Back To Course

Math 106: Contemporary Math9 chapters | 106 lessons

Watch short & fun videos
**
Start Your Free Trial Today
**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Maria Airth*

Maria has a Doctorate of Education and over 15 years of experience teaching psychology and math related courses at the university level.

Mathematical modelling simply refers to the creation of mathematical formulas to represent a real world problem in mathematical terms. This lesson reviews the creation and pitfalls of mathematical models.

Hi and welcome to this lesson on mathematical modelling. In order to understand mathematical modelling, it is first important to understand the term **modelling**. In the most broad definition of the word, modelling could be said to be showing an example of a scenario.

When a model is on the runway, he or she is showing an example of what the clothing would look like on a person. Many people enjoy building model cars or planes. Again, these models give an example of what real cars and airplanes look like. **Mathematical modelling** is the same - it simply refers to the creation of mathematical formulas to represent a real-world problem in mathematical terms. Join me, now, as we look closer at the use of mathematical modelling in real-world situations.

You're probably already aware of some very well-known mathematical models - those that give perimeter and area of a square. The models are simply the formulas *P* = 2(*L*) + 2(*W*) and *A* = *L* * *W* (*P* is perimeter, *A* is area, *L* means length and *W* means width). So, yes, these formulas are mathematical models because they are examples or representations of the image that can be used repeatedly with different values to obtain different results for the same scenario. Mathematical models can be used to model real-world scenarios as well as pure math scenarios.

If you were in charge of purchasing the fruit for your book group each week, how could you go about figuring out how much money was needed each week for your purchase? Well, one way would be to work it out from scratch each week. Or, you could build a mathematical model to assist you in getting your total faster each week.

Let's assume you have been doing this enough to know that you will need 3 apples, 2 oranges, and 4 bananas each time. But, the price of fruit changes slightly from week-to-week, so you can't just assume from one week to the next how much it will cost. You know that you will need to multiply the price of apples times 3, the price of oranges time 2, and the price of bananas by 4 each week.

This is the perfect start to a mathematical model. Here is a formula you might write to model this scenario: 3(*a*) + 2(*o*) + 4(*b*) = your total. Notice that I used the first initial of each fruit to represent the price. In math, you don't have to use *x* and *y* for variables, any letter can act as an unknown.

So, in our example, if we find one week that apples are $0.35 each and oranges are $0.25 each and bananas are $0.50 each, our model would work out to 3(.35) + 2(.25) + 4(.5) = $3.55.

If, the next week, oranges go up to $0.75 each, then we just replace this value in our model to work out the new cost. This mathematical model will work each week as we calculate the total cost of fruit for the group.

One thing to remember about mathematical models is that they are not always accurate. By that I mean that they are not necessarily precise in real-world scenarios. Take the example of the volume of a box. We know a simple mathematical model for determining the volume of a box is *L* * *W* * *H*, right?

This works fine in theory, but in **practice** (that is to say, in the real world actually doing the math) there is something missing. The original model does not take into account the actual cardboard itself. Depending on how thick or thin it is, the outer measurements are not the same as the inner measurements; for shipping purposes, the outer measurements of the box are noted, but for packing purposes, the inner measurements of the box are more important for volume.

A more accurate model for the volume of the box (for packing purposes) would have to take into account the thickness of the cardboard itself: if *t* is thickness, then volume = (*L* - 2*t*) * (*W* - 2*t*) * (*H* - 2*t*).

Similarly, in our fruit purchasing model, the model does not accurately take into account all of the possible expenses incurred to purchase fruit. A simple exclusion is the fuel required to travel to and from the fruit market. Another could be the expense for parking (if there are parking meters at the market).

So, you see, while a model is a close representation of the real world, it is not completely accurate. The more variables you can think of to add to your model, the more accurate the model will be.

We have seen that a **mathematical model** is just a representation of a real-world scenario in formula form. It follows from any **model**, which is an example scenario. To make a mathematical model, all you need to do is devise a formula to represent the variables in your scenario. This gives you one model to use in every instance of a similar scenario (such as our fruit purchase example).

Just as with more common physical models, mathematical models are not perfectly accurate. They are representations of a perfect scenario, but we all know the real world is not perfect. Just because a shirt looks great on the model, does not necessarily mean it will look good on me in the real world. To combat this accuracy issue with modelling, it is important to add as many variables into your model as possible. The more variables you have accounted for, the more accurate your model will be. Thanks for joining me. Bye.

You'll have the ability to do the following after this lesson:

- Define mathematical model
- Explain how to make a mathematical model
- Describe the limitations of mathematical models

To unlock this lesson you must be a Study.com Member.

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
14 in chapter 1 of the course:

Back To Course

Math 106: Contemporary Math9 chapters | 106 lessons

- Critical Thinking and Logic in Mathematics 4:27
- Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice 4:47
- Logical Fallacies: Appeals to Ignorance, Emotion or Popularity 8:53
- Propositions, Truth Values and Truth Tables 9:49
- Logical Math Connectors: Conjunctions and Disjunctions 3:39
- Conditional Statements in Math 4:54
- Logic Laws: Converse, Inverse, Contrapositive & Counterexample 7:09
- Reasoning in Mathematics: Inductive and Deductive Reasoning 7:03
- Reasoning in Mathematics: Connective Reasoning 8:16
- Polya's Four-Step Problem-Solving Process 7:52
- Mathematical Principles for Problem Solving 7:50
- The Three-Way Principle of Mathematics 5:49
- Solving Mathematical Problems Using Estimation 7:38
- Using Mathematical Models to Solve Problems 6:35
- Go to Mathematical Reasoning & Problem-Solving

- Developing Adaptable Teams & Employees
- Effective Delegation Skills for Supervisors
- ORELA Essential Academic Skills: Practice & Study Guide
- Math 108: Discrete Mathematics
- ORELA Elementary Education - Subtest II: Practice & Study Guide
- Developing Adaptable Employees
- Proactive Employees & Team Problem Solving
- Organizational Change Management
- Identifying Competencies & Training Needs
- Relations Between Labor & Management
- How to Request a CLEP Transcript
- CLEP Exam Dates & Testing Center Locations
- CLEP Scoring System: Passing Scores & Raw vs. Scaled Score
- Continuing Education Opportunities for Molecular Biology Technologists
- WV College & Career Readiness Standards for Social Studies
- Common Core State Standards in Ohio
- Resources for Assessing Export Risks

- Required Rate of Return (RRR): Formula & Calculation
- Fixed Phrases: Definition, Examples & Practice
- Why Do Workers Join Unions? - Benefits & Reasons
- Rigid Motion in Geometry
- Electronic Health Records & Evidence-Based Medicine
- Symmetry in Insects: Types & Examples
- Native American Mathematics: History & Mathematicians
- Behavioral Health Quality: Framework & Measurement
- Quiz & Worksheet - Animal Population Size
- Quiz & Worksheet - Psychoanalyst Anna Freud
- Quiz & Worksheet - Potassium Chromate
- Quiz & Worksheet - Understsanding Transaction Processing Systems
- Quiz & Worksheet - Decomposing Numbers
- Tourism Marketing Flashcards
- Tourism Economics Flashcards

- CEOE Oklahoma General Education Test: Practice & Study Guide
- Introduction to Organizational Behavior: Certificate Program
- AP Chemistry: Help and Review
- Common Core ELA Grade 7 - Speaking & Listening: Standards
- Common Core ELA Grade 7 - Writing: Standards
- Phylogeny and the Classification of Organisms: Homework Help
- Understanding Energy Resources
- Quiz & Worksheet - The Four Stages of the Listening Process
- Quiz & Worksheet - The Electron Shell
- Quiz & Worksheet - Global Literature from 1600 to 1900
- Quiz & Worksheet - Grammar & Pronunciation in Public Speaking
- Quiz & Worksheet - Adjectives, Adverbs, Nouns & Agreement Errors

- Style in Fiction: Dialect & Figures of Speech
- Application Development: Definition & Types
- How to Improve Reading Comprehension
- Homeschooling in North Dakota
- Colorado State Math Standards
- ADHD Advocacy Groups
- Wisconsin Science Standards for 4th Grade
- Missouri State Standards for Math
- Best Books for Young Adults
- Pi Day Project Ideas
- Pi Day Project Ideas
- What is Dual Credit?

Browse by subject