Presentations + Last Week = Awesome

Last week was awesome and I am excited to see what will be shared tonight. The ideas and lessons were great last week. I am set to use Denis' circle activity tomorrow. I just wanted to thank all of you that have shared activities and offered suggestions this semester. I have learned so many things this year and I am excited to use them next time I teach geometry.

Update on Wheel of Theo...
I was working on GSP assignments this week and in the Pythagoras section (Chp.8) It has a lesson on how to create the wheel using GSP. It also gives instructions for creating a tool. Denis asked about this in class. I had tried it, but I was missing the first part. The book says that you need to identify reference points before selecting the new parts.

See you tonight.
Is tonight pizza nigh??? or next week???

Wheel of Theo in the Gym

I just finished building the Wheel of Theodorus in the gym with my 4th period class. It went pretty well and the kids did a great job with their accuracy. They were a little out of control at times, but it was a nice activity for a Friday. Compared to the hand drawings we were right on target with the number of triangles that we could make without overlapping. The students were able to explain what we were doing to both the Principal and the Ast. Principal. The only thing I would do different is to tie the bottles together with something thicker so that you could see the string on the picture.

ARTICLES

Perimeter and Area:
This was a nice article and was similar to the activity that Bill shared in class last week. One part that really spoke to me was in the first paragraph. The following things were stated...
1. Students develop knowledge through interaction between the student and the knowledge
2. Students do not think like adults
3. Students learn well through social interaction
There is a lot of truth to these 3 statements.

Chp. 9 Exploring Connections between teaching, learning and assessing Mathematics for Understanding

I haven't finished this article, but if you are going to read on I would suggest this article. The teacher/researcher is focusing on opened-tasks. She had been a math consultant for 2 years and discusses the steps that it took to change her classroom.

Wheel Of Theodorus

This is a great activity that covers several objectives. Rational Numbers, Irrational Numbers, Geometry, and Pythagorean Theorem.
The activity starts with creating a unit of length. Once I have the unit I cut a unit by unit square out of the corner of a note card. This tool will act as a ruler for the students throughout the activity. Using the "ruler" start in the middle of a large piece of paper and make a right isosceles triangle that has legs one unit long and then connect the legs creating the hypotenuse. The next step is repeated as many times as you like. Make the previous hypotenuse the base of the new triangle and use the ruler to add a leg that is one unit long and is perpendicular to the base. Then connect the unit length leg back to the middle. Repeat, Repeat, Repeat.... I have my students use the Pythagorean Theorem to find the length of the hypotenuse for the first ten triangles. They see a pattern quickly and could give you the first ten hypotenuses without the work, but I make them show the work.
I only require that the students draw about 15 triangles, but many of them go much further than this. Several of them will make 50 to 60 triangles attaching extra papers everywhere to make it work. When the students finish drawing all of the triangles and the math, they spend some time decorating or adding on to the triangles.
See links below for examples
http://www.ldlewis.com/Teaching-Mathematics-with-Art/images/Wheels-of-Theo/Kyles-turkey.jpg
http://www.chatham-nj.org/156620131125737203/lib/156620131125737203/IMG_0198.jpg

This year I have thought of two different extensions.
a) Using GSP. I figured it would be pretty cool to make on GSP and it was :) I will post the file on the discussion board if you would like to see it.
b) The second activity has yet to be completed. I would like to take my class to the gym and use yarn and water bottles to build a large scale version of the Wheel of Theodorus. If I am successful, I will let you know.

I originally got this idea from an article in the Mathematics Teacher.

Bell Tower

I really enjoyed Monday night's class. It is nice to be able to go outside the classroom and see the concepts that we are discussing be applied to our surroundings. I especially liked the Bell Tower activity. I was actually quite surprised at how close our estimate was to the actual height of the bell tower. Using sketchpad to model the situation was also exciting because it allowed you to complete the problem without knowing anything about the tangent function. However, it did require me to think about scale (something that hadn't been part of the lesson).

Chp. 6 Linear Measurement

I was surprised at how poorly some of the students did on the activities. Especially the students were calling something 5 1/2 when it was only 4 1/2. I guess I understand the confusion, but it doesn't seem to make much sense. As I was reading this article I was reminded of my father-in-law who is always talking about teaching the grand kids "stuff." I think that response to him sometimes is "oh they are to young (1, 2, or under) they couldn't possibly learn something," however as I go through this article some to the issues are just misconceptions. My guess would be that not all of these students have a grandpa who is encouraging them to work with different toys or "equipment." I don't know if this is even making sense.......What I am trying to say is that this article really made me a believer of what my father-in-law does/says. He really is teaching our kids "stuff" that will be useful to them in the future.

GSP!!!!!!!!! IT WORKS

I was working with my students today on squares and square roots. We started the lesson with finding the area and perimeter of different rectangles and squares. Then I gave the students squares with a given area and asked for the side length and perimeter. They all did fine until the they got to the square that had area equal to 110 sq meters. Some said 55 and others said 10 point something....maybe 10.5 they said. We then checked a square that was 10.5 by 10.5 and the area was to big. So others suggested 10.4 and the conversation continued.
I had GSP pulled up on the SMARTboard to see if we could make a square that had area 110 and then measure the side lengths. I was going to have the square ready, but I decided to see if they could create a square as a class. The initial response from the students was to just draw a square. I said how and they said with a ruler and pencil. I told them the program didn't have a ruler that we would have to do something different. One person said, "use that line thing and just do one that looks right." This brought up some debate about whether or not our sides were the same or if we had right angles. We used the measure tool and found that we didn't. We decided to erase everything but the line segment. I gave them a hint and drew a circle using the segment on the screen. From there they were able to create the square. They knew that radius would help them and they knew it had to be perpendicular. The most surprising part was that the students were telling me to make another circle. They wanted another circle that had the same radius with the center at the other end of segment.
After creating the square we measured the side lengths and area. We manipulated the square to make it match the squares in the exploration of area and perimeter.
The most amazing part.........these were Freshman taking Pre-Algebra extended. If you don't know what that means....they are the lowest 30 kids of the freshman class. They were able to figure out GSP and some were saying...."do we get to do this." I was shocked. I usually hear "I'm not doing this, it is stupid."

Supplementary Angles / Colinear Angles

FYI I could not find a definition for supplementary angles that didn't involve the word "pair" or the phrase "two adjacent angles."
I also could not find collinear angles.
So I guess the proof needs revised.

I can see my blog now, I don't know what was wrong.