Marcos and I spent the hour reviewing and correcting his work on multiplying and dividing rational expressions. He was comfortable with the topics, with the exception of long division. We worked through some other examples, and he has 3 exercises to complete for homework. Marcos also asked me a few questions on his review sheet for his test tomorrow. I am confident that he will do well on it.

A rational expression can consist of a polynomial in both the numerator and the denominator. In order to simplify such expressions, we look to factor the polynomials, and then cancel the common factors in the numerator and denominator. This is the same as dividing the common factors to equal 1. Marcos should do well with this topic, as he understands factoring well. His assignment is (2-32 even)

Today, Marcos took the vocabulary quiz (15 words and expressions from textbook). I corrected his quiz. I gave examples in context about words spelled wrongly. Marcos will practice more( study and homework) his vocabulary and retake the quiz tomorrow. Marcos and I reviewed how to express frequency with adverbs. Then, Marcos wrote several examples about this topic.

Today, Marcos and I spoke about how to express frequency with adverbs with " Siempre, todos los dias, mucho, a veces, de vez en cuando, poco, rara vez, nunca. 1.These expressions are usually placed BEFORE the verb(Siempre, rara vez, nunca).2. These expressions are usually placed AFTER the verb ( mucho, poco). 3. Longer phrases can be placed at the BEGINNING or the END of the sentence (todos los dias, a veces, de vez en cuando). Then Marcos worked on activity 6 (textbook) writing true or false. Marcos was able to determine whether the statements were true or false (about Marco's routine). Example: A VECES contestas las preguntas de la maestra en la clase. Si, A VECES contesto en la clase.
Yo SIEMPRE contesto en la clase. ( If false, Marcos made it true.)

As the final exam is next Tuesday, we today began a review of the grammar that will be on the test viz: run-ons, fragments, subject-verb agreement, dangling modifiers, and pronoun-antecedent agreement. Marcos completed a number of grammar exercises on these topics, and we will continue reviewing grammar during the week. Our study of literature this year was selected mostly from the literary canon as opposed to popular fiction or science - fiction. In order to expand our reading selection, I discussed and distributed biographical information on Issac Asimov, the famous Columbia University educated science-fiction writer who wrote the "I,Robot" series of stories that is now a movie and part of popular culture. We discussed how prescient his fictional stories were,and I then distributed an Asimov short story ,"The Machine that Won the War", about Man's over reliance on computers. Marcos was quite familiar with "I Robot" ,but not with Asimov. For homework due Thursday, I assigned grammar exercises on agreement, reading the short story, and answering questions on the story. These questions focus on locating specific language in the text to support and draw inferences.

Marcos and I spent the first hour going over his Algebra review packet. He was able to figure out what he did incorrectly, as well as how to do the problems that he was confused about.
Our second session was spent on learning how to divide polynomials . When we divide a polynomial by a monomial, just write each term of the polynomial over the monomial and simplify. For dividing a polynomial by a polynomial, we need to use long division. Long division works the same way with polynomials as with regular numbers, but we must make sure that the polynomial is written in descending degree, and any missing exponents are written in with a coefficient of 0. Marcos' assignment is p.684 (1-25 odd)

The lesson began with a review and discussion of current news stories. Next, the economic concept of macroeconomics was introduced. Macroeconomic Performance was the topic presented. We spent the remaining time discussing GDP.

We began with a review and discussion of current news stories. Next, the tariff on Chinese imports was reviewed in detail. We then completed our review Of Market Structures (Chapter 7). Marcos demonstrated an exceptional understanding of the concepts discussed.

As the final exam next week will include an essay on "Anthem", we carefully reviewed Marcos' study guide answers on Chapters 11 and 12 which examine the novel's philosophy and theme. Marcos had some questions on Rand's use of the phrase " a creed of corruption" . In order to clarify that phrase we studied the language before and after the quote to assist him in locating in the textual basis for Rand's characterization. We additionally focused on Rand's explanation for the "collapse of society" being caused by the worship of the word "We". Marcos supplemented his study guide responses accordingly. Last, we reviewed the organization of his essay on "Gathering of Old Men" and Alice Wallker's " Tribute" and noted ways to better support and to organize the essay . For homework, I assigned rewriting the essay per my comments.

Rational Expressions can have polynomials in the numerators and denominators. They can be multiplied and simplified. We apply the rule of factoring (GCF, trinomials, difference of squares) to factor the polynomials. Then, if we have common factors in the numerators and denominators, we can cancel them out because they actually divide out to 1. Marcos and I worked through many examples, and had fun "cancelling" the common factors with much gusto!