Counting to Four

This is for anyone out there is a fan of Feist and this little ditty she lent to Apple to market their iPods:



Then, you will love to share this with your pre-schooler. Heck, I've watched it three times without my kids around!



I love when talented people put it out there for kids, and have a little fun themselves. That video was shot in one take! Doesn't it just make you want to go out and buy an album on iTunes?

Movie Review: Wall-E

Now, it is summer vacation, so I think it's all right to talk about the movies. And, this one is science fiction of sorts, and I hear the folks at Pixar like math an awful lot.

I loved it - totally mommy approved - my daughter smiled and asked questions throughout the whole movie. It looks so good that you can't even tell it's animated, but it also has great depth in the characters, meaningful messages, an optimistic ending, and plenty of fun to make it all palatable. When is the last time you laughed at a cockroach?

Wall-E is a loveable little guy, who finds joy in simple things, and keeps objects discarded long ago as his private treasures. Eve is sharp and sassy, and eventually comes around to see how wonderful Wall-E is. And he loves that she sees things differently than him, finding new ways to use his "treasures." Even without talking, their beeps and blips give us enough of a sense of human oooh-ing and aaah-ing, that we know exactly what they're saying. For characters without facial features, thye sure do have a lot of expressions.

The messages of the film are many, and blatant. True to the literary concept of sceince fiction, Wall-E uses the setting of the film to effectively communicate a warning. The earth has become so polluted, humans have fled to space, victims of the ubermarketing bombardment by BuyNLarge to consume and use everything - you decide which company(ies) may be having a finger pointed at them. What's nice about the future is that no one has to do anything - there is a robot for every task. The bad thing about the future is that no one has to do anything - humans have become blubbery, complacent beings with practically vestigial arms and legs. They're not bad, or evil, they've just been on vacation for 700 years, lounging around.The main "Directive" of the movie (to borrow a phrase from Eve), is to save a plant - a survivor among survivors and a harbinger of planetary healing. My daughter loves to rescue plants herself, and actually chose an Eve figurine as a souvenir over a Wall-E toy. The messages may be a little dire and a little in your face, but the story manages to stay very positive and optimistic, in large part because of its heroes, who manage to make an adventure out of the whole thing.

Now, as much as we loved the movie - it wasn't perfect. I personally liked it more than A Bug's Life, The Incredibles, and Ratatouille, but I liked Toy Story, Cars, Finding Nemo, and Monsters Inc. more. My reasons for liking those last three may be tied more to the way my daughter has loved them. We saw Nemo the first time we went out without her, and I may have been a little emotional when the baby fish got all but wiped out at the very start of the movie, Monsters Inc may have been responsible for my daughter's quick potty training, and Cars gets a big boost from it's great use of music, something Pixar films don't usually do.

I felt like there was so much attention to the realistic animation on Earth and in Space, that I was a little surprised, and not so amused, but the cartoonish appearance of the "humans." My daughter thought they were all babies. There were also a lot of opportunities to use some music to keep the story and the emotions of the movie "glued together" that I felt were missed. The movie was a little more political than a kid's film can usually get away with, which means that some people will surely not like it (if it doesn't line up with their politics), but since it gelled well with mine, I felt like it could still work. However, I forsee a little less popularity in general because of it.

SAT Tips and Tricks - Making up Numbers

I always say that math on the SAT is not hard, it's tricky. After all, the SAT is a reasoning test, not a math test. There's a subject test to cover the higher level math, and to test your straight up math skills. This test is supposed to test how smart you are - so it's only a plus if you can out-test the testers.

This post could otherwise be titled "How to avoid algebra." Really - and The College Board tells you about this strategy here, in their Official Guide to the SAT, which happens to be one of the books we use in our SAT prep courses at The Tutor Studio.

This strategy works for any questions where there are variables in the answer choices. Here's how it works:

Make up nice, simple numbers for any variables found in the answer choices. Avoid numbers like 0, 1, and 2, since they can give you funky answers. Use 100 if "percent" is even mentioned in the question. It may not make the problem easier, but it might, and it won't make the problem harder.

Use your numbers to work the problem - go through the story with your values.

Get an answer

Now, plug the numbers you made up into the answer choices until one of them gives you that same answer.

Here's an example:
There are 25 more men than women in the senior class. If n represents the number of men in the class, what fraction of the class is women?

A) (n+25)/n
B) (n-25)/n
C) n/(n+25)
D) n/(2n-25)
E) (n-25)/(2n-25)

First, try to do the algebra. Ugly, isn't it?
Now, let's make up some numbers. I'm going to use 100 for "n", which represents the number of men.

If there are 100 men, and there are 25 more men than women, then there are 75 women.

If there are 100 men and 75 women, then there are 175 students total.

So, the fraction women is 75/175

Now, let's try the answer choices - remember, I chose 100 as "n".

A) (100+25)/100 = 125/100 Nope
B) (100-25)/100 = 75/100 Nope
C) 100/(100+25) = 100/125 Nope
D) 100/(2x100-25) = 100/175 Nope
E) (100-25)/(2x100-25) = 75/175 Yep!

So, the answer is E (and it really is!)

Pi and i Throwdown

You see, i is the "imaginary number." That's right - your algebra II students will be learning about imaginary numbers.

It's not a strange as it sounds. The problem is that if you have a negative number under a radical (like the square root of -4), it just doesn't work. Because, there is no number times itself that equals a negative number (Even -2 x -2 = +4).

So, to get around this problem, mathematicians use i. The imaginary number is the square root of (-1), so i squared = -1. It allows you to proceed with a problem that would otherwise be dead. Now the square root of -4 is 2i (2 is the square root of 4, and i is the square root of -1). Hopefully, the imaginary number goes away later in the problem by cancelling out, or by squaring so that you end up with a real answer after all.

And, if you want to remember what's up with pi, click HERE

Calculators - Texas Instruments

Let me start this post by saying that kids should NOT learn to rely on a calculator to do their math for them. That said, a good calculator is a powerful tool for doing more complicated math and for performing tedious operations (after they have been mastered manually). Things that used to take mathemeticians all day to complete are being done routinely in high school classrooms around the world in a matter of seconds thanks to these little gizmos.

I am totally a fan of Texas Instrument Calculators. Almost all classroom teachers use them for demonstration, and they are by far the most popular among students. It is so hard to have different equipment than everyone elso around you, and Texas Instruments calculators are awesome anyway. The functions and placement of the buttons are as intuitive as they can be.

Another great thing about the TI series is that if you start out with a more basic calculator and upgrade as your math courses need you to, the functions don't change, there are just more of them. So, if you learn one of their scientific calculators, you'll be surprised at how much you already know how to do when you invest in a graphing calculator.

So long as students are using their calculators appropriately (read: they can do the math on their own, but use the calculator to check their work and speed up the process), here are the levels I recommend:

Elementary School (4th - 6th Grades)

TI-15 Explorer™ ($10 - $15)
What does an elementary school student need a calculator for? Nothing. However, it is imprtant to get familiar with the equipment, the same way you let your kids play computer games when they are younger, and then they know how to hack into your financial records by the time they're 10. The two line display is reason enough to give this calculator a try. Just make sure that they use it to verify and check, or to explore some higher level math concepts, and not as a shortcut to having good, solid, basic math skills. We all have to deal with fractions sometime!

Middle School (6th grade - pre-algebra)

TI-34 II Explorer Plus™ (Price $18-$23)
This is the middle school version of Ti's scientific calculator. It's an excellent training calculator. it pretty much does everything that the TI-36 does, but with the functions a middle schooler would need most often found on the the front (as opposed to under a menu). For example, there are lots of fraction functions that you would have to search for on the regular scientific calculator, but you have to search for trig functions (like sin, cos, tan), which would be found front and center on the TI-36.

High School, Scientific (Algebra, Geometry, and Algebra II, Chemistry and Physics)
High School students will not even find a graphing calculator useful until Algebra II, and will not find it neccesary until pre-calculus. These calculators are just enough power:


TI-30Xa (Price: $15-$20)
A super-basic scientific calculator. It can do all of the functions that a student through geometry and/or chemistry might need, but it doesn't have the 2-line display, so you can't see what you enter. That can be really confusing if you are entering more than a couple of operations. It's worth the few extra dollars for the TI-36X II.


TI-36X II (Price $20-$25)
Totally worth the extra $$$ compared to the TI-30. This is the most popular scientific calculator out ther, and there's a reason for it. It does everything a student taking math through alsgebra II and chemistry could ever need (except graphing), and it is very easy to use. The functionality is the same as the TI-83 and TI-84 graphing calculators, so when you finally decide to invest in the big calculator, you'll already know what to do. The two line display is great - you can see what you entered, and even edit it afterwards. This is absolutely my personal pick for a scientific calculator.


TI-36X (Price $20-$25)
This calculator is sleek and pretty, and has a few extra goodies, however it does not have the 2-line display. This alone makes the TI-36X II a better pick for about the same price.


High School, Graphing
High School students will not even find a graphing calculator useful until Algebra II, and will not find it neccesary until pre-calculus. These calculators are a must for any pre-calc, trig, or calculus students, and are worth the investment. Just make sure you give them a lecture about not losing these beauties, they're not cheap:



TI-83 (Price $99 - $129)
This graphing calculator is the standard. Everything you need, and if you get the "Plus" edition, you can hve a little more memory and even link to other other calculators to share extra programs. The thing is, that for about $10 more, you can get the upgraded version of the TI-83 - the TI-84, so you should.


TI-84 (Price $109 - $139)
This calculator is Just Right. This would definitely be my pick for a graphing calculator for a high school student. It has all the power you could need, and is still easy and intuitive to use, and it is permitted on all of the usual standardized test out there that allow a calculator. It is just like the TI-83, except you get a lot more memory and linking capability, including a USB cable for downloading even more "educational" software. Oh, and it comes in fun, funky colors and you can even get removable faceplates for it, just like your cell phone!


TI-89 (Price $119 - 149)
This calculator is so much power, it's confusing to use, and it's way different thatn the other TI calculators, so your teacher won't know how to use it either. There are no additional functions that a high school student could ever use compared to the TI-84. Don't buy this calculator just because it's the "top of the line." It is, if you're studying math or a physical science in college. For high school, stick to the TI-84.

All of these calculators are available at Office Depot, Staples, and Target. be sure to shop those back to school sales!

A Brief History of pi

This strange little number that your son or daughter may use for geometry problems is equal to about 3.14 or 22/7, but what does it mean, and why do we use it?

It turns out that all circles, no matter how big (a planet) or how small (an atom) have the same ratio of their circumferences to their diameters - pi. That means that if you measure how big around a circle is and how wide across it is, distance around divided by the width will always equal pi.

So far (at the time of posting), pi is a number that goes on, and on, and on, with no end to the decimal places in sight. It is a truly irrational number.

As long ago as 1900 BC, the ancient Babylonians estimated pi as 3.125, and the ancient Egyptians used a formula that 3.1605 - the pi ratio is even mentioned in the Bible!

"And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about." (I Kings 7, 23; II Chronicles 4, 2.)

But, it was good old Archimedes who, around 250 BC did a brilliant little math experiment. He started with a hexagon drawn around a circle and calculated the perimeter, then compared that to the area of a hexagon drawn inside the circle. Then, he used 7 sides, 8 sides, and kept going up to 96 sides. He figured out a pattern and came up with the ratio of the perimeter to the diameter equal to 223/71 < pi < 22/7.

In China, Around 480, a Chinese mathematician named Zu Chongzhi estimated pi as 355/113, and showed that it was between 3.1415926 and 3.1415927 using another Chinese mathemetician, Liu Hui's experiment (similar to Archimedes, but continuing to a polygon with 12288 sides). This value of pi would stand as the most accurate value for pi over the next 900 years.

One of the really cool things about pi is that it has been calculated by every kind of mathemetician, using arithmetic, geometry, trigonometry, and later even calculus, and all of these different types of mathematics arrived at the same answer.

You can find pi at home with a simple activity of measuring the width and distance around of circular objects, like different sized cans. To measure the circumference, use a piece of yarn to circle the outside of the can, trim it, and then measure the length of the string on a ruler. Divide the circumference by the width and see if you get something close to this:

3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510

But of course, you can always just go out for THIS when the math homework is finally done!

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