Trying Times

Okay, I admit it; I can’t do the 8th grade algebra!!!!! I managed to keep up with the 7th grade pre algebra studies, but with my new job of 30 hours a week, I did not have time to keep up with the 8th grade math this year. Fourth grade math has been keeping me busy.  My fourth grader has been having a tough time this year.  It seemed as though nothing was sticking, and I was having to put in a tremendous effort just to keep him afloat, at the expense of everything else.  I am talking about 4 hours of intense one-to-one assistance 5 days a week starting after 3 PM!! Oh what to do?!!
Since our budget doesn’t allow for any of the commercially available after-school study aid programs, like SCORE or Kumon, and we didn’t have time to get him to and fro anyway, I opted to go the cheapest route and have him tested through LA Unified, to see if there was any specific reason for his struggles that I had missed, besides the chronic sinus infection which seemed to impede his hearing.  I had his vision checked and he was borderline.  They recommended vision therapy for his “tracking” problem.  That’s a problem staying on the line when you are reading from a distance, for those of you who are unfamiliar with the term. Vision therapy?  I don’t even want to know how much that might cost or where we would have to drive for it.
  I spoke to the pediatrician regarding his struggles, and was given the number of a psychologist who works with children with learning disabilities, but since my son wasn’t acting out, becoming frustrated with the arduous hours of work, or failing, he wasn’t eligible. He recommended an Education Psychologist in Santa Monica who wanted $300 for a one hour consultation.
  My friend, who has a wonderful list of experts on call for myriad situations, recommended an Educational Psychologist in my area who works from home, but she charged $90.00 per hour. I said he’d have to be able to walk on water after one session.
  So after all of the testing was said and done, my son was rated perfectly normal and qualified for no public school study services.  I was looking for some suggestions on how to get him to grasp things a bit quicker.  Seven hours at school along with 4 hours after school was barely getting him by.  Get a student from the local college for $10/hr I was told.  Well, I never did pursue that because I was too overwhelmed to look into the matter further.  And, by the grace of God, after Christmas, my son seemed to have matured in some manner, because now, with the beginning of the New Year, he seemed to be able to memorize his spelling words, and regurgitate what we reviewed about photosynthesis and do quite well on his tests.  What a relief! He got a really nice report card and is feeling very good about his abilities.
  I think that with the summer babies, it just takes them a bit longer to catch up.  My wonderful sissy-in-law explained this phenomenon to me as she has two summer babies, and how true it is. Fortunately, my second grade daughter was on auto pilot, and had picked up writing in cursive, the final basics of reading and borrowing and carrying in math all with the expert guidance of her teacher.
  The twins in 8th grade were instructed to do or die.  No more mommy-will-proof-read-your-papers-and-make-them-grammatically-correct, and mommy-will-go-over-your-math-to-make-sure-you-are-getting-it business.  I was just too busy for that business with the 4th grader’s struggles and the new job away from home.  We were keeping afloat, and it helped that no one made All Stars or Tournament Team.

Then one of the twins somehow got lost in algebra, and no matter how hard I tried, I couldn’t get him back on board. It was uncanny.  They went to take their private high school entrance exams, and this boy scored in the upper 10% of all of the applicants, qualifying him for honors courses.  His twin brother, who can do the algebra, did not. Go figure. So how was he going to deal with honors geometry when he was failing the last part of algebra?
I spent hours downloading tutorials from the internet, trying to convince him that if he were to copy down the step-by-step equations that his teacher worked on the board to use as an example, it might help. All to no avail. He just put his head down, complained that he didn’t get it, and that I had to spend time with HIM to help!  I dragged out the Cliff Note algebra book to see if that would help. Try as I might, I had forgotten how to factor polynomials! It was tutor time. I went to work getting names and numbers. And quotes!  Aye caramba!  The going rate for a decent local college kid who knew the material was $45/hour!  And my son claimed all but four kids in his class had tutors!  How were they affording it?
  I soon realized that I was in the wrong line of work! Anyway, one of his buds had a tutor who came twice a week. I asked if he might be wiling to tutor two for additional pay.  Win win I thought. The two students would have a cut rate; the tutor would earn more per hour. Well my probablity guess was way off because this suggestion just incited a million phone calls between the other student’s mother, the tutor and I trying to set upon a price and a date.  I came to find out that the other student was getting quite a good deal, which was not being offered to me.  I got tired of the haggling and told that tutor adios. I then called my other friend who had suggested her tutor back when we were dealing with the fourth grader woes.  I called his cell; got a friendly voice and a flexible attitude and I hired him on the spot.  He arrived that night, on time, and went right to work for 2 hours with algebra boy.  My son was happy to report that he received a 91% on his test the following day.
Even though it takes me six hours of work to pay for two hours of tutoring, it is worth every penny if it works. It also saves about four hours of my time, which would need to be spent trying to explain something I don’t get, so mathematically speaking; I guess it all works out! Thank God for summer vacation. I think I need to take an algebra class so I can begin my tutoring career next year!

Algebra
From the 825 A.D. book, "ilm al-jabr w'al Maqa balah" (translated "The Science of Cancellation and Reduction") by the great Iranian Mathematician, Mohammed Ibn Musa al-Khowarizmi. After years of bad pronunciation by Europeans, it came down as "aljabra" and, eventually, "algebra"

Calculus
From the Latin "calculus" meaning "stone used for reckoning"

Cosine
From the complement of sine because it is 90 degrees out of phase.

Exponent
Means "placed out" from two Latin words: "ex" (out) and "pon" (place)

Fraction
From the Latin "fractus" meaning, literally, "broken"

Geometry
Greek word geometria from geo (earth) and metro (measure)

Logarithm
Means "proportional number" from two Greek words: "logos" (proportion) and "arithmetik" (number)

Why we use the letter "m" to denote the slope of a line
m is for the french verb "monter" which means to mount, to climb, or to rise

Percent
Means "by the hundred" from two Latin words: "per" (by) and "centum" (hundred)

Sine
From the Latin word sinus which means " folded cloth"

Trigonometry
Greek word "trigonometria" from Tri (three) gonia (angle) metro (measure)

Zero
From the Arabic "zefirum" meaning "empty"

***

Two seemingly meaningless numbers in the Bible are actually quite interesting.
153

"Simon Peter went up, and drew the net to land full of great fishes, an hundred and fifty and three: and for all there were so many, yet was not the net broken." (John 21:11)

153 is a neat number. Here are four reasons:


1. 153 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17
2. 153 = 1! + 2! + 3! + 4! + 5! (i.e., 1 + (1 x 2) + (1 x 2 x 3) + (1 x 2 x 3 x 4) + (1 x 2 x 3 x 4 x 5))
3. 153 = 13 + 33 + 53

4. 153 lies dormant in every third number. Take any multiple of three, sum the cubes of its digits, take the result, sum the cubes of its digits, take the results, etc. Believe me. You eventually get 153. Take 12, for example.
13 + 23 = 9.
93 = 729.
73 + 23 + 93 = 1080.
13 + 03 + 83 + 03 = 513.
Finally, 53 + 13 + 33 = 153.

220

In Genesis 32:14, Jacob gives Esau 220 goats ("two hundred she goats and twenty he goats") as a gesture of friendship.

The Pythagoreans, those math lovin' dudes from ancient times, identified 220 as a "friendly" number. What made it friendly? Well, 220, unlike most numbers, had a close friend, 284. Namely, each are equal to the sum of the proper divisors of the other. (wha'?) Proper divisors are all the numbers that divide evenly into a number, including 1 but excluding the number itself. The proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110. Add all those numbers and you'll get 284. Likewise, the proper divisors of 284 are 1, 2, 4, 71, and 142 and they sum to 220.

***

A somewhat advanced society has figured how to package basic knowledge in pill form.
A student, needing some learning, goes to the pharmacy and asks what kind of knowledge pills are available. The pharmacist says "Here's a pill for English literature." The student takes the pill and swallows it and has new knowledge about English literature!
"What else do you have?" asks the student.
"Well, I have pills for art history, biology, and world history," replies the pharmacist.
The student asks for these, and swallows them and has new knowledge about those subjects.
Then the student asks, "Do you have a pill for math?"
The pharmacist says "Wait just a moment", and goes back into the storeroom and brings back a whopper of a pill and plunks it on the counter.
"I have to take that huge pill for math?" inquires the student.
The pharmacist replied "Well, you know math always was a little hard to swallow." 

May 2, 2005
Next Post date June 6, 2005
Muslim Toilet (Remind me never to visit!)

You probably know that 3 squared + 4 squared = 5 squared. Those three whole numbers, known as "Pythagoras Triplets", satisfy the Pythagoras Theorem, a2 + b2 = c2. Did you know there are many more such whole number triplets? This article shows you one method of finding them.
Pythagoras of Samos (569 B.C. - 479 B.C.) was a great Greek mathematician who left us few documents to work with. However, the geometric theorems he and his followers developed had certainly made a big impact on modern geometry. .

His most well-known theorem in geometry, the Pythagoras Theorem, states that, for a right-angled triangle represented by three sides, a, b and c, where a & b form the right angle, and c is the hypotenuse, the equation:

a2 + b2 = c2

relates the three sides, and the inverse is also true. For example, a triangle with sides 3, 4 and 5 is right-angled, since
3 squared + 4 squared = 5 squared.

***

An engineer, a physicist and a mathematician are staying in a hotel.
The engineer wakes up and smells smoke. He goes out into the hallway and sees a fire, so he fills a trash can from his room with water and douses the fire. He goes back to bed.
Later, the physicist wakes up and smells smoke. He opens his door and sees a fire in the hallway. He walks down the hall to a fire hose and after calculating the flame velocity, distance, water pressure, trajectory, etc. extinguishes the fire with the minimum amount of water and energy needed.
Later, the mathematician wakes up and smells smoke. He goes to the hall, sees the fire and then the fire hose. He thinks for a moment and then exclaims, "Ah, a solution exists!" and then goes back to bed. 

***

Q: What will a logician choose: a half of an egg or eternal bliss in the afterlife? A: A half of an egg! Because nothing is better than eternal bliss in the afterlife, and a half of an egg is better than nothing.

***

The Evolution of Math Teaching
* 1960s: A peasant sells a bag of potatoes for $10. His costs amount to 4/5 of his selling price. What is his profit?
* 1970s: A farmer sells a bag of potatoes for $10. His costs amount to 4/5 of his selling price, that is, $8. What is his profit?
* 1970s (new math): A farmer exchanges a set P of potatoes with set M of money. The cardinality of the set M is equal to 10, and each element of M is worth $1. Draw ten big dots representing the elements of M. The set C of production costs is composed of two big dots less than the set M. Represent C as a subset of M and give the answer to the question: What is the cardinality of the set of profits?
* 1980s: A farmer sells a bag of potatoes for $10. His production costs are $8, and his profit is $2. Underline the word "potatoes" and discuss with your classmates.
* 1990s: A farmer sells a bag of potatoes for $10. His or her production costs are 0.80 of his or her revenue. On your calculator, graph revenue vs. costs. Run the POTATO program to determine the profit. Discuss the result with students in your group. Write a brief essay that analyzes this example in the real world of economics.

***


Top ten excuses for not doing homework:
* I accidentally divided by zero and my paper burst into flames.
* Isaac Newton's birthday.
* I could only get arbitrarily close to my textbook. I couldn't actually reach it.
* I have the proof, but there isn't room to write it in this margin.
* I was watching the World Series and got tied up trying to prove that it converged.
* I have a solar powered calculator and it was cloudy.
* I locked the paper in my trunk but a four-dimensional dog got in and ate it.
* I couldn't figure out whether i am the square of negative one or am the square root of negative one.
* I took time out to snack on a doughnut and a cup of coffee.
* I spent the rest of the night trying to figure which one to dunk.
* I could have sworn I put the homework inside a Klein bottle, but this morning I couldn't find it.

***

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