Ed Tech 4 Math

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

Over the weekend, my husband was at a local coffee shop and the change he received for his large hot mocha included a two-dollar bill.

The bill was crisp and clean; series dated 2003A, and looked like it had never seen the insides of a wallet.

And that got me wondering to when the last time was that I had seen a two-dollar bill.

 Two-dollar Tid-bits

I did a search about the two-dollar bill on the website for the U.S. Department of Treasury.  

 Here’s what I found on the FAQs about Currency denominations:

• The Federal Reserve System does not request the printing of the two-dollar bill as often as the others.
• The Series 2003A $2 bill was the last printed and bears the names of former Secretary of the Treasury John W. Snow and Treasurer Rosario Marin.
• As of April 30, 2007 there were $1,549,052,714 worth of $2 bills in circulation worldwide.

The modern two-dollar bill was issued in 1976 for the U.S. Bicentennial. I have one of those 590,720,000 notes as a memento of my birth year!

For the Teachers and Students

Browsing the U.S. Department of Treasury’s Education link, I found a plethora of other useful and interesting information for today’s youth and teachers.

I especially liked the For the Kids! where you can find kid-friendly websites on topics such as the White House, the U.S. Mint, and the Alcohol and Tobacco Tax and Trade Bureau.

Since my mind was on currency, I took a look at the U.S. Mint site and had fun reading about coin circulation facts and coloring the Arizona state quarter.  I also found many links for teachers, including lesson plans.

What are the Chances?

In 2004, 121,600,000 of the newest $2 bills, Series 2003A, were printed for the Minneapolis Federal Reserve Bank.  A new issue of Series 2003A $2 bills was printed from July to September 2006 for all 12 Federal Reserve Banks. In all, 220,800,000 notes were printed_1.

So, the single two-dollar bill that my husband encountered is one of 342,400,000 printed between 2004-2006.

Some say that it is bad luck if you come across a two-dollar bill.  Others say the two-dollar bill is fake.  And then there are some who are intrigued by the rarity and collect them!  My interest was certainly sparked by the rare occurrence.  Is yours?

References:

1.    United States two dollar bill. http://en.wikipedia.org/wiki/United_States_two-dollar_bill

So, I’m sitting in the conference room with two fellow instructional coaches, and I just showed them Wordle.  And all three of us are intrigued with how we can use this Internet based classroom tool.

Wordle is a tool for displaying words as a graphic image.  The size of the words is a relative indicator of their frequency of use. You can read more about Wordle on Ed-tech-4-Science.

In Wordle:  Seeing Science Images as Art, Dr. Rillero, I was immediately intrigued by what Wordle creates with text. Here’re my Wordle art for this blog:

So, why would a classroom teacher want to spend time on Wordle? 

The word analysis and count feature gives teachers important information as to how often academic content vocabulary terms are used in a text.  In regards to assessments, knowing how many times content vocabulary is used can help the teacher make sure he/she is using the same terminology in their instructional delivery.

This week is benchmark assessment week in the Avondale School District.  So, I immediately thought of the math assessments hundreds of students will be taking on Monday.

I thought it would be interesting to “see” what words were most often used in the 6^th grade assessment.  Knowing that this quarter’s focus was on fractions, I was expecting to see words related to fractions as the largest ones in the art creation.  

I should note that I included only the text for the questions stems, not the answers.  This is what I got:

I was really surprised that “ate” was one of the largest words.  Using the word count feature, I found out it was used 13 times.  “Multiply” was used 10.  This tells me that many of the fraction problems are given in the context of eating some type of food!  Maybe a redesign of some of these problems is necessary.  Fractions can be used in many other contexts! I wonder what kind of Wordle art the AIMS (Arizona Instrument to Measure Standards) practice tests would create?

In the Math Classroom

I can easily see a math teacher using the information provided by Wordle in a data analysis unit.  The word count provided with each Wordle art is a good source of data to be graphed and analyzed.  Students can use current event articles posted online from sources such as CNN, FOXNews or BearEssential News as the text, and do an analysis of the word usage.  The data can be interpreted (and displayed) in many different ways:  content vs. everyday language, frequency of word usage, or even determining the frequency of how many words with 3, 4, or 5 letters.   

The possibilities are vast with Wordle.  Share your thoughts and Wordle art with us!

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!