Two Examples of Proofs

I uploaded two more videos to YouTube today. They are both examples of how to use angle theorems to prove things. Here they are:

Four More Geometry Proofs

I completed 4 more Geometry proofs. My plan is to prove most of the theorems I go through with my Geometry class for YouTube and then I will also be adding some harder proofs as well. Tell me what you think and if there are any proofs you would like to me to add.

Alternate Interior Angle Theorem



Same-Side Interior Angle Theorem



Triangle Angle Theorem



Remote Interior Angle Theorem

New Squidoo Lenses Published

I have just finished two new Squidoo lenses. Squidoo is a pretty cool site that allows anyone to create a webpage about any topic. Check out my lenses and feel free to give it a thumbs up if you like what you see.

Writing Linear Equations

Graphing Linear Equations

Geometry Videos

Hello! Been awhile since I have posted, but I plan on sharing some of what I have been doing with my online videos and websites. Essentially, my new job has been wonderful, but also time consuming. Finally, I am to the point that I can start uploading new videos in an organized way and finish some of the work I started with the Algebra videos and website. My current goal is to focus my new video creation on Geometry videos, filling in Algebra videos when I have time and a need for my websites. Here are two Geometry videos I created today!

Interesting Facts on Factors

Asking a student to find all the factor's of an integer is a relatively simple and common task. Similarly, finding the prime factorization is often asked of our students. It is essential for methods of finding the GCF and LCM that are often taught. However, there are some other very interesting questions surrounding those topics.

• How many factors does an integer have?
• What is the sum of the factors of an integer?
• What is the product of the factors?
• How many odd factors does it have?
• How many even factors?

These questions are all answerable by looking at the prime factorization the integer in question. The following two videos show this process:

This is a great topic to share with your advanced students. It is a way to make prime factorizations more interesting.

My new job is going great. I am learning something new every day. It has been a great experience so far.

One Week Down

As I mentioned before I am started a new job this school year. The Sycamore School is a pre-school through eighh gradet gifted and talented school. I am teaching the fifth and sixth grade pre-algebra and the seventh and eighth grade Geometry classes. It was an amazing first week. I was told that the kids would constantly surprise me with what they know and the question's the ask. I must say they were entirely accurate. Here are some highlights:

• A 7th grade Geometry student was able to prove the square root of two is irrational. I didn't learn this until graduate school and I would imagine many of you have never done it.
• A 5th grader aced the pre-algebra pretest.
• A great dialogue in my 7th grade Geometry class about the definition of skew lines. In general skew lines are not very interesting, but, through their questions we were able to learn a lot about the importance of rigorousness in our definitions.

Professionally it has really challenged me. In my previous teaching assignments I have been able to, how shall I say it...fly by the seat of my pants? Not always, or even most of the time, but if I chose not to spend the time preparing, I could usually come up with very effective lessons on the fly. I am not able to do this at Sycamore. I have to have all my i's dotted and t's crossed as well as spending time considering ways to deepen the discussion beyond what is usually presented in a math class. I love it and am anxious to continue to pursue this challenge.

One of the issues with my new position is it is a long commute and a considerable amount of work. This will make it more difficult to continue to web activities, but I plan on building time into my schedule to continue them as I really enjoy it.

I hope all of you have had a great start to the school year!!!!

Grade Systems Part 4 - Testing

There were many things that bothered me about the structure of my undergraduate education program. One of those was that I was given no information on best practices in testing. Evaluating student performance is a vital component of every classroom. This happens in many ways and has many different names. Formative and summative assessments are two of the more recent names that have been applied to evaluating student learning. There are many things to consider when evaluating students.

• What types of questions should I write?
• Is it OK to use multiple choice? If so, when and how many?
• Should students be asked to explain their answers in a math class?
• How much should each question be worth?
• Should I give partial credit or not?
• How much of the test should be basic skills and how much should require higher order thinking skills?
• Should my tests be summative or formative?

The chair of the board of directors at my new school told a story that I think is important for educators and for this discussion. His son was reading a book that had a genie and the ensuing wishes in it. The son asked, "Dad, what would you ask for if you were given one wish?" The dad said he didn't know and turned the question back on his son. The son responded, " at first I thought I would ask what the meaning of life is, but then I thought maybe that is not the right question. So instead I thought I would wish to know the right questions to ask."

I think a big part of writing tests is about asking the right questions(not just the ones on the test). What are some of the questions that you think need to be answered by someone writing a test?