In this lesson, students are still working toward gaining fluency in writing equivalent expressions. The goal of this lesson is to highlight a particular common error: mishandling the subtraction in an expression like \(8-3(4+9x).\) To this end, students first analyze and explain the error in several incorrect ways of rewriting this expression. Then, they consider the effect of inserting parentheses in different places in an expression with four terms.
- Critique (in writing) methods for generating equivalent expressions with fewer terms.
- Generate expressions that are not equivalent, but differ only in the placement of parentheses, and justify (orally) that they are not equivalent.
- Write expressions with fewer terms that are equivalent to a given expression that includes negative coefficients and parentheses.
Let’s see how to use properties correctly to write equivalent expressions.
Access to index cards is suggested for students to need help isolating one expression at a time. They can use the index card to cover up nearby expressions.
- I am aware of some common pitfalls when writing equivalent expressions, and I can avoid them.
- 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.