There are many ivory towers for mathematicians, but applied mathematicians have a basic need to serve others, by helping solve real world problems. They are condemned to wander the world, masquerading as engineers. There are few, but that is good, because few are needed. They carry calculus, differential equations, matrices, and linear transformations like tools in their bag. They may share the explanation of tricks, but never pull them on others, because they know, it is the height of arrogance and abuse of talent to laud over and not serve others, less understanding than they.

Please do not be too hard on the ivory tower mathematicians; many of their flights of fancy-castles in the air have found practical application. There need to be both kinds.

A trick for you all that has practical application; when the balance in your checkbook doesn’t square with the bank’s number, it is a good common thing to look for the exact difference somewhere in your check register or on the bank sheet. That’s OK, and if you find it, that’s great.

But if not, before doing more, divide that difference, by nine. If it divides evenly, there is a good chance you have transposed two adjacent numbers somewhere; an easy error to, exasperatingly, overlook. No guarantees, just a possible clue to minimize the tearing out of hair!

Good Luck and Steady Winds

Trick for multipying by 11

Take the number you are multipllying 11 by......say 23 X 11. Take the first numerial of that number, 2, and place it to the right side of the answer, then take the second numerial, 3, and place it to the left side

of the answer, now add the two numerals together 2 + 3, which equals 5 and place it in the middle of the answer.....2 5 3. If the number is 29 X11, you still put the 2 to the left, the 9 to the right, add 2 + 9 which equals 11, so put the 1 in the middle and then add 2+1, so your answer is 319.

Another trick for multiplying with nines : Every answer equals 9

Example: 1 X 9 = 09  (0+9=9)

              2 X 9 =18 (1+8=9)

              3 X 9 = 27(2 +7=9)

              4 X 9 = 36(3+6=9)

              etc.

Also when you multiply in progression, the answer of the first numeral starts at zero, one, two, three,etc and the second numeral starts at 9 ,then 8, then 7 (look at the answers above to see numerical progression)

Here is a rhyme I taught when I was teaching multiplication and division of fractions that made it easy to remember what to do:

Multiplying fractions, no big problem

top times the top

and bottom times the bottom,

Dividing fractions, easy as pie

Flip the second number and multiply

EX: 1/2 divided by 1/4 = 1/2 X 4/1 = 4/2 =2

I always loved math. I thought it was a fun and wonderful game. My greatest achievement was teaching high level math as a volunteer at my son's elementary school. I set out to change an attitude about math being horrible, and I knew it had worked when more than one of the students (now in high school) I taught, would say aren't you that Math Superstar lady? Then they'd sing one of my math jingles or recite one of our tricks. By the end of the program, we had 98% of the students participating weekly in an extracurricular upper level math program. Let's get teachers who love math into the elementary level math programs to build solid basics for students!

Whitebuffalobk and and Sonnie Moonie are so right. When in a small college, I took all the math courses I could, from the engineering arm, not the sciences arm of the school, thus, unwittingly, creating an applied mathematics major for myself, where there was no formal one.

Had to go to the big university at the capitol to take my Graduate Record Examination (GRE). Consisted of a general part and then a second part in one’s major. Before each part, multiple choice answer sheets were handed out, that were to be marked. All students, (about 400 in the auditorium), got an idea of the difficulty of the questions to come, by the number of answers to be marked on the sheets. They were abuzz as the history and English majors had 300 +, the chemistry and physics majors nearly 200. Finally, the call came for math majors to come down and get their sheet. Only one other person got up and came down with me to each get our sheet. We gasped, as there were only 80 or so answer places.

I carefully noted where he sat back down way over on the other side and in front of me in the auditorium. I did my best, but when I got to the last five questions, I had never seen them before. However, I had been well grounded in applying the principles and slowly worked my way through them all, getting done with a modest time left before the buzzer. The other student worked right up to the end, before he turned in the question pamphlet and answer sheet.

I eagerly waited for him to come out to the foyer to talk about the test. Turns out, he was from the big University. To my surprise, he said he was pretty sure he had seen the tricks to most of those last ten tough questions, but couldn’t remember the tricks exactly. He struggled to guess as best he could, but ran out of time and didn’t even get to mark anything down on some of them.

It was the first of many clues I was to get in life, about tricks versus basics and applied mathematicians versus mathematicians.

(help in next email)

Math is full of patterns. If you look out for them, it makes it all a lot simpler.

As a math teacher myself...both high school and college level...are you going to try to memorize a trick to do every type of arithmetic problem?  Why not just learn how to do the problems correctly to start with.  Tricks and jingles which work with just a few problems may be "fun" but they do not create concept skills that build upon one another in high school math.  And when these students get into one of the upper-level math classes which expect this background to be in place, not only do they have an answer as to why a "trick" works, they often resent the teacher who is trying to get them to really learn a concept.  Math consists of more than just arithmetic and tricks.  It's an exciting, beautiful subject in its own accord.  Please treat it with the respect it deserves and stop trying to side-track students who could actually learn the subject matter with tricks.  Maybe then the failure level in freshman college level classes will finally go down.