### 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 1: Locate rational numbers on a number line.

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

1.2.PO 4: Determine the square root of an integer.

1.2.PO 6: Apply grade level appropriate properties to assist in computation.

1.2.PO 7: Apply the symbols "square root of" to represent square root, "±" to represent roots, "{}" as grouping symbols.

1.2.PO 9: Calculate the missing value in a percentage problem.

1.2.PO 11: Simplify numerical expressions using the order of operations with grade appropriate operations on number sets.

#### 1.3: Use estimation strategies reasonably and fluently.

1.3.PO 2: Use estimation to verify the reasonableness of a calculation. (e.g., Is 32 the square root of 64?)

1.3.PO 3: Express answers to the appropriate place or degree of precision. (e.g., time and money)

### 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: Construct box and whisker plots.

2.1.PO 3: Determine the appropriate type of graphical display for a given data set.

2.1.PO 4: Interpret box-and-whisker plots, circle graphs and scatter plots.

2.1.PO 5: Answer questions based on box-and-whisker plots, circle graphs and scatter plots.

2.1.PO 6: Solve problems in contextual situations using the mean, median, mode, and range of a given data set.

2.1.PO 8: Compare trends in data related to the same investigation.

2.1.PO 9: Solve contextual problems using scatter plots, box-and-whiskers plots, and double line graphs of continuous data.

2.1.PO 11: Identify a line of best fit for a scatter plot.

2.1.PO 12: Distinguish between causation and correlation.

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

2.2.PO 1: Determine the probability that a specific event will occur in a 2-stage probability experiment.

2.2.PO 2: Solve contextual situations using probability. (e.g., If the probability of Michelle making a free throw is 0.25, what is the probability that she will make three free throws in a row?)

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 all possible outcomes involving the combination of two or more sets of objects. (e.g. If you roll a 6 sided number cube 4 times how many possible outcomes are possible?)

### 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: Extend a grade level appropriate iterative or recursive pattern.

3.1.PO 3: Solve grade level appropriate iterative or recursive pattern problems.

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

3.2.PO 1: Describe the rule used in a simple grade level appropriate function. (e.g., T-chart, input/output model)

3.2.PO 2: Distinguish between linear and nonlinear functions, given graphic examples.

3.2.PO 3: Determine whether a graph or table are related to a given an equation of the form y=ax² where ‘a’ is a natural number.

3.2.PO 4: Identify independent and dependent variables for a contextual situation.

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

3.3.PO 2: Use variables in contextual situations.

3.3.PO 3: Translate a written sentence or phrase into an algebraic equation or expression and vice versa. (e.g., Three less than twice a number is 2n-3.)

3.3.PO 4: Translate a sentence written in context into an algebraic equation involving two operations.

3.3.PO 5: Translate a contextual situation into an algebraic inequality. (e.g., Joe earns more than \$5.00 an hour; therefore, x > 5)

3.3.PO 6: Identify an equation or inequality that represents a contextual situation.

3.3.PO 7: Solve one-step equations with rational numbers as coefficients or as solutions.

3.3.PO 8: Solve one-step equations that model contextual situations.

3.3.PO 9: Solve two-step equations with rational coefficients and integer solutions. (e.g., 3x + 5 = 11, 4x – 20 = 8)

3.3.PO 10: Graph an inequality on a number line.

3.3.PO 11: Solve a simple algebraic proportion.

3.3.PO 12: Solve applied problems using the Pythagorean theorem.

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

3.4.PO 1: Identify the slope of a line as the rate of change. (the ratio of rise over run)

### 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: Draw a model that demonstrates basic geometric relationships such as parallelism, perpendicularity, similarity/ proportionality, and congruence.

4.1.PO 2: Draw three-dimensional figures by applying properties of each. (e.g., parallelism, perpendicularity and congruency)

4.1.PO 3: Recognize the three-dimensional figure represented by a net.

4.1.PO 4: Represent the surface area of rectangular prisms and cylinders as the area of their net.

4.1.PO 6: Identify the properties of angles created by a transversal intersecting two parallel lines (e.g., corresponding angles are congruent).

4.1.PO 7: Recognize the relationship between inscribed angles and intercepted arcs.

4.1.PO 10: Identify corresponding angles of similar polygons as congruent and sides as proportional.

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

4.2.PO 1: Identify the planar geometric figure that is the result of a given rigid transformation.

4.2.PO 2: Model a simple transformation on a coordinate grid. (e.g. translate right four units and down two units)

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

4.3.PO 1: Use a table of values to graph a linear equation.

4.3.PO 2: Determine the midpoint given two points on a number line.

4.3.PO 3: Determine the distance between two points on a number line.

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

4.4.PO 1: Solve problems for the area of a trapezoid.

4.4.PO 2: Solve problems involving the volume of rectangular prisms and cylinders.

4.4.PO 3: Calculate the surface area of rectangular prisms or cylinders.

4.4.PO 4: Identify rectangular prisms and cylinders having the same volume.

4.4.PO 5: Find the measure of a missing interior angle in a triangle or quadrilateral.

4.4.PO 6: Solve problems using ratios and proportions, given the scale factor.

4.4.PO 7: Calculate the length of a side given two similar triangles.

### 5: Structure and Logic

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

5.1.PO 1: Describe how to use a proportion to solve a problem in context.

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

5.2.PO 1: Solve a logic problem given the necessary information.

5.2.PO 2: Identify simple valid arguments using if...then statements. (e.g., All squares are rectangles. If quadrilateral ABCD is a rectangle, is it a square?)

5.2.PO 4: Verify the Pythagorean theorem using an area dissection argument.

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.