The School Pad

Test test test

noreply@blogger.com (WhiteCloud1989) — Tue, 22 Jul 2008 00:17:00 +0000

Arithmetic Sequences

noreply@blogger.com (WhiteCloud1989) — Mon, 14 Apr 2008 20:03:00 +0000

Sorry I haven't written in 5 days. I've recently had an addiction to Squidoo and Helium. Hey. I like money after all.

However I'm working out a new writing schedule so that I can incorporate my new addictions without forgetting about my blog ♥

Here's a post I was working on:

Old class notes: MATH

Arithmetic sequences:

Recursive: Figuring out a sequence step by step
Explicit: Figuring out a sequence from a general formula.
Arithmentic: Common diference between the terms.
a) recursive: an = an-1 +d
b) explicit: an = a1 + d(n-1)

example:
-6, -2, 2, ....
a1,a2,a3,....

Common difference (d): +4.

Example:
Finding the 10th term recursively. (the slow inconvenient way)
Recursive: an = an-1 + 4.
That means if (for example) you want to find the 4th term (a4) you'd have a4 = a3 +4. That means you need to know a3 to find a4 (and you need to know a4 to find a5, etc..)
In short it means: start at the beginning and add.
a1, a2, a3, a4, a5, a6, a7, a8, a9, a10
-6, -2, 2 , 6 , 10, 14, 18, 22, 23, 30

Finding the 10th term explicitly. (the fast way)
explicit: an = a1 + 4(n-1).
a1 is the first term , which in this case is -6.
explicit: an = -6 + 4(n-1). So if you want to find the 10th term (a10), you'd have a10 = -6 +4(10-1).
which comes out to
a10 = -6 + 4(9)
a10 = -6 + 36
a10 = 30.

What if you're not given the first term? If you're given any term (and told what the term number is) you can still use this method. However you'll have to adjust. For example, if you were given the 4th term and needed to find the 10th term, in truth you make the 4th term become term 1, and the 10th term becomes term 6 (10-4).

What if you're not given the term numbers? Then you'll have to use Recursive. Sorry.

TI-83 Calculator Trick

noreply@blogger.com (WhiteCloud1989) — Thu, 10 Apr 2008 01:51:00 +0000

I once wrote a program for my Ti-83 that would use the Quadratic formula for me:
A=-B +-V(b2-4AC)
all over 2A

All you have to do is:

Turn your calculator on
Press the Prgm button
Go right twice to New
Press Enter (Create new)
Give it a name (ideally one your teachers won't recognize. I called it "Lupu")
Copy the code on the right.

What's with the colored words?
These are not words you write. These are words written within the calculator's library.
While you are writing your program, press Prgm again to see the library.

PS.The colons appear by pressing Enter.

Disp is found in the I/O section, 3d word.
-Go to Prgm.
-Go right once
-Go down twice (or press 3)

Pause is found in the CTL section of the library, 8th word.
-Go to Prgm
-Go down 7times (or press 8)

Prompt is found in the I/O section, 2d word
-Go to Prgm
-Go right once
-Go down once (or press 2)

What does this program do?
It will ask you for three numbers. These are a, b, and c.
In the equation:
5x^2 +3x + 4 =0
a=5
b=3
c=4
The equation MUST be in this format for you to enter the numbers in the right order.

The program will then step-by-step solve for x.
This means it's easy to copy the steps down.

For example:
if I enter:
1
3
2

It will say
"
-3
+-V()
1
/
2
"

so x= -3 +-V(1)
all over 2.

The program will pause at this point so you can copy this down.
It will then proceed to solve for x if you press Enter. If it's an imaginary answer it will crash and you just press Quit.
After all, you already have the hard part done.
If it's not an imaginary answer, it will tell you x.
Using this example, the program would continue and say
"Roots
-1
-2
"
So the roots of the equation would be x=-1 and x=-2

So what's this program good for?
Well it allows you to know the equation in Quadratic formula form without you having to remember or do any math, thus making you look as if you know your stuff. I'm good at math so I only used this because I was lazy, not because I didn't know it.

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Completing The Square

noreply@blogger.com (WhiteCloud1989) — Wed, 02 Apr 2008 23:20:00 +0000

Completing the Square
Yeah,
you know that annoying thing you probably have to do in Math B2, advanced algebra, or pre-calculus? Completing the Square? Well no worries, I'll explain it to you.

2x2+ 16x -10 = 8
1. Locate the x2 coefficient and take it out. 2. Move over any loose numbers. 3. Half the x coefficient and write it on the side (or keep in your head) 4. Square your result and add it both sides of the equation 5. Turn the x side into a square. If you don't know it off the top of your head, simply take the root of x (x2 -> x), take half of the x coefficient and add it (+ 4), and square the whole thing. Simplify the other side if needed. There, you've completed the square. You can then go on to solve for x if you want to.

Completing the square of quadratic functions of two variables: This is usually taught in multivariable calculus.

The square will of course be taken in respect to x in this example.
Need to take the square in respect to a variable other than x? It's the same

thing. If you don't feel comfortable you can also temporarily switch to x. The steps are exactly the same except you have an extra variable -that you treat as a constant. So....
2x2 + 16yx - 18y2 = 0

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Probability Part One

noreply@blogger.com (WhiteCloud1989) — Fri, 28 Mar 2008 02:04:00 +0000

What is probability?
Probability is the likelihood that something will happen. It is represented in terms of 0 to 1: O being no chance, 1 being the highest.

In Percentage mode, that would be 0% to 100%.

Part 1: One time probability.
If you throw a coin, the chances that you will get heads is 1 out of 2. That's because there are only 2 possibilities (heads or tails) and you only want heads (1). That means for each die, you have a 1:2 probability of getting heads.

However this is only for one time event. If you were to throw the die twice, you do NOT have 50% of heaving heads on both tries. You have 50% for the first try, and 50% for the second try, but not combined.

Part 2: When to add probabilities. (OR rule)
It's quite simple: The only time you add probabilities is if you're considering multiple items as ONE event. Basically, if in ONE turn you're considering an item OR an item [OR another item, etc..]

Example:
A bag contains 2 pennies, 3 nickels, 4 dimes, and 5 quarters. What is the probability that if you picked a coin at random it would be a penny OR a nickel?
The probability of getting a penny is 2: 14
The probability of getting a nickel is 3: 14.
The probability of getting a penny OR a nickel is 5:14.
PS, the 14 is the total of all the coins in the bag.

Side Lesson:
While the above lesson had a probability that couldn't end up the same (you can't pick up both a penny and a nickel if you only pick on coin), some OR probabilities will give you the possibility of getting either result! For example, the probability that a number between 1 and 10 is divisible by 2 OR divisible by 3 could have both sides met since there is the number 6 is divisible by both.
What do you do when something like this happens?

You use the regular OR rule first but you also subtract the possibility that you can have both.
So in this example:
Probability that a number is divisible by 2: 5:10 (2,4,6,8,10)
Probability that a number is divisible by 3: 3:10(3,6,9)
Probability of both: 1: 10 (6)
So the probability of getting a number divisible by 2 OR (and only or) divisible by 3 is:
5:10 +3:10 -1:10 = 7:10.

Part 3: When to multiply probability.
While it is nice to know the probability of a single event happening, it would be nicer to know the likelihood of a combination of events happening.
So if you want to find out the chance that you will get two heads in a row on two coin flips...
You find the probability of getting a Heads on a single coin flip (1:2)
and multiply by the probability of getting another Heads on the second flip (1:2).
So you get 1:2 * 1:2 = 1:4.

This is also know as the Counting principle.

Side Lesson:
If you're finding the probability of multiple things happening, but that when one thing happens , the next changes, it's slightly different.

For example:
You have a bag with a red toy, a green toy, and 2 blue toys.
What is the probability that if you have 2 draws, you will get 2 blue toys, but that when you pick a toy, you don't put it back in the bag?
Probability that you get a blue toy on the first try: 2 out of 4
Probability that you get a blue toy on the second try : 1 out of 3 (because there are now only 3 toys left, and only one is still blue).
Probability that you get two blue toys?
2:4 x 1:3 = 2:12 (or 1:6)

Part 4: Computations:
Finding the likelihood of at least a number of things happening.. This requires the use of COMBINATIONS (a lesson on that is not provided here. Your calculator might be able to do it).

First you find all of the possibilities. "At least" (or at most) imply that you could have multiple options.
Make a computation of the first option then add a computation of the second option.
You will then divide by the Computation of the total with the number of wanted items.

Example:
A bag contains 2 blue and 3 red marbles. 3 marbles are picked at random. What is the probability that at least 2 of the marbles are red?
At least means: 2 red and 1 blue <-first option
or
3 red and 0 blue. <-second option

Computation of first option: 3C2 x 2C1. There are a total of 3 reds but we want 2, the last marble would have to be 1 of the 2 blue marbles.

Computation of second option: 3C3 x 2C0. There are a total of 3 reds and we want all 3, we want 0 of the 2 blue marbles.

Computation of total: 5C3. We have 5 marbles total but we only pick out 3 marbles.
3C2 x 2C1 + 3C3 x 2C0
5C3

Part 5: The likelihood that something will not happen.
This actually shouldn't have a lesson of its own. It's really the same as the AND & OR rule except that your outcome will be the probability that something will NOT happy.

So the probability that you will not get a heads on a coin flip is 1:2.

If you can't find the probability of something not happening (like if you're given a word problem that only tells you the probability of something happening) , it is simply 1-P(something).
or 100% - P(something)%

What does this mean?
Example:
The probability of Daniel getting an A on his test is 90%. What is the probability that he will not get an A?
Answer: 10% (100-90).

Example 2:
The probability of Daniel getting an A on his test is 90%, the likelyhood of his parents giving him money as a reward for an A is 75%. What is the probability that he will NOT receive money as a reward for his grade.

First find the probability of him getting an A AND his parents rewarding him.

90% * 75 % = 67.5% (.9 * .75 * 100)

The likelihood of him NOT receiving an award for his test score is
100% - 67.5% = 32.5%

This lesson covered basic, and some intermediate, probability rules. A separate lesson on BAYES' rule, and other weird probability will be given. Permutations weren't included in this lecture because just about anything you can do with permutations can be done with the Counting Principle & AND rule &OR rule. I might included them in Probability part Deux.

Well that's all for now. I probably won't write another lesson for a week or so. They're supposed to be only an extra feature to the blog after all :P

A Guide to Stem-And-Leaf Plots

noreply@blogger.com (WhiteCloud1989) — Wed, 26 Mar 2008 04:49:00 +0000

Since I am a math lover, I will also provide math lessons. If you wish for a certain topic to be covered, simply comment it.
PS. I made the mistake of thinking these were called tree diagrams when actually they're called stem and leaf plots. :D. That's why all of the pictures are off. I've fixed all of the text but I don't feel like fixing the pictures.
Why do they have to use so many tree references in math?

A guide to Stem and leaf plots.
I think this should be taught in the 5th grade.

All of the grades within a test are given below, organize the grades into a Stem and leaf plot.

Simply reorganize the numbers
Decide on a cut off point. I chose the units digits because they're the ones that change the most.
Locate the lowest and highest numbers (35 and 100)
Start your base, or roots, (left) with 3 and end with 10. I started at a 1 because it was 12:44 AM and I wasn't thinking right, and now I don't feel like editing the picture.
Add the missing numbers of the roots on the right side in order to represent their full meanings. (so 8|2,4,7 stands for 82,84, and 87)
Be sure to show an example in your "Legend".

What are those colored boxes? They're repeated numbers.

Having this chart allows you to know many things:

1. What is the range?
A range is the lowest value and the highest value.
So the range is (35,100).

2. What is the mode?
The mode is the number that is most repeated. In this case that would be 98 because there are 3 occurences?

PS. If you have a diagram where the two different numbers have the most occurences, both numbers are the modes.
EG. 56,67,89,89,89,90,90,90,91,91,100. In this example, there are two modes: 89 and 90.

3. What is the median?
The median is the number in the middle. simply "cross off" one letter at the top, then one in the bottom (then top, then bottom, etc..) until you are left with either 1 or 2 numbers. If you're left with only one number, that's the median. If you're left with 2 numbers, you have to average them.
In this case the median is 84.

4. What is the mean?

A "mean" is an average of everything.
First add all of the numbers and find the sum: 1379
Then count how many numbers there are:17
Divide and that's the mean: 81.12

Further Exercises:
You can download two further exercises (with answers and explanations) right here.

This is nice, but what's it good for?
I'm sure some of you noticed the post saying that this was a rather slow method- and it is! However Stem-and-leaf plots are important in the elementary/middle school section because they provide a basic picturesque understanding of statistics. They are the perfect introduction to statistics. As far as the fact that excel is faster, the whole point is to be able to do them without computers. While computers are nice, understanding a concept is crucial to understanding what good the concept is for. I do agree that once a person has a good understanding of Stem-and-leaf plots, the fundamentals for statistics are set.

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A way to not lose your pens

noreply@blogger.com (WhiteCloud1989) — Sat, 22 Mar 2008 13:39:00 +0000

Notepad with a hanger pen attached. This notepad is usually left on my night-table.

You know those people who , if you give them a brand new box of 30 pens, they'll only have 5 left by the end of the month? Well I'm one of those people. How do I lose them? I have NO idea; I don't lend them out much so that can't be the reason. I've usually just brushed it off as "the spirit living in my room steals my things" (no, I don't believe in ghosts, this is just my way of explaining to my mom why I never have pens and pencils).

Well, guess what?
I bought a set of FOUR pens a few weeks and I still have them!!!
My secret?
Hanger pens.

A "journal" that I keep in my schoolback, in which I write down notes for classes with few sequential notes required (like computer science, or math). Notice the hanger pen?

Some, well probably none, of you may remember a Tip of the Day on my Twitter box. I sometimes leaves tips on my twitter - located in my sidebar, nice pink box that says "Twitter". Sometimes I leave notices to posts, or ideas for future posts, or just daily happenings, but I do occasionally leave a Tip of The Day.

One of them was : " Tip of the day: Hanger pens. Pens with caps that can attach to notepads laying around the house can help you fight off writer's block."

and I've decided this tip was worthy of its own post.

A full-fledged notebook, with a hanger pen. No, I don't mind it being yellow. I've never understood people who couldn't read letters they could see. If it's easily visible, then it's readable. This yellow is easily visible, therefore I don't mind using it. This notebook would be used for a class with loads of sequential notes, like health or history.

Hanger pens aren't the only things you can attach.
See my wallet?
It has a hanger pen and a bunch of mini index cards attached. Those mini index cards are stacked within a plastic (that came with) and all linked with a ring. That means I can write down

homework
stuff to buy
stuff to do

directly on my wallet (aka, the thing I carry around the most).

The fact that the caps are attached to the notebooks means that I have to pens back in their proper spot after using them. Also, the fact that the pens are attached means that I don't have to look for a pen, just for my notebook/notepad.
Now if only I could find hanger pencils.

These particular pens are made by Paperchase ©. I think I'm going back to Borders soon to get more because I LOVE them.

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Firefox Plugins for Language Students

noreply@blogger.com (WhiteCloud1989) — Wed, 19 Mar 2008 04:26:00 +0000

The 2nd installment of the Firefox Plugins for Students.

If you're wondering, no I don't test these out. First I make a list of all of them, then I read the full descriptions to find out what they do, then I look at the reviews AND the discussions. If I feel an add-on is worth the download after going through all of these, I put it on my list.

Occasionally I will try out an add-on if I have absolutely no way of knowing if it is good, but usually I'll just ignore the add-on.

Typing tools:

anykey-Allows typing into phonetic Russian, Ukrainian, Amharic, Arabic, Armenian, Hindi Davangari, Hebrew, Mongolian, greek

abcTajpu-Type in accented letters, international characters or symbols (Mostly european characters)

Multiple languages tools:

FoxLingo-Web page translation, translated search, text translation, tools to help learn languages. 45 languages. A must have.

gTranslate- The usual alternative for foxlingo due to compatibility issues.

Wordlearner toolbar- this toolbar will help you learn words in any language while you surf the web.

English

MSTS Dictionary- english dictionary. Just select a word, right click ,and lookup. You'll get a thorough definition in far less time than it would to go on dictionary.com.

ESL

Backword-See a word you don't know? Just click on it and find out how to pronounce it, what it means, and save the paragraph it belonged in for future study.

Irregular Verbs- learn english irregular verbs (aimed for French learners, but could also be used to help other learners)

english proverbs - Write out an English proverb on the status bar. Hover to find out its equivalent in the language you've chosen. There are 9 languages available.

East Asian languages

multiple

East Asian Translator - translates web pages and selected passages in chinese, english, japanese, and korean. You need to get East Asian languages enable in XP.

Japanese
Perapera-kun - A popup japanese word translator. It shows the meaning and what kind of sentence part it is; furigana comes as well when looking up kanji. You need to have a japanese dictionary installed in FF first though (read the info page to find out which).

furigana injector -Looks up the readings for kanji words and inserts them as furigana

Chinese

Chinese Perapera-kun - A popup chinese word translator. You have the meaning as well as the phonetics of the word. It works with both Simplified and Traditional characters. You can export words to study later. Read the info page to find out where the get the dictionary required to use this.

Vietnamese

vnDict -Vietnamese Dictionary Extension.

Other languages:

simpletranslate (german)-German Dictionary Extension

EHTip (croatian)-Croatian Dictionary Extension

Sozlook (turkish)-Turkish Dictionary Extension

©Image MIT OpenCourseWare

Plugins for the Math, Health, and Busy Student.

noreply@blogger.com (WhiteCloud1989) — Tue, 18 Mar 2008 01:55:00 +0000

This is the first of many entries for my FireFox Plugins for Students Series.

Plugins for the math & statistics student
These are plugins for math & statistics students. These can help you do your homework even if you're too lazy to get the tools you're supposed to use.
Graphing Calculator Toolbar-Enter up to 5 equations into this toolbar and then view the graph and table of values right on firefox.

Status-bar Scientific Calculator - click on the icon to display the textbox and enter your expression. It does a lot of things a 'real' scientific calculator does.

Plugins for the Health student
calorie count plus toolbar - search calories and nutrition info; keep track of what you eat; make sure you stay on your healthy eating track.

Plugins for the busy student
ReminderFox - Think of this as a mini calendar. And when you need to be reminded of something, a pop up will appear. So if you're an internet addict who keeps losing track of time, you can finally set yourself an alarm right on your browser and get yourself to school! (or wherever)

Reload Every - Need to have something constantly reloaded but can't press refresh all the time? This thing is for you. You can choose the refresh rate.

Downthemall- Download every link on the page. You can use filters to only download certain links, or certain types of links (images only, actual links only, combinations, etc..)

Roboform- Automatically fill out sign-up forms, checkboxes, and radio buttons.

Autofill forms: Alternative to Roboform.

auto toggle tabs- A timer automatically changes from one tab to the next. I could see a
few uses for this for people who participate in
ptc/ptp/ptr/autosurf/manualsurf sites.

Update scanner - Monitors web pages for updates.

PDF Download - Stops PDF files form automatically loading (and slowing down) your browser. YOU get to approve the PDF files first. No more will your browser slowdown/freeze because you clicked a link to an unknown PDF file.

Teach about real life

noreply@blogger.com (WhiteCloud1989) — Sun, 02 Mar 2008 04:35:00 +0000

Most people would agree that it is a parent's job to teach his child about everyday things. However, the truth is some people aren't great at parenting and will not do so.

Take me for example.
I am 19 and I didn't even know how to take the bus until 6 months ago. About one month later, I learned how to take the train. I still have no idea how to use a bank account; I can't drive; I don't know how to do the laundry; I have no charisma for retail (aka, the only real job I've ever had); I can't cook much; I don't know how to fix a computer (and my father's a computer nerd).
Academically however, I am amazing. Whether it be math, or english, or history, or even woodshop, I've done very well. It isn't a lack of intelligence-it's a lack of parenting.

My mother would do everything for me and my brother. My father would leave the parenting to my mother. Because of that we've always been slow to learn "common sense" and common tasks.

How nice it would have been to have learned some of that stuff at school.
So teachers, please, for the sake of children of parents who forget to teach important stuff...please. Have a lesson once a semester or so about real life stuff.

There are already schools who do some of that. Everything I've learned so far about cooking and baking I've learned from my 7th grade Home Economics class. However ONE class isn't enough.

Example:
All 4th graders learn about bus safety, bus cards, bus etiquette, bus map/time reading on March 21st.
All 5th graders have a special class once a week where they learn "driving rules" but instead use bikes or [cool] tricycles. You could even set up fake signs in the playground.

I will be posting project ideas every once in a while.

Ideally (in my mind) a student should have one of these "seminars" once a year. Some seminars should be done at least twice: once while in early elementary school, once while in late middle school . They could be anything from a little 30 minute lecture to a full blown project! It doesn't matter the size, as long as they're taught while little as well as while grown.