I asked the student to complete four adding-fractions-with-different-denominators problems. He answered all the problems correctly, even converted improper fractions to appropriate mixed numbers. His answers were neatly written out, and he simplified all fractions to lowest terms. We reviewed similar problems during the lesson.
The student also accurately analyzed a short, descriptive story. He was tasked to select details from the story that appealed to different senses: sight, touch, taste, hearing. He correctly placed details he selected into the appropriate sensory category; he rightly said that no details of the story described the taste of anything.
He read a short story passage and answered five multiple-choice questions based on the facts of the story. He answered all the questions correctly.
I asked the student to simplify 6 fractions to lowest (simplest) terms. He simplified 5/6 fractions correctly. The one fraction he missed had a GCF of 4; he initially simplified the fraction by 2 and stopped. When I reminded him that he had two even numbers in the fraction, he corrected the mistake quickly and understood his error. I will incorporate these problems into future sessions for additional practice.
The student and I continued to work on adding fractions with different denominators. I showed him three distinct methods for adding fractions with different denominators: the long-handed method, which involves finding the LCM for the two denominators, multiplying the quotient of the new denominator divided by the old denominator by the old numerator to calculate the new numerator for each fraction, then adding the numerators together; the short-hand multiply add method, which involves multiplying the two denominators to get the new common denominator, then cross multiplying the numerator and denominator of each fraction to create two new numerators, before finally adding the numerators together and simplifying the final fraction to lowest terms; third, the opposite denominator method, which involves multiplying the numerator and the denominator of each fraction by the denominator of the other fraction to create two fractions with a common denominator. The numerators can then be summed together and the fraction can be simplified.
The student and I solved two problems with each method. I asked him if he preferred a method. He said that the short-handed multiplication or the opposite denominator multiplication method might appeal to him. I assigned him some problems to complete for homework, with the instruction that he could choose whatever method suited him best. It will be interesting to see what method he favors.
The student and I briefly reviewed converting improper fractions to mixed numbers. He seems to understand the conversion, and I will incorporate it into future lessons as well.
In addition, the student favors calculating answers mentally; while he has shown a certain adeptness for it, I encouraged him to write out his calculations and solutions to avoid errors as the problems grow more complicated.
During a game of mathematician cards (think of the card game war, but the numbers can be combined using different mathematical operations, or a spontaneous word problem can be created using the two numbers), I asked the student to solve some word problems with fractions: Brandon has two-fourths of a candy bar. He eats one-fourth of the candy bar. How much does he have left? He correctly answered this question and others similar to it. Once I cover multiplication and division with fractions, I will steadily incorporate word problems into our lessons. I want the student to focus on mathematical methods initially; once he is confident with them, he can build his skills decoding word problems. His ability to answer these problems without any visual support suggests he is capable of decoding word problems.
I modeled mapping with a short-story passage; I wrote a phrase to describe the information in each paragraph in the margin. I answered the questions with the student assisting me; I read a question aloud, then asked him to point to the paragraph where I might find the information. He identified the correct paragraph 5/5 times, and he selected the answer to each question with the same accuracy.
I asked the student to read a passage to himself, use mapping, and then answer the five-multiple choice questions that followed the passage. He used mapping correctly; his phrase notes were well-written. He answered 4/5 questions correctly. The question he missed required him to sum a length of time described in the passage; he missed a portion of the total when he read, so he answered the question incorrectly, despite looking in the correct paragraph. This was a minor error; he undoubtedly understood how to do the problem. I reinforced the idea that mapping is a supplemental technique; that is, it is not a substitute for careful reading, nor is it intended as a "shortcut"ù; it is meant to engage the student and quicken their look-backs into the text.
The student and I also read short passages to use context clues skills. He read two passages silently. Each passage required him to fill-in two missing words in the passage. He answered the questions correctly.
Next, I asked the student to read two passages that required him to use the context of the paragraph to define the meaning of a bold-type word. He answered the questions correctly.
I discussed the features of good descriptive writing with the student and gave him a model descriptive paragraph built from two general, "telling"ù statements. I had prepared a packet for him; the packet was centered around the idea that good descriptive writing "shows"ù instead of "tells"ù; this means that descriptive writing describes something in a way that the reader can visualize it, or imagine touching it, tasting it, listening to it. I started with three statements about surfing "I like surfing. It is fun. It is truly a unique experience."ù After reading these statements, I asked the student if he found the statements boring. He confirmed his disinterest, and I reciprocated it with the caution that boring writing is always discarded by readers; The three statements tell the reader that surfing is fun, but do nothing to describe it or explain why it is fun. I told the student, "After reading a good paragraph about surfing, the reader should be inspired to surf, to measure their own experience against the writer's experience."ù I laid out a few features of descriptive writing for him, each focused on how to use a specific part of speech (e.g., use concrete nouns: nouns that refer to things the reader can really interact with, instead of abstract words like experience. Verbs should describe actions and help the reader visualize the action of the storyteller; avoid overusing "to be"ù verbs; if you do use a "to be"ù verb make sure it is surrounded by more vivid verbs in the paragraph.) I read through two versions of the initial statements about surfing transformed into descriptive paragraphs. One version had a "to be"ù verb (was), but the verb was surrounded by better verbs "planted,"ù "split"ù etc. I asked the student to analyze, in words, what made this paragraph superior to the first three statements. His analysis pinpointed a key feature of descriptive writing: "It makes you feel like you are really surfing. I get a picture in my head."ù Descriptive writing doesn't need to tell about an experience; the experience is recreated by showing. The final version of the paragraph contained no "to be"ù verbs and used figurative language to create lasting images. I discussed the figurative language sentences in detail with the student. I asked him if he was familiar with similes and metaphors. He knew of similes, but was less certain about metaphors. I will be sure to address figurative language in writing in future sessions.
As a small assessment, I wrote a general, non-descriptive sentence and asked the student to write a descriptive sentence in place of it. I wrote: I saw the bear and ran.
He wrote two alternate versions of the sentence. His final version used descriptive language to create suspense about the moment of seeing the bear. I will begin the next lesson with a similar activity, and, in addition, I will email the student's mom a list of prompting questions she can ask him after reviewing his writing, if she thinks his writing needs additional details.
Note: The student sometimes writes without punctuating his sentences or forgets to capitalize the first letter at the beginning of a sentence. I will review these lessons with him, and also go over rules for using conjunctions and building complex sentences (so his writing will begin to show varied sentence structure). After he writes his next descriptive paragraph, I will edit it with him (by edit I mean check and correct grammar) to ensure he has a firm grasp on these grammar rules.
I gave the student a writing assignment to complete at home. I gave him two statements: "I like paddle boarding. It is fun." I asked him to recast the "telling"ù statements in a "showing"ù (descriptive) paragraph. I told him that I want to understand how it feels to paddle-board; I want to live the experience through his writing. I let him take home the packet we worked through during the lesson to use as a guide for his own writing.
Note: I emailed the student's mom links to three different short YouTube videos on adding fractions with different denominators. Each video shows one of three methods the student and I discussed during this lesson. I will also email a list of prompting questions for his writing assignment by Sunday, so he has had a chance to complete a draft independently."