In this lesson, students have a chance to recall one way of understanding equivalent expressions, that is, the expressions have the same value for any number substituted for a variable. Then they use properties they have studied over the past several lessons to understand how to properly write an equivalent expression using fewer terms. We are gently building up to students being able to fluently combine like terms, though that language is not used with students yet.
- Apply properties of operations to justify (orally and in writing) that expressions are equivalent.
- Generate an expression that is equivalent to a given expression with fewer terms.
- Interpret different methods for determining whether expressions are equivalent, and evaluate (orally) their usefulness.
Let's see how we can tell that expressions are equivalent.
- I can figure out whether two expressions are equivalent to each other.
- When possible, I can write an equivalent expression that has fewer terms.
To expand an expression, we use the distributive property to rewrite a product as a sum. The new expression is equivalent to the original expression.
For example, we can expand the expression \(5(4x+7)\) to get the equivalent expression \(20x + 35\).
factor (an expression)
To factor an expression, we use the distributive property to rewrite a sum as a product. The new expression is equivalent to the original expression.
For example, we can factor the expression \(20x + 35\) to get the equivalent expression \(5(4x+7)\).
A term is a part of an expression. It can be a single number, a variable, or a number and a variable that are multiplied together. For example, the expression \(5x + 18\) has two terms. The first term is \(5x\) and the second term is 18.