Lesson plan for Grade Six
Teacher : Tanaka Hiroshi

Subject : Feel for the way of developing mathematical lessons in which the little changes
between the “goals” are conscious
1. Unit: Connection to secondary school (extension of the unit of proportion and inverseproportion)
2. About the subject<restoration of lessons which centre on students’ “question”>
Where should we place the “goal” and “summary” in a lesson, and could they really help thestudents? These questions request serious discussion. I heard that in some areas, writing the“goal” and “summary” on the blackboard formally has become a task for teachers and has beenon the check list for developing lessons. But if we think dispassionately, it is impossible to raise
the students’ attainment by only writing down the “goal” and “summary” exactly.
Recently I have heard a lot of agony from the young teachers as they are forced to follow somefixed steps and hard to get their students excited in the class.
Depend on the exact “goal”, sometimes it would spoil the fun of the whole lesson if the teacher
writes down the “goal” first. Furthermore, sometimes students would not be able to think of themost important things if the goal has been written on the blackboard first.
Same for the “summary”, many teachers have already experienced that let students to write
down what teacher has written does not really help to develop the students’ abilities, although
their notebooks may seem to be nice. So I think there is no fixed form for how to present the“goal” and “summary”.
I wonder whether other people also feel the danger like me of developing lessons mainly by thefixed form, despite what have been researched in our country have higher quality.
Although it sounds hackneyed, if we do not treasure the process that students raise their own“questions” during the problem solving activity, explain and summary them by their own words,
we could not actually develop students’ abilities. These years private enterprises have also beenemphasizing the importance of task setting ability, because more and more new employees are
only able to deal with the work which has be given to them, lacking the ability to decide whatshould be done next by themselves. In the world of education, we should also make an effort totry to set the questions raised by students during the introduction of teaching materials as thecurrent task, and place the true “goal” from the middle of the lesson.
The students’ attainment is the ability to learn. The lessons which have been developed attachingimportance to students’ willingness, treasure the very moment when students create theirquestion.
Once more, it is required to change the concept of teaching like this.
<the goal changes little by little>
From students’ perspective, the tasks which they are dealing with keep changing during thelesson. Some of them appear while students try to understand teachers’ question, and somearise from students’ thoughts. Because these little changes of tasks that raised by the 40 students
diffuse and convergence in the classroom, teachers are required to have a high level of skill indeveloping the lesson. As specialists of education, teachers should be conscious of these changes.
If teachers are conscious of this, they would try to develop the lesson while checking the littlechanges of “goal”. With this consciousness, teachers would make sure that students who seem tobe falling behind could also join in the activity. I think lessons that developed with theconsciousness of these “little changes of goals” are able to deal with students’ individual
differences and ability differences.
3. About the learning in this lesson
For the sixth grade, we have finished the contents of textbooks and enter the period of summaryand extension after the middle of February. The textbook which our school used has the thirdbook as the connection to secondary school. I designed this lesson to confirm the position of thelearning of proportion and inverse proportion by examine various phenomenon of functional
relations, as the extension of the unit of proportion and inverse proportion.
4. The development of this lesson
Objective of this lesson:
Know that there are lots of rules behind the phenomenon that one number changes following
another one, in addition to proportion and inverse proportion. And be able to summarize thesame and different points of each one.
learning activities

teacher’s role in supporting the activities

1. Think of the rule of the changes
2 → ？ → 4
T : “If I put 4 into this box, what number willcome out?”
S: “Maybe 6?”
S: “Maybe 8?”
S: “It should be 16, isn’t it?”
2. Investigate every caseExample: 6 comes out after 4 has been putted
in
0

12

3456

7

2

3456789

T: “Under what condition would the numberschange like this?”
S: think of the concrete case
3. Find out that there are different graphs witha same pair of numbers
01

2
4

3

4
2

56

7

Have the students understood that thenumbers change by the same rule in the box?
Is every student aware of the fact that there
are several kinds of rules could change 2 to 4?

Could the students recall some specificrelationships from the completed graph? Infact, some of them have been learned before.
Students can look up in their notebook.
This is the first time that students see
relationships like get 2 from 0.
From different viewpoint, the phenomenon
that one number increase and the other one
decrease could be thought different.
It could be thought that they have a fixed
produce like inverse proportion or have a fixedsum.
Maybe some students do not feel like creating
inverse proportion relationship from numbersin this case. But I want them to review theirlearning.