Think of numbers beyond how a child does. Counting seems important early on. The child may say, "I am five." Five might mean something as if it were a person, place, or thing. "I listen to 105.3 on the dial," or "We leave at 5." This is one example of where other languages might beat out English with the phrase "I have five."

Questions and explanations mature while growing up. With age, numbers begin to differ from nouns, to become more like adjectives, to take place alongside other adjectives like hot and cold, green and blue. For me, I didn't care about such language until hearing my (second) calculus teacher Mr. Fee tell the class the "what 'five' was" decades ago.

He recalled to the class a time his graduate work when the set of numbers they had been using expanded from the exclusive ( -∞, +∞ ) to the inclusive [ -∞, +∞ ]. Note the change from the parentheses to the brackets. He joined his classmates afterward for a lunch on the grass (on the lawn, not on the weed) where they were confused as to what it was they were now adding on, and they were having trouble visualizing infinity as a destination rather than as a direction. One frustrated student said he could understand a number like five, but putting bounds on infinity was beyond him.

Mr. Fee then asked, "what is five?" and then had to reinforce his question as the math group looked at him as asking a silly question, but they could not answer what 'five' was. None of them could explain what five was anymore than they could explain what infinity meant. Adjectives can't explain themselves without a noun. No different than explaining what blue is without finding something blue to point at.

That same week in time was spent trying to explain what a mole of atoms was to a student pursuing pre-law with a poor chemistry grade blocking his path. After an *hour* of adjective and noun review, comparing moles to fives and dozens and so on, the block went away, the remaining test scores were superior and excellent instead of poor, and there never was a second tutoring session. Good for me.

Like math, language allows for time spent thinking either down to earth or up in the clouds. This is why people claim to see "poetry in math." The graduate math class members eating their sandwiches missed keeping their language skills sharp. If you have a difficult time explaining that five is a person, place or thing, then you might consider numbers to be adjectives most all the time until working it all out later through more complex studies.

As adjectives, numbers modify nouns, you can mix it up. Remove the anxiety of solving word problems. Keep numbers in their place.

Working with adjectives is a skill and can be flexed with exercise. Memorize multiplication tables. Estimate square roots. Practice long division. Add fractions. Multiply prime numbers, Learn to use all the keys on the calculator or calculator app. Type out your own tables, posting the hard to memorize sections to access on mobile later on at your leisure. Doing so saves the weight of carrying a textbook or flash cards around. Posting privately keeps your problem away from the public, away from your superiors, and avoids the accompanying "what that for?" question from others on the browse.

Solutions are built rather than piled high. Cancel out small numbers first, leaving the multiplication and division of larger numbers for later. Making good use of algebra, look for choices that deal with the smaller pieces before working out the larger ones. Checking small work is easier than large work. Come to rely on algebra to check work differently, rearranging the terms. This may be more productive than to check twice calculations made the same way. Act like a musician and stop to work out errors rather than only repeating the good spots when practicing drills.

Keep an open mind when working with numbers. While the result may be a comprehensible number like 5 of something, getting to the result may take the solution into outer space. Calculating the number of times to stop to fill an auto with gas over a long trip may produce a result of 4.1 stops, which is the wrong answer because you can not make one tenth of a stop. You would need to make 5 stops, or 4 stops if starting with a full tank. Calculating the diameter of a measuring wheel of 1-meter circumference involves using the irrational number *pi*. Calculating the future value of 5 dollars in 5 years earning 5 percent interest compounded continually involves using the irrational number *e*. The tangent just short of a right angle is infinite, the Tangent of a right angle is undefined (division by zero). The trigonometry function "sin 0° / 0" equals 1 (a different kind of division by zero). Graphing the function "** x**² + 1" (sum of two squares) never factors for zero like "

With numbers and operations put into the equation, the remaining pieces are dealing with algebraic variables. Variables and the nouns they represent are collectively referred to as "the unknowns," which is just as good as any other name to call what they are.