Today we started a new chapter on Logarithms. We began by taking notes on the board reviewing some old concepts on inverses. We recalled some inverses are multiplication/division, cubing and cube-rooting, and what we're leading up to is exponentials and logarithms. We reviewed some common exponential properties like 25^1/2 is like the square root of 25, and 4^-2=-16. Then we started with exponential form, lableling the base and the power. I showed JPaul how to go from exponential form to logarithmic form and vice versa. He practiced on his own. Then we used that technique to solve logarithms such as: log3(27)=3. JPaul got the hang of it but will need more practice to be fluent with it.

JPaul worked on completing his test today. At the end of the class he turned it in and we reviewed it. He got an 81%. He made a few of the same errors for not using the Plus/Minus technique when solving quadratic equations. Other errors came from simplifying radicals incorrectly and getting stuck. I had JPaul rework the problems he missed. He understood where he made mistakes.

We continue discussing mid-term planning and discretionary financing needs.

Discuss how lakes and ponds are created through tectonic activity or glaciation.
Examine how tectonic activity can create either high salinity lakes and ponds by land rise in the ocean, or fresh water lakes and ponds through land splitting in deep fissures which fill with water. Indicate how glacial movement scrapes large depressions in the land which fill with water. Examples are the formation of the
Great Lakes in the US.
Discuss how atmospheric water is essential to global distribution, especially in arid areas. Analyze how extreme droughts can occur which kill people, cattle and crops. These droughts are made worse by increased population and water use. Indicate how topsoil can blow away, soil can harden and become impenetrable, leading to runnoff and flooding when the drought is ending.

JPaul reviewed short-term financial planning and we began our lesson on mid-term financial planning.

JP took a synthesis essay test during today's session.

Today he completed two activities from StudySpanish.com, about comparatives and superlatives in Spanish. After that, we watched the video: Los comparativos on YouTube.

Today he worked on the basic quiz on StudySpanish.com about the preterite tense.

Today he completed pages 56-57 and 58 of the book. He learned five new verbs and had to conjugate them in the present and preterite tense.

We reviewed and edited the first paragraphs of JP's synthesis essay based on 6 sources that discuss nuclear energy. JP created a great thesis statement about people's hesitancy to embrace or fear of new technology . We added a clarifying sentence to the first paragraph and then edited his discussion of his first source, a graph. Next, we discussed how to use two other sources to bolster the argument. JP had a very good grasp how to use the sources and completed the body of his second paragraph by both citing an opposing view and yet negating its relevance to his thesis. We will continue working on completing the essays within the time allotted by AP exam over the next months.