In this Grade 8 lesson from Saxon Math Course 3, students learn how to add integers — including positive, negative, and zero values — using number lines, real-world contexts like temperature and debt, and sign rules for determining the sum. The lesson also introduces collecting like terms, helping students simplify algebraic expressions by combining terms with the same variable. These foundational skills support students in solving equations and working with algebra throughout Chapter 4.
Section 1
📘 The Language of Algebra: An Introduction
This course introduces the foundational rules of algebra. You'll learn how to work with integers and variables to solve increasingly complex real-world problems.
To begin, we'll establish our foundation by learning the rules for adding integers and using them to simplify algebraic expressions by collecting like terms.
Section 2
Addition with Two Integers
To find the sum of addends with different signs:
To find the sum of addends with the same sign:
Think of adding integers like a game of tug-of-war on a number line! When signs are different, the team with the greater absolute value wins and gets to keep its sign, with the final score being the difference between their strengths. When signs are the same, they're on the same team, so just combine their power and keep the sign!
Section 3
Like terms
Like terms have identical variable parts, including exponents. The variables may appear in any order.
Imagine variables are secret family names. The term 3xy is from the 'xy' family, and so is yx since the order of variables doesn't matter! But x^2y is a different family because the exponent changes the name. You can only combine terms that belong to the exact same family tree, including their exponents, to keep things tidy.
Section 4
Collecting like terms
We combine or 'collect' like terms by adding their numerical coefficients. The variables do not change.
Think of collecting like terms as sorting your laundry. You can only combine socks with socks and shirts with shirts. In algebra, you combine terms with the exact same variable part, like 'x' with 'x' or 'ab' with 'ab'. The number in front, the coefficient, just tells you how many of each item you have collected.
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Section 1
📘 The Language of Algebra: An Introduction
This course introduces the foundational rules of algebra. You'll learn how to work with integers and variables to solve increasingly complex real-world problems.
To begin, we'll establish our foundation by learning the rules for adding integers and using them to simplify algebraic expressions by collecting like terms.
Section 2
Addition with Two Integers
To find the sum of addends with different signs:
To find the sum of addends with the same sign:
Think of adding integers like a game of tug-of-war on a number line! When signs are different, the team with the greater absolute value wins and gets to keep its sign, with the final score being the difference between their strengths. When signs are the same, they're on the same team, so just combine their power and keep the sign!
Section 3
Like terms
Like terms have identical variable parts, including exponents. The variables may appear in any order.
Imagine variables are secret family names. The term 3xy is from the 'xy' family, and so is yx since the order of variables doesn't matter! But x^2y is a different family because the exponent changes the name. You can only combine terms that belong to the exact same family tree, including their exponents, to keep things tidy.
Section 4
Collecting like terms
We combine or 'collect' like terms by adding their numerical coefficients. The variables do not change.
Think of collecting like terms as sorting your laundry. You can only combine socks with socks and shirts with shirts. In algebra, you combine terms with the exact same variable part, like 'x' with 'x' or 'ab' with 'ab'. The number in front, the coefficient, just tells you how many of each item you have collected.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter