This post is to simply state the obvious for those of you checking the blog. I have not been posting this week, because I have been consumed with learning as much as I can about the new Interactive Whiteboard that we not have in our classroom. This one tool has the potential to engage students at a deeper level than many of them have ever seen before. I am familiar with another a similar program, but this “bad boy” is the BOSS. The only reason that I say similar is for their similar intentions. This one uses the ActivInspire platform which doesn’t just intend, IT DELIVERS!
View this video for just a snapshot of the possibilities that will be seen in the 21st Century classroom.
Circles are something that have been around (pun intended) for quite some time in the students’ educational experience. They are expected to remember all of the vocabulary associated with circles, i.e., center point, diameter, radius, arc, chord, central angle, and sector. To the best of my knowledge, the only new vocabulary term that was introduced today is tangent. This is simply a line that touches the circle at exactly one point.
The main focus of our study is using various equivalent representations to calculate the measure of central angles by degrees. These representations are simply percents, decimal, and fractions. This is by no means new math; it is just math used in a new way.
Today’s study wrapped what we have learned so far this year around the backdrop of the the Martin Luther King Memorials “Stone of Hope.” We discussed the man, the events of his life, and how he was a “Stone of Hope” carved from a “Mountain of Despair.” For instance, our discussion began by explaining the astounding volume of individuals that participated in the March on Washington. An estimated 250,000 + individuals rallied at the Washington Monument to undergo the 0.8 mile march to the Lincoln Memorial.
We discussed that on that day alone marchers walked an aggregate 200,000 miles. This is enough distance to hike the entire Appalachian Trail 91.7 times. Further still, had each of these 250,000 individuals been placed equidistant along the trail’s 2180 miles, they would have stood just 46 feet apart. However, students were even more amazed to discover through proportional mathematics just how massive the Stone of Hope actually is.
We used the known height to calculate the stone’s estimated thickness and depth. We calculated its approximate volume in cubic feet. We, then, used that computation to determine its approximate weight based on the understanding that solid granite weighs 168 lbs./cubic foot. I later called the Monument to determine just how close our mathematics were. However, neither the National Park Service person nor the monument employee with which I spoke knew the actual measurements. Each one referred me to the other agency. I will try again tomorrow, and see if I can get to someone else that might know.
An individual traveling to a foreign country who could not speak the language would not be near as successful as one which could speak in the native tongue. The same is true with mathematics and specially geometry. There are numerous terms and symbols that make up the mathematical language around geometry. Therefore, we will be taking vocabulary tests throughout our geometry study. The first one will take place tomorrow. It will cover the first three sections of Chapter 8 and include a few additional terms that are not mentioned in the text.
Most of today is a review of sixth grade material. However, the vocabulary is vitally important to a students understanding of the concepts at hand. If a student can not “speak the language” if you will, that student can not be successful to a great degree.
Today’s discussion is all about the building blocks of geometry. Students must understand the vocabulary and the way things are labeled to fully understand the content.
We are wrapping up chapter 5 with a review. We worked the reviews in class on Thursday and will grade them today in class. The test will be tomorrow, and then, it’s off to Chapter 8 to begin our three unit study of Geometry. This is my favorite portion of the the year. Geometry is where math began to make sense for me as a young learner. I could see it, manipulate it, and in some instances, even hold it in my hands.
We are spending the entire week working with constructions. Students will create congruent figures, bisect them, and even copy them using nothing more than a compass and a straight edge. This week will provide concrete representations of geometry principles. Thus, students will begin the study of geometry after the break with a good understanding of definitions, and geometric relationships. The address below is to a website that has step by step tutorials.
This concept is another viable use of proportions. We simply set a scale factor (model measurement : actual measurement) as a proportion to an object. The video on the Videos Tab is a great resource for this lesson. The main thing to remember is to set up both fractions of the proportion as model : actual.
The use of ratios is extremely valuable in geometric thinking. For instance, an architect cannot draw a house plan using a 1:1 scale, or the plan would take up the same amount of space as the house. This proportional relationship allows us to determine missing lengths through comparative mathematics. We show what we know and use that information to compute what we do not know.
The vocabulary and geometric symbols are vitally important to keeping everything easy to follow. 5-7 Corresponding Figures
