Homework # 2 Part One: Read the classroom vignette below, take some time to reflect on what you read. Draw or attach a picture that best represents the thoughts during your reflection. Students in a first-grade class with no previous experience with fractions are given the following problem. Sherelle and Tyrone got 7 brownies at school. Miss Carolyn told them that they could share the brownies as long as they each got the same amount. How many brownies would each person get? The teacher printed the problem on a piece of paper for each child. Everyone had a pencil but no other materials. She read the problem several times for the children. After about two minutes, Johnetta, had something to say. Johnetta: This is impossible! They are going to have to give the brownies back. Ms. Murphy: Why do you think that? Johnetta: Either Sherelle gets more or Tyrone gets more and Miss Carolyn said they had to be the same! Tommy: Miss Carolyn must have made a goof. Ms. Murphy: (holds up 7 pieces of brown construction paper that she had hidden under her chair.) Can we pretend that these are the 7 brownies? Sherelle and Tyrone, come on up here. You lucky kids are the ones who are getting the brownies, but you can only get them if you share them equally. Tyrone took the 7 pieces of construction paper from Ms. Murphy and passed them out to Sherelle and himself, until they each had 3 pieces. He had 1 piece of paper left. Tyrone: That one is left. If I take it, I have more, and if Sherelle takes it, she has more. Ms. Murphy: I wonder if it is impossible. Miss Carolyn did say that they had to have the same. I wonder if there is anything we could do? long pause in which the children don’t say anything. In our family, sometimes we don’t have enough for everyone to get a whole cookie. Like if we go to Subway and get cookies for dessert. I think those cookies are just too big and too expensive so I don’t buy one for each person. Maybe if just Dan and I are going for cookies, I might just buy one cookie. Does that ever happen in your families? The children all said yes. What do your moms do when that happens? Nadia: They break off little pieces for each person. Ms. Murphy: Yes, anything else? Simon: They give us each half. Ms. Murphy: Half --- what does that mean? Simon: Half, like if you make 1 cookie and break it into 2. Ms. Murphy: I wonder if that could help us with . . . Ava: interrupting Oh, that’s what Sherelle and Tyrone could do. Share the last one. Ms. Murphy: Tell me more about that. Ava: Is it ok if I ruin this paper? Ms. Murphy: Sure. Ava: she tries to carefully tear the paper into two equal pieces I am trying to make it the same. They could do this, make 2 little brownies and each gets 1 little brownie. Ms. Murphy: Wow, does that give you some ideas of what they could do? Ava: Yes. They could each get 3 big brownies and a little brownie. Simon: They each get 3 brownies and a half brownie. Ms. Murphy: Ava, what do you think, do they each get 3 brownies and a half brownie? Ava: Yes, that would work! Don’t forget to draw your reflection on the scenario above. Part Two: Read the chapter titled “Equal Sharing Empson” and complete a reflective reading response. • • • Part One: Summarize o In a summary, your goal is to communicate the main ideas of the article and leave out the details. (This should only require a sentence or two to complete.) Part Two: React o What did you think or feel as you read this article? ▪ What things pushed your thinking further? What did you disagree with? What questions do you have about the information presented in the article? Part Three: Synthesize o Make connections between what you read and other readings or your own experiences as a teacher or a student. ▪ Are this author’s ideas about teaching and learning similar to your own ideas and experiences? ▪ What similarities (or differences) do you see between this reading and other readings from the course? ▪ How might this reading influence your future teaching? Part Three: Build on the reading 1. Solve the problem below using two different methods (not every solution needs to be a fraction in lowest terms). 24 children want to share 8 brownies equally. How much brownie will each child get? 2. Use the terms provided in the table on page 25 and explained in the chapter to try to identify the strategy name that matches each of your solution methods in question 1. Part Four: Complete the problem below. Find the fraction of the whole rectangle (on the next page) for each numbered section. Explain how you found each answer. 1 3 2 Section 1: Fraction of the whole ____________ Explanation . . . Section 2: Fraction of the whole ____________ Explanation . . . Section 3: Fraction of the whole ____________ Explanation . . . Part Five: The following question was given to a class. Use the answers below, lettered a-e, to answer the questions, numbered 1-5. Five children want to share 13 cupcakes equally. How much cupcake should each child get? 1. Choose two of the answers below. Say if they are correct or incorrect. a. 13/5 b. 2 + ½ + a little more c. 2 + 1/5 + 1/5 + 1/5 d. 2 + 1/2 + 1/10 e. 2 + 3/5 2. Explain how they may have come up with the given solution. You may use any representation (example: picture, number line…) to help in your explanation. 3. List at least two ideas they misunderstood or understood. 4. Research and list two misconceptions associated with this topic. Please reference your information source. 5. Write two question you would ask to further the peers thinking?
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