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) 

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) 

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) 

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) 

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) 

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) 

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) 

Sharing/Make Time LCM on Number Lines 
One student suggests using the LCM method on a double number line diagram. (2:48) 

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) 
