Lesson: Bus Problem
Student
 Teacher
 Extensions
Setting the Stage
  • Have the students sit in groups
  • Hand out the student page

Doing the activity

Students should be encouraged to solve the problem in their own way. For example, if they decide to use a calculator they may get 438/30 = 14.6 or .08684 etc (See Figure 1) depending on whether they interpret 438/30 as 30 into 438 or vice versa. Actually, if I was guessing I probably would go for the incorrect interpretation since 438/30 looks so much like 


Students will usually discard the strange looking number (.068 etc.) and use the answer with a whole part (14.6). Long division done the usual way yields:
                                                          _____                            ____
30 ) 438   = 14 R 18 or 30 ) 438 = 14.6
which are also popular answers to this problem. Again, sense making is not taken into consideration when students answer 14 R 18 or 14.6 buses. To help students understand and learn more deeply the the division algorithm an activity like The Lineup: Who doesn't Belong and Why would help. 
                                                                           __
Suggested lineup: 4 รท 16, 1/4, 4.0, .25 and 16 ) 4

Debrief

 

A good solution for students still struggling with problem solving with division is to answer this question in a sensible and more understandable way like the solution below (Figure 2).



Figure 2

The student would see more clearly why 15 buses (not 14.6) are needed. Of course, this process is not as efficient as knowing what to do with the quotient after dividing, but it's a meaningful step in the right direction.