### 1: Calculations and Estimations

#### 1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

1.1.1: Order, model, and compare positive rational numbers (fractions, decimals, and percentages)

1.1.3: Understand rates and ratios as comparisons of two quantities by division

1.1.4: Differentiate between rates and ratios and express both as fractions

1.1.5: Solve problems by calculating rates and ratios

1.1.6: Locate positive rational numbers (fractions, decimals, and percentages) on a number line

1.1.7: Apply equivalent forms of fractions and decimals to solve problems

1.1.8: Determine equivalent forms of fractions, mixed numbers and improper fractions

1.1.10: Identify prime and composite numbers less than 100

#### 1.2: Compute fluently and make reasonable estimates

1.2.1: Develop and analyze algorithms for computing with fractions and mixed numbers

1.2.2: Add and subtract fractions with like and unlike denominators

1.2.3: Understand linear, area, and discrete models to multiply and divide fractions

1.2.4: Solve problems involving common percentages

1.2.5: Convert mentally among common decimals, fractions and percentages

1.2.6: Apply grouping symbols to simplify calculations and evaluate expressions

1.2.7: Develop and use strategies to estimate the results of positive rational number computations and judge the reasonableness of results

1.2.8: Use referent numbers in estimating answers to adding and subtracting fractions and mixed numbers (e.g., 2 1/4 + 3/8 < 3, since both 1/4 and 3/8 are less than 1/2)

#### 1.3: Understand meanings of operations and how they relate to one another

1.3.1: Use the inverse operations of addition and subtraction to solve problems and check solutions involving adding and subtracting fractions and mixed numbers

1.3.2: Apply the associative, commutative, and distributive properties to simplify computations with positive rational numbers

### 2: Statistics and Probability

#### 2.1: Select and use appropriate statistical methods to analyze data

2.1.1: Find, use, and interpret measures of center and spread

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

2.2.1: Determine experimental probability of an event from a set of data

2.2.2: Express probability using fractions, ratios, decimals, and percents

2.2.4: Determine the number of possible combinations of two or more classes of objects (e.g., shirts, pants and shoes)

#### 2.3: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

2.3.1: Design experiments and simulations to determine experimental probability of different outcomes

2.3.2: Understand that experimental probability approaches theoretical probability as the number of trials increases

2.3.3: Recognize and understand the connections among concepts of independent outcomes, picking at random, and fairness

2.3.4: Represent and interpret the outcome of a probability experiment using a frequency distribution, including determining experimental probabilities

#### 2.4: Develop and evaluate inferences and predictions that are based on data

2.4.2: Predict the outcome of a probability experiment by computing and using theoretical probability

### 3: Algebraic Relationships

#### 3.1: Understand patterns, relations, and functions

3.1.1: Represent, analyze and determine rules for finding patterns involving positive rational numbers with tables, graphs, words, and when possible, symbolic rules

#### 3.2: Represent and analyze mathematical situations and structures using algebraic symbols

3.2.1: Develop an understanding of different uses of variables (e.g., as a placeholder for a specific unknown, as representative of a range of values)

3.2.3: Describe and interpret relationships using information from tables and graphs including coordinate graphs (first quadrant)

#### 3.3: Use mathematical models to represent and understand quantitative relationships

3.3.1: Model and solve contextualized problems using various representations such as graphs, tables, and equations

3.3.2: Recognize and represent direct variation using tables and graphs

#### 3.4: Analyze change in various contexts

3.4.1: Investigate how a change in one variable relates to a change in a second variable

### 4: Measurement

#### 4.1: Understand measurable attributes of objects and the units, systems and processes of measurement

4.1.1: Select the most appropriate unit to measure area and perimeter

#### 4.2: Apply appropriate techniques, tools, and formulas to determine measurements

4.2.1: Determine measurements of length and perimeter to the nearest eighth inch (for length less than one foot) and nearest inch (for lengths greater than one foot)

4.2.3: Develop and use formulas for finding perimeter and area of polygons

4.2.4: Calculate the area and circumference of a circle using pi as well as common approximations of pi (e.g., 3.14, 22/7)

4.2.7: Recognize that two-dimensional shapes having the same perimeter may have different areas and that shapes having the same area may have different perimeters

4.2.8: Analyze how changes in area of a figure affect the dimensions of the figure

4.2.9: Use referents to make estimates of area and evaluate the reasonableness of the estimate (e.g., estimate area of classroom by measuring area of one floor tile)

4.2.10: Calculate rates (e.g., miles per hour, simple interest, people per square mile) to solve problems.

### 5: Geometry

#### 5.1: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

5.1.1: Identify, describe, compare and classify polygons by their sides and angles

5.1.2: Identify and represent the radius, center, diameter, chord and circumference of a circle

5.1.3: Identify combinations of angles that are complementary or supplementary and determine their measures

5.1.4: Use properties of polygons to determine the lengths of sides and perimeters

5.1.5: Develop, understand, and apply the property of the sum of the measures of the interior angles in a polygon as well as the sum of the exterior angles

#### 5.2: Use visualization, spatial reasoning, and geometric modeling to solve problems

5.2.1: Model, sketch, draw and label polygons, circles (including the center, radius, and diameter), complementary angles, supplementary angles, vertical angles, and adjacent angles

5.2.2: Identify and describe the intersection of two or more geometric figures in the plane (e.g., the intersection of a circle and a line)

#### 5.3: Specify locations and describe spatial relationships using coordinate geometry and other representational systems

5.3.1: Plot polygons on coordinate graphs (first quadrant)

#### 5.4: Apply transformations and use symmetry to analyze mathematical situations

5.4.1: Build or sketch a shape that has a given number of lines of symmetry, or rotational symmetries (e.g., sketch a simple polygon with a given number of lines of symmetry)

Correlation last revised: 10/24/2008

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