Lesson 3 of 6
Objective: SWBAT solve problems related to route finding, elapsed time, and the four operations.
My students, like all students in the west, live in cities without a subway system so I run this video of a subway train crossing a bridge to start the lesson. I ask them a to write responses to at least one of the general and one of the mathematical questions (below) in their journal.
1. Do you think you'd like riding on a subway? Why or why not?
2. Why do some cities have subways (New York, Boston, Washington, D.C.) and others (Phoenix, Miami, San Diego) don't?
3. What is the purpose of a subway?
1. Do you think travelling by subway from, for example, home to a movie theater, is faster or slower than going by car? Why?
2. Do you think walking in the city is ever faster than taking a subway?
3. How many miles per hour (what speed) do you think cars drive in our town/city? On the highway? What do you think the maximum speed of a subway might be?
There are two types of problems students will work on today, problems with elapsed time and story problems that involve multiplication, division, addition or subtraction.
If you would like to create your own problems, this interactive map makes it easy to zoom in on certain areas and stations, or use can project or print this (Metro Map (color) or this Metro Map (b&w). I prefer to have students involved in the problem creation, so this is the way I do it: I have one student pick a starting station, for example, Foggy Botton on the red line. I have another student pick and ending station, for example, Woodley Park/ Zoo, which is also on the red line. I go into the trip planner, but don't project it, as it gives the "answer". I tell them when the next train arrives and give them the total trip time. They need to calculate the end time.
Then we work through the second step, which has to do with whether or not the elapsed time is enough for certain events to occur. I create these problems on my own based on basic math facts. Examples:
If Rene can do 30 jumping jacks in one minute, how many can he do on his ride from ------ to ------. (If the subway car is empty! Otherwise that would really bother the other riders.)
Claudia writes on paragraph of her story every 8 minutes. How many paragraphs will she write on her trip from --------- to ------------.
If you'd like to go through some prepared examples, here are a few in this Guided Practice Metro Math.
Note: Some of the subway trips have a transfer. In this case, the students need to add in the time of both legs of the trip AND the time between trips that is spent waiting in the Metro station.
The word problems in the Metro Math Independent Practice require flexible, multi-step thinking on top of the computational skills. One area to watch for in particular in these multi-step problems is confusion over how to apply division. Some students are habituated to completing the calculation (for example, 3 x 5 = 15) and assuming that they are done. That's one of the many points of word stories such as these. They are not done until all components of the question have been answered. My role in this part of the lesson is to circulate and confer with students, asking them questions at their level to push their thinking further.
I ask students to share, with a partner, something about this lesson that they had a breakthrough with (e.g., didn't understand initially but persisted and understand now), something with which they are still struggling, or something they would do differently if they were teaching the lesson.