In this lesson from OpenStax Prealgebra 2E, students learn how to add integers, including both positive and negative numbers, using two-color counter models and number line strategies. The lesson builds skills in simplifying expressions with integers, evaluating variable expressions, and translating word phrases into algebraic expressions. Real-world applications such as temperature, elevation, and banking help reinforce the concept of integer addition in context.
Section 1
📘 Add Integers
This lesson introduces adding positive and negative numbers. You'll learn the rules for adding integers with the same or different signs, then apply these skills to simplify expressions, evaluate variables, and solve real-world problems.
First, you’ll see how to model integer addition using visual examples. Then, you'll jump into practice cards to master simplifying and evaluating expressions.
Section 2
Model addition of integers
We will model addition of negatives with two color counters. We let a blue counter represent a positive and a red counter will represent a negative. If we have one positive and one negative counter, the value of the pair is zero. They form a neutral pair.
Section 3
Simplify expressions with integers
When the signs are the same, the counters would be all the same color, so add them. When the signs are different, some counters would make neutral pairs; subtract to see how many are left.
Section 4
Evaluate variable expressions with integers
To evaluate an expression means to substitute a number for the variable in the expression. Now we can use negative numbers as well as positive numbers when evaluating expressions.
Section 5
Translate word phrases to algebraic expressions
All our earlier work translating word phrases to algebra also applies to expressions that include both positive and negative numbers. Remember that the phrase the sum indicates addition. The phrase increased by also indicates addition.
Section 6
Add integers in applications
Solving applications is easy if we have a plan. First, we determine what we are looking for. Then we write a phrase that gives the information to find it. We translate the phrase into math notation and then simplify to get the answer. Finally, we write a sentence to answer the question.
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Section 1
📘 Add Integers
This lesson introduces adding positive and negative numbers. You'll learn the rules for adding integers with the same or different signs, then apply these skills to simplify expressions, evaluate variables, and solve real-world problems.
First, you’ll see how to model integer addition using visual examples. Then, you'll jump into practice cards to master simplifying and evaluating expressions.
Section 2
Model addition of integers
We will model addition of negatives with two color counters. We let a blue counter represent a positive and a red counter will represent a negative. If we have one positive and one negative counter, the value of the pair is zero. They form a neutral pair.
Section 3
Simplify expressions with integers
When the signs are the same, the counters would be all the same color, so add them. When the signs are different, some counters would make neutral pairs; subtract to see how many are left.
Section 4
Evaluate variable expressions with integers
To evaluate an expression means to substitute a number for the variable in the expression. Now we can use negative numbers as well as positive numbers when evaluating expressions.
Section 5
Translate word phrases to algebraic expressions
All our earlier work translating word phrases to algebra also applies to expressions that include both positive and negative numbers. Remember that the phrase the sum indicates addition. The phrase increased by also indicates addition.
Section 6
Add integers in applications
Solving applications is easy if we have a plan. First, we determine what we are looking for. Then we write a phrase that gives the information to find it. We translate the phrase into math notation and then simplify to get the answer. Finally, we write a sentence to answer the question.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter