SWBAT calculate elapsed time on a number line.

This lesson connects calculating elapsed time in a real world setting, using actual train schedules.

10 minutes

I want to be sure certain students have a clear understanding of what is a schedule and what is the purpose of a schedule. I begin by asking the students to explain what a schedule is, what it's used for. I want to make sure they are using descriptions involving time and describing activities that occur at specific times.

Then I ask students to describe our daily schedule at school, and to help them frame this with a concrete understanding to think of what our classroom schedule looks like. The students are able to explain that our daily schedule includes starting math around 9:00, and that we go to lunch at 11:00. They are also aware of many other details including the start time for school, and the schedules for specials (art, music, computers, and physical education).

I ask the children to think about their own daily schedule, and to consider what time they get up, eat breakfast, and the schedule for after school and sports activities. The sports reference also cued students to realize they have game and practice schedules.

My next question to the class is, *"H**ow long is one of your games?"* I explain to the students they will be working on elapsed time, using a number line to calculate the elapsed time.

I then ask the students, *"How do you explain elapsed time?"* The responses include, "It starts at one time and then it ends," "When you get up and when you go to school," "What time something begins, and then the next thing begins." One student explains it as, "The time from one place to the next." Since we are going to be using train schedules, I focus the students on this explanation to introduce the train schedule.

Students in my class live in an urban area, but not one with many trains. This type of schedule is unfamiliar to students, so I decide to guide them through reading a schedule together.

20 minutes

I pass out a copy of a train schedule for each student. I chose to give each student their own copy of the schedule because the printing is small, and I have some students who need larger print. I explain how the schedule shows train numbers, cities, and departure times from each location. Projecting the schedule really helps to navigate the explanations. I chose to use a train schedule to provide a context and a real world application of elapsed time that is emphasized by the Common Core Standards.

I begin by modeling, with instructions, how to fold a piece of white copy paper in half vertically, or hot dog style, two times. Then we do it together. The folded paper creates narrow sections that divide the work space into columns.

I ask students to locate two times on the train schedule:

- The departure time of the first train leaving from Elburn (I deliberately select the first town).
- That train's arrival time in Melrose Park.

Using an open number line drawn on the board, this elapsed time problem is solved together using the friendly numbers that fall between 4:48 and 5:43. As a class we added using these increments:

- 4:48 + :02
- 4:50 + :10
- 5:00 + :43

The students then add the total minutes to calculate the elapsed time of 53 minutes between the two stops.

I then ask the students to determine the travel time from Melrose Park to the Olgilvie Transportation Center, on the same train. This train arrives at 6:28.

Some of the students create a second number line, due to space limitations, others chose to keep the two problems separate for their own organization and understanding. A few students continue the same number line. The friendly number intervals we create to calculate elapsed time for this journey are:

- 5:43 + :02
- 5:45 + :15
- 6:00 + :10

Students are then asked to determine the elapsed time for the entire train ride from Elburn to the Olgilvie Transportation Center. The students are adding 45 minutes and 27 minutes to find a time of 82 minutes. This allows for discussion about how we write this using hours and minutes.

The students, due to prior lessons, are able to explain that there are 60 minutes in an hour.

82 minutes minus 60 minutes is 22 minutes. The elapsed time would be one hour and twenty-two minutes.

15 minutes

I ask the students to look at the train schedule for train number 32. I explain to the students I need to know which train is faster so I can compare the elapsed times.

The students create new number lines, using the same strategy of moving to a friendly number to make it easier to add. A few of my students add:

- 7:11 + 1:00
- 8:11 + 0:12

Other students add:

- 7:11 + 0:04
- 7:15 + 0:45
- 8:00 + 0:23

Although the two strategies are both correct, the students using the first example are able to complete the task more quickly. Their comparison was that the second train was a faster trip between the two locations.

5 minutes

Now students work independently. I give them the choice of selecting the train stops and trains. They are to calculate the elapsed time and record the number line on their paper. The students choose a partner to work with in class, and this allows them the opportunity to talk through the steps and process their thinking with another student.