triangle.

#### 3.4: Analyze change in a variable over time and in various contexts.

3.4.PO 1: Determine slope, x-, and y-intercepts of a linear equation.

3.4.PO 2: Solve formulas for specified variables.

### 4: Geometry and Measurement

#### 4.1: Analyze the attributes and properties of two and three dimensional shapes and develop mathematical arguments about their relationships.

4.1.PO 1: Identify the attributes of special triangles. (isosceles, equilateral, right)

4.1.PO 2: Identify the hierarchy of quadrilaterals.

4.1.PO 3: Make a net to represent a three-dimensional object.

4.1.PO 4: Make a three-dimensional model from a net.

4.1.PO 6: Solve problems related to complementary, supplementary, or congruent angle concepts.

4.1.PO 7: Solve problems by applying the relationship between circles, angles, and intercepted arcs.

4.1.PO 8: Solve problems by applying the relationship between radii, diameters, chords, tangents or secants.

4.1.PO 9: Solve problems using the triangle inequality property.

4.1.PO 11: Determine when triangles are congruent by applying SSS, ASA, AAS or SAS.

4.1.PO 12: Determine when triangles are similar by applying SAS, SSS, or AA similarity postulates.

4.1.PO 13: Construct a triangle congruent to a given triangle.

4.1.PO 14: Solve contextual situations using angle and side length relationships.

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

4.2.PO 1: Sketch the planar figure that is the result of two or more transformations.

4.2.PO 2: Identify the properties of the planar figure that is the result of two or more transformations.

4.2.PO 3: Determine the new coordinates of a point when a single transformation is performed on a planar geometric figure.

4.2.PO 4: Determine whether a given pair of figures on a coordinate plane represents a translation, reflection, rotation, or dilation.

4.2.PO 5: Classify transformations based on whether they produce congruent or similar figures.

4.2.PO 6: Determine the effects of a single transformation on linear or area measurements of a planar geometric figure.

#### 4.3: Specify and describe spatial relationships using coordinate geometry and other representational systems.

4.3.PO 1: Graph a quadratic equation with lead coefficient equal to one.

4.3.PO 2: Graph a linear equation in two variables.

4.3.PO 3: Graph a linear inequality in two variables.

4.3.PO 4: Determine the solution to a system of equations in two variables from a given graph.

4.3.PO 6: Determine changes in the graph of a linear function when constants and coefficients in its equation are varied.

4.3.PO 7: Determine the distance between two points in the coordinate system.

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

4.4.PO 1: Calculate the area of geometric shapes composed of two or more geometric figures.

4.4.PO 2: Calculate the volumes of three-dimensional geometric figures.

4.4.PO 3: Calculate the surface areas of three-dimensional geometric figures.

4.4.PO 4: Compare perimeter, area, or volume of figures when dimensions are changed.

4.4.PO 6: Find the area of a sector of a circle.

4.4.PO 7: Solve for missing measures in a pyramid. (i.e., slant height, height)

4.4.PO 8: Find the sum of the interior and exterior angles of a polygon.

4.4.PO 9: Solve scale factor problems using ratios and proportions.

4.4.PO 10: Solve applied problems using similar triangles.

### 5: Structure and Logic

#### 5.1: Use reasoning to solve mathematical problems in contextual situations.

5.1.PO 2: Determine whether a given procedure for solving an equation is valid.

5.1.PO 3: Determine whether a given procedure for solving a linear inequality is valid.

#### 5.2: Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions and recognize their applications.

5.2.PO 4: Analyze assertions related to a contextual situation by using principles of logic.

5.2.PO 7: Create inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

5.2.PO 8: Critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

5.2.PO 13: Construct a simple formal or informal deductive proof.

5.2.PO 14: Verify characteristics of a given geometric figure using coordinate formulas such as distance, mid-point, and slope to confirm parallelism, perpendicularity, and congruency.

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.