# How to make a mathematical model: 9 Steps (with pictures)

Using mathematical language to describe a system is what constitutes a mathematical model. Not only the natural sciences and engineering disciplines use mathematical models, but also biology, economics, and sociology. Mathematical models can range from simple to complex. If you want to learn how to build a mathematical model, keep reading this article.

## Steps

### Part 1 of 2: Prepare to Make a Mathematical Model

#### Step 1. Determine what you want to know

What is the goal of creating a model? Make a list of the information you want to find when using the model. It is important that you ask yourself this question before creating the model or you may end up creating a model that does not meet the objective.

• Do you want to predict something? Do you want to find out how to regulate something? Do you want to do something else?
• For example, imagine you want to know how much space you have in a storage unit so you know how many boxes you can put in it. You will need to create a model to predict how much space is on the storage drive.

#### Step 2. Determine what you already know

What information do you already have? Make a list of the information you have already found. As you make your list, decide which pieces are most relevant and which pieces are not.

• You should also make a list of any information you can assume based on what you already know.
• Keep in mind that you may need to take steps to find the information you need.
• To find out how much space you have in your storage unit, you will need to measure the height, width, and length of the unit.

#### Step 3. Determine the physical principles that govern the model you want to create

Should you consider factors like gravity, volume, time, etc.? Take note of any factors that you will need to consider when creating the model.

• To determine how much space you have on a storage drive, you will need to find the volume.
• You will also have to remember that there will be some wasted space, as some objects can be uneven and that will make it difficult to take advantage of every inch of the storage unit.

#### Step 4. Identify the equations you will have to use to find your answer

What equations and formulas will you need to find your answer? How will you apply these equations and formulas? Make sure you have a clear understanding of how to connect the information you have into the equation.

### To find the volume of the storage unit, you will have to use the equation volume = height x width x length

#### Step 5. Find out if others have made the model

There is no need to reinvent the wheel if someone else has developed a model that can meet your goal. Check in your textbook or ask your teacher. Just remember to make sure someone else's model works for you.

### To get an idea of how to find the volume using the equation you have identified, check your textbook or ask your teacher

#### Step 6. Create a diagram of your model

A simple mathematical model may not require a diagram. However, if you create a complex model, a diagram can help determine if your model will work. Draw a diagram that represents the actual model you plan to make.

### Part 2 of 2: Make a Mathematical Model

#### Step 1. Create the model

Once you have finished the planning phase, you should be able to create the model. Use the diagram, the information you already have, and other information to make your mathematical model. Make sure to check your notes frequently to ensure accuracy.

• Make sure your model represents the actual relationship between the information you are trying to achieve.
• To make more advanced models, you will have to use a computer program.

#### Step 2. Test your model

It is important to check the validity of the model results before you try to do anything else with the model. Apply the information and see if the model is valid. Are the results what you expected? They have senses? Can the results be repeated?

### Solve the equation volume = height x width x length to determine if the results make sense. Repeat the solution to determine if the results can be repeated

#### Step 3. Determine how the model can be improved

To make your model useful for additional applications, you need to consider how it can be improved. Are there any variables that you should have considered? Are there any restrictions that need to be set? Try to find the best way to improve your model before using it again.

• For example, if you want to have 1 meter (3 feet) of room to walk through the storage unit, you can adjust the equation to account for that space. Just deduct the space you will lose from the appropriate number in your equation. In this case, you can adjust your equation to read like this: volume = height x (width - 3) x length.
• After you've identified ways to improve your model, make the changes and test it again.