# Expression Word Problems Worksheets

Algebraic expressions are great for helping us understand any situation that involves data or quantities. Once we understand the system, we can analyze these quantities to best understand what makes it tick. If we would like to manipulate or change that system, we can easily model this situation and understand what needs to be done to make that happen. You run into many different types of problems in all ways of real life where this strategy can help you make good choices. This series of worksheets is filled with expression based word problems that will help you learn how to manage these very quickly and effectively.

### Aligned Standard: Grade 6 Expressions and Equations - 6.EE.A.2c

- Cubic Volume Step-by-step Lesson- This is a neat trick that I never thought about before!
- Guided Lesson - We have you evaluate expressions with known variables and create expressions.
- Guided Lesson Explanation - The word word problem requires a bit of thought.
- Practice Worksheet - There are many word problems. Also note that there are still ten problems, even though it has some weird numbering in it.
- Absolute Value Inequalities Five Pack - Solving for x was never as much fun as this.
- Matching Worksheet - Match the expression to the word problem that it represents.

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

### Homework Sheets

The first two are the standard problems that you will see for this standard. The third sheet I thought on for some time.

- Homework 1 - What is the volume and area of a cube with sides that measure 12/3 feet?
- Homework 2 - The volume of a cube can be expressed as: volume = (length of sides)cubed
- Homework 3 - The area of a cube can be expressed as: area = 6 (length of sides)squared.

### Practice Worksheets

Each sheet starts with word problems and then moves to just basic problems.

- Practice 1 - David has 9 more shirts than the James. James has s shirts. Write the expression that shows how many shirts David has?
- Practice 2 - There were S students in the classroom and 25 more students came to the classroom. Write an expression that shows how many students are in the classroom.
- Practice 3 - Mary has c candles. Nancy has 24 more candles than Mary. Write an expression for how many candles Nancy has.

### Math Skill Quizzes

The quizzes were written in a similar fashion to the practice sheets.

- Quiz 1 - Robinson has 5 rabbits. His friend bought m more rabbits. Write an expression that shows how many rabbits Robinson has now.
- Quiz 2 - Harry has 8 more ice cream cones than Brown. Write an expression that shows how many ice cream cones Harry has.
- Quiz 3 - Baker has z balloons. Nelson has 16 more balloons than Baker. Write an expression that shows how many balloons Nelson has.

### Writing Expressions to Model Scenarios

Math is a great tool to help us better understand our environments and make relatively accurate predictions. Sometimes like weather forecasting, it does not always hold up due unforeseeable shifts or changes. More times than not, it will be helpful to make more quality consistent decisions.

There is a basic strategy that we encourage you to use when developing these expressions. It all starts with defining the quantities that you are working with. Some of these quantities will be unknown to you and therefore serve as the variable in your expression. Other values will be consistent and as a result be represented by constants. The second step is to define how all these quantities relate to one another in the situation. This helps us identify the operations that will be taking place in our expression. When I review a word problem, I like to outline the values and how everything relates. It makes it much easier to translate into math.

Here is an example word problem, see if you can model the situation using math:

Jason jogged for 50 miles in the month of September. He ran the same distance every day. Write an expression to represent the distance he ran each day.

**Solution:** We begin by exploring all the quantities. In this case that would be the 50 miles and number of days (30) in the month of September. The one factor we do not know the value of (unknown) is the distance that she ran each day. We can name that variable with any symbol of our choice, I’ll choose the letter D. In the end we have identified:

50 miles, 30 days, D (distance each day)

Now we look at how these things relate. We know that the total value of all the jogging was 50 miles. Being the end value indicates that it is found by itself on one side of the equal symbol. We then work on how the number of days and distance each day would interact. They would be factors of one another which means that we would multiply them. So our final answer would be 30D = 50.

## A Reminder: What Are Math Expressions?

Math expressions are mathematical sentences that have at least one operation and two terms. There terms can take on many different forms and sequences. The consist of signed numbers, coefficients, constants, and variables. This is where we use variables and numbers to identify a problem. Now, a variable is a symbol we use to represent an unknown number. The most common symbols used are the letters x and y. The goal of these expressions is to communicate a value of something or model a scenario with math.

Let us consider an example. 12 + x = 16, We must find the unknown x of this expression. One of the great aspects of equations is that you can constantly manipulate them as long as you perform the same operation or action to both sides of the equal sign. With this in mind, to find out the unknown here, we can just subtract 12 on both sides of the equal sign.

12 + x - 12 = 16 - 12, On the left side, 12 - 12 will be cancelled out and become zero. While on the right side, 12 will be subtracted from 16 to get an answer 4 from it. The resultant expression becomes x=4, The expression above means that the unknown variable x is 4.