This is an optional lesson to practice identifying and writing equivalent expressions using the distributive property. If your students don’t need additional practice at this point, this lesson can be skipped (or saved for a review days later) without missing any new material.
- Draw a diagram to justify that two expressions that are related by the distributive property are equivalent.
- Explain (orally) how to use the distributive property to identify or generate equivalent algebraic expressions.
- Use the distributive property to write equivalent algebraic expressions, including where the common factor is a variable.
Let's practice writing equivalent expressions by using the distributive property.
- I can use the distributive property to write equivalent expressions with variables.
Equivalent expressions are always equal to each other. If the expressions have variables, they are equal whenever the same value is used for the variable in each expression.
For example, \(3x+4x\) is equivalent to \(5x+2x\). No matter what value we use for \(x\), these expressions are always equal. When \(x\) is 3, both expressions equal 21. When \(x\) is 10, both expressions equal 70.
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.