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Whole Unit Lesson Study −6th Grade
Mathematics:
“Proportion”− How a study
(research) lesson fits in a unit ★Recording of all lessons taught in a unit★ |
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Whole Unit Lesson Study Part II・Details −Contents
of Meetings (Record of the first lesson and its discussion)− |
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8/9(Wed.) |
Meeting 1 |
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Agenda |
Item
1: Goal of mathematics education
at our school and its relationship to the whole unit lesson study Item 2: Discussion of the unit, “proportion
and inverse proportion” Item 3: Setting up agenda for the next
meeting |
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Contents of
the discussion |
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About item 1 |
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How far the 6th grade students need to progress in
learning about the concept of “proportion and inverse proportion” ・
Helping students understand the concept of proportion using
charts, graphs, and mathematical expressions ・
Reading charts and understanding them are important skills that
are necessary not only in the field of mathematics but also other
fields. Therefore, we need to
help students foster such skills through manipulative activities. ・
Developing lessons and expanding them, focusing on the
understanding of two changing values. |
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About item 2 |
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How far do the students need to progress in learning about making
graphs? The two periods reserved
in the unit instructional plan are too short to allow the students to acquire
the skills for reading and making graphs ・
The main goal of mathematics education at our school is fostering
students’ reasoning skills and mathematical thinking abilities, therefore,
these two items should be the focus and skills for making graphs should be
selective and only the important content should be touched. ・
It is better to provide a point of view of proportion and inverse
proportion to the students. ・
It is ideal to incorporate manipulative activities for understanding
of the characteristics of proportion and inverse proportion. |
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☆ Confirmation of common understanding of item 1 and 2 |
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・
Teach proportion and inverse proportion at the same time. ・
Use charts as the center of learning activities. ・
Help the students understand the characteristics of proportion
and inverse proportion through manipulative activities. |
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About item 3 |
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All the participants of the meeting will think about how to
develop the lessons that follow the first lesson. |
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8/10(Thu.) |
Meeting
2 |
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Agenda |
Item 1: Confirmation of what they discussed
during the last meeting Item 2: About the instructional plan |
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(1)
How to deal with
proportion and inverse proportion. (2)
About
experiments that students conduct during the second lesson. (3)
When to
summarize the characteristics of proportion Item 3: Confirmation of homework for the next
meeting. |
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Contents of the discussion |
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About item 2(1) |
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Do not include the topic of “inverse proportion” in this unit and
focus on only the topic of “proportion” and develop the unit instructional
plan. ・
The main characteristic of proportion that the students need to
understand is regular (constant) changes of two values. |
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About item 2(2) |
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Is it necessary to have experiments during the second lesson? ・
Experiments should be done during science lessons and students
need to focus instead on investigating values. ・
It is okay to do experiments; creating charts is a necessary and
meaningful activity for students’ learning. |
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About item 2(3) |
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It is necessary to think about how far do we want the students to
understand the characteristics of proportion. |
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About item 3 |
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Think about “hatsumon” (a question or action that promotes
students’ active thinking) to include during the introduction of the lesson. ・
Make a list of as many two-value relationship that look like
“proportion” but actually are not |
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☆ Confirmation of common understanding of item 2(1) |
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Focus on only one kind of relationship between two values, i.e.
“one value increases and the other value also
increases,” (increase–increase two-value relationship) and ask students to
find the rules of the relationship. ・
This unit will deal with only “proportion.” (“Inverse proportion” will be taught
some other time in a different unit. ・
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☆ Confirmation of common understanding of item 2(2) |
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Lesson 1: Ask students to find as many “increase-increase two-value
relationship” as possible. Lesson 2: Conduct experiments with weights and
springs. Summarize the results
in the charts and make a list of insights gained from the charts. Lesson 3: Investigate the characteristics of
“proportion.” Lesson 4: Solve application problems on “proportion” |
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☆ Confirmation of common understanding of item 2(3) |
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Help the students to understand the characteristics of
“proportion” in a certain order.
The mathematical expression that describes the relationship of
“proportion” will not be introduced until the end. |
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※ We developed an instructional
plan for this unit based on the contents of discussions from the two
meetings. |
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Instructional Plan(11 lessons) |
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Small Units |
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Goal |
Development |
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Phase 1: Finding many different functions (relationship
between two values). (1 lesson) |
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○ Be able to find
increase–increase two-value relationship |
○ The students will be asked to look for phenomena that shows
increase–increase two-value relationship from their surroundings. |
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Phase 2: Finding out the relationship between the
stretch rate of a spring and the number of weights. (2 lessons) |
A B |
○ Be able to make
charts with dates collected from the experiment. ○ Students will
enthusiastically try to find rules of the relationship between the stretch
rate of a spring and the number of weights from the charts they create. |
○ Investigating the relationship between the stretch rate of a
spring and number of weights during the experiment and create charts using
the data collected. |
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Phase 3: Investigating other kinds of two-value
relationships by thinking about or comparing with the rules that the students
discovered through the experiment with springs and weights (4 lessons) |
C D E F |
○ Be able to
create charts based on many different relationships between values. ○ Be able to find
the relationship between values from charts. ○ Be able to
understand the relationship between two values: i.e.,when value x increases
by 2 times or 3 times the corresponding value of Y also increases by 2 times
and 3 times. ○ Be able to
write expressions to show a
“proportion.” |
○ Develop charts
with data and identify a chart that shows the same kind of relationship as
the relationship of two values that they studied during the previous lesson. ○ Think about the
reasons why we can say the relationship between two values showed on two
charts are similar. ○ Through
comparative activities, the teachers help the students organize the meaning
and characteristics of proportion.
The teacher also helps them think about or develop expressions that
show the proportional relationships. |
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Graphs of
“proportion” (2 lessons) |
G H |
○ Be able to show
proportional relationships on graphs. ○ Be able to
understand a graph of “proportion”:
They are |
○ Show
“proportion” on a graph. ○ Think about the characteristics of graphs of proportion. |
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Phase 4: Exercise problems dealing with “proportion” |
I J |
○ Make sure the
students learned the contents of this unit. |
○ Do the exercise
problems in the text book and aid materials. |
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8/17(Thu.) |
Meeting 3 |
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Agenda |
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Item 1: Confirmation of what they discussed. Item 2:
Discuss the introduction section of the first lesson. |
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Contents of the discussion |
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About Item 2 |
・
We will ask students to put away their textbooks. Presenting some
kind of picture/diagram to the students to provoke images of changes of two
values. ・
Example of phenomena should be coming from the students’ school
life in order for them to associate the learning activity with their real
life, which is more meaningful for them. ・
We should not limited ourselves to only the phenomena that show
the proportional relationship of two values. We should include other kinds.. | |||||||