(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

In the future this will contain narratives and other information about the Domain.

## 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-06.NS.01

 6th Grade MAT Targeted StandardsDomain (NS) The Number SystemCluster: Apply and extend previous understandings of multiplication and division to divide fractions by fractions MAT-06.NS.01 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.). How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

## Student Learning Targets:

### Reasoning Targets

• I can interpret quotients of fractions.

### Skills Domain (Performance) Targets

• I can solve word problems involving division of fractions by fractions.
• I can compute quotients of fractions.

## Resources

### Websites

#### MAT-06.NS.02

Domain (NS) The Number System
Cluster: Compute fluently with multi-digit numbers and find common factors and multiples

MAT-06.NS.02 Fluently divide multi-digit numbers using the standard algorithm.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

***MAT-5.1.22 Divide multi-digit numbers by two-digit numbers with or without remainders

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-06.NS.03

 6th Grade MAT Targeted StandardsDomain (NS) The Number SystemCluster: Compute fluently with multi-digit numbers and find common factors and multiples MAT-06.NS.03 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

## Student Learning Targets:

### Skills Domain (Performance) Targets

• I can add multi-digit decimals.
• I can subtract multi-digit decimals.
• I can multiply multi-digit decimals.
• I can divide multi-digit decimals using the standard algorithm for each operation

## Resources

### Websites

#### MAT-06.NS.04

Domain (NS) The Number System
Cluster: Compute fluently with multi-digit numbers and find common factors and multiples

MAT-06.NS.04 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two wholenumbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

For example, express 36 + 8 as 4 (9 + 2).

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-5.1.18 Determine least common multiple

**MAT-6.1.5 Generate a list of factors, prime factors, and multiples

• **MAT-7.1.3. Use prime factorization to determine the greatest common factor and least common multiple
• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-06.NS.05

 6th Grade MAT Targeted StandardsDomain (NS) The Number SystemCluster: Compute fluently with multi-digit numbers and find common factors and multiples MAT-06.NS.05 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

## Student Learning Targets:

### Knowledge Targets

• I can explain the meaning of 0 in each situation.
• I can describe quantities having opposite directions or values.

### Skills Domain (Performance) Targets

• I can use positive and negative numbers to represent quantities in real-world context.

## Resources

### Websites

#### MAT-06.NS.06

Domain (NS) The Number System
Cluster: Apply and extend previous understandings of numbers to the system of rational numbers

MAT-06.NS.06 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

• a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
• b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
• c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

***MAT-6.2.4 Use ordered pairs to locate a point on a coordinate plane

**MAT-5.1.5. Place integers on a number line

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-06.NS.06.a

Domain (NS) The Number System
Cluster: Apply and extend previous understandings of numbers to the system of rational numbers

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

MAT-06.NS.06.a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

#### MAT-06.NS.06.b

Domain (NS) The Number System
Cluster: Apply and extend previous understandings of numbers to the system of rational numbers

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

MAT-06.NS.06.b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

#### MAT-06.NS.06.c

Domain (NS) The Number System
Cluster: Apply and extend previous understandings of numbers to the system of rational numbers

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

MAT-06.NS.06.c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

#### MAT-06.NS.07

 6th Grade MAT Targeted StandardsDomain (NS) The Number SystemCluster: Apply and extend previous understandings of numbers to the system of rational numbers MAT-06.NS.07 Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world.  d. Distinguish comparisons of absolute value from statements about order.

## Student Learning Targets:

### Knowledge Targets

• I can explain inequalities used in real world situations.
• I can define absolute value.

### Reasoning Targets

• I can compare two numbers on a number line based on their locations.
• I can express the comparison of two numbers using inequality symbols.

### Skills Domain (Performance) Targets

• I can graph an inequality on a number line.
• I can explain inequalities used in real world situations.
• I can use absolute value to describe magnitude or size in real world situations.

## Proficiency Scale

Please refer to the proficiency scales for standards MAT-06.NS.07a | MAT-06.NS.07b | MAT-06.NS.07c.

## Resources

### Websites

#### MAT-06.NS.07.a

 6th Grade MAT Targeted StandardsDomain (NS) The Number SystemCluster: Apply and extend previous understandings of numbers to the system of rational numbers Understand ordering and absolute value of rational numbers. MAT-06.NS.07.a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

## Student Learning Targets:

### Reasoning Targets

• I can compare two numbers on a number line based on their locations.
• I can express the comparison of two numbers using inequality symbols.

### Skills Domain (Performance) Targets

• I can explain inequalities used in real world situations.
• I can graph an inequality on a number line.

## Resources

### Websites

#### MAT-06.NS.07.b

 6th Grade MAT Targeted StandardsDomain (NS) The Number SystemCluster: Apply and extend previous understandings of numbers to the system of rational numbers Understand ordering and absolute value of rational numbers. MAT-06.NS.07.b Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3°C > –7°C to express the fact that –3°C is warmer than –7°C.

## Student Learning Targets:

### Knowledge Targets

• I can explain inequalities used in real world situations.

## Resources

### Websites

#### MAT-06.NS.07.c

 6th Grade MAT Targeted StandardsDomain (NS) The Number SystemCluster: Apply and extend previous understandings of numbers to the system of rational numbers Understand ordering and absolute value of rational numbers. MAT-06.NS.07.c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.

## Student Learning Targets:

### Knowledge Targets

• I can define absolute value.

### Reasoning Targets

• I can use absolute value to describe magnitude or size in real world situations.

## Resources

### Websites

#### MAT-06.NS.07.d

 6th Grade MAT Targeted StandardsDomain (NS) The Number SystemCluster: Apply and extend previous understandings of numbers to the system of rational numbers Understand ordering and absolute value of rational numbers. MAT-06.NS.07.d Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.

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## Proficiency Scale

 Score Description Sample Activity 4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. - 2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). 2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). - 1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). 1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). - 0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). 0.0 Even with help, the student demonstrates no understanding or skill. -

## Resources

### Vocabulary

• List

#### MAT-06.NS.08

 6th Grade MAT Targeted StandardsDomain (NS) The Number SystemCluster: Apply and extend previous understandings of numbers to the system of rational numbers MAT-06.NS.08 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

## Student Learning Targets:

### Skills Domain (Performance) Targets

• I can solve real-world problems by graphing points in all four quadrants.
• I can find the distance between points with the same first or second coordinate.