## Thursday, March 21, 2019

### Math is Communication

In science and engineering, math is a vital part of communicating the ideas related to any observation or situation. Sloppy or incomplete expressions of math only tell part of the story.

To properly tell the math story, it is necessary to 1.) begin with the formula. The formula establishes the relationship between all of the things that are part of the situation. The next thing is to 2.) plug in the values of the various variables. This tells the specific story. Lastly, 3.) simplify and reduce the math (solve the problem).

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So, the steps in summary are:

1. Write the formula.
2. Plug in the values.
3. Solve.

It is important to fully accept that the math is a story. Math is a way to communicate the relationship between different quantities and properties. Math is the whole movie.

Just jotting down some numbers and coming up with an answer is like the movie trailer. It doesn't tell the whole story.

It is noteworthy that telling the math story is very similar to solving a math problem. Telling the story is only different in that it begins with the relationship between the parts, whereas solving a problem begins with the question, then identifies the relationship between what is given and what is asked to be found.

Math is often the most efficient way to explain the relationship between things and to show, when they interact, what happens. Suppose that a situation was described as follows:

A 10 newton force acts on a  5 kg box unopposed. What is the rate of acceleration.

Without math, using only words (and in the style of epic fantasy) here's what we would have:

Long, long ago, when the foundations of the universe were being created, the Creator deemed that there would be a universal relationship between the force acting upon an object, its mass, and the rate at which the force would accelerate it. So it came to pass that the rate of acceleration would be proportional to the force acting upon the object and inversely proportional to the mass of the object.
Some time later it occurred that there was a 5 kg box. Upon this box a force was applied and the magnitude of that force was 10 newtons. The relationship of force and mass resulted in the box changing velocity, accelerating from rest at a rate of 2 meters/second every second.

Now, with math, the same story:
F = ma
10 N = 5 kg • a
10 N / 5 kg = a
2 m/s/s = a
The story is the same, but the telling is different. Math tells the story of science and engineering.

It is vital to note that each line of the solution is a sentence in the math story, and every sentence must have a verb. In the case of math, the verb is the equal sign. Therefore, every line of the solution needs to have BOTH sides of the equation AND the equal sign, or else the story is not being told well.

SUMMARY

The math story begins with the formula, the relationship between all of the variables involved., The next part of the story is the insertion of the specific values into the formula. The conclusion of the story is the algebraic / arithmetic solution and reduction.

Tell the whole story!

1. Write the formula.
2. Plug in the values.
3. Solve (making sure to use complete math expressions that include the equal sign).