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Domain: Standard Code 3.NF2a Teacher Name: 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-Updated Lesson for Adults Critical Area/Standard: Students will be able to represent a fraction 1/b on a number line What are your mathematical goals for diagram by defining the interval from zero to one as a whole and partitioning it into b equal the lesson? (i.e., what do you want parts. students to know and understand about Students will be able to use the number line to compare fractions. 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? Tools: Number lines, picture of a fruit smoothie, math journals, posters, markers, pencil, adding machine tape Grouping: Students will work in cooperative learning groups; “Think-Pair-Share” can be utilized during this task. Record and Report: Oral reports using the poster to demonstrate findings. Introductory Activity: Picture of a smoothie; explain that fruit juice is often used in a smoothie. Divide students into groups. Anticipatory Set: Review/Prior Knowledge: Review the number line from zero to one. Demonstrate with juice, “How many cups in a pint, quart, gallon, etc.” Actual Task/Problem/Assignment: Task: Brent uses 5/6 cup of fruit juice to make his fruit smoothie, Lauren uses 2/3 cup of fruit juice for her fruit smoothie, and Gary uses 3/4 of a cup for his fruit smoothie. Who uses the most fruit juice in their fruit smoothie? PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK Materials Number lines, picture of a fruit smoothie, math journals, posters, markers, pencil, As students work independently or in adding machine tape small groups, what questions will you ask to— Getting Started: Explain your reasoning behind the way you divided up your number line. help a group get started or make Show me….. progress on the task? Draw me a picture….. focus students’ thinking on the What does this mean….. key mathematical ideas in the task? assess students’ understanding of Assessment; students must show their work and be able to explain their thinking behind the key mathematical ideas, problemdiagram or number line. solving strategies, or the representations? Students will be able to justify their answers. advance students’ understanding of the mathematical ideas? How will you ensure that students remain engaged in the task? 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? What will you do if a student (or group) finishes the task almost immediately? How will you extend the task so as to provide additional challenge? Monitor groups as they explore. Offer suggestions if necessary. Early Finisher Options: i.e. Explain how/ why… a. Mom wants a diet smoothie with only half as much juice. Using each child’s recipe, label where the diet smoothies would fall on the number line. PART 3: SHARING AND DISCUSSING THE TASK How will you orchestrate the class discussion 1. Do you see a connection between ……. so that you accomplish your mathematical Following the activity, students will come together and debrief as a class. goals? Present solutions and justify their thinking. Which solution paths do you want to have shared during the Could you have used a different method? Explain. class discussion? In what order will the solutions be presented? Why? List other times when we would need to know how to measure a liquid. What specific questions will you ask so that students will— Students are engaged, actively participating, and able to justify their thinking. 1. make sense of the mathematical ideas that you want Task extension: The fruit smoothie recipe makes 2 cups for each person. Brent uses 5/6 cup of them to learn? fruit juice to make his fruit smoothie, Lauren uses 2/3 cup of fruit juice for her fruit smoothie. 2. expand on, debate, and question And Gary uses ¾ of a cup for his fruit smoothie. The remaining ingredients in the smoothie, the solutions being shared? ice cream and berries, are used in equal amounts. What is the amount of berries and ice cream 3. make connections among the used in each smoothie? different strategies that are presented? *Begin with the 3rd grade task and then move on to the adult question about total recipe. 4. look for patterns? (Compare and order) 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?