What is math modeling?
Math modeling is the powerful process of using equations to understand real-world situations, solve practical problems, and even predict the future—often without us realizing it.
Author
Tess Loucka
Published:
December 2025
Key takeaways
- • Math modeling is behind almost every scientific and mathematical discovery.
- • Math modeling is the process of solving real-world problems with original equations.
- • There are seven main steps to making a mathematical model, but since the process involves plenty of trial and error, it is okay to repeat steps numerous times.
How do meteorologists predict the weather? How do urban planners create traffic lights that manage the flow of traffic? How do companies calculate the optimal price they should charge for their products?
The answer is math modeling.
Math modeling is the process behind the world’s greatest discoveries and scientific achievements, yet most people don’t know what it is!
If you want to know how math has shaped the world around us, you need to know math modeling.
But what is mathematical modeling, and how can you use it yourself?
What is math modeling?
Mathematical modeling is the process of visualizing a real-world situation using math. The goal is always to create a model that helps you understand the situation more thoroughly—and in some cases, predict the future!
If you want to understand or solve a real-world problem, mathematical modeling is the answer.
But that definition is a bit vague. What is a model in mathematics? What does a mathematical model look like?
Well, a mathematical model is, most of the time, just an equation or system of equations, created using real-world data.
A very simple mathematical model, for example, could be a + b = c, which visualizes the fact that adding two numbers together creates a third number.
What is the process of math modeling?
Just like the scientific method, math modeling has specific steps and goals to check off as you go. There are seven steps to the math modeling process.
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Establish a real-world problem
The point of mathematical modeling is to create an equation that helps you understand and solve practical problems. So, the first step in the process is to figure out what real problem you want to try solving.
Math modeling is used in countless areas of life, such as determining the optimal manufacturing process for a company, calculating flight paths, estimating car value, or managing a bank account.
So, choose a problem or question you want to answer, big or small. This will be the focus of your math model.
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Identify the variables
Every problem has variables.
Want to figure out what your pet’s favorite food is? You’ll need to think about a) the food type, b) the speed at which your pet eats their food, and c) other visual signs of enjoyment in your pet.
What about trying to predict tomorrow’s weather? You’ll need to consider a) barometer readings, b) the current weather state, c) wind patterns, d) the types of clouds you can observe, etc.
Whatever the problem is, think about the specific variables or data points you need to collect in order to find a solution.
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Research
After establishing your problem and defining variables, it’s time to gather some data. You can collect data through many methods, including observation, surveys, experiments, or information found online.
For instance, if you want to estimate the value of your house in 5 years, you’ll need to research the values of houses like yours. What do other, similar houses sell for? What do houses in my area sell for? How have house values changed in the last 5 years? What do economists predict will happen to the country’s economy in the near future?
Finding an answer to your big question requires asking a lot of little questions! But the more questions you ask and the more research you do, the more accurate your math model will be.
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Make assumptions
This step may seem contradictory, but it’s essential to the modeling process! After completing your research, you’ll probably have a better idea of what the solution to your problem may be—in other words, an assumption.
What trends are you noticing in your research?
Questions like that can help you build the foundation of your math model. But don’t worry if your assumption is wrong. It’s not about right or wrong; it’s about having a foundation to work from.
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Make your model
At this stage, you’re ready to come up with your math model—your equation(s).
The type of math you use here fully depends on the problem you’re trying to solve. If your problem is especially complex, don’t be afraid to ask a teacher for help.
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Analysis
Now that you’ve created your model, it’s time to test it out! This is the fun part, when you can use trial and error to tweak your model until it’s perfect.
Try to solve your problem using your model, and if something doesn’t seem to be working, this is your chance to go back to the drawing board and create something that works. Most models don’t work perfectly on the first try, so don’t feel discouraged.
Keep going until you’re happy with it.
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Report your results
The most satisfactory part of mathematical modeling is being able to report your results. Turn your results into a data table, a short paper, a chart, a video, or any other method that you think would work best.
If your results aren’t 100% accurate, don’t beat yourself up. Just go back to step 2 and try again!
What are examples of math modeling?
Math modeling is simply the process of creating equations to solve real-world problems. Therefore, it is used in hundreds of thousands of ways, everywhere you look, wherever you go.
Scientists use math modeling to create equations that send astronauts into space. Medical scientists use math modeling to predict the spread of diseases. Investors use math modeling to calculate the risks and rewards of potential investments.
The list goes on.
In math class, you’ve probably come across many math models without even realizing it. For instance, how do you calculate the area of a rectangle?
At one point in time, someone wanted to measure a rectangular area but didn’t know how. So, they created their own math model, tested it, and eventually came up with the equation area = length x width.
The same thing is true with the Pythagorean theorem, the slope-intercept formula, the quadratic formula, and so many others.
These equations are ingrained in mathematics now, but at one point in history, they were just math models that had to be tested.
For more practice with equations and mathematical models, try practice questions in math workbooks or math programs and websites. If you’re a student, your teacher is your best resource.
Keep practicing, and maybe someday you can come up with an equation that will change the world.
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About the Author
Tess Loucka
Tess Loucka discovered her passion for writing in high school and has not stopped writing since. Combined with her love of numbers, she became a math and English tutor, focusing on middle- and high-school-level topics. Since graduating from Hunter College, her goal has been to use her writing to spread knowledge and the joy of learning to readers of all ages.
