**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.

**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.

**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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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