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Domain: Statistics & Probabiity Standard Code: 6.SP.4 & SP.5.c Teachers: Liz Roberts, Sherry Hammond, Candis Clayton Adapted from: Smith, Margaret Schwan, Victoria Bill, and Elizabeth K. Hughes. “Thinking Through a Lesson Protocol: Successfully Implementing High-Level Tasks.” Mathematics Teaching in the Middle School 14 (October 2008): 132-138. PART 1: SELECTING AND SETTING UP A MATHEMATICAL TASK Students will be able to display numerical data to give meaning; give quantitative measures (mean, What are your mathematical goals for median, center, spread, interquartile range) as well as, describe patterns and deviations. the lesson? (i.e., what do you want students to know and understand about mathematics as a result of this lesson?) What are your expectations for students as they work on and complete this task? 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? How will the students work— independently, in small groups, or in pairs—to explore this task? How will students record and report their work? How will you introduce students to the activity so as to provide access to all students while maintaining the cognitive demands of the task? Expectations: All students will be engaged and on-task. Materials/Resources/Tools: pencils, paper, task sheet, calculator, & any manipulatives students may choose to help them solve the problem. Groupings: Students will work either with partners or in groups no larger than 4. Recording: Students will record the information on their task sheet & in math journal. Launch: Questions for students— 1. How many of you have cell phones? 2. How many of you are allowed to send and receive text messages? 3. How many texts do you think you send each month? (estimate) Show a video clip of “texting grandma” http://www.youtube.com/watch?v=ySR3hpieiQc Explain story/task & give task sheets to students. PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK Sub-task A As students work independently or in What is the task asking you? small groups, what questions will you What do you already know about the task? ask to— How could you represent the data? Could you draw a picture or a graph, etc.? help a group get started or make What have we done in the past that could help you with this task? progress on the task? For struggling students: What does “unlimited texting” mean? focus students’ thinking on the Sub-task B key mathematical ideas in the How can you show the highs/lows/differences in numbers of texts each day? task? assess students’ understanding of What does average mean? How do you figure that out? key mathematical ideas, problem- What was the least number of texts and what was the most number of texts? What info is needed? What info is not needed? solving strategies, or the What have we done in the past that could help you with this task? representations? advance students’ understanding What do the parts of your picture, chart, plot mean? For struggling students: How do you make a “box & whiskers plot”? What parts do we need? of the mathematical ideas? How do we find the average? What is a quartile? What is an outlier? For advanced students, demonstrate at least one more way to represent/prove your answer(s). Sub-task C How many texts will Tina’s mom need to pay for from the month? Is there anything else the task is asking you? How will you ensure that students remain engaged in the task? See above questions. What assistance will you give or what questions will you ask a student (or group) who becomes quickly frustrated and requests more direction and guidance is solving the task? For advanced learners who finish early--Present additional task as follows: What will you do if a student (or 1. Change the number of free texting minutes to 350 per month group) finishes the task almost 2. Cost of texting 351-500 messages is $.25 immediately? How will you 3. Cost of texting from 501-up messages is $.35 extend the task so as to provide 4. Now how much money would Tina need to earn to pay her mom back? additional challenge? PART 3: SHARING AND DISCUSSING THE TASK This task could have a variety of pathways to the solution. How will you orchestrate the class discussion so that you accomplish your Students will be chosen to present and defend their solutions (based upon the methods they mathematical goals? used) to demonstrate a variety of solution pathways. Students will be asked to listen/watch Which solution paths do you want and record different methods in their math journals. to have shared during the class discussion? In what order will Solution Pathways: histogram, dot plots, box & whisker plot, algorithm, and other ideas. the solutions be presented? Why? What specific questions will you ask Order of presentation: struggling students or students with limited/basic understanding, so that students will— students with “popular” solution pathways, students demonstrating abilities to think “outside 1. make sense of the the box” or abstractly with more complex solution pathways. mathematical ideas that you want them to learn? Questions: 2. expand on, debate, and question 1. What did you know before that helped you solve this investigation? the solutions being shared? 2. Which solution pathway made the most sense to you and why? 3. make connections among the Which method was most helpful in solving the task? different strategies that are 3. How were the strategies similar? How were they different? presented? 4. What patterns did you notice? 4. look for patterns? 5. What is one more situation where you could use a box & whisker plot? 5. begin to form generalizations? What will you see or hear that lets you know that all students in the class understand the mathematical ideas that you intended for them to learn? All students need to participate during the “exploration”. Students need to recognize and use correctly median, mean, upper/lower quartiles, cluster(s), and outliers. Students need to associate quartiles with “25%” and describe the various parts of their data using appropriate vocabulary. SP.4 and SP.5.c Tina’s Texting Tragedy Sub-task A Tina’s mom is mad, really mad! She signed her daughter up for a cell phone on the family plan. She didn’t sign her up for unlimited texting. But you guessed it, Tina texted a lot. When her mom got the bill, she was furious. The bill listed the number of texts Tina sent each day. How can her mom display the data from the bill to show Tina how serious and upset she is? Number of texts sent each day Sun 17 23 20 33 30 Mon 20 17 18 14 17 Tues 22 19 34 5 39 Wed 18 15 22 10 Thur 8 17 19 45 Fri 19 7 11 17 Sat 23 38 22 26 Sub-task B What was the average number of texts Tina sent every day? Create a box-and-whiskers graph to chart the daily numbers of text messages. Show the median, upper and lower quartiles. What does each quartile represent? Identify any outliers and clusters and what they represent. Sub-task C Tina’s mom’s plan allows for 200 texts a month for free, but any texts after that cost $.25 each. How much will Tina have to earn to pay her mom for all those extra texts? How many will Tina want to limit herself to each day in the future to make sure this never happens again?