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The Three-Way Principle of Mathematics

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  • 0:01 Three-Way Principle of…
  • 0:21 The Sample Problems
  • 0:48 Verbal Principle
  • 1:42 Graphical/Visual Principle
  • 3:08 By Example
  • 4:49 Lesson Summary
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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.

What methods are there to solve and understand mathematical problems? This lesson will review three methods to understand mathematical problems (verbal, graphical, and by example). Each will be illustrated with examples.

Three-Way Principle of Mathematics

Hi. Today, we are going to be talking about the three-way principle of mathematics. Basically, there are three ways to solve a problem in math: verbally, graphically, or by example. In this lesson, we will discuss each of these principles by solving sample problems using each type.

The Sample Problems

To really illustrate how you can use each of the three principles to solve problems, I think it would be great to have two very different styles of math problems and work each out using each principle. So, here are the two samples we will focus on through the lesson:

  • Mathematically speaking, what is a set?
  • 2x = 20, solve for x.

Let's see how each principle can help us solve these problems.

Verbal Principle

The verbal principle literally refers to working through a problem using words to talk or write out the solution. The first sample question was mathematically speaking, what is a set? The verbal solution to this is to write it out. A mathematical set is a group of numbers or items that are grouped together based on a stated standard of inclusion. It is indicated by brackets.

The second sample is similar: 2x = 20, solve for x. Verbally, we might say, 'This means 2 times what number equals 20. Knowing that 2 tens is 20 gives us our answer. x must equal 10 because 2 times 10 is 20.' Solving things verbally can be time consuming and takes a real understanding of the concept before you even get started. The other methods help when you don't necessarily know the subject matter as well.

Graphical/Visual Principle

Solving a problem graphically means to show the problem in a visual way. In math, we tend to think of drawing graphs, charts, or diagrams, but any visual representation of a problem is also a form of graphical illustration. Any type of picture or drawing out the problem is a form of solving the problem using the graphical principle.

Back to sample question one: mathematically speaking, what is a set? We could draw the concept of a set by imagining a set of cows and drawing a circle around just the cows in this picture:

Visually representing a set
picture of animals with cows circled

Now we can visually see that a set is a grouping together of items based on a pre-stated condition (here, the pre-stated condition was that the animal had to be a cow).

The second example, 2x = 20, solve for x, is perfect for a graph. We will just need to graph the line y = 2x, and then find the value of x when y is 20. Draw your x and y-axis and label the vertices. Then, complete the graph of the line. Once you have drawn the line, find the point where y = 20; you will see that the value of x at that point is 10. The graph helps you see that you are doubling your x value each time, which could help you come to your answer before actually having to calculate each product.

Graphically representing an equation
graph of y equals two x

By Example

To solve problems by example, you do just what it sounds like: create examples to illustrate the solution. Here are a few examples of a set:

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