Alexa worked through right triangles where she had to find the degree of an angle using trig functions. She successfully completed the angles. I reminded her about the Triangle Angle Sum Theorem, which can be used to find the third angle of the triangles. She simply subtracted the acute angle that she found from 90, and this gave her the third angle in the triangle. Finally, we talked about the Pythagorean Theorem, which she remembered as a^2 + b^2 = c^2. She used the Pythagorean Theorem to find the missing side of her triangles.

Brief overview of the biogeochemical cycles in the biosphere and why they are critical..

Alexa and I continued to work on her essay for the novel. Today I reviewed the rules for MLA citation. I also presented how to format a block quote using MLA. I did one as an example for Alexa. Then she did one herself so that I was sure she understand how to format one correctly. We continued drafting the essay.

View and discuss the biogeochemical cycles which occur in an ecosystem

. These include the nitrogen cycle, the water cycle, and the carbon cycle.

Review the drawings in her sketch book.

Alexa was absent today

Review the place of producers, consumers, and decomposers in the ecosystem. Relate how the energy flow goes from sun-producer-consumer-decomposer. Define trophic level and stress that at each level, less and less of the energy originally captured by producers becomes available. There is an energy loss at each trophic level. Show a pyramid of biomass, discuss the biomass difference at each level and relate that to the energy difference.
Invert the pyramid to show how unstable it can become.Discuss and question the effect that changing the biomass in one level has on the biomass (creatures) in a second level. Stress that the changes in population decrease in one level will lead to population decreases in all levels, with harmful results.

Alexa asked for clarification on her homework question. She was not sure how to do the inverse function on the calculator. I explained, and she got the correct answer. I then sent her a sheet on inverse trig functions, and explained how to work the problems. She has to complete 5 of them on her own by Monday.
We then looked at 10.8 Practice on Inverse Functions. Given a triangle with 2 sides, she had to find one of the acute angles of the triangle. This required her to determine which trig function to use. She could then use the rule of triangle sums to find the 3rd angle of the triangle.

Continue Drawing. Photograph pages from her sketchbook.

Continue her pages in the sketchbook...