# Example Descriptions for Study Lesson Plans 1

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4 D. Instructional sequence for the unit: Example from a first grade subtraction lesson (Tsuta Elementary School, Hiroshima, Japan) Guidelines for Instruction (12 lessons) Section 1: To understand how to formulate an expression (risshiki) for subtraction when borrowing (kurisagari) is involved, and how to calculate through concrete manipulative activity... (4 lessons) 1st lesson: To think about calculation methods for subtraction when borrowing is involved (This period) 2nd lesson: To foster a better understanding of the subtraction-addition method (genkaho) by calculating 12 minus 9 (12-9). 3rd lesson: To foster a better understanding of the subtraction-subtraction method (gengenho) by calculating 13 minus 4 (13-4). 4th lesson: To learn how to select the most efficient method of subtraction depending on the given numerical values. Section 2: To apply subtraction with borrowing to different situations in problems......(3 lessons) 1st - 3rd lessons: To increase proficiency to solve problems using subtraction with borrowing when you have differences and remainders. Section 3: To make cards containing subtraction with borrowing problems and practice using the cards when calculating......(3 lessons) 1st - 3rd lessons: To master the calculation process by enjoying playing games and using the calculation cards. Section 4: Review......(2 lessons) 1st - 2nd lessons: To review what the students have learned by doing exercises. III. Lesson Information B. Goal(s) of the study lesson Example from a 2nd grade lesson (Greenwich Japanese School, Greenwich, Connecticut) 1. To solve some new problems, using knowledge acquired in the previous 8 lessons (learning to draw different triangles and quadrilaterals; distinguishing squares, rectangles, right triangles, and other plan figures; and discussing and understanding the definitions and characteristics of these figures). 2. To foster students individual motivation for learning and to excite their spirit of curiosity by letting them engage in activities that require previously learned knowledge, skills, and approaches. C. How this study lesson is related to the lesson study goal Example from a 7 th grade lesson (Greenwich Japanese School, Greenwich, Connecticut) This lesson is a higher potential lesson, which requires using the previously learned concept of measuring a sector and thinking about finding the area of the side of a cone, which has a curved surface. The majority of my students are not good at examining and thinking about solids without having concrete objects. Therefore I planned this lesson to ask the students to actually measure a model of a cone in the classroom to help each individual student to think about the problem more easily. I hope this activity will not be 4

5 carried out using student trial and error, but rather will be based on the student s previously learned knowledge. Using this knowledge and having good foresight, thinking out, and coming up with good ideas can help the students discover a higher mathematical solving process. I think this experience can be shared and jointly owned by the students. D. Process of the study lesson Example from a first grade subtraction lesson (Tsuta Elementary School, Hiroshima, Japan) Learning Activities and Questions [hatsumon] 1. Grasping the Problem Setting The other day we went leaf collecting, didn t we? What kind of leaves did you get? That s right. You collected 12 leaves from the big Ginkgo tree at the Shinto shrine and drew the faces of the people in your family on the leaves. Expected Student Reactions Red and brown leaves There were miscanthuses and persimmon trees, too. I collected chestnuts, too. The pictures turned out pretty funny. I collected so many leaves that I have some left over. Teacher Response to Student Reactions / Things to Remember Give praise to the students who did great job reporting their answers and raising their hands at various situations during the lesson. Remind the students that they collected only 12 Ginkgo leaves after they changed the location. Check out beforehand how many people are in each student's family. Evaluation* a. Are the students positively trying to recall the event? How many leaves did you use for drawing faces, Student A? How many leaves did you use for drawing faces, Student B? How many leaves did Ms. Nishi use for drawing faces? Ms. Nishi collected 10 leaves and drew 5 faces." "How many leaves are left over?" A: 4 leaves. Oh, we had a new baby the other day, so 5 leaves. B: Because my family is 4 people, so 4 leaves. Ms. Nishi: 5 leaves. 5 leaves Well, (by using fingers) it is 5 leaves. Make sure that all the students know that Ms. Nishi collected only 10 leaves. Make students understand the problem setting and the teacher is looking for students to answer the questions by using subtraction. Remind them of the supplementary numbers of 10. b. Do the students understand they can solve these problems using subtraction? c. Were the students able to solve the problem 10-5? 5

6 Did everyone have leaves left over? (Yes) there were (leaves) left over. I had a lot of leaves left over. I had 8 leaves left over. 2. Presentation of the Problem Format 1.) presenting the format and using it on previously learned subtraction situations (without regrouping) Wow, you guys are great! You were studying math even during your Life Studies (a mixture of Social Studies and Science) lesson. What kinds of calculations (of the four: addition, subtraction, multiplication or division) were you doing? Were the problems you did in your head like this one? It s great, isn t it? Well, what calculation do I need to use? Subtraction. Point out to the students that they are using arithmetic not only during the arithmetic period, but in a lot of other situations too. Based on the conversations with the students, present some subtraction problems that they already know how to solve. By reviewing these problems, help students understand the situation of the subtraction problem. ********************* collected Ginkgo leaves. And then s/he drew pictures of his/her family on the leaves. How many leaves are left over? ********************* What do you think? What should we write in the blanks? I don t know what will be in the blanks. I don t understand. It must be the name of the person who collected the leaves. They are the number of leaves collected and the picture drawn. When you present the problem, confirm what the necessary conditions are. b. Did the students understand what would be in the blanks in order to complete the problem? b. Were the students able to fill in the blanks with appropriate numbers and think about the problem? 6

7 What would you write in the blanks if it is Ms. Nishi's case" It is Ms. Nishi collected 10 Ginkgo leaves. And she drew 5 pictures of her family on the leaves. How many leaves are leftover? What is the expression (shiki) for this problem? What is the answer? It is It s 5. No, it s 5 leaves. Now let s do Ms. Tsukuda's family. Ms. Tsukuda collected 12 leaves just like everybody did. Ms. Tsukuda's family has 2 members so she drew faces on 2 leaves." "Could you make a problem with Ms. Tsukuda's family?" Do you understand? What expression did we use to get the answer? "What is the answer?" How did we find the answer? It is Ms. Tsukuda collected 12 Ginkgo leaves. And she drew 2 pictures of her family on the leaves. How many leaves are leftover? It is It is 10. I subtracted 2 from the 2 of 12. Change the numerical values in the problem little by little and confirm that you want them to use subtraction when they have a situation where they have to find the remainder. Remind them of subtraction of two digit numbers without borrowing and confirm that in this case they subtracted the numbers in the ones positions from each other to find the answer. b. Were the students able to fill in the blanks with appropriate numbers and think about the problem? c. Were the students able to do the calculation of 12-2? 2.) Using this format to set up the main problem of the lesosn Now let s do the Student C's family. How many faces did Student C draw on the leaves? C: I drew 7 faces on the leaves. 7

10 4. Polishing (Neriage) and Presenting Individual Solution Methods Please teach how you came up with the answer clearly to the other students in the classroom. Are there any other ways to find the answer? ( Why did you break 12 up into 10 and 2? ) ( Why did you break 7 up into 2 and 5? ) Yes, yes, there are. Why did you break 12 up into 10 and 2? Why did you break 7 up into 2 and 5? During the time the teacher walks around the classroom to see how the students are doing (kikanjunshi) I will take some notes on how the students are thinking. And I would like to ask the students to present in the order of (b), (c), (d). (refer to the student's expected solution methods above in the column "Expected Student Reactions") Ask the students to ask questions when they don t understand what other students presented because of lack of explanation. If the students do not ask any questions, the teacher will ask questions (so the explanation will be clear). a. Could the students present their own ideas in a loud voice? a. Could the students listen to their friends presentations carefully? b. Did the students understand there are many ways to solve subtraction problems that involve borrowing? 5. Summary and Announcement for the Next Lesson Let s try to solve 12-5 using whatever method you like. "What do you think the best way is to solve 12-9?" "Let's try to find out what method is the best in the next lesson." I will do it the same way I did it before. I wonder if the solution that K used is more convenient? I will try to do it the way that N did. I won't know until I do it. Well, I think method (b) is the best. I think method (c) is faster. I want to try to solve it. When the problem is posed, the teacher tells the students whose case they are dealing with (to be consistent with the other problems). Take notes on the students who are listening to their friends presentations and trying to solve the problem in a different way than they did before. Try to incorporate these observations into the next lesson. (Ask the students c. Could the students solve the problem using the method that they understood and agree with each other? 10

11 to write the student s name who s solution method they liked, in order to solve the practice problem in the handout) a. Will the students be motivated to learn the following lesson? Try to help and lead the students who are still using the method of subtracting numbers one by one from 12 to the method of breaking up 12 into 10 and 2 and subtracting the numbers one by one from 10 and counting the remaining numbers (because this method will lead to the way of thinking on "Subtraction-Addition" method). * Each heading alphabet (a, b, c, and d) in the column "Evaluation" corresponds to the four categories of goals for this lesson. E. Evaluation Example from a 5th grade lesson (Greenwich Japanese School, Greenwich, Connecticut) Were the students able to find many kinds of per unit quantities by using the data given to them (area of land, area of forestry, and population) Were the students able to compare, think out, and investigate the situation in Japan and the U.S, using calculated numbers? 11

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