The student simplified six fractions to lowest terms and identified the greatest common factor (GCF) for each fraction. He answered 5/6 questions correctly. For the fraction 16/76, he initially simplified the fraction using a GCF of 2. However, the resulting fraction, 8/38, could have been simplified further. When verbally prompted to recheck his work, he wrote all the factors for the numerator and the denominator, and correctly identified 4 as the GCF. I also showed him how he could have simplified his original answer, using a GCF of 2, to get the correct answer of 4/19.
The student corrected one of his rate calculations from the previous lesson. The problem required him to calculate the total number of miles traveled and the average miles per hour traveled. He calculated the hourly rate of travel perfectly, however, because of an error in calculating partial products, his final distance calculation was incorrect. He redid the problem his way: dividing the total time in half, multiplying a known rate by half the total time, and then doubling that partial product. I showed him an alternate method of multiplying the hourly rate of travel by the total number of hours. He was observant and verbally summarized the method once I finished.
We further discussed similar triangles in greater detail. He understood from the previous lesson that similar triangles have at least two congruent angles, and the length of their sides are always in equal ratio. However, I wanted him to recognize scaling: the idea that triangles can be different sizes but still have a similar shape. We discussed scaling and I pointed out that each pair of similar triangles were the same shape, but different sizes. We also discussed the meaning of corresponding angles and, after looking at example triangles with marked corresponding, we agreed that corresponding angles are angles in the same position.
Take Home Work
He took home three similar triangle problems; I reviewed one exceptionally challenging problem with an embedded triangle. We identified the two separate triangles, and I marked the larger one with a highlighter.
Reading and Writing:
I reviewed the differences between the active and the passive voice. He did not remember all the differences between the two voices, and he incorrectly said, "One is in the past." I corrected him and showed him an example of a sentence first written in the passive voice, and then rewritten in the active voice, but both written in the past tense. He read through eight sentences and identified the voice of each sentence "active or passive" and the agent of action. He identified the voice correctly in 7/8 sentences. He incorrectly said that the sentence "It gets colder here in Winter"ù was written in the passive voice. I used this opportunity to discuss an idiosyncrasy of English: getting cold or getting hot is often interpreted as an action, because conditions are changing. He identified the agents of action for active voice sentences perfectly, however, he identified the subject of the passive voice sentences initially. When I reiterated the directions to him, he corrected his errors. Some sentences did not have agents of action: "The problem was solved."ù For these sentences, he always identified the subject, but I explained to him that no one is identified as the doer of the act. He understood this distinction and changed his answers accordingly.
Take Home Work
The student took home a worksheet relevant to this activity. He must rewrite sentences in the passive voice to the active voice. Some sentences are already written in the active voice to check if he can truly identify the differences in voicing.
We exchanged questions from our Loch Ness monster articles. He wrote a total of 15 questions. Many of his questions were references to specific facts in the text, and he also asked fill-in the blank style questions. According to him, I answered 8/15 of his questions correctly. He also answered 8/15 of my questions correctly. My summary of his article was brief, but it included an overview of the article. He answered many "all of the above"ù style questions correctly, which suggests he was able to not only remember facts from the reading, but correctly understand the commonality among them as well.
I reviewed his summary of a Chupacabra article from the previous lesson. I told him that he included many important details from the article, including an illustrative quotation, but his summary needed to be better organized and also reference and describe the theme of the article. I gave him a sample summary I had written. I asked him to reread his summary, then read mine and highlight any information in my summary that was not included in his own. He highlighted a factual detail in my summary that wasn't in his own, but he did not highlight the sentences that referenced the theme of the article. We discussed why and how it is important to mention the theme or main idea of an article when summarizing it, as the theme indicates the reason the article is written, its general message. The message is the framework for facts, so it must be included in any summary of facts.
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