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Lesson Plan (PDF)
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Lesson Video (Quicktime)
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List of Episodes (PDF)
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You may download the above files for your own use (information)
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This lesson study features a 50 minute lesson given at Sapporo City Maruyama Elementary School in a class of 40 third grade students. It is one of a sequence of lessons.It is the fourth of a sequence of 13 lessons. The preceding lesson considered the product 20 times 3 and the children were encouraged to calculate the number of black circles in the array below. In the figure the total is (10 times 3) plus (10 times 3), which is 30+30, giving 60.
The current lesson is planned in detail in the Lesson Plan (above) and sets out to encourage children to use their previous knowledge to solve a problem to calculate how many circles in a new array (which they will find is 23 times 3). The plan is to find different methods for doing this, to consider which are complicated and which are easier and, if any child suggests column multiplication, to link this into the practical activities with 3 rows of 23 black circles. The longer term goal is to make the children aware of the advantages of column multiplication building from meaningful experience related to practical examples.
Note how the teacher starts at the left-hand side of the board with the problem, writes up the development of the lesson, circling important points in yellow, so that the whole lesson structure is seen on the board at the end of the lesson.
| In the current lesson, Mr Muramato introduces the new problem, as the children attempt to predict what it is, based on their previous experience.
The problem is presented in the clip and at the end, the children expect a smaller copy for them to calculate. |
The problem: start 01:58, length 1:20. |
| After establishing the problem is to calculate 23x3, the children are encouraged to work on their own. Mr Muramato walks around as they work for about five minutes. He establishes who has finished and who has not, and then invites children to explain their ideas. Initially all the ideas relate to subdivision of 23 either into 20 plus 3 or 10 plus 10 plus 3. The clip shows the first response. | Amon sees 23 as 20+3 : start 10:45, length 2:18. |
| Every response is greeted with approval, except possibly one boy, who sees the whole array as 30+30+9. Although he has ‘seen’ the whole problem as two sub-arrays of ‘3 rows of 10’ being 30 and a sub array of 3 rows of 3 being 9, he is told quietly that he hasn’t finished yet and must write it all down. | Amano ‘not finished’: start 21:56, length 1' 10" |
| One response suggests that the 2 in 23 can be considered as 2 ten-yen coins. | Using 10-yen coins: start 25:18, length 2:00 |
| After some seventeen minutes devoted to examples of splitting 23 into 20, 3 or 10, 10, 3, one child suggests that no-one has proposed anything different. | I noticed something: start 33:53, length 1' 2" |
| After this intervention, several different possibilities are suggested, including 11+12, 9+9+5 and 11+11+1. The teacher encourages the children to talk through each one. The clip shows the complication of the split into 9+9+5. | 3x9, 3x9, 3x5: start 38' 13", length 2:15 |
| The teacher has found that some children have used the standard vertical form of laying out the problem. He encourages one of them to explain her idea. He then links the vertical form to the other methods using pictures and places a picture by the vertical sum for direct comparison. After this there is a 5 minute session summarizing the lesson in which Mr Muramato gets the children to read the purpose of the lesson from the board and to suggest a form of words to describe the lesson. The whole board is laid out from left to right with the main ideas of the lesson enabling the children to see the full argument and to make their own notes. |
vertical form: start 42:08, length 4' 2" |