# Creating and Identifying Equivalent Expressions Worksheets

This is a topic that not many students see a great deal of value in. This is a great skill to have under your belt when we begin to work with more complex algebra skills. It will help us learn to solve equations and satisfy systems. In the end, this is a critical skill that we should mastery at the most basic level. You need to spend a good deal of time familiarizing yourself with the concepts of constants, coefficients, and powers to best know how to manipulate all of the different aspects that are available to you.

### Aligned Standard: Grade 6 Expressions and Equations - 6.EE.A.3

- Identifying Equivalent Expressions Step-by-step Lesson- Start off a nice solid multiple choice question.
- Guided Lesson - See if the first question has you scratching your head! A similar questions has been on three national tests for this standard.
- Guided Lesson Explanation - We thought that these need to be explained deeply.
- Practice Worksheet 1 - Time to see if the value of formulas throws kids off a bit.
- Practice Worksheet 2 - The expressions get a bit more complex here.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Examples are provided with each of these sheets to help students along when they are doing the work alone.

- Homework 1 - Find the missing value in the expression that would make the statement true.
- Homework 2 - Which expression is equal to the expression 3(x + 2y + 4)?

### Practice Worksheets

You fill find just about every different way possible to ask these question in here.

- Practice 1 - Which expression(s) are equivalent to 5(x - y)+ 3 ? Draw a line to match them.
- Practice 2 - Find the missing value in the expression so that they will be equal.
- Practice 3 - Find the "?" value in the expression so that they will be equal.

### Math Skill Quizzes

By request, I setup the first quiz in a more formal format.

- Quiz 1 - Write an equivalent expression. Create your own.
- Quiz 2 - Fill in the following blank: 4l – 8m + 24n = 4(l – 4m +____-)
- Quiz 3 - Is the expression true or false? Interpret what has been put in play or you.

### How to Determine If Math Expressions Are Equivalent

When two things are equivalent, they look the same. However, this is not the case in mathematical expressions. While the may both have the same end value, they may look completely different. Mathematical expressions are a finite combination of well-organized symbols and numbers according to the context of the problem. There is an infinite number of ways to represent equivalent mathematical expressions. But is it also easy to identify them? Two expressions are said to be equivalent when they are the same. Though they may look different, when you plug in the same variables into both the expressions, they will give you the same result upon simplifying.

It is not always easy to identify either the given two mathematical expressions are equivalent or not. Let's find out an easy way to do it.

Consider this example: X^{2} - 9 = (x + 3) (x - 3)

In this example, both expressions are the same. When you simplify the right-hand side of the equation, you will get the same expression. Similarly, when you substitute the value of x with the same number on both sides, you get the same answer. It shows that both these two math expressions are equivalent.

As we see in that example, when we are trying to establish equivalency, we must simplify as far as we can. We can often establish this through two common strategies. The first is by using the distributive property. If you remember back that is where a sum or difference is multiplied by a fixed value, variable, or coefficient. When you recognize those factors, you can often remove them from both sides of equal or at least reduce them. The second strategy is to identify factors and remove them from each expression. This is one of the most used tactics for reducing values. Put it to good use for yourself.

You can also use this establish or write your own equivalent expression. We often write these when we are actually doing the calculations by hand. When a computer, phone, or calculator is not handy generating these values can be helpful to create values that are the same exact, but in a much less complicated format. You will find this pretty common when you graduate high school.