or Not to Plug |

This page is a collection of ideas, advice, and good problem solving principles gleaned from my own personal study of mathematics and teaching experience. It is not intended to be scholarly, exhaustive, or in any way super elegant, merely a group of items that I wish to put in one place so that I can refer students to a written reference. If it serves as a help to them in even a minor way, it will have been worth the trouble to provide it here. Check back from time to time, in case I add items in the future. Thanks.

Something much better and more universally understood the world over (remember: math is studied internationally!) is the term "** substitute**," or perhaps "

Let's leave "plug" for the end of the electrical cord used to connect your TV set to the wall outlet. (Besides, on the lighter side, "plug" is another name for an old, broken-down horse. Ugh!)

It's really quite simple to know. If you can "count" the items referred to, use "number." A problem that I was working on recently involved the "number of soldiers" that were marching. To say the "amount of soldiers" sounds a bit strange to the ear.

The word "amount," therefore, is used when you can't count, as in the "amount of milk in a glass." Of course you could count the "number of glasses of milk" or the "number of fluid ounces in the glass," but that's different. You're counting glasses, not the milk itself.

Above I explained the words "amount" and "number". Here we will look at two words often used with them when we compare things: ** less** and

When we are comparing countable things, using number, we should say "fewer". Example: "There are fewer cookies on my plate than on yours." [Do NOT say: "…less cookies…".]

On the other hand, use "less" when "amount" is involved. Example: "There is less milk in my glass after I drank some of it."

However, you might use "fewer" with milk if you're counting glasses of milk. Look: "There are fewer glasses of milk on this table than on that one." That's because we're counting the number of glasses, not the amount of the milk.

Another set of terms that often are used improperly by many people is ** expression**,

First, an algebraic ** expression** is merely some combination of numbers, letters, and operations symbols (such as the signs for addition, subtraction, etc.). Some simple examples would be these:

The principal difference that distinguishes expressions from the other two is the absense of the equals sign (=).

From that last statement, we might conclude that ** equations** (and

Finally, we might think of ** formulas** as special equations that have a general and useful purpose, like the formula for finding the "

But they usually take this style:

Some common formulas would include:

perimeter of a rectangle ... p = 2(l + w)

area of a circle ... A = pi * r^2

volume of a cube ... V = e^3

And let's not forget one very famous formula developed by Einstein ... E = mc^2

Here is how I use it with a simple example, finding the perimeter of a rectangle whose length is 16 and whose width is 9.

FF: | p = 2(l + w) |

SS: | p = 2(16 + 9) |

CT: | p = 2(25) |

.. | p = 50 The perimeter is 50 units. |

In other problems, our measurements can be were more theoretical, or "in the mind", as it were. The length of a hypotenuse of a right triangle with legs of 5 and 6, for example, could be properly stated as "sqrt (61)", without any need to give a decimal approximation. This because the decimal form of sqrt(61) is not a terminating decimal, but rather is of infinite length and has no repeating group of digits.

At other times, when a fraction like 3/7 is used or is the end result, you might just as well leave your results that way. Because any decimal equivalent can only be approximate, or involve complicated repeating decimal notation; yet the fraction is quite "exact" and simple to manage.

Always use small numbers whenever possible. |

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Don't multiply until you have to. |

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DECIMALS ARE DUMB, FRACTIONS ARE FANTASTIC, BUT WHOLE NUMBERS ARE A WHOLE LOT BETTER. |

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