Distributive Property (Factoring) Lesson Plan

Overview

In this lesson, we will introduce how to write expressions in factored form for `7`th graders. Using the box method to review distributive property can help students make connections with factoring as well. Students will practice factoring expressions with `2` and `3` terms. You can expect this lesson with additional practice to take one `45`-minute class period.

Grade 7

Expressions, Equations, And Inequalities

7.EE.A.1

How to Teach Writing Expressions in Factored Form

Warm Up

Students should review the distributive property to simplify the expressions. Students may use different methods to show their work, such as drawing arrows or the box method.

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Review the methods students chose to simplify each expression. It may be helpful to review the box method with students if they do not offer it on their own to help them with factoring later:

Comparing Expressions

Ask students how they might go from their simplified expression to the given expression. Some students may recognize that the value outside of the parentheses is the greatest common factor. Using the box method when reviewing student methods may help students better understand how the values are all related.

Area model or Box method

To help students connect the distributive property to factoring, use the box method with the first example. Having the expression written in the box for students can help them recognize that they are trying to find what would be outside of the boxes. Based on students’ current knowledge, give them a minute or two to try and write the expression in factored form.

It is quite okay if students factor out some common factor (other than `1`). As students share their work, they will notice that students might have factored out `2, 3,` or `6`.

If students are not sure where to start, ask students which of the three gray boxes would affect both `6x` and `18`. This can help students recognize that they need to figure out what can be divided by both numbers first.

Using the box method to factor with positive values will be a review from `6`th grade, so make sure students can write the expression as `6(x + 3)` from the box method before moving forward.

Factoring with subtraction

Encourage students to use the box method to try and factor the expression. As students try this problem, they should also check their work with a partner or table group.

Factor `24y - 9`

Some students may opt to think through these problems without drawing the box. For some students, they may accidentally lose the negative in front of the constant. Encourage students to check their work by using the distributive property with their expression in factored form.

Factoring with multiple variables

With this example, remind students to be mindful of their signs! Allow students some time to factor the expression and check with a partner.

Factor `-12x - 27y`

Students should recognize that the variables are different, so they just need to focus on the numbers. Because both values are negative, students may factor out a negative automatically. For students that do not factor out the negative, it will be important to compare the two forms. Let students know that if the first term is negative in an expression, then they will generally want to factor out the negative sign.

Factoring with three terms

Encourage students to see if they can use the box method to help them factor the expression. Students should recognize that their box needs to be `1\times 3` instead of `1\times 2`.

Factor `18xy - 48x + 24`

This example requires students to consider the `\text{GCF}` for three numbers, which will likely cause some potential misconceptions:

Students may only find the `\text{GCF}` for `2` of the `3` numbers. Remind students that they must be able to divide all of the terms by the same thing in order to factor.
Students may be tempted to factor out a variable. Remind students that the variable they want to factor out would need to be with every term in order to be factored out.

Factoring out a variable

In this example, students have to factor out a variable as part of the `\text{GCF}`. Some students might naturally see it while some students might not. A class discussion will help students to learn from each other.

Factor `12xy - 32x`

Writing Expressions in Factored Form Practice

After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of mild, medium, and spicy practice problems for writing expressions in factored form. Check out the online practice and assign to your students for classwork and/or homework!