Get Math Mammoth Clock for free - CurrClick promotion

UPDATE: The promotion is extended till the 15th of this month so that all can enjoy it (they've had some problems with so much traffic).

I'm sure most of you already know about this... CurrClick is having a mother's day promotion where they have 20 homeschool titles for a free download... and one of them is my Math Mammoth Clock book.

Just click here to download some of them -- or all of them! (You'll have to register if you haven't already.)

My opinion on Saxon math

Someone asked me recently of my "review" of Saxon math.

I'm sorry if this sounds harsh. But the truth is, I really don't want to do a comprehensive review of it. It just goes so much against my way of teaching and thinking about math.

Saxon math presents a concept in a lesson, then has a few exercises about it, and the rest of the lesson is review of previous concepts.

The NEXT lesson usually is not on the same topic as the previous lesson. It jumps around in topics tremendously. One lesson on geometry, next on fractions, next on addition, next on large numbers. It's unbelievably disjointed. And THAT feature I find unacceptable.

How can kids get a coherent view of mathematics studying that way?

I like how professor Hung-Hsi Wu has worded it (emphases and the additional note are mine):

"But I think that what perhaps disturbs me the most about Saxon is to read through it, I myself do not get the feeling that I am reading something that when that the children use it they would even have a remotely correct impression of what mathematics is about. It is extremely good at promoting procedural accuracy {Maria's note: this means teaching procedures such as the correct motions of the long division algorithm, or what to do to find the lowest common denominator, etc.}. And what David says about building everything up in small increments, that's correct, but the great pedagogy is devoted, is used, to serve only one purpose, which is to make sure that the procedures get memorized, get used correctly. And you would get the feeling that-I think of it as a logical analogy-you can see the skeleton presented with quite a bit of clarity, but you never see any methods, your never see any flesh, nothing-no connective tissue, you only see the bare stuff.

A little bit of this is okay, but when you read through a whole volume of it really I am very, very, uneasy. There are lots of things in it that I admire, but something that is so one-sided-you think once more about yourself and you think about what happens if this thing gets adopted. There might be lots and lots of children using it. And suppose that hundreds of thousands of students are using this book and they go through four years of it. Would you be willing to face the end result? That here are hundreds of thousands of students thinking that mathematics is basically a collection of techniques.

That impression by the way is very easy and is almost obtained-you get it by looking at the topics. There is no rhyme or reason about the sequencing of the topics. For example, the things are really broken up. The report gives the examples. One of the grade levels, grade four or grade five, has exactly two sections on probability (that's right two sections). They belong together and without a doubt there is no increase in sophistication or techniques, and yet I think they are separated by 200 pages. When I do this I want to emphasize that I do not single out one or two examples. I am trying to describe through one or two examples the overall the overriding impression that I have. And when that happens, you get the feel that if my students use this, how could they not get the idea that mathematics is just a collection of techniques? If that is the case, what happens to them when they go on to middle school, and then to high school, and after that, God forbid, you might be facing them in your freshman calculus classes. And that is a frightening thought!

References: http://www.arthurhu.com/2003/11/antisax.txt

http://www.pdkintl.org/kappan/k0111jac.htm

Teacher appreciation week

I should have posted this earlier but forgot. I even missed one day!

Learning A-Z is having an open house this week; you can access their family of websites for free, one site per day.

The writing site is for today. Vocabulary site is coming up soon, and so is their science site. Lots to explore and download.

Gas price math

Today I just stumbled upon two sources discussing the price of gas in a comparative sense; one was a line graph comparing it to the past, the other was a world-wide comparison.

Both were interesting; and a resourceful teacher can now make all kinds of problems based on the data. First based on the list of gas prices in various countries, for example these come to mind. (And I'm just giving you ideas for a lesson on gasoline lesson; I'm not providing answers but if some of you want to, feel free to comment.)

• Approximately how many-fold is the price of gas in Bosnia-Herzegovina as it is in the USA? In Egypt? In Venezuela?



• If your mileage is 25 miles per gallon, find the price of driving a 120-mile trip in Germany and in the USA.

Looking at the inflation adjusted gas price in 2008 dollars now. Just reading the graph:

• When was the price of gas at its lowest? At its highest? How much was it?



• Find the price of gas (approximately) in 1930, 1960, and 1990 by reading the graph.



• If you overlook the peaks of the late 1930s and early 1980s, describe the general trend in the price of gas from 1918 till about 1999.
  How many dollars did the price change over that period?

Then into percents:

• If you overlook the peaks of the late 1930s and early 1980s, describe the general trend in the price of gas from 1918 till about 1999.
  How many percent was this change?
• What was the price of gas (approximately) when it was at its cheapest in the 1990s?



• How many percent did the price drop from 1981 to that low point of 1990s?



• How many percent has the price risen from the low point of 1990s till now?

And so on! Feel free to change the questions as you see fit and use them with your students.

A simple triangle problem

Someone sent in this very simple question (a student?).

Leg b of the right triangle is twice as long as the base a.
If the area is 36 cm squared, what is the length in of the leg b?

A little bit of algebra helps in this problem.

FIRST strive to make a picture. Need a right triangle, the leg twice as long as the base. Here in my picture things aren't exactly to the scale, but it suffices for illustration purposes:


So we actually know that b = 2a.

The area of a triangle here is base times height over 2, and remember the height is the other leg, and it's twice the base:

area = ba/2 = (2a)(a)/2 , and this is 36 (given).

So we get our equation:

(2a)(a)/2 = 36

a² = 36

a = 6.

The leg b is therefore 12 cm long. check: Legs are 12 and 6, so the area is 12 * 6 / 2 = 36.

Points on math education

I've been lazy lately when it comes to blogging and I'm sorry for that. I've been sort of taking time off from computer work and painting some windows since it just needs done at our house. I view it sort of as "therapy", since it's so different from the computer work and I just take my time and I don't have to think that hard. I like painting.

Anyways, I foud something really nice at Mathmom's. She's written, I feel, an excellent piece about problems in math education in elementary grades. Her point of view is of classroom instruction, but it's still really relevant even for homeschoolers. Some excerpts:

On calculators:

But to be honest, as much as I hate calculator use in school, in this age of calculators and computers, efficiency at hand computation is not, IMO, the most critical math skill for kids to learn. I am NOT saying that it should be ignored, or that kids should be allowed to skip it, and just use calculators in class (see rant linked above). But it is not, IMO, the be all and end all of math education, nor is it a prerequisite, IMO, for studying anything else.

What I consider even more important is a strong sense of number. I want kids who know immediately when the answer they got (either by hand computation or with a calculator) is way off. I want kids who have an instinctive understanding of the distributive law before it is ever formally taught or named (12 sevens is obviously the same as 10 sevens and 2 more sevens). I want kids who know when the amount of change handed to them makes no sense. I would rather have a kid who can multiply 64 x 25 mentally (by halving 64 twice and doubling 25 twice, to see that it's equal to 16 x 100 = 1600) than a kid who can sit down and carry out the long multiplication with pencil and paper, by rote.

I feel that we need to consider several things when it comes to calculators. It's best when the kids can do mental calculations and do paper-and-pencil methods, including understanding why they work. Calculators should be used judiciously, but used. Like she mentions, number sense is of paramount importance so that kids can estimate their answers and tell if the calculator "got it wrong" (e.g. they punched wrong buttons).

On spiraling curricula:

Steve is right that a spiral curriculum can lead to a lax attitude of "it's ok if they don't master this now, because they'll see it again later" that goes on ad infinitum, and the kid never masters anything. This is clearly no good. But the solution isn't necessarily to take away the spiraling for those who need it, IMO. The solution is to have limits - for example, it's ok if they don't completely "get" long multiplication when it's previewed in 3rd grade, or even when it's introduced more formally in 4th, but they have to get it when it's reviewed in 5th, or they shouldn't move on.

This sounds like a really sane approach.

She also talks about including non-routine problems for ALL students to solve. I definitely recommend this practice and have written about it before! MathMom gives several good reasons for this:

1. First, it provides a fabulous way of helping students to appreciate the uses of the procedures and skills they have learned or are learning.

2. Second, this is the kind of thing that "real mathematicians" do! ... A "mathematician" does not sit down and solve 25 ratio and percent word problems, knowing exactly which skills are required to perform the computations. Instead, she investigates "puzzles", looks for interesting patterns makes new discoveries, generalizes results.

3. Third, it develops self esteem and confidence.

4. Fourth, it builds transferrable problem solving skills.

Read it all at Ramblings of a math mom: Math wars.

High school geometry - a review

It's done! Finally! Took me some time to finish this review, perhaps because it involved three products:

• The book Geometry: A Guided Inquiry. As the name suggests, this book is based on letting students learn about theorems and their proofs in the setting of "guided inquiries" or interesting problems. It is quite unique in its approach.


• A Home Study Companion which includes solutions and about 300 interactive demonstrations


• Geometer's Sketchpad - dynamic geometry software.

This review isn't just what you typically find on the web; someone called it an "exquisite in-depth review". It's fairly long... with sample pages and other pictures, examples, and more.

I encourage you to read it even if you don't need a high school geometry book right now... because you'll get valuable insight just HOW GOOD geometry instruction can be, how the book handles proof, or what to think about an axiomatic vs. discovery based geometry text.

Review of Geometry: A Guided Inquiry with Geometer's Sketchpad and Home Study Companion.

Free math videos...

...for this week only!

MathTV.com is letting us test-drive (public beta) their new website for FREE for one week only:

http://www2.mathtv.com/

Hundreds of videos on pre-algebra, algebra, trig, and calculus topics. Even in Spanish.

Brain rules

This was an interesting website, and can give you some insight into how our brains work -- which is always a good thing to know, to enhance learning!

It is based on a book, which explores the 12 brain rules in detail. These rules or principles have to do for example with exercise, sleep, stress, how our memories work, and so on.

On the website you can read and watch little videos about each. Warning: the video about "attention" is illustrated by an immoral "attention getter". But you will glean some good ideas and learn pretty interesting stuff in the others; I enjoyed most of it:

Brainrules.net/the-rules

It's been quiet...

at my blog lately and I'm sorry for that. But, I have something in the works.

I'm working on a review of a "three-combo" geometry curriculum for high school geometry:

• The textbook Geometry: A Guided Inquiry


• Geometer's Sketchpad - a dynamic geometry software


• A Home Study Companion to accompany the book, which includes solutions and dynamic illustrations with Sketchpad

I enjoy doing geometry. This book has problems that "evolve" from one to the next, leading to important conclusions. Then it has really interesting projects, and many of them can naturally be constructed with Geometer's Sketchpad, which is lots of fun - for me anyway.

The problem is, I cannot afford to take the time to study and solve all these projects and interesting problems, but just to pick and choose one here, another there.

Anyhow, I hope to complete this review within a week.

Backwards math

This is just a really cute story of a 3rd grader who on her own figured out a way to do "backwards math"...

Backwards math

Kindergarten math

People occasionally ask me about kindergarten math, and if I'm going to write kindergarten level books for the Math Mammoth series. The answer is no, I don't feel there's any need for me to write books, because there already exist plenty of good materials for these very basic and easy concepts.

BUT I did write a comprehensive article about what you can do in kindergarten math, including many games you can play, and what basic concepts should be covered in order to prepare for 1st grade.

Problem solving & math as an art

Continuing on a litlte bit more with my thoughts concerning Lochart's Lament.

Lockhart starts out his lament with a comparison: WHAT IF music teaching only consisted of learning to write music, write notes on paper, and only after high school level would students be allowed to actually hear and make music? WHAT IT art instruction would consist of "paint by numbers" until high school, which is when they'd actually start applying paint...

Lockhart remarks that if he wanted to destroy a child's natural curiosity and love of pattern-making, "...I simply wouldn't have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education."

He calls school mathematics "pseudo-mathematics", where emphasis is on the accurate yet mindless manipulation of symbols.

These are, of course, very strong words. I don't fully agree... I don't feel all that's done at school would be pseudo-mathematics or mindless manipulation of symbols. Really, you CAN teach addition so that it makes sense, and we need to learn the symbols for it (5 + 6 = 11).

Lockhart uses the triangle example that I blogged about before to illustrate how mathematics is an ART:

"To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion -- not because it makes no sense to you, but because you gave it sense and you still don't understand what your creation is up to; to have a breakthrough idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive."

I can see where he's coming from... yet I wouldn't put down so harshly all that is done within school mathematics. There IS a place for drills, for computation practice, for studying algorithms, measuring units, and so on.

Lockhart says, "The main problem with school mathematics is that there are no problems." Here I agree. We should add GOOD PROBLEMS - or true problem solving to our lessons. I don't mean "exercises"...

"But a problem, a genuine honest-to-goodness natural human question -- that's another thing.
How long is the diagonal of a cube? Do prime numbers keep going on forever? Is infinity a number? How many ways can I symmetrically tile a surface? The history of mathematics is the history of mankind's engagement with questions like these, not the mindless regurgitation of formulas and algorithms (together with contrived exercises designed to make use of them).

A good problem is something you don't know how to solve. That's what makes it a good puzzle, and a good opportunity. A good problem does not just sit there in isolation, but serves as a springboard to other interesting questions. A triangle takes up half its box. What about a pyramid inside its three-dimensional box? Can we handle this problem in a similar way?"

In other words, good problems do not simply practice a technique or idea that the student just saw used in an example. Notice: a good problem is such that you don't initially know how to solve it.

Now, this does not mean kids shouldn't solve "routine" problems or exercises, because ONLY by having KNOWLEDGE of techniques and concepts can new, non-routine problems be tackled.

But I'd recommend you take some time, perhaps a day every two weeks, where your math lesson consists of problem solving so that your students CAN experience this kind of problem solving process that leads them to conjecture, to investigate, to THINK hard, fail first but persevere, to justify their thoughts -- to come up with proofs.

It is of course even better if a teacher can lead the teaching with such good questions or problems even more often, such as starting the lesson with an interesting problem that leads to a new concept. But I realize not all of us can do that, and that it may take more time than direct instruction. If you can give them at least a glimpse of it sometimes, feel proud, because then you've done better than many.

... For good problems, check some resources here.

Carnival of Homeschooling - the April fool's day edition

Carnival of Homeschooling is up at Why Homeschool. This one is the April fool's day edition, and Henry has sprinkled the carnival with juicy stories of past April fool's day jokes from BBC or others.

Check also Denise's entry for subtracting mixed numbers.

Kindergarten question

How to teach subtraction in the kindergarten with the tens place values and in horizontal sequence, for eg, 20-5=? They know to count their fingers, from the smaller number to the bigger number, but when the fingers are not enough to count, then what?

I'm not sure kindergartners are necessary ready for this. I would ONLY do these types of problems with concrete help.

Get a 100-bead abacus. Instruct them to first "make" 20 or show 20 on the abacus, and then move 5 away. Then "see" how many are left.

This online abacus is also really good for illustrating such.

Once they've done 20 - 5 and many other problems, you can ask if they notice a similarity in these problems:

10 - 5

20 - 5

50 - 5

70 - 5

etc.

But if some don't, wait till 1st grade. Practicing problems that "cross the ten" without manipulatives, such as 23 - 5 or 71 - 9, can wait even till 2nd. I realize kids might be able to do them by counting down, but to learn effective strategies for solving these kind of problems, children need a good foundation of place value (tens and ones), and that doesn't come immediately.

I'd use addition problems first, and a little easier ones, such as

20 + 7

44 + 2

62 + 7

and so on. These can help cement the place value concept as well, if you approach them right, such as, "62 has 6 tens and 2 ones, and then you add 7 more ones. Can you do that on the abacus, or with your ten-bundles and sticks, etc.?

With subtraction, try problems that "stay" within the same ten, such as 65 − 3. The idea is to use concrete aids and help them see they don't need to "touch" the whole tens when subtracting, so it's really similar to doing 5 − 3.

But still, I feel even this is not essential for kindergarten but can wait till first grade.

Giveaway!

Today I have something a little different from the "norm": a giveaway!

All you have to do to take part is go visit Homeschool Boutique, find a T-shirt you'd like to win (these shirts mostly carry homeschool slogans), and then either leave a comment below mentioning the shirt you'd like to win, or email me with your choice.

Just one note: whichever way you do it, make sure I can contact you/find your contact info easily.

We will choose 2 winners by drawing. This contest ends Sunday, April 5, 2008.

Placement tests for Math Mammoth LightBlue Series

I've just added to the site placement tests for the Math Mammoth complete curriculum (LightBlue Series), for grades 1-4. These are actually end-of-year tests. They could also be used as diagnostic tests, to see what content areas a child might be lacking in .

A problem to solve about multiples

Here's one more problem from the collection that John Morse sent me.

144, being a multiple of itself, naturally ends with ...144.

What is the next greater multiple of 144 ending in ...144?

I chose this problem because solving it doesn't require knowing any concepts beyond multiplication and multiples.

I solved this problem kind of a "crude" way; however upon thinking my solution through, it is fairly accessible to even younger students, because it doesn't use more sophisticated concepts.

Basically I considered the problem as finding ABC (A, B, and C are digits), or possibly a longer or shorter number such as 144 x ABC ends in 144.

  144
x ABC
-----

I systematically checked what C can be in order for the answer to end in 4.

I found only one possible digit works.

Then I systematically checked what B can be, knowing that C must equal 6 -- and found two possible digits: 2 and 7.

After that, I stumbled upon the right answer since I simply checked what is 26 x 144, 76 x 144 and 126 x 144. The last one is the multiple we're looking for - it is 18,144.

Like I said, this method IS accessible to students who have mastered multiplication algorithm.

---

Another solution, essentially by John Morse:

This one uses the concept of a "digital root", which means essentially the remainder when dividing a number by 9. You can find it out by adding the digits of a number until you get a sum less than 10.

For example, the digital root of 28,294 is found this way: 2 + 8 + 2 + 9 + 4 = 25; 2 + 5 = 7.
When finding the digital root (or divisibility by 9), you can always "cast out nines" or any combination of numbers adding up to nine - in other words, omit them from the total sum. In the above example, it's enough to add 2 + 8 + 2 + 4 = 16; 1 + 6 = 7 to obtain the digital root.

We're looking for a multiple of 144 that ends in ...144. Since 144 is a multiple of 16, ITS multiples will also be multiples of 16. Similarly, 144 is a multiple of 9, thus ITS multiples will also be multiples of 9 (divisible by 9).

Then, we do know our number will be greater than 1,000. The number we look for is (some thousands) + 144 since it must end in 144. Since 144 is a multiple of 16, those whole thousands tacked to our multiple must be also be multiples of 16. 1000 is NOT a multiple of 16, whereas 2000 (and its multiples, all having even-number thousand's place digits) ARE multiples of 16.


Hence, it remains to find the digits in front of ...144 such that they, placed together, form a multiple of 9 AND 2. The least such digit pair is 1 & 8, putting even digit 8 in the thousands's place, and thus forming 18144.

Lockhart's Lament

Recently there's been a lot of talk about an essay written by mathematician/teacher John Lockhart, called Lockhart's Lament. Some people praise it, some are more skeptical.

Lockhart's Lament makes for good reading and he raises some really interesting points, so I can heartily recommend reading it.

Personally I don't fully agree with every statement he makes there. But his MAIN point concerns mathematics as an art, and how we should teach it.

I went ahead and copied a part of the essay below. This is direct quote from the essay, presenting a VERY GOOD example with the triangle problem.

---

So let me try to explain what mathematics is, and what mathematicians do. I can hardly do better than to begin with G.H. Hardy's excellent description:

A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

So mathematicians sit around making patterns of ideas. What sort of patterns? What sort of ideas? Ideas about the rhinoceros? No, those we leave to the biologists. Ideas about language and culture? No, not usually. These things are all far too complicated for most mathematicians' taste. If there is anything like a unifying aesthetic principle in mathematics, it is this: simple is beautiful. Mathematicians enjoy thinking about the simplest possible things, and the simplest possible things are imaginary.

For example, if I'm in the mood to think about shapes-- and I often am-- I might imagine a triangle inside a rectangular box:



I wonder how much of the box the triangle takes up? Two-thirds maybe? The important thing to understand is that I'm not talking about this drawing of a triangle in a box. Nor am I talking about some metal triangle forming part of a girder system for a bridge. There's no ulterior practical purpose here. I'm just playing. That's what math is-- wondering, playing, amusing yourself with your imagination.

....

The mathematical question is about an imaginary triangle inside an imaginary box. The edges are perfect because I want them to be-- that is the sort of object I prefer to think about. This is a major theme in mathematics: things are what you want them to be. You have endless choices; there is no reality to get in your way.

On the other hand, once you have made your choices (for example I might choose to make my triangle symmetrical, or not) then your new creations do what they do, whether you like it or not. This is the amazing thing about making imaginary patterns: they talk back! The triangle takes up a certain amount of its box, and I don't have any control over what that amount is. There is a number out there, maybe it's two-thirds, maybe it isn't, but I don't get to say what it is. I have to find out what it is.

So we get to play and imagine whatever we want and make patterns and ask questions about them. But how do we answer these questions? It's not at all like science. There's no experiment I can do with test tubes and equipment and whatnot that will tell me the truth about a figment of my imagination. The only way to get at the truth about our imaginations is to use our imaginations, and that is hard work.

In the case of the triangle in its box, I do see something simple and pretty:




If I chop the rectangle into two pieces like this, I can see that each piece is cut diagonally in half by the sides of the triangle. So there is just as much space inside the triangle as outside. That means that the triangle must take up exactly half the box!

This is what a piece of mathematics looks and feels like. That little narrative is an example of the mathematician's art: asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations. There is really nothing else quite like this realm of pure idea; it's fascinating, it's fun, and it's free!

Now where did this idea of mine come from? How did I know to draw that line? How does a painter know where to put his brush? Inspiration, experience, trial and error, dumb luck. That's the art of it, creating these beautiful little poems of thought, these sonnets of pure reason. There is something so wonderfully transformational about this art form. The relationship between the triangle and the rectangle was a mystery, and then that one little line made it obvious. I couldn't see, and then all of a sudden I could. Somehow, I was able to create a profound simple beauty out of nothing, and change myself in the process. Isn't that what art is all about?

This is why it is so heartbreaking to see what is being done to mathematics in school. This rich and fascinating adventure of the imagination has been reduced to a sterile set of "facts" to be memorized and procedures to be followed. In place of a simple and natural question about shapes, and a creative and rewarding process of invention and discovery, students are treated to this:



"The area of a triangle is equal to one-half its base times its height." Students are asked to memorize this formula and then "apply" it over and over in the "exercises." Gone is the thrill, the joy, even the pain and frustration of the creative act. There is not even a problem anymore. The question has been asked and answered at the same time-- there is nothing left for the student to do.

Assortment of links and news

I have quite a collection of links and stuff people have sent me. Hopefully everyone will find something of interest!

---

Esp. for teachers

• LearnHub is a network of communities, each one built around a specific subject.
  
  You can do all kinds of stuff: upload videos, author pages using a simple editor, upload your powerpoint presentations, create tests and track users' progress, combine lessons, tests, and activities into a restricted access course, complete with e-commerce integration. Learnhub also includes live tutoring, live video, voice, whiteboard and document sharing.
  
  If you want to teach something online, this website sounds really interesting.



• WorksheetLibrary.com contains
  thousands of worksheets for all school subjects and levels. This is a subscription service, but you'll find some free worksheets in every area.

For all math enthusiasts

Some math software!

• First of all, some real "heavy" machinery for serious computing:
  
  SpaceTime 3.0 is now available for Windows, Pocket PC, Smartphones, and Palm handhelds. It is the most powerful mathematics software available for mobile devices at very affordable prices and has many of the features of top commercial programs such as Mathematica and MATLAB including a built in scripting engine.


• From the same place, MyCalculator is a free scientific calculator for Windows, Pocket PC, Palm handhelds.

For all of us who like to voice our opinion (or vote)

There is one week left in the contest for images to represent the Carnival of Homeschooling. So go vote - only seven days left!

Vote for whatever size image
Vote for medium size image

Math Mammoth Introduction to Fractions

A new book for the Blue Series, Introduction to Fractions has simple fraction lessons with lots of picture-based visual exercises, and small denominators.

Learn more at the above link.

7 things you'd never guess about me

I got tagged by Sol for a meme "7 things about me you'd not likely guess".

Here goes:

1. When I was in elementary school, I wanted to become a nurse (probably because my mom was one).

2. When in middle school, I wanted to become an elementary school teacher. I was pretty sure I'd do that. Math was NOWHERE in my mind. I didn't mind math but I didn't think of it as anything especially interesting either. In fact, I wouldn't have chosen math had it not been for some coincidences...

3. One happened in 9th grade. One of the math teachers (who didn't teach me) saw my score in the national 9th grade math competition, and persuaded me to choose the longer math course for high school... Originally I was going to go with the short math, no physics, and two languages. So I changed the shorter math course to the long one.

4. Another strange coincidence: when high school started (10th grade), the first day of school I was told they had accidentally put me in the wrong class... that because I had the longer math course without physics, that I'd belong to the group "B" and would have to change OR take physics. My friends were in the group "A" so I didn't want to go to group "B". So I chose physics and dropped one foreign language. So this is how I "ended up", as if by accidents, with the right background (physics and math) in the high school to be able to study math in the uni.

5. My math teacher in 10th grade (1st year of high school) was really nice and good and kept talking how there is going to be a lack of math teachers in years to come. During that year I figured I would study math after high school.

6. I almost became a piano teacher as well, because I was studying it half-time alongside math. But one sunny morning it was as if something went to my ears and I couldn't stand any loud noises at all, surely not my own banging of a grand piano in a small room. The doctors never found anything and suspected some kind of an infection went to my ears from a cold I had had two months previous. To this day, it is a mystery what exactly happened but it "killed" my piano teacher career.

7. All through my growing up and schooling, I always thought I'd work for the school system. My dad worked for the postal system, my mom was a nurse, all my friends parents worked for someone else... Thus, it NEVER crossed my mind I would become an entrepreneur, independent of the "systems". But here I am, doing just that.

If you have a blog and like this meme, consider yourself tagged!

Movies of math in the real world - FuturesChannel.com

I delved into this fascinating website just this past week, and I heartily recommend you visit it, too!

Most math teachers have faced the age-old question, "When will I ever need this?", especially when kids get into algebra and more. Well, FuturesChannel.com has the answer - in the form of short movies, lesson guides, and worksheets.

The topics are just fascinating, from skyscrapers, roller coasters, endangered animals, to inventing, the subway, bakery, bicycle design, etc.

For each movie, there is a worksheet or several for the student that concentrates on some math topic that is needed in the field shown in the movie.

Some samplings:

100,000 computers a day
A rare and fascinating look inside the world's largest computer manufacturer, Dell Inc., where thousands of computers are custom-built and shipped around the world every day. From the call center to the inventory system to the assembly line and beyond, one thing is certain: The whole operation relies on a variety of math skills every step of the way.

Inventing with Polygons
This guy had some really interesting stuff! Inventor Chuck Hoberman uses polygons to build amazing expandable structures.

Structural Engineering
To design buildings that don't fall down, you need to know how your materials will respond to forces such as gravity, wind, and earthquakes.

The Bakery
Whether it's fractions or measurement or division, a key ingredient to this baker's success is math, making each one of his pastries, cakes and breads as delicious as the last.