(NS) The Number System Categories All categories Not categorized Prioritized Standards (EE) Expressions and Equations (G) Geometry (NS) The Number System (RP) Ratios and Proportional Relationships (SP) Statistics and Probability

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# The Number System

## Narrative for the (NS) The Number System

The standards within the Number System domain require students to apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

## 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.NS.01

 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.01 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. a. Describe situations in which opposite quantities combine to make 0. b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. d. Apply properties of operations as strategies to add and subtract rational numbers.

## Student Learning Targets:

### Knowledge Targets

• I can plot integers and rational numbers on a number line.

### Reasoning Targets

• I can represent addition and subtraction problems on a number line.

### Skills Domain (Performance) Targets

• I can add and subtract integers.
• I can add and subtract rational numbers.

## Resources

### Vocabulary

• integer
• rational number
• absolute value
• opposite

#### MAT-07.NS.01.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 addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. MAT-07.NS.01.a Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

## Student Learning Targets:

### Knowledge Targets

• I know that opposite numbers combine to make zero.

### Reasoning Targets

• I can describe situations where opposite numbers combine to make zero.

## Resources

### Vocabulary

• opposite

#### MAT-07.NS.01.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 addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. MAT-07.NS.01.b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

## Student Learning Targets:

### Knowledge Targets

• I can show that a number and its opposite are additive inverses.

### Reasoning Targets

• I can represent addition of rational numbers on a vertical or horizontal number line using the sign of the value being added to determine direction.
• I can describe sums of rational numbers in real world contexts.

## Resources

### Vocabulary

Positive, Negative, Opposite, Additive Inverse, Absolute Value, Integer, Rational Numbers.

#### MAT-07.NS.01.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 addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. MAT-07.NS.01.c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

## Student Learning Targets:

### Knowledge Targets

• I can show the distance between two rational number on the number line is the absolute value of their difference
• I can use the additive inverse to write a subtraction problem as an addition problem

### Skills Domain (Performance) Targets

• I can subtract rational numbers in real world contexts.

## Resources

### Websites

• Try searching - integer addition, integer subtraction, rational numbers, rational numbers addition, rational numbers subtraction
• www.bigideasmath.com
• Chapter 1 - Integer addition and subtraction sections
• Chapter 2 - Rational numbers addition and subtraction sections

### Vocabulary

• rational number
• integer
• absolute value
• opposite

#### MAT-07.NS.01.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 addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. MAT-07.NS.01.d Apply properties of operations as strategies to add and subtract rational numbers.

## Student Learning Targets:

### Skills Domain (Performance) Targets

• I can add rational numbers
• I can subtract rational numbers

## Resources

### Vocabulary

• Integer
• rational number
• absolute value
• opposite

#### 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

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