### 7.NS: The Number System

#### 7.NS.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.

7.NS.1.a: Understand that the additive inverse of a number is its opposite and their sum is equal to zero.

7.NS.1.b: 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.

7.NS.1.c: Translate between the subtraction of rational numbers and addition using the additive inverse, p − q = p + (−q).

7.NS.1.d: Demonstrate that the distance between two rational numbers on the number line is the absolute value of their difference.

7.NS.1.e: Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to add and subtract rational numbers.

#### 7.NS.2: Extend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers.

7.NS.2.a: Understand that the multiplicative inverse of a number is its reciprocal and their product is equal to one.

7.NS.2.b: Understand sign rules for multiplying rational numbers.

7.NS.2.c: Understand sign rules for dividing rational numbers and that a quotient of integers (with a non-zero divisor) is a rational number.

7.NS.2.d: Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to multiply and divide rational numbers.

7.NS.2.e: 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.

#### 7.NS.4: Understand and apply the concepts of comparing and ordering to rational numbers.

7.NS.4.a: 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.

7.NS.4.b: Use concepts of equality and inequality to write and explain real-world and mathematical situations.

### 7.RP: Ratios and Proportional Relationships

#### 7.RP.2: Identify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams, verbal descriptions, and real-world situations.

7.RP.2.a: Determine when two quantities are in a proportional relationship.

7.RP.2.b: Recognize or compute the constant of proportionality.

7.RP.2.c: Understand that the constant of proportionality is the unit rate.

7.RP.2.d: Use equations to model proportional relationships.

7.RP.2.e: 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.

### 7.EEI: Expressions, Equations, and Inequalities

#### 7.EEI.4: Apply the concepts of linear equations and inequalities in one variable to real-world and mathematical situations.

7.EEI.4.a: Write and fluently solve linear equations of the form ax + b = c and a(x + b) = c where a, b, and c are rational numbers.

7.EEI.4.b: 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.

7.EEI.4.c: Write and solve two-step linear inequalities. Graph the solution set on a number line and interpret its meaning.

7.EEI.4.d: Identify and justify the steps for solving multi-step linear equations and two-step linear inequalities.

### 7.GM: Geometry and Measurement

#### 7.GM.2: Construct triangles and special quadrilaterals using a variety of tools (e.g., freehand, ruler and protractor, technology).

7.GM.2.a: Construct triangles given all measurements of either angles or sides.

7.GM.2.b: Decide if the measurements determine a unique triangle, more than one triangle, or no triangle.

#### 7.GM.4: Investigate the concept of circles.

7.GM.4.a: Demonstrate an understanding of the proportional relationships between diameter, radius, and circumference of a circle.

7.GM.4.b: Understand that the constant of proportionality between the circumference and diameter is equivalent to π.

7.GM.4.c: Explore the relationship between circumference and area using a visual model.

7.GM.4.d: Use the formulas for circumference and area of circles appropriately to solve real-world and mathematical problems.

#### 7.GM.6: Apply the concepts of two- and three-dimensional figures to real-world and mathematical situations.

7.GM.6.a: Understand that the concept of area is applied to two-dimensional figures such as triangles, quadrilaterals, and polygons.

7.GM.6.b: 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.

7.GM.6.c: Decompose cubes, right rectangular prisms, and right triangular prisms into rectangles and triangles to derive the formulas for volume and surface area.

7.GM.6.d: Use the formulas for area, volume, and surface area appropriately.

### 7.DSP: Data Analysis, Statistics, and Probability

#### 7.DSP.1: Investigate concepts of random sampling.

7.DSP.1.a: Understand that a sample is a subset of a population and both possess the same characteristics.

7.DSP.1.b: Differentiate between random and non-random sampling.

7.DSP.1.c: Understand that generalizations from a sample are valid only if the sample is representative of the population.

7.DSP.1.d: Understand that random sampling is used to gather a representative sample and supports valid inferences about the population.

#### 7.DSP.5: Investigate the concept of probability of chance events.

7.DSP.5.a: Determine probabilities of simple events.

7.DSP.5.b: Understand that probability measures likelihood of a chance event occurring.

7.DSP.5.c: Understand that the probability of a chance event is a number between 0 and 1.

7.DSP.5.d: Understand that a probability closer to 1 indicates a likely chance event.

7.DSP.5.e: Understand that a probability close to ½ indicates that a chance event is neither likely nor unlikely.

7.DSP.5.f: Understand that a probability closer to 0 indicates an unlikely chance event.

#### 7.DSP.6: Investigate the relationship between theoretical and experimental probabilities for simple events.

7.DSP.6.a: Determine approximate outcomes using theoretical probability.

7.DSP.6.b: Perform experiments that model theoretical probability.

7.DSP.6.c: Compare theoretical and experimental probabilities.

#### 7.DSP.7: Apply the concepts of theoretical and experimental probabilities for simple events.

7.DSP.7.b: Develop both uniform and non-uniform probability models.

7.DSP.7.c: Perform experiments to test the validity of probability models.

#### 7.DSP.8: Extend the concepts of simple events to investigate compound events.

7.DSP.8.a: Understand that the probability of a compound event is between 0 and 1.

7.DSP.8.b: Identify the outcomes in a sample space using organized lists, tables, and tree diagrams.

7.DSP.8.c: Determine probabilities of compound events using organized lists, tables, and tree diagrams.

7.DSP.8.d: Design and use simulations to collect data and determine probabilities.

7.DSP.8.e: Compare theoretical and experimental probabilities for compound events.

Correlation last revised: 9/16/2020

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