Reason # Nineninenine to own a Calculator

I know you've been working hard this week and reading a lot so I'll keep this brief. Here's one final PSSA style question:

Why in Mathopolis would you get one of these?

a. You need a clock.
b. You've got mad math skills and you want to practice them.
c. You like Nines.
d. You are so cool your friends need to wear a sweater when they hang out with you.

This one is from the Triple Nine Society (if you search for that you can find out more info.)

Stay radical!

A Day Late, but Still Irrational

A good friend of mathematical accuracy, Adam, sent us this gem in honor of Pi Day (3/14). Come to think of it, Adam is a fabulous name- one of the few that implies a mathematical operation.




If a mathematical superhero didn't have the ability to fly, they'd surely be driving this model- the Mazda Mathmobile.

Winter Comes to an End, but Bad Math Doesn't

Next week is the start of PSSA season. I guess that means we get to hunt the PSSAs. Wouldn't that be great. Anyways, I have no idea what the weather will be next week, but I hope the temperatures (and attitudes) stay positive.

Since the Mathman morning announcements have been reduced like the greatest common factor between the numerator and denominator (i.e. cancelled) for a while, I've had some time to head out into the "real world" and fight bad math at every intersection.

It didn't take long for me to find this example:



Wow. Sounds like a fabulous toy (THAT YOU SHOULD NEVER BRING TO SCHOOL). I mean, who wants to take the effort to throw a snowball?

Anyways, If I'm going to plop down >$20 on a piece of plastic I want to know how well it works. So I went looking for some information and found:

Ad copy #1:

The 50 Foot Snowball Launcher.

STOP RIGHT HERE! 50 FOOT SNOWBALLS! RADICAL!

This toy blaster makes and launches softball-sized snowballs up to 50', allowing rapid, long-range assaults during neighborhood snowball confrontations.

Wait a second... It doesn't launch 50 foot snowballs, it launches smaller snowballs up to 50 feet. That's a bummer.

Ad copy #2:

Snowball Blaster by Wham-O
*Snowball Maker/ Launcher
*Makes and launches Snowballs up to 80 feet (24 meters)
*Compelling Box Packaging

So does it launch snowballs 50 feet or 80 feet (24 meters)?

Ad copy #3:

Product Description:
Protect your turf and defend your snow fort with a snowball maker and launcher

Snow toy makes and launches Snowballs up to 50 feet (16 meters)

By this point I was really confused. The numbers don't match.

Why?

A: My guess is probably poor font choice. When I looked at the actual package it appeared to say "80ft (16m)". This advertising ploy was pure genius. That's because 80 feet is much farther than 16m. Here's some math:

Since 1 meter = 39.37 inches it follows that

1 m .... ..... 16 m
----------- = --------- = (approx.) 52.5 ft.
39.37 in.... 629.92 in

We could also check the 80 feet and figure out how many meters that is.

Since 1 in = 2.54 cm, 12 in (1 ft) = 30.48 cm. So,

1 ft.... .... 80 ft
----------- = --------- = (approx.) 24.4 m
30.48 cm.. 2438.4 cm

The poor font choice for the 5 or 8 made the 50 or 80 very confusing. The PSSA graders probably would have ruled that "ILL" for illegible. Definitely less than a proficient score would be awarded to this product.

In conclusion, since you CAN'T use this at school, why bother paying >$30 for something so impractical? Something that would be much handier (and much less money) would be a scientific calculator with a fraction button. That, coupled with a bit of conversion common sense (CCS) would allow you to figure out that the claims made for this toy are at best confusing.

Keep your eyes open, #2 pencils sharp, and leave the snowballs at home.

Until next time,
Stay radical.

I <3 Doing Things the Hard Way

"I used my calculator."

I would be willing to bet this is most frequently used statement in the math classes around BJHS. This little phrase has become the new magic word, bumping "Please" off of the #1 spot. (I realize the phrase is more than one word, but the fluidity with which many say "I used my calculator" makes it almost one word.) The truth of the matter is, statistically speaking, over 1/3 of the Junior High students cannot use this phrase truthfully.

The BJHS Math Dept. (otherwise known as The Department of Accuracy and Justice) has collected data about calculator ownership from all of the homerooms throughout the school. The results: at least 470 students out of 1300 (rounded to the nearest 100) don't own a calculator.

470
---- = .3615 = 36% cannot use the statement "I used MY calculator." accurately.
1300

The strange thing is that many students would have difficulty in calculating the decimal and percent above without a calculator.

What is also puzzling about this situation is how many of the BJHS students own cell phones or iPod/ mp3 players compared to those who own a calculator. It's perplexing because nobody uses "I used my cell phone." or "I used my iPod." to describe how they solved a math problem. It's really weird that people wouldn't own a calculator as they probably have math homework around 4 out of 5 days (80%) of the week.

All of these observations don't even account for the fact that a scientific calculator with a fraction (A b/c) button only costs $10-$15 and is so much more useful throughout the school day than either a cell phone or mp3 player. Owning and using your OWN calculator may even make math a bit easier for you- that is unless you have mathematical superpowers which allow you to calculate at the speed of light (approximately 186,000 miles per second).

So let's summarize: Cost < a monthly cell phone bill. Usefulness > an iPod. It sounds like calculator ownership is something everyone should experience.

So the message is: If you really love doing math for fun DON'T own a calculator. It will take you a lot longer to do your math work so you'll feel a sense of accomplishment knowing you did ALL the work and didn't take the easy way out.

How Good is Your Memory?

So you think iPhone is the greatest thing ever.

Think again.

A long time ago-in a galaxy far, far, away, people thought they had the greatest video game system ever. The year was 1977. While that may sound like the age of the dinosaur for those of you who can't remember life without texting or cell phones, it's not really that long ago. As a matter of fact, statistically speaking, you'll probably live longer than 2 billion seconds or over twice that amount of time.

Anyways, in 1977, the first successful home video game systems came into play. (I know some of you can't imagine life without video games, but people did survive.) The first widely available video game system was the Atari (later to be called the Atari 2600). The Atari was out long before any of the Playstations, Nintendos, or XBoxes. If you don't know what I'm talking about, look up "Atari" sometime when you're not texting inequalities on your phone. (Example: Dude, 1<3 Don't Stop Believing - it's my favorite song on my iPod- it is so da bomb).

You may ask, "Why would I care about 1977? That's like, last century." Well, stick with me young Jedi for you have a lot to learn. (-not only did the Atari come out in 1977, but Star Wars did as well.)

Ok, so why was the Atari so revolutionary (even if it was 1977)? I'm glad you asked.

The Atari cartridge was revolutionary because it had 4K of memory. That's 4,000 bytes (actually 4,096, but we're going with 4,000). Remember from typing class that 1 character equals about one byte. For 1977 that was pretty amazing. For 2009, that's pretty lame because the basic iPhone has 4GB of memory.


So the PSSA style question is: "How many Atari cartridges would fit on an iPhone?"

A. A whole lot. (or ITL)
B. IDK. (otherwise known as ITL)
C. I'm not quite sure, but 1 <3 learning so let's figure it out.
D. Don't select this choice, it's just on here to be a distraction. (or ITL to read and eliminate this choice)

I hope you chose "C."

First of all some background information: (this would be on a formula sheet, padawan)

1K = 1000 bytes
1MB = 1000K
1GB = 1000MB

Now to use the force (i.e. math) to figure things out: (note the ..... are just placeholders because Mathman stinks at page formatting in html.)

1 cartridge..... C cartridges
--------------- = ------------
4 K............... 1000K

Solving for C (by using cross products and proportions) gives us:

1*1000=1000

1000/4=250 cartridges in 1000K (or 1MB)

Now,

250 cartridges..... N cartridges
------------------- = ---------------
1 MB ................ 1000 MB

Solving for N gives,

250*1000=250000

250000/1=250000 cartridges in 1000MB (or 1GB)

Since the iPhone we're comparing to is 4GB, that would hold 250,000*4 = 1,000,000 Atari cartridges.

Big deal, you say, the iPhone I want is still the greatest thing EVER.

For now.

Let me leave you with the next up and coming unit of measure. The terabyte (TB) is coming and it's 1000GB. It's going to make your iPhone go the way of the Atari.

Stop Me if You've Heard This One Before

Here's a joke for you:

Bill Gates walks into a room and everyone becomes a millionaire, on average.

Hilarious, huh?

I see the mail piling up right now: "Dear Mathman. I don't get the joke." or "Dear Mathman, it's too hard to understand that joke." or even, "Dear Mathman, that's a dumb joke. Pencil tapping is waaayyy cooler." (maybe if you're actually really good at pencil tapping)

Well, it isn't a dumb joke, because you have to understand the three M's to get it. What are the three M's you ask. Is that, like, 150% better than Eminem? (most certainly). Do they melt in your mouth, not in your hands? (It does take a long time in the microwave to melt the candy shell, but that's a story for another time.)

The three M's are measures of central tendency, or the mean, median, and mode. Measures of central tendency (the three M's), refer to "average". Most people get the mode. That was a bit of a joke in itself as mode refers to the most frequent data values in a set. That doesn't help us much with the Bill Gates joke since he's probably the only one person in the room with enough money to buy a planet.

The median refers to the middle value of a data set. Once again, since Mr. Gates is only one data value, one person with no money in their pockets would cancel his cash right out.

That leaves mean as being the only hope to make this joke funny. Never underestimate the power of an outlier. A quicky wiki left me with Bill being worth somewhere around $58 billion in 2008. That's $58,000,000,000 in standard notation or 5.8 x 10 to the 10th power dollars. Do you realize how big that is? That's 58,000 groups of $1,000,000 each. That's enough cash to pay someone (who's awesome at it) to pencil tap for you while you do your math homework.

Since it takes $1,000,000 to be a millionaire, Bill Gates could offset 57,999 other people in the room who wouldn't even have enough money to buy their own pencil to tap and pull the mean to $1,000,000 a piece. That would buy a whole lot of pencils for each person so they could stop absconding them from Mr. Krack's pencil box.

Here's the definiton for mean:

sum of all the values
--------------------------- = mean
total number of entries

In our case:

$58,000,000,000
------------------------ = $1,000,000
58,000

Just to put that in perspective: Heinz Field seats 64,000 people. That means we'd need 64,000-58,000 = 6,000 more millions of dollars to make everyone in Heinz Field (on average) a millionaire. That amount of money we'd need to spread over 63,999 people is 6,000 x $1,000,000 = $6,000,000,000. So the average amount those (other than Bill Gates) 63,999 people would need is $6,000,000,000 / 63,999 = $93,751.46. I'm taking a guess here that most people don't have this much money kicking around. (Personally, I am good for the $.46 of my share.)

To me that makes this problem even more interesting since Bill himself could cover 58,000 out of the 64,000 people in the stadium and most likely we still wouldn't be able to make everyone in the stadium millionaires since we wouldn't have enough money.

One man has the capability to make the "average" of:
58,000
----------- = 90.625%
64,000

of the population of Heinz Field millionaires, while the rest of us 63,999 people would have a hard time covering the remaining 9.375% of the money to raise the average of the population of Heinz Field to the status of millionaires.

Possibilities vs. Probabilities

Citizens of the Junior High: The PSSAs are coming soon. That can only mean one thing:

Free breakfast.

You've probably heard the saying, "There's no such thing as a free lunch." Well, that's because there are way too many possibilities for breakfast.

Lets's consider the options you had for choosing your breakfast: Orange or apple juice (much to the dismay of Mathman, espresso isn't one of the options here) and a breakfast item of a Cocoa Puffs cereal bar, Trix cereal bar, cinnamon sugar donut, apple, banana, or the ubiquitous "Honey Bun".

If we were to quickly calculate the possibilities for the number of breakfasts we'd have:

Orange juice and Cocoa Puffs cereal bar
or Trix cereal bar
or cinnamon sugar donut
or apple
or banana
or "Honey Bun"

Apple juice and Cocoa Puffs cereal bar
or Trix cereal bar
or cinnamon sugar donut
or apple
or banana
or "Honey Bun"

So there are 12 possibilities for breakfast.

There's a simpler way of finding out how many ways to choose breakfast. Think about it 2 ways for juice, 6 breakfast items = 12 possibilities.

2 and 6 to get 12. Multiplication must be the secret operation.

Now, we can also consider that picking a juice doesn't effect the choice of a menu item. So choosing a juice and a breakfast item are independent events.

Now that we have considered the possibilities, let's consider the probability of choosing a particular breakfast. Let's look for P(apple juice, Trix cereal bar). The P() stands for probability of what's in the (). The P(apple juice, Trix cereal bar) is 1 result of 12 possibilities or a 1/12 chance. We could also get here by taking the P(apple juice)= 1/2 and P(Trix cereal bar) = 1/6. Once again, use the secret operation of multiply to get 1/12.

So the odds of getting Mathman's favorite breakfast of espresso and chocolate chip and banana pancakes is P(espresso, banana pancakes) = 0*0 = 0 since the P(espresso)=0 and the P(banana pancakes)=0.

Let's end on a positive note: the P(staying radical)= 1 or 100%. That's the only way to be.

It's All in the Merchandising

Introducing our new weapon in the fight against ignorance:



Welcome the Algebratz.

I've read the PSSA manuals. I see nothing against using the Algebratz.

You Probably Should Read Closely

Greetings citizens of the Junior High. It has recently come to my attention that many of you are slightly confused about two types of probabilities- theoretical and experimental. Well, I'd like to help you figure out the difference between the two.

First up: theoretical probability. This is simply an educated guess at what will happen in a situation. For instance, the theoretical probability that citizens of the Junior High will wash their hands after using the restroom to help prevent the spread of the "stomach flu" is 1 or 1/1 or 100%. It should be a sure thing, especially since there are signs stenciled on the walls that say "Please Flush" and "Please Wash Hands". You can refer to this probability as P(washing hands). Simple hand washing after using the restroom can limit the spread of the "stomach flu", which really isn't a flu at all, but often an e. coli bacterial outbreak.

In essence, a theoretical probability is just a hopeful prediction.

Now, we'll take a look at an experimental probability. This type of probability is a ratio based on the number of favorable outcomes out of the total number of trials. Quite simply, we conduct an experiment and observe what happens. For our example, if we notice that the water ran 5 times for 8 people leaving the restroom we can conclude that the experimental probability is 5/8 = 5 out of 8 = .625 = 62.5% of the people using the restroom washed their hands.

In many cases the theoretical and experimental probabilities are not equal. Often times the experimental probability is greater than the theoretical probability.

Unfortunately, in our example, the best we can hope for is that the experimental probability matches the theoretical probability. Especially since everyone can read the writing on the wall- "Please Wash Hands".

We are not even going into theoretical and experimental probabilities of the "Please Flush" signage.

Citizens of the Junior High, remember: Only you can wash your hands.

Pick a Winner?

Dear Mathman,

My friends and I are starting a chapter on probability. We were wondering, Do you pick your nose?

Sincerely,
Laura



Dear Laura,

I'm not sure exactly what you are referring to by "Do you pick your nose?" It sounds like this sentence is in the present tense and an ongoing process, so I'd have to say the answer is "No.", as I didn't have any kind of option in choosing my nose. BUT, If I indeed did have several equally likely noses to choose from- let's say 4, the odds I would have chosen my current nose are 1 in 4 = 1/4 = .25 = 25%.

Life is full of choices; You can pick your friends but you can't pick your nose.

Stay radical,
Mathman

Don't Leave Math Behind.

We use language everyday. As great as words are though, they sometimes get put into sayings that have different meanings. For instance: "Cool" could refer to temperature, or it could refer to something that is "Groovy", "Awesome", or even "Radical". This makes English a bit confusing to someone who has the capability to time travel.

Language is great, however, because without it we wouldn't be able to ask such timeless questions as "Why did the chicken cross the road?" or "What were you thinking?" We also wouldn't be able to make such statements as "I'm hungry." or "Employees must wash hands before returning to work."

Recently, language has been compacted by the phenomenon known as texting. LOL. BFF. FAQ. These acronyms are so common the most people know their meanings immediately and don't have to think about what they mean.

That's great and all, but that leaves math out of the equation for the most part. I mean, if English gets texting, shouldn't math get digiting? It's not really fair that they get all the abbreviations when we're stuck with + for add, - for subtract, x for multiply, and / for divide. That's sooooo middle ages.

It's time, citizens of the Junior High, to start bringing math back into the 21st century.

Announcing our new acronym: (drum roll please) SIF

Do you know what it stands for? How about: Slope-Intercept Form. What is Slope-Intercept Form you ask? It's a form you fill out that has the slope and the y-intercept in it. It's the same form ALL the time, just the slope and intercept get filled in.

SIF: y=mx+b, where m is the slope (rise over run) and b is the y- intercept, the place where the graph crosses the y-axis.

Say it with me:SIF.

Stay radical, or at least keep being a regular quadrilateral.

Valentine's Day Question for the All Knowing Mathman!!!

Dear Mathman,

I have a major problem and I need your help. With Valentine’s Day quickly approaching, I have this special someone that I need a gift for. I am not the romantic but I want to do something special, so I need some suggestions of what to get. Let me know if you have any thoughts.

Thanks,

Cupid





Dear Cupid,

I have the same problem. What do you buy that special someone to show her/him that you really care? Here are some great ideas that have gotten me out of some tough problems.

Ruler, compass, protractor, a slide rule, up-to-date formula sheet, scientific calculator with fraction button and directions (great to help on the PSSA test), but the one gift that will really show you care is a pass to Math Help at the BJHS every Tuesday and Thursday. The gift of knowledge cannot be replaced. It is a gift for that special someone to continually grow. With this gift, the person’s love will continue to grow exponentially. A solid base/foundation is important with everything especially in math. I encourage everyone to give this special gift to everyone.

Thanks,

Mathman