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#### 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.

# Ratios and Proportional Relationships

## Narrative for (RP) Ratios and Proportional Relationships

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.RP.01

Domain (RP) Ratios and Proportional Relationships
Cluster: Understand ratio concepts and use ratio reasoning to solve problems

MAT-06.RP.01 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-6.1.1 Use a fraction to represent parts of a whole, division, or a ratio

**MAT-7.1.1 Use ratios and proportions to represent relationships

• *** 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.RP.02

Domain (RP) Ratios and Proportional Relationships
Cluster: TOPIC

MAT-06.RP.02 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of$5 per hamburger.”

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-8.5.6 Solve problems involving rates; i.e., speed equals distance divided by time (miles per hour)

• *** 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.RP.03

 6th Grade MAT Targeted StandardsDomain (RP) Ratios and Proportional RelationshipsCluster: Understand ratio concepts and use ratio reasoning to solve problems MAT-06.RP.03 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems including those involving unit pricing and constant speed. c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

## Student Learning Targets:

### Knowledge Targets

• I can convert ratios to percents.

### Reasoning Targets

• I can determine the relationship between two or more ratios.
• I can determine equivalent ratios.
• I can determine equivalent relationships between ratios.
• I can compare equivalent ratios to find missing values in a table.
• I can solve real world problems involving ratios and rates.
• I can solve real-world problems involving ratios and percents.
• I can determine if rates are equivalent.

### Skills Domain (Performance) Targets

• I can make tables of equivalent ratios relating quantities with whole-number measurements.
• I can graph points of equivalent ratios on a coordinate plan.
• I can calculate unit rates.
• I can manipulate units appropriately when multiplying and dividing.
• I can establish ratios to convert measurements within a system.

## Proficiency Scale

Please refer to the proficiency scales attached to standards MAT-06.RP.3b | MAT-06.RP.3cMAT-06.RP.3d |

## Resources

### Websites

#### MAT-06.RP.03.a

 6th Grade MAT Targeted StandardsDomain (RP) Ratios and Proportional RelationshipsCluster: Understand ratio concepts and use ratio reasoning to solve problems Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. MAT-06.RP.03.a Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

## Student Learning Targets:

### Reasoning Targets

• I can determine the relationship between two or more ratios.
• I can determine equivalent ratios.
• I can determine equivalent relationships between ratios.
• I can compare equivalent ratios to find missing values in a table.

### Skills Domain (Performance) Targets

• I can graph points of equivalent ratios on a coordinate plane.

### Product Targets

• I can make tables of equivalent ratios relating quantities with whole-number measurements.