In about 6 hours Eastern Standard Time, the magnificently decorated New Year’s Eve Ball will once again descend 77 feet (23 meters) over the course of a minute₁ to symbolize the passage of time while millions of people gather together to ring in the year 2009.

There haven’t been too many New Year’s Eves that I haven’t witnessed this televised traditional event.  And as a kid, was always awed by how the ball would drop as time ticked away on the television screen.  Since the dawn of the new millennium, the New Year’s Eve ball has truly been a magnificent piece of artwork from the designers at Waterford Crystal, and I am ever more still eager to watch its brilliance descend from the heights of the New York skyline.

2009 gets a make-over

This year, the ball is a 12 foot (in diameter) geodesic sphere based on a truncated icosahedron, weighing in at 11,875 pounds.  It is covered by 2,668 Waterford crystals and illuminated with 32,256 LED lights (about 3 times more than last year). And even will all this, the ball is more energy efficient than ever, consuming only the same amount of energy per hour as it would take to operate two traditional home ovens₂.

I can’t wait to see the show that will be put on this year as the ball descends, and with the enhancement of technology is capable of producing 16 million colors and billons of kaleidoscope patterns.  It’s sure to be a spectacular show!

In the classroom

The design and new facts of the New Year’s Eve ball lends itself to a variety of math problems to be solved.  One in particular that comes to mind is in regards to the overall surface area of the ball.

The New Year’s Eve ball is not quite a sphere, it’s a geodesic sphere (think of EPCOT at Disneyworld).  Its surface is made up of many triangles, with these triangles having different dimensions because of the curvature of the sphere₃.  So, we would need to know the dimensions of every kind of triangle and how many of those different triangles to calculate the surface area.

But, if we simply considered the New Year’s Eve ball as being a sphere, we can use the formula .  After the calculations, we find the surface area is approximately 452.39 square feet.

S = 4(Pi)r².  With what we know about the 2009 ball, our radius is 6 feet.  Therefore, S = 4(Pi)6²

What if we were to fill the New Year’s Eve ball with a bunch of confetti?  How much confetti can the ball hold?

As with surface area we have a formula that we can use to fine the volume: V = 4/3(Pi)³

I’d much rather explore the volume of sphere with a 3-D interactive animation that helps me to build conceptualization of the concept.

Adaptive Curriculum offers such a resource in “Volume of a Sphere.”  In this Activity Object dynamic modeling is used to derive the formula for the volume of a sphere from the formula for the volume of a pyramid.  As the user changes the number of pyramids in the sphere they observe the relationship between the sum of the volume of the pyramids and the volume of the sphere.  The visualization of deriving this formula assists students in understanding where the formula came from and also strengthens reasoning abilities.  The final visualization reminds me a little of the New Year’s Eve ball!

For more on the New Year’s Eve ball:

• Time’s Square Alliance
• Modern Marvels: New Year’s Eve Ball Drop
• New Year’s Eve Ball Grows Bigger and Brighter

References:

1. Times Square Ball.  http://en.wikipedia.org/wiki/Times_Square_Ball  Retrieved December 31, 2008.
2. Time’s  Square Alliance.  http://www.timessquarenyc.org/nye/nye_ball.html   Retrieved December 31, 2008.
3. Geodesic dome. http://en.wikipedia.org/wiki/Geodesic_dome   Retrieved December 31, 2008

So, I bet you were wondering what happened with the 8^th grade students from Mr. K’s class? 

Well, plans changed.  As they do so often in our daily lesson plans!

I ended up spending Friday afternoon with Mr. K and two of his 7^th grade classes.

The focus of the week’s lessons was on probability, and Mr. K was still determined to use Adaptive Curriculum as part of his instructional delivery with the SmartBoard.

Adaptive Curriculum has a few Activity Objects for probability:

• Probability with Tree Diagrams
• Find the Given Probability
• Playing with Probability
• Analyze Experimental Probability Using Graphs
• Experimental and Theoretical Probability

After briefly previewing these Activity Objects with Mr. K during his morning prep period, he decided to use “Find the Given Probability.”

Mr. K had success in both his classes in using this Activity Object.  One of my favorite moments was when we first started the Activity Object and all the students were dead silent and watching the SmartBoard as the introduction was given.  After some time went by and students were being given a chance to come up to the SmartBoard, I heard comments of “Oh, you got it!” and “That’s awesome!”  It got even better when students were working together with each other to solve the problems and could barely stay in their seats for want of getting to the SmartBoard and solve the problem!

At the end of the lesson, Mr. K asked the students to reflect on their learning.  Here’s what a few students had to say:

“I learned an easier way to do probability.  The good thing about the activity is that you’re basically making your own problems.  It was really fun.  I loved the project.”  W. B

“I learned to use probability in a better way.  It gives a good challenge.  I really liked it.”  P. G.

“I learned that you have to multiply the smaller probabilities to get a final one.  I liked the animations and interactive learning.  I would recommend this program to any math teacher.”  J. G.

Sometimes you just need a new way to “see” the math.

On Monday, I observed what was to be an 8^th grade math lesson on solving for angles of triangles. 

I watched Mr. K’s 50-minute class period go by with homework being corrected and recorded, a few problems from the homework reviewed, and a start at classifying triangles.

In the middle of explaining the relevant terms (scalene, isosceles, acute, obtuse, etc.) Mr. K stopped, as there appeared to be some confusion about the relationship between the interior angles of a triangle.  So, he had the students cut out a triangle and complete the following:

• Label each angle as 1, 2, and 3.
• Cut off the corners of the triangle, making sure you can still read the numbers.
• Arrange the cut corners by matching angles 2 and 3; and then angle 1 to 2.

After this, students were asked to observe the arrangement.  The conclusion was that the sum of the angle measurements in the triangle totals 180 degrees, and that was true for all triangles.  This can be observed because the straight edges of the triangle all match up and form one edge, or a straight angle.

Here’s a clip from TeacherTube on this same activity:

 Triangle Angle Sum

The triangle activity Mr. K had the students complete was a good way to review previous learning.  It was hands-on and focused on conceptualization.  In fact, it was already used in the direct instruction of the lesson the previous week.

But, the lesson just didn’t seem to go the way Mr. K wanted.

Maybe it was because Monday was the first day back after the Thanksgiving break or maybe it was that these 8^th grade students just weren’t interested in math on a Monday morning.  Or maybe they just needed to “see” the math in a different way.

I talked to Mr. K after the lesson about the overall engagement of the students and the activity they worked on, and I asked him to stop by my office after school as I had a resource to show him that I thought would help him in his next lessons.

We looked at Adaptive Curriculum’s “Type of Triangles” in which dynamic modeling is used to create different triangles so that students can observe the changes in angle and side measurements as it relates to classification. 

I chose this Activity Object not just because it focuses on the content being addressed in Mr. K’s lesson, but it allows for excellent use of Mr. K’s Smart Board, which would allow the students to get more engaged and involved in the lesson about the relevant vocabulary.

The plan was that we would use this Tuesday with his two classes. 

This morning, we played around with “Types of Triangles” a little bit more and also looked at “Interior and Exterior Angles of Triangles.”  Mr. K was excited about both of these Activity Objects and we played and discussed them for about 40 minutes.  Mr. K decided that he wanted to spend some more time with these Activity Objects before using them with the class and we made a new plan to use them on Friday.

I’m excited that Mr. K is excited! And I’m looking forward to spending more time in his classroom on Friday. 

I’ll let you know how it goes with the students on Friday and how Adaptive Curriculum’s Activity Objects allowed students to “see” math in a new way. 

Check back this weekend for an update on the lesson!

Tired of playing the same old board games or just sitting around watching movies?

Try Blokus!

This multi-award winning (2004 Teacher’s Choice Award and Mensa Best Mind Game Award of 2003, just to name a few) is one of the best board games that I have come across!

Blokus, a game of strategy, was created in 2000 by Bernard Tavitian, a French mathematician.  The game stems from the Four Color Theorem and the use of polyominoes as the pieces, and is a bit reminiscent of Tetris.  Not only is this game highly engaging and competitive, it builds on your spatial reasoning and logic skills.

Winning the game may seem simple:  be the first to place all your pieces (polyominoes) on the game board.

The only restriction is that each new piece you place on the board must touch another piece of the same color only at the corners (hence the connection to the Four Color Theorem)! 

If you don’t have time to run out to the store before Thanksgiving Day arrives, you can play online and compete against players around the world.

Or, you can download Blokus World Tour (for a small fee) and play on your computer.  The graphics and competitions are much better at Blokus World Tour and you just can’t help but to keep playing until you win each of the different tournaments.  I’m currently at playing Tournament 6 – The Berlin Showdown – where best out of five of the Classic 2 Player and Duo games wins you the tournament.

Once you begin playing, I guarantee that you’ll be hooked!  And hopefully you’ll get to claim the title of being the first player in your family to place all their pieces on the board!  A title I proudly hold! 

Oh, did I mention that you get 50 bonus points if the very last piece you place is the single square piece?

Read more about what people are saying about Blokus at Blogus.