Thinking Systematically Grade 6 (Japan)
From APEC HRDWG Wiki
Teacher Atsutomo Morii's lesson “Thinking Systematically” was captured on video for the 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, and demonstrates teaching students to find the value of two quantities that satisfy two conditions. Students are asked to determine the number of pencils and ballpoint pens bought if the total number of items purchased was 10 and the total price was 460 yen. The lesson plan and full lesson video are available below. Video highlights with descriptions and analysis are available at the end of this page.
[High Performing Economy  ] [Demonstration Practice  ] (see Resource Types)
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Lesson Video in Quicktime (Coming Soon) (Video Clips and Highlights Available below) |
List of Episodes (Coming Soon) |
Lesson Goals
The goals of the lesson are for students to:
- notice that using a table helps them to understand how to solve the problem
- use a table to organize, categorize, and investigate numerical data in a logical order and
- find a pattern in the table that enables solving the problem using calculations
Selected Video Clips
The clips below are selected from the full list of episodes. The Full Lesson Video may be downloaded for further study.
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.
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Description of Video Clip |
Video Links |
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There is a short opening stage in which the teacher gives some hints to the class about what they might be doing today. He posts on the white board a picture of a pencil and a ball-point pen. He asks students what they might expect to pay for each item. Some students comment that the lesson will be about costs and possibly about total costs. |
Posing the problem (1 of 6)
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The specific problem for today’s lesson is now stated. It is posted on the board. The teacher asks students what they think needs to be done. Some students propose specific groupings of pencils and ball-point pens. After a short discussion, students agree that a table needs to be used. Setting up a table is now considered in detail. The teacher posts cards showing Number of ball-point pens, Number of pencils, and Total cost. He says, “We need a table like this.” This step ensures that everyone is on the same track. Getting the first entry involves some discussion about whether zero can be used. It is accepted that (10, 0) – ten ball-point pens and zero pencils – will be the first entry. Total cost of this combination is 700 yen. A second entry is prepared on a separate card showing (9, 1) and its total cost of 670 yen. |
Understanding the problem (2 of 6)
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Students write the problem in their notebooks and go about completing the table. Some students also complete and place on the board separate cards showing the total cost for specific ordered pairs. One incorrect entry is noted by the class and is removed from the board. |
Individual Work (3 of 6)
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This main part of the lesson concludes with the teacher checking students’ notebooks for progress on their tables, and by asking if all possible entries have been posted on the board. Several more cards need to be prepared and these are placed on the board. Some students have noticed from their own tables that the total cost falls by 30 yen as one goes from one ordered pair to the next – that is, as one less ball-point pen is replaced by a further pencil. The teacher then asks students to identify the solution to the original problem. This is given as (2, 8) – that is, two ball-point pens and eight pencils. The teacher asks if there are any other possible solutions. Someone proposes a solution involving decimal values. This kind of solution is not considered realistic. It is possible that the lesson might have ended here. |
Class Discussion (4 of 6)
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However, there is a further and final stage of the lesson that consists of reviewing the solution process. One student draws a straight-line graph relating the number of pencils and the number of ball-point pens. The teacher shows another way of making a graphical representation. At this stage the solution process is reviewed using the motto “HaKaSe” (Fast, Simple and Accurate) which students are familiar with. Students are not convinced that using a table is the quickest way of finding a solution. |
Further Discussion (HaKaSe) (5 of 6)
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Some students come up with a pair of linear equations that permit one to compute a solution once the constraints have been identified. Whether everyone understands this algorithmic approach is not discussed. This method depends on being able to use the 30 yen difference. This is where today’s lesson concludes and where it might be taken up tomorrow. |
Summary (6 of 6)
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