Apply and extend previous understandings of numbers to the system of rational numbers. 

NC.6.NS.7 Understand ordering 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. 

Apply and extend previous understandings of numbers to the system of rational numbers.

NC.6.NS.5 Understand and use rational numbers to: 

• Describe quantities having opposite directions or values.

• Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. 

• Understand the absolute value of a rational number as its distance from 0 on the number line to: 

• Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. 

• o Distinguish comparisons of absolute value from statements about order. 

NC.6.NS.9 Apply and extend previous understandings of addition and subtraction. 

• Describe situations in which opposite quantities combine to make 0. 

• Understand 𝑝𝑝+𝑞𝑞 as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. 

• Understand subtraction of integers as adding the additive inverse, 𝑝𝑝−𝑞𝑞=𝑝𝑝+(–𝑞𝑞). Show that the distance between two integers on the number line is the absolute value of their difference. 

• Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. 

Apply and extend previous understandings of numbers to the system of rational numbers. 

NC.6.NS.6 Understand rational numbers as points on the number line and as ordered pairs on a coordinate plane. 

a. On a number line: 

• Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself.

• Find and position rational numbers on a horizontal or vertical number line. 

b. On a coordinate plane:

• Understand signs of numbers in ordered pairs as indicating locations in quadrants. 

• Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. 

• Find and position pairs of rational numbers on a coordinate plane. 

Apply and extend previous understandings of numbers to the system of rational numbers. 

NC.6.NS.9 Apply and extend previous understandings of addition and subtraction. ● Describe situations in which opposite quantities combine to make 0

• Understand 𝑝𝑝+𝑞𝑞 as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. 

• Understand subtraction of integers as adding the additive inverse, 𝑝𝑝−𝑞𝑞=𝑝𝑝+(–𝑞𝑞). Show that the distance between two integers on the number line is the absolute value of their difference. 

• Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. 

NC.6.NS.6 Understand rational numbers as points on the number line and as ordered pairs on a coordinate plane. 

a. On a number line: 

• Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself.

• Find and position rational numbers on a horizontal or vertical number line. 

NC.6.NS.8 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. 

NC.6.NS.6 Understand rational numbers as points on the number line and as ordered pairs on a coordinate plane. 

• a. On a number line: o Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. o Find and position rational numbers on a horizontal or vertical number line. 

• b. On a coordinate plane: o Understand signs of numbers in ordered pairs as indicating locations in quadrants. o Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. o Find and position pairs of rational numbers on a coordinate plane. 

NC.6.NS.7 Understand ordering 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.