Problem Solving: Writing 1-Variable Equations

Have you ever wondered how much just an individual item costs when the price stated is for more than one item, such as 3 for $11.99?


Standard(s) Supported: 6.EE.B.6, 6.EE.B.7, 7.EE.B.4 and HSA.CED.A.1

What is a 1-Variable Equation?

A 1-variable equation is an equation that has only 1 specific variable in the equation, such as x. The specific variable may occur multiple times in the equation (2x + 4 – 3x = 7x) and the specific variable may be within non-like terms (5x vs. 2x2). No matter what, to make a 1-variable equation, only the same variable will be present throughout the equation.

What is a 1 variable equation.pdf

This fundamental will only focus on 1-variable equations with like terms. When you study quadratics and polynomials later in your math career, you will get to experience 1-variable equations with non-like terms. And when you study systems of equations you will get to experience multi-variable equations.

If you forgot what makes an equation, an equation, check out the fundamental Equations vs Inequalities!

What is problem solving in math?

There are many strategies used for problem solving. Overall, once you hit pre-algebra the key focus in problem solving includes:

1) Identify what you know (are given) in the problem

2) Identify what is unknown (typically the part of the problem in the question)

3) Define your variable(s) (choose a variable to represent the unknown(s))

4) Create a model (could be writing an equation, creating a graph, making a table)

5) Solve your model to calculate the unknown(s)

6) Check your work

Let’s face it, problem solving is not easy and remembering all the above steps when you are first starting out can seem like a lot. So, this site is going to focus on the strategy that uses the acronym CUBES. If you have used CUBES before in math, you may notice that the below CUBES chart looks a little different than it did in the early years of math. Why? Because as you progress through math and learn more, your techniques and strategies need to grow right along with you.

CUBES - general method to help problem solve and write equations

CUBES.pdf

Need a refresher on translating the written word to math? Check out the fundamental Lost in Translation: translating from the written word to math!

Let’s see how the CUBES strategy can help us problem solve when writing 1-variable equations.


How do you problem solve and write 1-variable equations?

Example 1: using CUBES and writing 1-variable equations

Example 1.pdf

Example 2: using CUBES and writing 1-variable equations

Example 2.pdf

Did you notice in example 2, that the equation did not answer the question? Sometimes you have to solve for the cost of a single item to find the cost of multiple items.

Need help with combining like terms? Check out the fundamental Simplifying Expressions!

Why do we learn to write 1-variable equations in math?

Equations used in careers will not always look as formal as in your math class. Many times, you use the same or similar equations, so the math becomes intuitive over time. An air traffic controller essentially uses the equation distance = rate * time (d = rt) when making sure planes landing and departing a runway will not be on the runway at the same time. In reality, an air traffic controller does not have the time to do the math for every landing and departure. They must rely on their intuition and gained knowledge through years of math education and experience. A lot of the skills you gain in math class will become intuitive over time to the point you won’t even realize you are using math in your everyday life.

What’s next? As you learn more concepts in math, the problem solving gets more complex. Once you start learning about linear relationships you will learn how to problem solve using linear relationships. Check out the fundamental Problem Solving: Linear Equations!