Multiplication Algorithm Grade 3 (Japan)

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Hideyuki Muramoto's lesson for 3rd grade on Multiplication Algorithm in Japan was captured on video for an APEC Education Network (EDNET) project called Classroom Innovations through Lesson Study. The lesson is an example of using the Lesson Study process of professional development in the teaching of Mathematics. The lesson plan and full lesson video are available below. Video highlights with descriptions and analysis are available at the end of this page.

Lesson Overview

The lesson was taught by Hideyuki Muramoto with support of Kazuyoshi Okubo. The CRICED, University of Tskuba, owns the copyright of the Lesson Plan and the Full Lesson video. The Full Lesson Video was directed by Masami Isoda and the List of Episodes and clips were developed by David Tall. This 50-minute research lesson was presented at Sapporo City Maruyama Elementary School to a class of 40 third grade students. 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 to the practical activities. The longer-term goal is to make the children aware of the advantages of column multiplication building from meaningful experience related to practical examples.

[High Performing Economy Dotblue.jpg] [Demonstration Practice Dotpurple.jpg] (see Resource Types)

Lesson Plan

Lesson Video in Quicktime

(Video Clips and Highlights Available below)

   List of Episodes 

Key Points:

  • The array method offers a powerful visual approach to explain multiplication in terms of groups of items. The above example shows that 60 can be expressed as 20 groups of 3 items or 3 groups of 20 items, which also illustrates the commutative property of multiplication. In this problem, the challenge is for the students to show an array that represents 63.   
  • 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.

Video Clips and Highlights from the Lesson

The video clips are selected from the full List of Episodes. The Full Lesson Video may be downloaded for further study. The streaming video version requires Adobe Flash (free download at Flash).

The following video is an example of a research lesson used during the lesson study cycle. Wiki users may use this video to experience a part of the cycle and can hold a post-lesson discussion with their colleagues after watching this video to continue the lesson study process.

Description of Video Clip

Video Links

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 of the problem for them to calculate the number required.

The problem (video 1 of 7): 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 (video 2 of 7): start 16:45, 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’ (video 3 of 7): 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 (video 4 of 7): 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 (video 5 of 7): start 33:53, length 1:02

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 (video 6 of 7): start 38:13, length 2:15

The teacher has found that some children have used the standard vertical form of laying out the problem. In the clip, 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 the episode shown, 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 (video 7 of 7): start 42:08, length 4:02

Multiplication Algorithm Grade 3 – Teacher Hideyuki Muramoto

Back to Classroom Innovations through Lesson Study.