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Domain: Operations and Algebraic Thinking Standard Code: K.OA.3 Teacher Name: Salem Hills CCA Task Title: My Pretty Garden 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 What are your mathematical goals for Students will show multiple ways for the number ten to be decomposed into two parts, and then draw the lesson? (i.e., what do you want students to know and understand about a representation 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? Expectation: Use manipulatives to explore combinations of number and then represent one solution pictorially. Materials needed: Paper, crayons, pencil Make available a variety of manipulatives (such as two-color counters, connecting cubes, etc) Students should work independently, creating their own product. Product: Student will represent their solutions using drawings and/or equations. Background Knowledge: Discuss the types of gardens the students have seen. Task: “Shaylin is planting a garden and wants to have 10 flowers. Some are red and some are yellow. What might her garden look like?” PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK As students work independently or in Explore: Students will explore ways to make combinations of ten, then will choose one small groups, what questions will you combination and represent it on paper as flowers in a garden. Illustrations should include an ask to— equation. Teacher is circulating to assess understanding and is asking leading questions to further help a group get started or make understanding. progress on the task? focus students’ thinking on the - What could you use to help you figure out this problem? key mathematical ideas in the - If your fingers/counters/crayons are flowers, how many of them are red and how many are task? yellow? assess students’ understanding of key mathematical ideas, problem- - How did you know (blank number of flowers) were red? - How did you get that answer? (Did you use manipulatives? Fingers? Addition/subtraction?) solving strategies, or the representations? 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? If students get frustrated or stuck, teacher can suggest the student count 10 two-sided counters, then have the student drop them on the table in front of them. Continue with leading questions, such, “What do you see?” Extension: - Student can find all combinations of 10 - Student can write an equation for each combination of 10 - Student can find 3 parts of 10 (ex: 3 and 3 and 4) or increase the total to a larger number PART 3: SHARING AND DISCUSSING THE TASK How will you orchestrate the class discussion so that you accomplish your As teacher observes student work, look for: mathematical goals? - Student who used/did not use manipulatives Which solution paths do you want - Student who used addition/subtraction to have shared during the - Student who used drawings class discussion? In what order will - Different combinations of 10 the solutions be presented? Why? What specific questions will you ask so that students will— Debriefing Questions: 1. make sense of the - Why did you do it that way? mathematical ideas that you - Why did you choose that manipulative? want them to learn? - Can you show us how you got started? 2. expand on, debate, and question - Did anyone else do it the same/different way? the solutions being shared? 3. make connections among the different strategies that are presented? 4. look for patterns? 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?