Math Is... Beautiful...

I have taught the Theodorus Wheel Project for three years now, and I have never seen the quality of work that I saw this year! The work of these children was so outstanding, I just had to share it! For those who don't know, the Wheel is another way of teaching the concept that irrational numbers can be found on a number line. What we did was start by making an equilateral right triangle (both legs were an inch long). We then found the length of the hyponenuse of this triangle using the Pythagorean Theorem. then we made another right triangle using the hypotenuse from the first right triangle and another 1-inch leg. We found the next hypotenuse and repeated the procedure. After every triangle we drew, we used a compass to draw an arc back to our initial number line. Where the arc touched the number line showed where that irrational number falls on a number line. The interesting thing is that as we continued this procedure, a visual and numerical pattern emerged, like a spiral staircase. The task I gave the students was to keep drawing triangles until they got all the way back around to the number line, and then to create a new picture from the design they saw. Like I said, they did a fantastic job applying this concept. But, the pictures are above. You can see it for yourself!

This week, we will start working on the first of our algebra concepts, solving equations in one variable. We are getting closer and closer to the CRCT with each passing day. You should know that ALGEBRA makes up about 50% of the items covered on the test, so let's work hard going forward, guys! See ya in the Red Hallway, Knights! 801, SECOND TO NONE!!!

The Big Wheel Keeps On Turnin'...

Hi guys! I know you are enjoying your time off (I certainly am!) but I thought I would go ahead and recap the past week and let you all know what we will be doing when we return from the break.

As I said in the last post, I was somewhat disappointed in the test scores for my Pythagorean Theorem Test when I administered it on November 13th. So we reviewed that test this past Monday and I gave a retest on Tuesday. We did better (an average of 4 more questions right than we did the first time, for an average increase in score of about 14 points), but we could have done even better than that. On the plus side, I had a lot more "A's" than I have had in recent memory, and we welcomed FOUR new members of the 100 club (J. Ware, D. Franklin, A. Rudd, and B. Spikes)! Congratulations!

After the test, we spent the rest of the week working on the Theordorus Wheel Project. This is a combination of art and mathematics, where the students make a series of right triangles that rotate around a single point. This project also illustrates where irrational numbers fall on a number line. The first triangle you drew was an equilateral right triangle (both legs are 1 inch long), but after that, one of the legs gets longer and longer. The effect looks like a spiral staircase if you are looking straight down on it. Several of you are in different stages of completing the wheel, but remember, you must have a minimum of SEVEN triangles with SEVEN math problems on the back of your sheet and SEVEN properly drawn arcs in order to get a minimum passing grade. To get a "B", the "wheel" must make one complete revolution, and you need a matching number of math problems on the back of your paper as the number of triangles it takes to get your wheel all the way around. If you want an "A", the wheel must be colored in, and if you want an "A+", you will make your wheel a part of a larger picture that you draw in. Remember that this project is worth TWO test grades, so this is your opportunity to make or break your grade in my class.

When the week ended, we weren't quite finished with the wheels, so Monday of next week will be dedicated to getting the work finished. Tuesday is the deadline to get this work completed. The best wheels will be laminated and posted outside my classroom for all the other students to see! After that we will begin our preliminary efforts in algebra, looking at solving equations in one variable. Remember that when we get back, there are only three more weeks remaining until the Christmas Break. That's three more weeks to get your grades up as high as you want them to be. Let's get after it, Knights! Let me add that this week, you may go to http://www.myskillstutor.com/ and start working on the concepts we have taught thus far that you may have been having trouble on. Your user name is your GTID number, and you know your password. Remember the site name is ecma01. Let me know if you have any questions. I hope you and your families have a blessed, safe and truly wonderful Thanksgiving! Have a LOT of fun and be ready to get back to work on next Monday. Until then, see ya in the Red Hallway, Knights! 801, SECOND TO NONE!!!

HAPPY THANKSGIVING!!!

Getting RIGHT with TRIANGLES

Last week, we got more into our study of right triangles. We learned that the Pythagorean Theorem is used to find the missing length of a side of a right triangle. If you have to find the length of one of the legs, you have to turn the Pythagorean Theorem into a subtraction problem, but if you are finding the length of the hypotenuse, you use the Theorem in its original form. Remember to take the square root of the sum or difference! If the radical is not a perfect square, you must attempt to simplify it! We have been using our "bullets" (2, 3, 5, 6, 7, and 10) for some time now, but we have also introduced our "small squares" (4, 9, 16, and 25) in our attempts to simplify the radicals we have been coming up with. You use the small squares after you have gone through all the bullets. Remember also, that when you are simplifying radicals, your goal is to pull the greatest perfect square out of the radical you are simplifying, take the square root of that perfect square, and express your answer as a multiplication problem of the square root and the bullet you used (now expressed as a radical). For example, the "square root of 75" is not a perfect square, so it must be simplified. 75 is the product of 25 x 3, so you would change the radical to "the square root of 25 x 3". Then you give each factor its own radical, and the problem becomes "the square root of 25 times the square root of 3". Then you take the square root of 25 (when you use it, you lose it!), and your answer (the simplified form) is "5 times the square root of 3".

In addition to all that, we reviewed the concept that the interior angles of any triangle always add up to 180 degrees. This is important because if the measure of any of the angles is missing, you can find what it is by simply adding the other two angles and then subtracting the sum from 180. In the case of right triangles, it's even simpler! Since a right triangle has one 90 degree angle, the other two angles have to add up to 90. So to find the missing angle in a RIGHT triangle, you just take the measure of the acute angle that you see and subtract it from 90, and that will give you your missing measure! (See how much stuff we did last week?)

The week culminated with a test, and I must say that we as a team did not do as well as I would have liked, so we will be working more on these concepts on Monday, and for those who wish to do so, I will have a retest on Tuesday. THEN we will begin one of my FAVORITE projects in the 8th Grade curriculum, the THEODORUS WHEEL! Wait until you see it (and create one of your own!)! It is SO cool, and it will help you understand the concept of irrational numbers even better than you do now. So, until next week, see you in the Red Hallway, Knights! 801, SECOND TO NONE!!!

Triangulating Pythagorus

Hey guys, another week has come and gone! Doesn't it seem like the year is just flying by?

This past week, we moved from working exclusively on radicals to the Pythagorean Theorem, where we will be for the next few days. This theorem was named after the mathematician who first formulated it, Pythagorus. He correctly surmised that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. In other words, as we say the formula in class, "a squared plus b squared equals c squared". You can use the Pythagorean Theorem to find the missing length of any side of a right triangle. I want to reiterate that the Pythagorean Theorem only applies to right triangles. It doesn't work with the other kinds of triangles.

While we were working on the Pythagorean Theorem, we did take a day to review the other types of triangles (obtuse, acute and equilateral) in teaching the fact that the sum of the interior angles in any triangle is 180 degrees. This is useful information because if you don't know the measure of one of the angles, you can easily find it by adding up the measures of the other two angles and subtracting from 180. In the case of a right triangle, you have to remember that the other two angles add up to 90 degrees, since a right triangle already has one 90-degree angle. So if it's a right triangle, all you have to do is subtact the missing angle from 90.

Besides this new information, we continue to review all that we have learned about probability, outcomes, exponents, and radicals. I'm repeating again, for the benefit of you who read this blog regularly, that there WILL be a test coming up this week (Friday the 13th!) on everything that we have covered up to this point, so start studying now so you will be ready for it. This coming week, in fact, will be about reviewing for this test. Remember that tests count for 40% of the overall grade, and the better you do on your homework, classwork, and quizzes, the better you will do on the tests!

As a final note, this Wednesday is Veteran's Day, and there will be no school on that day. While I know you are glad about that, you should know that this holiday holds a particularly special meaning for most of your teachers on Team 801. Mr. Shelton and I are veterans of the US Army. Mrs. Jones, your reading teacher, served in the US Navy, along with her husband, who teaches Naval JROTC for Central High School in Phenix City. Mrs. Tolbert is a veteran of the US Air Force. Mrs. Myers' husband is currently serving in the US Army as a Lieutenant Colonel (he's a high-ranking officer). Since I went to West Point, ALL of the young men and women with whom I went to school have served in the Army, and several hundred of them are still in uniform. The men and women who wear the uniform have given up a lot so that you and I can live in the freedom and comfort that we do. While you are enjoying your day off on Wednesday, be sure to think about them, and if you get the chance, thank one of them for what they do for us. I know that a lot of you have parents who are serving in the Army, so when you get a chance to see them, Wednesday is an opportunity for them to get an extra-big hug from you. Believe me, they will appreciate it.

Well, that's all I have for now. As always, I'll see you in the Red Hallway, Knights! 801, SECOND TO NONE!!!

By the way, Congratulations to Mrs. Myers for being named Teacher of the Year for East Columbus for the 2009-2010 School Year!!!

RADICAL Mathematics!

What a week we had last week! I think that this was the most challenging week of instruction we have had so far this year, but I am confident that you all will learn the concepts we have taught, as long as we keep practicing and working at it! This past week, we learned how to simply radicals that are not perfect squares, and how to add and subtract, and multiply and divide, expressions which contain radicals in them. Remember, when you are simplifying radicals, you are not trying to put things together, you're trying to take things apart. There is a perfect square in the radical you are simplifying, and your job is to find it and bring it out so that the radical is simplified into a smaller form. Remember also that when adding or subtracting radicals, the key thing is for the radicals to match. If they don't match, you have to simplify the radicals first so that they DO match, and THEN you can add or subtract the numbers in front of the radicals. Multiplying and dividing the radicals is a different matter, though. All you have to remember there is "Inside Inside, Outside Outside". That means multiply or divide everything OUTSIDE the radical with everything OUTSIDE the radicals, and everything INSIDE the radicals with everything INSIDE the radicals. Then simplify the radical if you have to. Parents, I know this might sound a bit confusing, but if you ask your children to show you the notes I have had them copy and have given them, it may just clear up the confusion a bit. I know this concept has been challenging this week, but I assure you, we are not done working on this standard. We will keep practicing at it.

Now coming up this week, we will be working on the Pythagorean Theorem. Now before you go tying your tongue up in a knot trying to pronounce those big words, I'll make it simple for you: this week we are going to start working on right triangles! We will be working on finding the lengths of the sides and the interior angles of these triangles, based on information that we have been given beforehand. The tool we will use to get these answers is the Pythagorean Theorem. If I've peaked your curiousity, but you still have no idea what I'm talking about, come see me in class and I'll show you. Parents, while I'm on this point, I would like to appeal to you to make sure your children are in school and on time. That way, they won't fall too far behind if they miss anything. I'm not advocating that you come to school when you are sick or anything like that! I'm just saying that I can't teach you if you are not here, and I miss you when you're gone! So with that, I'll see ya in the Red Hallway, Knights! 801, SECOND TO NONE!!!

Of squares and roots...

Another week has come and gone, and I'm sure you all enjoyed this past week, if for nothing else because it was a SHORT one! To recap, last week, we got more into our study of squares and square roots. I taught you all the following points: every positive number has two square roots, a positive one and a negative one. Secondly, I taught you three situations that you would see which would require you to simplify square roots. We also continued to work on and study exponents, scientific notation, and all the standards in probability which we studied before we got into square roots. The week culminated with Test-takin' Thursday (I didn't know that all of my colleagues had also scheduled tests for that day, but I'm sure you all did fine).

This week, we will learn how to add, subtract, multiply and divide expressions which have square roots, and then we will get into our next GPS Task for this nine weeks, exploring what we have learned about exponential powers of 10. See ya in the Red Hallway, Knights! 801, SECOND TO NONE!

We're Baaaaack!

Hey guys, sorry it's been a minute since I last posted. I get home and my weekends get so busy that I sometimes run out of time to recap and preview on the weekends. That's why I am doing this posting now, before I even leave the school!

This past week, we left our study of scientific notation and turned our attention to square roots. To recap, scientific notation is a shorter way of writing very LARGE or very small numbers. You do so by writing a factor (a number) that is greater than or equal to 1 but less than ten, and then multiplying it by power of 10. The key thing to remember is that the exponent of that power of 10 does NOT signify how many zeroes are in front of or behind the numbers. The exponent ONLY means how many times you have to MOVE THE DECIMAL. Remember also that you DO have to move the decimal, or you have not truly rendered the number in scientific notation. If you need to review this a little more, come see me after school on Wednesday of next week.

From scientific notation, we moved into the beginning of our study of radicals and square roots. Again, let me clear up a common mistake: the square root of a number is NOT just taking it and trying to cut it in half. You have to ask yourself, "What number can I multiply BY ITSELF to get the number under the radical?" For example, the square roots of 25 are 5 and -5, because 5 x 5 = 25 and (-5) x (-5) = 25. Remember that when you see the radicand sign, you are only supposed to name the POSITIVE square root of the number. We spent a little time having you all make a chart of your perfect squares and square roots all the way out to the number 25. Make sure you don't lose that chart! You will need it for some time to come! One last review point I want to make here: remember that the square root of a perfect square is the length of one side of the square. This information will come in handy for you later on in the year.

Next week, we will pick up where we left off. We'll learn how to find radicals on a number line, how to simplify expressions that have radicals, and how to add and subtract radical expressions. This is where the school year gets REALLY interesting, so make sure you are here to get in on all the fun! See ya in the Red Hallway, Knights! 801, SECOND TO NONE!!!