The student completed a long division problem showing all his work. He followed the steps correctly and calculated the correct quotient. I also asked him to check his answer using the algorithm from previous lessons: quotient x divisor + remainder = dividend. He completed the check successfully; he also identified the dividend, divisor, and quotient for the problem. He is getting more confident with this method. In the next lesson, I will add more division problems to his review sheet (to be completed at the beginning of the lesson). In the last lesson, he took a significant amount of time to complete the two long division problems, so I limited the division problems to enable us to review and cover other math topics.
Next, I asked him to compute the ratios between two shapes arranged in rows. He answered all the problems correctly. He calculated the total number of shapes for each shape very efficiently. For each set of two shapes, he computed a part-to-part ratio and a part-to-total ratio. He computed all ratios correctly and expressed the simplified ratios correctly as well. I showed him how to use a single row to compute the simplified ratios of part-to-part and part-to-total, so he will always have a way of checking his simplification.
Lastly, he and I discussed a ratio word problem I had given him last week. His calculation was impeccable, and he answered the question in appropriate units, even devising another way to formulate the answer (eggs in dozen capacity cartons vs eggs in half-dozen capacity cartons).
I asked him to read two versions of two different sentences: one sentence written in the passive voice, the other in the active voice. I asked him to explain how the sentences differed; he incorrectly said "one is in the past tense; the other is in the present tense) Once I corrected this error, saying both were in the past tense, we talked about how "in one sentence the subject is receiving the action, in the other the subject is doing the action). I then asked him which sentence created a clearer picture of action; for both sentences, he identified the active voice version.
He read three sentences, each containing a bold-type word. He was asked to identify a synonym for the boldfaced word. He answered 2/3 questions correctly. All words were words he missed during his initial assessment; he was asked to identify a synonym for "immense"; the sentence he read described how surfers look for waves that are "uniquely immense, because each wants to break the record for catching the biggest wave"; he chose "wide" instead of "huge" as a synonym; he explain himself, saying that width is what makes a wave big; I told him to think like a surfer; surfers look for tall waves, and there is a context clue that could be a synonym for tallest, the "biggest"; when we talk about a wave being immense, or big, we are talking about hugeness or tallness, not width. Surfers never talk about catching the widest wave. When I pointed out the context word "biggest" he understood that "huge" was the best synonym.
He and I will exchange articles and write questions based on the two articles again. He will also write a summary of his article; this summary will allow me to teach him about the active voice, and to examine the comprehensiveness of his natural writing. I gave him a word-problem worksheet on rates, which are directly related to ratios, so he can practice using ratios. I will ask him if his rates can be rewritten as simplified fractions in the next lesson."