### 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: Express fractions as ratios, comparing two whole numbers. (e.g., ¾ is equivalent to 3:4 and 3 to 4)

1.1.PO 2: Compare two proper fractions, improper fractions or mixed numbers.

1.1.PO 3: Order three or more proper fractions, improper fractions or mixed numbers.

1.1.PO 4: Determine the equivalency between and among fractions, decimals, and percents in contextual situations.

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

1.2.PO 3: Apply grade level appropriate properties to assist in computation.

1.2.PO 7: Add or subtract proper fractions and mixed numbers with unlike denominators with regrouping.

1.2.PO 8: Demonstrate the process of multiplication of proper fractions using models.

1.2.PO 9: Multiply proper fractions.

1.2.PO 10: Multiply mixed numbers.

1.2.PO 11: Demonstrate that division is the inverse of multiplication of proper fractions.

1.2.PO 12: Divide proper fractions.

1.2.PO 13: Divide mixed numbers.

1.2.PO 15: 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 4: Estimate and measure for the area and perimeter of polygons using a grid.

### 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 a histogram, line graph, scatter plot, or stem-and-leaf plot with appropriate labels and title from organized data.

2.1.PO 5: Find the mean, median (odd number of data points), mode, range, and extreme values of a given numerical data set.

2.1.PO 7: Compare trends in data related to the same investigation.

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

2.2.PO2: Express probabilities of a single event as a decimal.

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: Make predictions from the results of student-generated experiments using objects (e.g., coins, spinners, number cubes, and cards).

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 a combination of 3 sets of 3 items, using a systematic approach. (e.g., 3 different shirts, 3 different pairs of pants, and 3 different belts)

2.3.PO 2: Determine all possible arrangements given a set with four or fewer objects using a systematic list, table or tree diagram when order is not important.

### 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 recursive pattern, using symbols or numbers.

3.1.PO 2: Extend a grade level appropriate iterative pattern.

3.1.PO 3: Solve grade level appropriate iterative 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)

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

3.3.PO 1: Evaluate expressions involving the four basic operations by substituting given fractions for the variable. (e.g., n+3, when n= ½ )

3.3.PO 2: Use variables in contextual situations.

3.3.PO 3: Translate a written phrase to an algebraic expression. (e.g., The quotient of m and 5 is m/5 or m ÷ 5.)

3.3.PO 4: Translate a phrase written in context into an algebraic expression. (e.g., Write an expression to describe the situation: John has x pieces of candy and buys three more. x + 3)

3.3.PO 5: Solve one-step equations with one variable represented by a letter or symbol, using inverse operations with whole numbers.

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

3.4.PO 1: Identify values on a given line graph or scatter plot. (e.g., Given a line showing wages earned per hour, what is the wage at five hours?)

### 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: Classify polygons by their attributes. (e.g., number of sides, length of sides, angles, parallelism, perpendicularity)

4.1.PO 3: Classify prisms, pyramids, cones, and cylinders by base shape and lateral surface shape.

4.1.PO 4: Classify three-dimensional figures by their attributes.

4.1.PO 5: Compare attributes of two- dimensional figures with three-dimensional figures.

4.1.PO 6: Draw triangles with appropriate labels.

4.1.PO 7: Identify supplementary or complementary angles.

4.1.PO 8: Identify the diameter, radius and circumference of a circle or sphere.

4.1.PO 9: Draw a two-dimensional shape with a given number of lines of symmetry.

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

4.2.PO 1: Identify reflections, and translations using pictures.

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

4.3.PO 1: Graph a polygon in the first quadrant using ordered pairs.

4.3.PO 2: State the missing coordinate of a given figure in the first quadrant of a coordinate grid using geometric properties. (e.g. find the coordinates of the missing vertex of a rectangle when two adjacent sides are drawn)

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

4.4.PO 2: Determine the appropriate tool needed to measure to the needed accuracy.

4.4.PO 6: Solve problems involving the perimeter of polygons.

4.4.PO 7: Determine the area of triangles.

4.4.PO 8: Distinguish between the perimeter and area in contextual situation.

4.4.PO 9: Solve problems for the areas of parallelograms (includes rectangles).

4.4.PO 10: Identify parallelograms having the same perimeter or area.

### 5: Structure and Logic

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

5.1.PO 2: Analyze algorithms for computing with decimals.

#### 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 simple logic problem from given information. (Which of three different people live in which of three different colored houses?)

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.