This webpage provides the research products of the
"Project IMPULS" (2011-2022) at Tokyo Gakugei University.

Speed 2

Title Speed 2
Lesson Plan
Movie File of the entire Lesson Movie
Revision number 1
Author(s) Takeo Takahashi
Date 2014.09.05
School Koganei Lower Secondary School attached to Tokyo Gakugei University
Instructor Takeo Takahashi
Grade Elementary School G-6(12 years old)
Summary The teacher shows the table below showing distances and times of 2 bullet trains. He asks which one is faster, "Nozomi" or "Hayate". Students work independently on the problem. Then he takes up students' ideas. He asks why they divided time and distance by the same number. One student shows a tape diagram that indicates division of the distance into equal parts of the distance. The teacher shows the time and the distance have proportional relationships. And students shows the ways of making LCM. Lastly, the teacher defined the distance "distance per hour" by the distance traveled over 1 hour. And he mentioned the distance traveled over 1 minute is called "distance per minute". (45:05)

    Distance(km) Time(hour)
Nozomi   630     3
Hayate    480     2

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Introduction/Posing Problem The teacher shows distance and time of the bullet trains "Nozomi" and "Hayate". Then he asks which one is faster. (3:58) movie
Solving Problem Students work independently on the problem that the teacher posed. While students work on the problem, the teacher observes how each student is solving the problem, and considers in what sequence the various solution strategies may be shared and discussed. (0:33) movie
Sharing/Make Time 1h in Expressions The teacher asks for the answer first. Students share that "Hayate" is faster. Then one student shows a way that makes the time 1 hour. They share that the one that goes farther is faster if the times are equal. (3:35) movie
Sharing/Make Time 1h on Number Line The teacher asks if the students have something to add. One student shows a way of making the time 1 hour by using a double number lines diagram. She divides 3 by 3 to make 3 hours to 1 hour and also divides 630km by 3 for "Nozomi". She shows the same way for"Hayate". (2:00) movie
Sharing/Make Time 1h on Figure The teacher asks why we divided 630 by 3 but not by 4. One student shows a way of making the time 1 hour on the double number line diagram. And he says we divide 630 km into 3 equal parts. The teacher shares with the students that on the double number line, 1 hour is 210 km, and 2 hours is 420 km. (5:29) movie
Discussion/Proportional Relationships The teacher shows that we halve the distance if we halve the time and we double the distance if we double the time. He asks what we call such relationships, and students respond, "Proportional Relationships". The teacher shares that two numbers are in a proportional relationship when one number doubles and the other also doubles, when one triples and the other also triples and so on. Then he adds 1/2 times and 1/3 times too. (3:51) movie
Sharing/Make Time LCM in Expressions The teacher asks for different ideas to solve the problem. Students shows a way of using the LCM of the times. (2:55) movie
Sharing/Make Time LCM on Number Lines One student suggests using the LCM method on a double number line diagram. (2:48) movie
Summary The teacher reviews the previous lesson and reminds students about "distance per second". Then he defines "distance per hour" this time by the distance traveled over 1 hour. And he notes that distance traveled over 1 minute is called "distance per minute". (1:41) movie

Project International Math-teacher Professionalization Using Lesson Study(IMPULS)