Ch 11 - Integers

NC Standards -- The Number System

Math Study Jams - Integers

Math Scoring Guide - Practice Questions

Lessons

Exploring Integers
Comparing and Ordering Integers
Adding Integers
Subtracting Integers
Multiplying Integers
Dividing Integers
Solving Equations with Integers
Graphing in the Coordinate Plane
Application of Integers
Graphing Functions

Rational Numbers

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.

11-1, Exploring Integers

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.
Distinguish comparisons of absolute value from statements about order.

11-2. Comparing and Ordering Integers

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.

11-3, Adding Integers

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.

11-4, Subtracting Integers

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.

11-5, Multiplying Integers

Not on EOG.

11-6, Dividing Integers

Not on EOG.

11-7, Solving Equations with Integers

Solving Equations with Integers
Application: Budget

11-8, Graphing in the Coordinate Plane

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.

11-8, Graphing in the Coordinate Plane

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.

11-9, Application of Integers

Finding Profit or Loss
Drawing and Interpreting Graphs

11-10, Graphing Functions

Completing a Function Table
Graphing a Function
Application: Salaries

What you must be able to do...

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.
- Distinguish comparisons of absolute value from statements about order

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.

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.

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

Describe situations in which opposite quantities combine to make 0.
Understand 𝑝 + 𝑞 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, 𝑝 − 𝑞 = 𝑝 +(– 𝑞). 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.