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Studying Classroom Teaching as a Medium for Professional Development: Proceedings of a U.S.-Japan Workshop (2002)

Chapter:Appendix D: A Plan for the Lesson on Division by a Two-Digit Number

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Suggested Citation:"Appendix D: A Plan for the Lesson on Division by a Two-Digit Number." National Research Council. 2002. Studying Classroom Teaching as a Medium for Professional Development: Proceedings of a U.S.-Japan Workshop. Washington, DC: The National Academies Press. doi: 10.17226/10289.
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Suggested Citation:"Appendix D: A Plan for the Lesson on Division by a Two-Digit Number." National Research Council. 2002. Studying Classroom Teaching as a Medium for Professional Development: Proceedings of a U.S.-Japan Workshop. Washington, DC: The National Academies Press. doi: 10.17226/10289.
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Page155
Suggested Citation:"Appendix D: A Plan for the Lesson on Division by a Two-Digit Number." National Research Council. 2002. Studying Classroom Teaching as a Medium for Professional Development: Proceedings of a U.S.-Japan Workshop. Washington, DC: The National Academies Press. doi: 10.17226/10289.
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Page156

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1 ~ t- . - 1. Topic of the lesson: division by two-digit numbers. The first lesson out of nine lessons in the unit "Division".) 2. A plan for the entire unit (nine lessons) (~) Regularities of divisions (two lessons) Methods to find the answer to expressions like "128 . 16" (this lesson). Divisions by "tens" and by "hundreds." (2) Division by a two-digit number (six lessons). Dividing by a two-digit number. How to check the results of divisions. Division by a two-digit number that needs an adjustment of a supposed quotient. Stan(lar(1 algorithm for "(three-(ligit) . (two-(ligit)." (3) Summing up the unit (assessment) (two lessons). 3. Objectives of the lesson Fin(ling the methods to get the answer to the (livision "128 . 16" by students themselves. - Understanding the regularities of divisions such as, '~he answer remains the same when we divide both the divisor and dividend by the same number" or "By making a (livisor half, the answer becomes (louble." 4. Development of the lesson

Main Learning Anticipated Remarks on Activities Students' Responses Teaching Posing today's · presenting a · drawing a figure of the problem situation · talk about the previous problem problem; class activity of planting · the expression for getting the answer is bulbs on the school 'We are going to "128 - 16/' ground plant 128 bulbs of · show a picture and tulips into 16 · using a number line model to the students planters. The same · If neeclecl, ask questions number of bulbs to those students who are to be planted could not understand the in each planter. problem well; How many bulbs · what is the unknown? will be planted in · can you clraw a figure? each planter?" · what if we change the numbers in the problem? Students' · finclingoutthe way (0) By guessing · givehintstothose problem to get the answer to (1 ~ By thinking how many "16s/' are there in 128 ? students who can not solving on their the expression 128 - 16 - 16 - 16 - = 0 find a solution own 128 - 16 (a repeated subtraction) (2) By substituting numbers into the expression At x 16 =128 by turns, we can get the answer. 1 x 16 = 16,2 x 16 = 32, 3x16=8,... 8x16= 128 (3) "Divicling by 16/' means cliviclecl first by 8, anclthenLy2. 128- 16= 128-~8x21=~128-81-2= 16-2=8 (~) Divicling both cliviclencl and divisor by the same number like 2 or A. 128- 16=~128-21-~16-21=6A -8=8 (5) When the divisor is multiplied by 2, the quotient becomes half; 128 - 2 = 6A, 128 - ~ = 32. So, we can get the answer of 128 - 16 as a half of 128 - 8 APPE N DIX D · ask the students to explain how and why the methods do work · request another method for those students who got one method

Main Learning Anticipated Remarks on Activities Students' Responses Teaching Whole-class · presenting the ideas Focus on the following ideas to integrate the · pick a naive method like discussion you came up with stuclents' methocls. guessing first and listen to the · by estimating the number, find the number that other stuclents' ideas applies to the equation; using 1` x 16 = 16 x 1` · focus on the regularities Repeated subtraction falls into this iclea) of division · comparing the · thinking by two steps methods presented · using multiplication table, applying the to find the regularity (If we make the number of planters connections half, the number of bulbs also becomes half) among them · which method might be more effective? Summing up · reflecting on the · when we clivicle both the cliviclencl and divisor regularities of by the same number, the answer remains the division we found same · so, we can get the answer to division by a two- cligit number, in certain cases, by reducing it into division by a one-digit number Applications · try the other cases divisions by 12 or 18, by applying the so on regularities · 96 - 1 2 = (96 - 2) - (1 2 - 2) = AS - 6 · 96 - 12 = (96 - 3) - (12 - 31 = 32 - ~ and · give such expressions like96- 120r 1~- 18as examples APPE N DIX D

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The Mathematical Sciences Education Board (MSEB) and the U.S. National Commission on Mathematics Instruction (USNCMI) took advantage of a unique opportunity to bring educators together. In August 2000, following the Ninth International Congress on Mathematics Education (ICME-9) in Makuhari, Japan, MSEB and USNCMI capitalized on the presence of mathematics educators in attendance from the United States and Japan by holding a two and a half--day workshop on the professional development of mathematics teachers. This workshop used the expertise of the participants from the two countries to develop a better, more flexible, and more useful understanding of the knowledge that is needed to teach well and how to help teachers to obtain this knowledge. A major focus of the workshop was to discuss teachers’ opportunities in both societies -- using teaching practice as a medium for professional development. Another focus of the workshop addressed practice by considering the records of teaching, including videos of classroom lessons and cases describing teachers and their work. These proceedings reflect the activities and discussion of the workshop using both print and video to enable others to share in their experience

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