Algebraic Expressions
Lessons in this chapter
About Algebraic Expressions
An Introduction to Algebra and Algebraic Expressions is where letters arrive, and the shift is smaller than it looks: a variable is a placeholder for a number, and every rule that applied to numbers still applies.
Identify Patterns and Parts of Algebraic Expressions gives the vocabulary: terms, coefficients, variables, constants. In 3x + 5, the 3 is the coefficient, x is the variable, 3x is a term and 5 is a constant, and having the names makes every instruction afterwards readable.
Evaluate Algebraic Expressions substitutes a value and calculates, which is the safest way into algebra because it is arithmetic with one extra step. Write Algebraic Expressions from Verbal Descriptions goes the other way, and the order-sensitive phrases are the trap: “five less than x” is x − 5, not 5 − x.
Apply Properties of Operations to Simplify Expressions and Apply the Distributive Property to Simplify Expressions carry the familiar properties into the new notation. Combining like terms works because 3x + 2x is three of something plus two of the same thing.
Factor Algebraic Expressions Using the Greatest Common Factor is the distributive property run backwards, and it is where the GCF work from earlier in the year pays off: 6x + 9 becomes 3(2x + 3).
All six lessons in this chapter open as 6th grade math worksheets inside the page. Evaluate Algebraic Expressions, Write Algebraic Expressions from Verbal Descriptions and Apply the Distributive Property to Simplify Expressions each give math problems worked one at a time and marked as you go. They are free to try, with no login needed for your first 3.
Frequently asked questions
Identify Patterns and Parts of Algebraic Expressions names the pieces, terms, coefficients and variables, so there is vocabulary to work with. Evaluate Algebraic Expressions substitutes a value and calculates, and Write Algebraic Expressions from Verbal Descriptions runs it the other way, from a sentence to an expression, which is the step most children find hardest. Apply Properties of Operations to Simplify Expressions and Apply the Distributive Property to Simplify Expressions then rewrite expressions without changing their value, and Factor Algebraic Expressions Using the Greatest Common Factor reverses the distributive step. The chapter sits in the Common Core domain Expressions and Equations (6.EE).
A letter standing in for a number. It is a placeholder, and every arithmetic rule that applied to numbers still applies to it.
3x and 5 are terms, 3 is the coefficient, x is the variable, and 5 is a constant because its value never changes.
x − 5, not 5 − x. The order-sensitive phrases are where most translation errors happen, and subtraction is the one that bites.
Adding terms with the same variable. 3x + 2x is 5x, because three of something plus two of the same thing is five of it. 3x + 2y cannot be combined.
Find the greatest common factor of the terms and pull it out. 6x + 9 has a GCF of 3, so it becomes 3(2x + 3). It is the distributive property reversed.