This activity gives students first-hand experience in relating ratios of time and distance to speed. Students time one another as they move 10 meters at a constant speed—first slowly and then quickly—and then reason about the distance traveled in 1 second.

Double number lines play a key role in helping students see how time and distance relate to constant speed —allowing them to compare how quickly two objects are moving in two ways. They can look at how long it takes to move 10 meters (a shorter time needed to move 10 meters means faster movement), or they can look at how far one travels in 1 second (a longer distance in one second means faster movement).

Along the way, students see that the language of “per” and “at this rate,” which was previously used to talk about unit price, is also relevant in the context of constant speed. They begin to use “meters per second” to express measurements of speed.

As students work, notice the different ways in which they use double number lines or other means to reason about distance traveled in one second.

Invite previously selected students to share how they reasoned about the distance traveled in 1 second. It may be helpful to discuss the appropriate amount of precision for their answers. Although dividing the distance by the elapsed time can result in a quotient with many decimal places, the nature of this activity leads to reporting an approximate answer.

During the discussion, demonstrate the use of the phrase meters per second. If it comes up naturally in students’ explanations, emphasize it. 

Discuss how we can use double number lines to distinguish faster movement from slower movement. If it hasn't already surfaced in discussion, help students see that we can compare the time it takes to travel the same distance (in this case, 10 meters) as well as the distance traveled in the same amount of time (for example, 1 second).

Explain to students that when we represent time and distance on a double number line, we are saying that the object is traveling at a constant speed or a constant rate. This means that the ratios of meters traveled to seconds elapsed (or miles traveled to hours elapsed) are equivalent the entire time the object is traveling. The object does not move faster or slower at any time. The equal intervals on the double number line show this steady rate.

In this activity, students analyze a situation in which two people travel for the same amount of time, each at a constant speed, but go different distances. The use of double number lines is suggested, but not required.

Monitor students’ work and notice the different ways in which students compare speeds. For the first question, students may use meters per second or compare the distance traveled in the same number of seconds. For the last question, they may draw a double number line for each of the scenarios being compared, or calculate each speed in meters per second.

In the digital version of the activity, students can choose to use an applet to create double number lines to represent given quantities, explore the problems, and solidify their thinking. The applet is the same as the one in an earlier lesson about grocery shopping.

Select students who reasoned differently to share their thinking. Some students will know that Diego ran faster, simply because he ran farther, but this reasoning is not always correct. Han runs farther but is slower than Diego because he had more time. Be sure to attend to both distance and time when making the comparison. Help students draw connections between the different ways they represented and reasoned about the problem.

During the discussion, keep as much emphasis as possible on the concept of meters per second.