### 1: The Number System

#### 1.1: Extend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line.

1.1.1: Understand that the additive inverse of a number is its opposite and their sum is equal to zero.

1.1.2: Understand that the sum of two rational numbers (p + q) represents a distance from p on the number line equal to |q| where the direction is indicated by the sign of q.

1.1.3: Translate between the subtraction of rational numbers and addition using the additive inverse, p − q = p + (−q).

1.1.5: Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to add and subtract rational numbers.

#### 1.2: Extend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers.

1.2.2: Understand sign rules for multiplying rational numbers.

1.2.3: Understand sign rules for dividing rational numbers and that a quotient of integers (with a non-zero divisor) is a rational number.

1.2.4: Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to multiply and divide rational numbers.

1.2.5: Understand that some rational numbers can be written as integers and all rational numbers can be written as fractions or decimal numbers that terminate or repeat.

#### 1.4: Understand and apply the concepts of comparing and ordering to rational numbers.

1.4.1: Interpret statements using less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), and equal to (=) as relative locations on the number line.

1.4.2: Use concepts of equality and inequality to write and explain real-world and mathematical situations.

### 2: Ratios and Proportional Relationships

#### 2.2: Identify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams, verbal descriptions, and real-world situations.

2.2.1: Determine when two quantities are in a proportional relationship.

2.2.2: Recognize or compute the constant of proportionality.

2.2.3: Understand that the constant of proportionality is the unit rate.

2.2.4: Use equations to model proportional relationships.

2.2.5: Investigate the graph of a proportional relationship and explain the meaning of specific points (e.g., origin, unit rate) in the context of the situation.

### 3: Expressions, Equations, and Inequalities

#### 3.4: Apply the concepts of linear equations and inequalities in one variable to real-world and mathematical situations.

3.4.2: Write and solve multi-step linear equations that include the use of the distributive property and combining like terms. Exclude equations that contain variables on both sides.

3.4.3: Write and solve two-step linear inequalities. Graph the solution set on a number line and interpret its meaning.

3.4.4: Identify and justify the steps for solving multi-step linear equations and two-step linear inequalities.

### 4: Geometry and Measurement

#### 4.4: Investigate the concept of circles.

4.4.2: Understand that the constant of proportionality between the circumference and diameter is equivalent to π.

4.4.3: Explore the relationship between circumference and area using a visual model.

4.4.4: Use the formulas for circumference and area of circles appropriately to solve real-world and mathematical problems.

#### 4.6: Apply the concepts of two- and three-dimensional figures to real-world and mathematical situations.

4.6.1: Understand that the concept of area is applied to two-dimensional figures such as triangles, quadrilaterals, and polygons.

4.6.2: Understand that the concepts of volume and surface area are applied to three-dimensional figures such as cubes, right rectangular prisms, and right triangular prisms.

4.6.3: Decompose cubes, right rectangular prisms, and right triangular prisms into rectangles and triangles to derive the formulas for volume and surface area.

4.6.4: Use the formulas for area, volume, and surface area appropriately.

### 5: Data Analysis, Statistics, and Probability

#### 5.1: Investigate concepts of random sampling.

5.1.1: Understand that a sample is a subset of a population and both possess the same characteristics.

5.1.2: Differentiate between random and non-random sampling.

5.1.3: Understand that generalizations from a sample are valid only if the sample is representative of the population.

5.1.4: Understand that random sampling is used to gather a representative sample and supports valid inferences about the population.

#### 5.5: Investigate the concept of probability of chance events.

5.5.1: Determine probabilities of simple events.

5.5.4: Understand that a probability closer to 1 indicates a likely chance event.

5.5.5: Understand that a probability close to ½ indicates that a chance event is neither likely nor unlikely.

5.5.6: Understand that a probability closer to 0 indicates an unlikely chance event.

#### 5.6: Investigate the relationship between theoretical and experimental probabilities for simple events.

5.6.1: Determine approximate outcomes using theoretical probability.

5.6.2: Perform experiments that model theoretical probability.

5.6.3: Compare theoretical and experimental probabilities.

#### 5.7: Apply the concepts of theoretical and experimental probabilities for simple events.

5.7.3: Perform experiments to test the validity of probability models.

#### 5.8: Extend the concepts of simple events to investigate compound events.

5.8.1: Understand that the probability of a compound event is between 0 and 1.

5.8.2: Identify the outcomes in a sample space using organized lists, tables, and tree diagrams.

5.8.3: Determine probabilities of compound events using organized lists, tables, and tree diagrams.

5.8.4: Design and use simulations to collect data and determine probabilities.

5.8.5: Compare theoretical and experimental probabilities for compound events.

Correlation last revised: 1/5/2017

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