So, after writing on how I enjoyed “Notes on a Triangle,” I read the chapter *on Re-viewing and Seeing Differently *and discover that it is about the film and how the students studied the triangles from the film clip! (Funny how things work in life…) I especially like the chapter’s section on how the students noticed that numbers could be triangles: not only were the students constructing triangles from numbers, but they were also forming patterns. Once the students noticed their pattern (the relationship between the increasing length of the hypotenuse and the total number of dots needed to construct the triangle), they were able to use mathematical language and symbols in order to predict the next number in their triangular sequence. This exploratory lesson allowed for a natural progression to take place in the classroom;building on students’ prior knowledge of triangles affords them a better opportunity to make real world connections (triangles made from squares, soccer drill formations, pyramids, etc.) I was then reminded of a word from earlier in the year: *oikos*. Jennifer’s students were creating a sort of **family** with their number sense: They were able to relate to, and understand that the mathematics they were attending to was **connected**. The students also seemed to view the classroom as a family, or **home**: They were confident and comfortable exploring and questioning their **environment. **

When I become a teacher, I want my students to feel like their classroom is a type of home. I want them to feel comfortable asking questions and challenging themselves. To do this, I need to create an environment that fosters problem solving and open ended questioning. I want to make mathematics more hands on, more interactive, and more engaging; it is through discovery that deep connections can be made.

Sidenote: Notes on a triangle has a partner: dance squared-here is the link: http://www.youtube.com/watch?v=yXL4DP_3dJI