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Unformatted text preview: © Gloriana González and Adam Poetzel, all rights reserved Problems about Norms Read and think about all of the problems. Do #1 and then choose two of the three other problems to complete. Use the rubric about establishing norms for mathematical work to answer the questions. Submit your answers electronically through Moodle and bring a hard copy of your answers to class for discussion. 1. Mr. Bennett assigns this problem to his students in his trigonometry class on the first day. “Two vertical walls of adjacent apartment buildings were exactly 12 meters apart. Two ladders were placed in the space between the two buildings. One ladder started at the base of “wall 1” and rested 5 meters up on “wall 2.” The other ladder’s base was touching “wall 2” and rested 9 meters up on “wall 1.” How many meters above the ground did the two ladders intersect? a. Draw a diagram. b. Solve the problem. c. Anticipate two possible mistakes that students could potentially make. d. What kinds of mathematical dispositions could Mr. Bennett promote with this problem? While working on the problem in class, several opportunities presented themselves that Mr. Bennett could have possibly used to help establish some classroom behavioral and/or mathematical norms. Choose two of the situations below and script what you would say to the class in order to take advantage of the teachable moment f. Terrel shouts to Steve across the room, “Steve, do you remember how to tell if triangles are similar?” g. Emily asks if she can get a ruler and protractor to help solve the problem. h. Olivia’s group says, “We have no idea how to start the problem, we give up.” i. April explains to the class, “I started out wanting to find the one angle on the bottom so I used the TAN button on my calculator.” Andre jumps in, “Aren’t you supposed to use the SIN button with that triangle?” 1 © Gloriana González and Adam Poetzel, all rights reserved € 2. Ms. Mendoza gave asked her students in her Algebra I class wants to start a discussion about differences between graph of y = x 2 + 4 x + 1 and the graph of y = − x 2 − 4 x + 1. She thinks that it would be valuable to give students some time to work on their own before they start the discussion. €
a. What are important characteristics of the graphs that she should expect to surface in the discussion? b. What could Ms. Mendoza tell students to prepare them to work on their own? Script a few lines of what you might say to the class. c. After the discussion has ended, what kinds of habits of mind and dispositions about working with graphs could she underscore? d. Script a paragraph about what should Ms. Mendoza tell students at the end of the discussion regarding strategies for thinking about the graphs of quadratic functions. 3. On the first day in his pre
calculus class, Mr. Orr gave students a problem about exponential growth of a bacteria culture. The problem says: There are 3,000 bacteria in a culture. After 3.5 hours, the bacteria had doubled. a. Find an equation for the number of bacteria after t hours. b. What was the amount of bacteria after 15 min? c. When can you expect to have 30,000 bacteria? a. Solve the problem. b. Irene looks in the index in the back of the book, and finds the chapter on exponential growth. Then, she tells Judy, “It’s in chapter 5”. How would you use this opportunity to teach students about a classroom norm? c. Mr. Bennett hears that Johnny says to Peter, “I guess that problem is about your backpack because it is full of germs.” Sue tells Johnny, “Shut up! You are such a bully.” How would you use this situation to hold students’ accountable for their behavior? d. Script a few lines of what you might say in this situation. 2 © Gloriana González and Adam Poetzel, all rights reserved 4. Ms. Short gave her geometry students a problem on one of the first days of class. She had them work in small groups to create a context for establishing norms. The problem says: “Find the area and the perimeter of each shaded region.” 2m 2m a. Solve the problem As she walks around the class, she noticed how students are approaching the problem and some asked her questions. Script a few lines of what she might say to those students? b. Lena: “Ms. Short, do we have to show our work or can we just do it on the calculator?” c. Pablo: “Can we draw stuff on the diagram?” d. Khloe: “We think this problem can’t be done. We don’t have enough information to solve it.” 3 ...
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This note was uploaded on 12/15/2011 for the course CI 401 taught by Professor Poetzel during the Fall '11 term at University of Illinois at Urbana–Champaign.
 Fall '11
 Poetzel

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