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Name of Task: Tongue Twister Task: Three witches wished three wishes, but which witch wished which wish.* Your Task: In your small groups, collect and organize data that will help you develop a function, f(x), that models the relationship between the number of times this tongue twister is spoken and the smallest total time it takes to say it. Then use your f(x) to predict: 1. f(35) 2. x if f(x) = 70 Some preliminary questions to discuss in your groups: What clarifying or simplifying assumptions, if any, are you making about this task? Do you expect the function to be linear, exponential, or neither? How will you collect and organize your data? How will you use your data to create a function that models the relationship? What does f(35) mean in the context of this task? What does x if f(x) = 70 mean in the context of this task? Your write-up for this task should include: 1. 2. 3. 4. 5. 6. Written answers to the preliminary questions Any tables and graphs you used, Details about how you used data to mathematically develop your function. Your function (clearly marked) Predictions for the two values (clearly marked) After the predictions are tested in class, write a paragraph accounting for any differences between your predictions and the actual measurements. Extension: Explore how the function would be if different if you modified the tongue twister procedure as follows: The first person says the tongue twister once, the second twice, the third four times, and so on. Find the time required as a function of the number of people. *Substitute any tongue twister of your choice. 1 Alignment to Content Standards: Alignment to Practice Standards: Mathematical Goals: What do you want students to know and understand about mathematics as a result of this lesson? Prerequisite Knowledge: What definitions, concepts, or ideas do students need to know to begin to work on the task? Accessing Prior Knowledge: What questions will you ask to help students access their prior knowledge and relevant life and cultural experiences? Task Solutions: What are all the ways the task can be solved? Anticipated Student Solutions: Which of these methods do you think your students will use? Anticipating Misconceptions: What misconceptions might students have? What errors might students make? Resources/Tools: What resources or tools will students have to use in their work that will give them entry into, and help them reason through, the task? Structure: How will the students work—independently, in small groups, or in pairs—to explore this task? How long will they work individually or in small groups or pairs? Will students be partnered in a specific way? If so, in what way? Questions that Assess and Advance Student Learning: How will you help a group get started on the task? How will you focus student thinking on the key mathematical ideas in the task? How will you assess student understanding of key mathematical ideas, problem-solving strategies, or the representations? How will you advance student understanding of the mathematical ideas? How will you encourage all students to share their thinking with others or to assess their understanding of their peers’ ideas? Reminder: The questions you ask should keep the task at a high level, not push kids toward a particular solution path, turning the task into an opportunity to practice procedures. Selection: Sequencing: What solution paths do you want to have shared In what order will the solutions be presented? during the class discussion? Why? Connect: What specific questions will you ask so that students: Make sense of the mathematical ideas you want them to learn? Expand on, debate, question, the solutions being shared? Make connections among the different strategies that are presented? Look for patterns? Begin to form generalizations? Extensions of the Task: What will you do tomorrow that will build on this lesson? 2