Thinking Through a Lesson Protocol (TTLP) Template s32

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 What are your mathematical goals for Students will…. the lesson? (i.e., what do you want Represent and solve multiplication equations using illustrations and use of models (e.g. arrays) 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 will use a 13ft.x13ft. Bedroom to equate and solve to find the products of each item. students as they work on and Area of each item: Bed-42 sq. ft., dresser-36 sq. ft., night stand-12sq.ft., rug-10 sq. ft., and book complete this task? shelves-24 sq. ft.  What resources or tools will students have to use in their The student will work in small groups using; graph paper, ruler, or linking cubes to complete the work that will give them following procedures. entry into, and help them 1. Choose either graph paper or linking cubes to show your work. reason through, the task? 2. Find the factors of each bedroom item that best fits the bedroom area.  How will the students work— 3. Determine which factors for each item that will be best for the bedroom with adequate walking Independently, in small groups, or space. 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 Large group discussion about items that go into a bedroom and the size of the bedroom. Student may students while maintaining the refer to their own background knowledge to visualize items in their own bedroom and participate in cognitive demands of the task? the discussion. PART 3: SHARING AND DISCUSSING THE TASK PHAowRT w 2:ill SyUPou PoORrchTINGestrate ST theUD classENTS’ EXPLORATION OF THE TASK Adiscussions students so w thatork iynodue paccenodmplishently oyourr inmathematical small gr goups,oals? what 1. Represent the area using an array. 2. Using the term for furniture in square feet. questionsWh wichill so youlution ask pto—aths do you  What shapes will fit best in the bedroom area space of 13ft.X 13ft. 3. Why is the solution of each item of furniture using comparisons greater  helpwan ta t ogr haoupve gsharedet star tdeudr oring  What are all the possible sizes for each number of bedroom items? the than or less than the bedroom area provided? make progress on the task?  List all the information you know. class discussion? In what 4. Every number represented as a rectangle.  focus students’ thinking on  How do you know you’ll have enough room for all your bedroom items? theorder will the solutions be presented? Why? key mathematical ideas  Win htheat stpaecski?fic questions will  assyoue ssask stu sod thatents’ stu dents will— 1. make sense of the understanding of mathematical ideas that key mathematical ideas, you want them to learn? problem- solving strategies, 2. expand on, debate, and or the representations? question the solutions  advance students’ being shared? understanding 3. make connections among of the mathematical ideas? the different strategies that are presented? How will4. y loouo ensk foru rpea tthatterns? students remain engaged in 1. Area of bedroom in square feet? 5. begin to form the task? 2. Area of each piece of furniture in square feet? generalizations?  What assistance will you 3. Area needed for walking space? give or what questions 4. Compare areas to answer questions. 5. Model a number in factorization. What wwillill y youou s eeask or a hear that lets 6. Model skip counting if needed. you knowstu dthatent al(orl stu grodup)ents w inho the class becomes quickly frustrated and understand the mathematical ideas thatDraw or model a visual representation of the furniture in the room. How many square you interenqduestsed for m themore d tirecto learn?ion and guidance is feet is used for walking space? 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 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.