We open with partner talk to solve how much time between now (8:49 a.m.) until we go to specials (11:15 a.m.). I chose this problem because it's real and interesting to students, and is abstract enough to challenge students when they calculate in their heads. Our classroom does not have an analog clock, and this problem allows me to introduce using a number line to make it EASY to find the elapsed time.
Student think is varied, all somewhere within an elapsed time of 2 hours to 3 hours. Based on this response, I can tell the students are looking at the hours of 8 and 11, and yet there is some confusion in determining the minutes.
We have used number lines throughout the year in my classroom, and one student asks, "Is there a way to do this on a number line?" This indicates they realize they will be adding and subtracting with time, and this was a skill we used with the number line.
Because I want students to practice calculating elapsed time on a number line, I use a flip book format to increase their interest in the task. I also gave the students the option of using colored markers for added interest.
First, I model the number line on the document camera with three examples including how much time we will be spending on math, and how much time students are out of school each day. The first example includes calculating time in minutes only, but the calculation does require computation past an hour mark. The second example includes calculating hours and minutes, including moving past midnight.
In my class we are working on math from the current time of 9:04 until 9:38. I write the current time of the our math activity at the beginning of a number line. It is important to reinforce the reason we set up a number line with 9:04 (start time) marked on the left side of the line (we are adding, so we need room to have numbers increase).
We add one minute to make a friendly number of 9:05. We then count by tens to get to 9:35. The last amount added is three minutes to get to 9:38. As each movement on the number line is made, we write the increment above the curved line jump in time format. The numbers for the jumps on the number line are then added to determine the elapsed time.
In each example, I ask the students to determine our "jumps" by asking questions about the increment to move on the number line. The first example provides them with the opportunity to move using minute and ten minute increments for the first one. The second example uses two hour, one hour, and half hour increments.
We create three scenarios, using number lines in a flip book format. I chose this format since it transforms a paper and pencil task into a more engaging activity for the students. Each scenario includes creating and determining the elapsed time using a number line, and writing a sentence to describe the context. The Common Core standards emphasize creating a real-world context, so I use scenarios similar to students' everyday lives. The scenarios include:
How long for __________
The elapsed time of a day in high school.
The length of a train ride between two stops.
Students complete the final example on their own. This student explains his process for using a number line and determining the elapsed time of the train ride.
As some of the students struggle with the last scenario involving the train. I model the problem for them using an analog display clock. This large clock is clearly marked with minute marks and five minute increments. I then ask the students to verbalize how to solve the elapsed time on a number line.
The students discover they had completed the problem differently from what I displayed and modeled for the class. This provides the students with the opportunity to share with a partner how they solved this problem. I observe students changing their solutions based on the what they had learned from their peers.