We worked a major problem in proving that a figure whose sides connect the midpoints of the sides of a rectangle is a rhombus. This was a breakthrough problem in that it related the abstract to the concrete via coordinate geometry. We finished off with several simpler problems.

We worked through a lengthy proof of a theorem stating that there mid segment of a trapezoid is (a.) parallel to the two bases, and (b.) has length equal to the mean of the lengths of the two bases.

* Review.
* Vocabulary: Boutiques 2.
* Conjugation: Immediate Past.
* Reading: Armee Suisse.

Will and I explored many facets of Scotland, particularly as it relates to the effects of the Industrial Revolution. Will read a brief history of Scotland, and we talked about it's politics, economic and social policies, and the way it fits politically and finically within the UK. We briefly touched on several Scottish philosophers whose ideas became prominent during the Industrial Revolution. Finally, we read a website written about the upcoming Scottish independence vote (in September) and we discussed the implications for independence in terms of economics and social policies.

We discussed the Divine Ratio (also known as the "golden ratio" or "golden mean." We explored its occurrence in architecture (the pyramids, the Parthenon, gothic cathedrals of Europe, etc.) nature (chambered nautilus, spiral galaxies, various flowers) art, music and mathematics. We found the ratio of two consecutive terms of the Fibonacci sequence approaches the Divine Ratio 1.618... to one.

I had a lesson planned for Will this morning to explore the economic and political philosophies which emerged from the Industrial Revolution. He was absent today.

Will read about and explained the chain reaction resulting from the processes of the Industrial revolution. We then discussed the causes of urbanization and explored the lives of workers in factories, including the hardships of women and children. We compared and contrasted the working and middle classes of the time, and explored how the factory system and mines changed work. Finally, Will and I discussed the connections between IR workers and modern day migrant farm workers, and the Luddites and their modern day equivalent, technophobes or persons who eschew technology.

Today I began by returning Will's graded midterm exam (89/100) and going over it with him. Thereafter we spent considerable time discussing possible topics for Will's research paper, which will be due in October. After mentioning a number of topics in which we was interested, Will seemed most keen on researching and writing about some aspect of tobacco's role in US history. I told him that was a wonderful topic and proceeded to model for him how to do online research concerning this topic. I printed one of the searches, which contained several sources that WIll might want to consult. Will said that he would make progress on researching his paper topic, including a library visit, this weekend. We then began a brief overview of Chapter 9, which is to be discussed in detail next week. Finally, we conferred about the new time slot for Thursday sessions (per Connie), as well as my anticipated absence from 9/30/14 through 10/7/14.

N/A

We began our exploration in this area with a discussion of plotting trapezoids in the Cartesian plane. We used the white board extensively to illustrate examples. The problem drill we did yesterday served as an excellent starting point as Will is now quite comfortable with graphing in the xy plane.