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Domain: Operations and Algebraic Thinking Standard Code: 4.0A.1 What’s in your Bedroom? Teacher Name: Rochelle Nyberg, T.aysha Bundy, Kathy Miles, Muretta Grimm 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…. What are your mathematical goals for Represent and solve multiplication equations using illustrations and use of models (e.g. arrays) the lesson? (i.e., what do you want Students to know and understand about Find factors of each bedroom items. 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? Students will use a 13ft.x13ft. Bedroom to equate and solve to find the products of each item. Area of each item: Bed-42 sq. ft., dresser-36 sq. ft., night stand-12sq.ft., rug-10 sq. ft., and book shelves-24 sq. ft. The student will work in small groups using; graph paper, ruler, or linking cubes to complete the following procedures. 1. Choose either graph paper or linking cubes to show your work. 2. Find the factors of each bedroom item that best fits the bedroom area. 3. Determine which factors for each item that will be best for the bedroom with adequate walking space. Large group discussion about items that go into a bedroom and the size of the bedroom. Student may refer to their own background knowledge to visualize items in their own bedroom and participate in the discussion. PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK As students work independently or in small groups, what questions will you ask to— What shapes will fit best in the bedroom area space of 13ft.X 13ft. help a group get started or make What are all the possible sizes for each number of bedroom items? progress on the task? List all the information you know. focus students’ thinking on the How do you know you’ll have enough room for all your bedroom items? key mathematical ideas in the task? assess students’ understanding of key mathematical ideas, problemsolving strategies, or the representations? advance students’ understanding of the mathematical ideas? How will you ensure that students 1. Area of bedroom in square feet? remain engaged in the task? 2. Area of each piece of furniture in square feet? What assistance will you give or 3. Area needed for walking space? what questions will you ask a 4. Compare areas to answer questions. student (or group) who becomes 5. Model a number in factorization. quickly frustrated and requests 6. Model skip counting if needed. more direction and guidance is solving the task? What will you do if a student (or Draw or model a visual representation of the furniture in the room. How many square feet is used group) finishes the task almost for walking space? immediately? How will you extend the task so as to provide additional challenge? PART 3: SHARING AND DISCUSSING THE TASK How will you orchestrate the class discussion so that you accomplish your mathematical goals? Which solution paths do you want to have shared during the class discussion? In what order will the solutions be presented? Why? What specific questions will you ask so that students will— 1. make sense of the mathematical ideas that you want them to learn? 2. expand on, debate, and question 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? 1. Represent the area using an array. 2. Using the term for furniture in square feet. 3. Why is the solution of each item of furniture using comparisons greater than or less than the bedroom area provided? 4. Every number represented as a rectangle. What’s in Your Bedroom 1. Taysha has a square bedroom that measures 13ft. x 13ft. She recently moved and will put the following furniture pieces into her new room providing adequate walking space. Bed: 42 sq. ft. Nightstand: 12 sq. ft. Dresser: 36 sq. ft. Rug: 10 sq. ft. Bookshelf: 20 sq. ft. Variation: How many different ways can you rearrange her room? Extension: Students choose their own items in their bedroom room and solve. Answer: Room: 13x13 = 169sq.ft. Bed: 42sq.ft. Factors: 1x42, 2x21, 3x14, 6x7 Nightstand: 12sq.ft. Factors: 1x12, 2x6, 3x4 Dresser: 36sq.ft. Factors: 1x36, 2x18, 3x12, 4x9, 6x6 Rug: 10sq.ft. Factors: 1x10, 2x5 Bookshelf: 24sq.ft. Factors: 1x24, 2x12, 3x8, 4x6 Walking Space = 45sq.ft.