Simplifying Expressions Lesson Plan

Overview

In this lesson, we’ll introduce the concept of simplifying expressions for `7`th graders by comparing expressions that need to be simplified. We’ll specifically call out the similarities and differences so students can recognize why certain expressions need to be solved differently than others. We’ll finish off the lesson with a partner activity! You can expect this lesson to take one `45`-minute class period.

Grade 7

Expressions, Equations, And Inequalities

7.EE.A.1

How to Teach Simplifying Expressions

Warm-up

Start the lesson by sharing slide one of the slideshow, where students will compare two expressions by discussing what they find to be the same and what they find to be different.

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Give students a few minutes to think about possible answers. After a few minutes, start having students share their responses with the class. Students may have all sorts of responses ranging from the expressions being in different colors to one expression having a set of parentheses.

Equivalent expressions

After students have shared, we want to ask some more targeted questions. Here’s what you’ll want to bring up:

Green expression: The “`x`” and “`2x`” can be combined to make “`3x`”.
Blue expression: Apply the distributive property, so multiply the “`3`” by each term inside of the parentheses: `3x + 6`
What do both of these expressions have in common? The expressions are equivalent.

This warm-up activity allows students to work with the distributive property and practice combining like terms in preparation for this lesson on simplifying expressions.

Increase the complication

Next, give a more complicated expression that combines distributive property and combining like terms. The other complication is dealing with a subtraction before the part that needs the distributive property.

Collect answers from students and list them on the side of the board. Students can volunteer to explain how they got to their answers. And, of course, as you combine two skills, students might forget how to combine or distribute.

Order of operations

A common mistake students are likely to make is to do `12-3` - both because it is easy to do and also because it is the first thing that comes up. Have a conversation about the need to follow the order of operations.

Rewrite subtracting as adding the opposite

Here are two issues that are likely to come up with this example.

Distribute the `3` instead of the `-3` and write the expression as `12 - 12x - 6`.
Distribute the `3` instead of the `-3` and write the expression as `12 - 12x - (-6)`.

There are different opinions on how to teach students to avoid these mistakes. We recommend that we practice rewriting every subtraction as adding the opposite. Here is what it would look like:

You could rewrite all the subtractions because it will help in distributing correctly and combining like terms. But at the least, students should do this for all subtractions outside the parentheses. Some students don't want to rewrite, which is fine too - as long as they have a process that works for them.

Formalize the process

Share a slide that captures the process. While most students will have figured out a process that works for them, some will want a formal reference sheet that they can use while simplifying expressions.

You might want to tell students that you can rewrite `18+ -12x` as `18-12x` - that typically, a simplified expression is without a double sign.

Class practice

Work on the next few problems with students on the board so that students get the hang of identifying expressions. With more complicated expressions, students might want to simplify each part and then put it all together.

Here is an example of how you would capture student thinking. You would want to be super-organized since this is an opportunity for you to model how they should do it.

The last practice problem is `3-(5+4w)`. Students might come up with ways to handle this. However, you should also give them a process in case they are unsure.

Sorting game

Once completed with the practice problems, pass out the partner activity where students will work together to sort the cards with the expression and their simplified form. Check over the matches as students complete them.

Simplify Expressions 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 simplifying expression activities. Check out the online practice and assign to your students for classwork and/or homework!