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#### MAT-07.NS.02

 7th Grade MAT Targeted StandardsDomain (NS) The Number SystemCluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers MAT-07.NS.02 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret products of rational numbers by describing real-world contexts. c. Apply properties of operations as strategies to multiply and divide ational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

## Student Learning Targets:

Skills Domain (Performance) Targets

• I can multiply and divide integers.
• I can multiply and divide rational numbers. (This includes work with positive and negative fractions and decimal numbers.)

### Vocabulary

Integer, Rational Numbers, Terminating Decimals, and Repeating Decimals.

#### MAT-07.NS.02.a

 7th Grade MAT Targeted StandardsDomain (NS) The Number SystemCluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. MAT-07.NS.02.a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

## Student Learning Targets:

### Reasoning Targets

• I can relate the properties of multiplication of fractions to the multiplication of rational numbers.
• I can interpret products of rational numbers by describing real world situations.

### Skills Domain (Performance) Targets

• I can use the rules for multiplying signed numbers to determine the sign of the product.

## Resources

### Vocabulary

• integer
• rational number

#### MAT-07.NS.02.b

 7th Grade MAT Targeted StandardsDomain (NS) The Number SystemCluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. MAT-07.NS.02.b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret products of rational numbers by describing real-world contexts.

## Student Learning Targets:

### Reasoning Targets

• I can explain why dividing by zero is undefined.
• I can interpret quotients of rational numbers by describing real world situations

### Skills Domain (Performance) Targets

• I can use the rules for dividing signed numbers to determine the sign of the quotient.

## Resources

### Vocabulary

• product
• quotient
• integer
• rational number

#### MAT-07.NS.02.c

 7th Grade MAT Targeted StandardsDomain (NS) The Number SystemCluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. MAT-07.NS.02.c Apply properties of operations as strategies to multiply and divide rational numbers.

## Student Learning Targets:

### Skills Domain (Performance) Targets

• I can multiply rational numbers using the properties of operations.
• I can divide rational numbers using the properties of operations.

## Resources

### Vocabulary

• Integer
• rational number
• product
• quotient

#### MAT-07.NS.02.d

 7th Grade MAT Targeted StandardsDomain (NS) The Number SystemCluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. MAT-07.NS.02.d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

## Student Learning Targets:

### Knowledge Targets

• I know that the decimal form of a rational number terminates or repeats.

### Skills Domain (Performance) Targets

• I can convert rational numbers into decimals using long division.

## Resources

### Vocabulary

• decimal
• fraction
• rational number

#### MAT-07.NS.03

 7th Grade MAT Targeted StandardsDomain (NS) The Number SystemCluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers MAT-07.NS.03 Solve real-world and mathematical problems involving the four operations with rational numbers.

## Student Learning Targets:

### Skills Domain (Performance) Targets

• I can add rational numbers
• I can subtract rational numbers
• I can multiply rational numbers
• I can divide rational numbers
• I can simplify expressions with absolute value elements
• I can apply the order of operations to solve problems
• I can write word problems into mathematical notation

## Resources

### Vocabulary

• rational number
• absolute value

# Ratios and Proportional Relationships

## Narrative for (RP) Ratios and Proportional Relationships

The standards within the Ratios and Proportional Relationships Domain require students to analyze proportional relationships and use them to solve real world and mathematical problems.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-07.RP.01

 7th Grade MAT Targeted StandardsDomain (RP) Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems MAT-07.RP.01 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, If a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ½ / ¼ miles per hour, equivalently 2 miles per hour.

## Student Learning Targets:

### Knowledge Targets

• I know that a ratio is a comparison of two quantities using division
• I can identify equivalent ratios
• I can write a ratio in lowest terms

### Reasoning Targets

• I can create equivalent ratios
• I can write ratios to represent practical problems

### Skills Domain (Performance) Targets

• I can calculate a unit rate.

## Resources

### Vocabulary

• unit rate
• ratio
• rate

#### MAT-07.RP.02

 7th Grade MAT Targeted StandardsDomain (RP) Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems MAT-07.RP.02 Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

## Student Learning Targets:

### Knowledge Targets

• I can understand that a proportional relationship is when two ratios are equal

### Reasoning Targets

• I can determine when a proportional relationship is being represented
• I can determine that ratios are proportional if their cross products are equal

## Resources

### Vocabulary

• ratio
• proportion
• cross products

#### MAT-07.RP.02.a

 7th Grade MAT Targeted StandardsDomain (RP) Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems Recognize and represent proportional relationships between quantities. MAT-07.RP.02.a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

## Student Learning Targets:

### Reasoning Targets

• I can determine if two quantities are proportional using a variety of methods (tables, graphs, diagrams, equations, or verbal description

## Resources

### Vocabulary

• ratio
• proportion
• cross product

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