Writing Algebraic Expressions: FREE Practice Pages

Grab this print-and-go set of worksheets for some quick and easy writing algebraic expressions practice! Includes 3 pages plus answer keys!

My teaching career has been focused in elementary school. But with the decision to homeschool my children, I’m now getting to teach some middle school subjects.

My oldest started a sixth-grade math book this year. I’ll be honest: there have been a few problems I’ve really had to think through and use number sense to figure out. I’ve loved the challenge, and the opportunity to learn more with him.

This week we jumped into a little bit of algebra. I LOVE algebra, and it was fun to sit with him and discuss how to write and evaluate algebraic expressions.

I wanted him to have a little extra work with this skill, so I created these algebra word problems!

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This is a guest post from Rachel of You’ve Got This Math.

Algebraic Expressions Prep-Work

Don’t you just love activities that don’t require prep-work? Well these word problems that have children creating algebraic expressions and then evaluating them require no prep-work.

Simply print off the pages you need, and that’s it.

What is An Algebraic Expression?

So what is an algebraic expression?

According to A Maths Dictionary For Kid’s, you can describe an algebraic expression in three ways:

  1. It is a mathematical phrase that uses both numbers and variables
  2. Though it may have basic operations and grouping symbols, it does not have equality or inequality signs.
  3. Finally, both sides of an equation are expressions.

If you’re looking for more in depth lessons and practice with algebra, you may be interested in my Algebra Essentials Lesson Collection.

Writing an Algebraic Expression:

Now that we know what an algebraic expression is, it’s time to create one.

  • Begin by giving your children a simple statement like, “Susan has three times as many books as Sally.”
  • Next, you can ask, “How many books does Susan have?”

Well, we don’t know how many books Susan has, because we don’t know how many books Sally has. When we don’t know a key piece of data, we can use a variable to represent the unknown.

In this case, our variable will stand for how many books Sally has.

  • Now, ask your children to write an expression using a b to represent how many books Sally has.
  • Therefore, the expression b x 3 represents how many books Susan has.

Evaluating an Algebraic Expression:

Now it is time for the fun part: evaluating the expression.

And this is easy. Now we are just putting in a number where the variable is, since it is no longer an unknown.

Let’s go back to our statement about Susan and Sally. We created an algebraic expression b x 3 or 3b to show that Susan has three times as many books as Sally.

Now, tell the children that you found out that Sally has 12 books. Now we can easily solve this problem. All we need to do is replace the variable with an actual number:

12 x 3 = 36

Therefore, Susan has 36 books.

FREE Algebraic Expressions Worksheets:

This set of worksheets provides practice with both of these steps.

Each problem starts with a set of facts.

For example, one problem states that a worker gets paid $100 dollars a day and $0.50 per mile he drives. We will use this statement to write our algebraic expression.

At this point we don’t know how many miles he has driven, so we will use m to represent how many miles he drives.

Now when I look at the statement I know that I will have to multiply the miles he drives by $0.50.

m x $0.50 or 0.5m can be used.

But I’m not done. I also know he gets $100 per day. So I need to add $100 to my algebraic expression.

This makes my expression: 0.5m + 100


Now let’s evaluate this algebraic expression.

The next line tells me how many miles he drove –> 245 miles.

So we evaluate the expression with 245 miles. This gives us:

(0.5 x 245) + 100

Following order of operations, we multiply first, and then add another $100:

0. 5 x 245 = 122.5

122.5 + 100 = 222.5

Therefore, the driver made $222.5 that day.

That’s it. Now you have a simple activity to get your young ones working on writing algebraic expressions and then evaluating them.

If you enjoy this lesson, become a Math Geek Mama+ member and gain access to the entire library of engaging math lessons like this one, hundreds of math games and low-prep practice worksheets for grades 5-8!

Learn more about Math Geek Mama+ right HERE.

Find more resources to help kids understand algebra vocabulary and translate algebraic expressions here.

{Click HERE to go to my shop and grab this FREE set of Writing Algebraic Expressions Worksheets!}

About the author: Rachel is a homeschool mom to four little ones, ages 2 to 6. She is a former public elementary teacher, and has recently begun blogging at her page You’ve Got This.

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