Name: Lee Arthur
Student Exploration: Distance-Time Graphs
Vocabulary: speed, y-intercept
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)Max
ran 50 meters in 10 seconds. Molly ran 30 meters in 5 seconds.
1. Who ran farther, Max or Molly? Max
2. Who ran faster? Molly. Explain: Molly had covered the distance at a higher rate of work than max.
This is as 30m/5 seconds = 6m/s, whilst 50m/10 seconds = 5m/s. 6m/s > 5m/s
Gizmo Warm-up
The Distance-Time Graphs Gizmo shows a graph and a runner
on a track. You can control the motion of the runnerby
manipulating the graph (drag the red dots).
Check that Number of points is 2, and that under Runner1 both
Show graph and Show animation are turned on.
The graph should look like the one shown to the right –one
point at (0, 0) and the other point at (4, 40).
1. Click the green Start button on the stopwatch.
What happens? Runner 1 (red) starts running, with the
graph displaying the distance he covered relative to the time.
2. Click the red Reset button on the stopwatch. The vertical green probe on the graph allows you to
see a snapshot of the runner at any point in time. Drag it back and forth. As you do, watch the
runner and the stopwatch.
A. What was the position of the runner at 1 second? 10 meters.
B. What are the coordinates of the point on the graph that tells you this? (1, 10)
C. When was the runner on the 30-meter line? 3 seconds.
D. What are the coordinates of the point on the graph that tells you this? (3,30)
2019
, Get the Gizmo ready:
Activity A:
• Click the red Reset button on the stopwatch.
Runner position
• Be sure the Number of points is 2.
In the Gizmo, run the “race” many times with a variety of different graphs. (The red points on thegraph can
be dragged vertically.) Pay attention to what the graph tells you about the runner.
1. If a distance-time graph contains the point (4, 15), what does that tell you about the runner?(Be
specific, and answer in a complete sentence.) As the x coordinate represents the time spent running
and the y coordinate represents the meters ran, this shows that in 4 seconds(x=4) the runner ran 15
meters (y=15). This gives us a speed of 15m/4s = 3.75m/s.
2. Look at the graph to the right. Notice where the green probeis. If
you could see the runner and the stopwatch at this moment, what
would you see?
The runner would be running backwards, and would
currently be at the 20 meter mark.
3. Look at the image below, from the Gizmo. What must be true about this runner’s graph?
X= 3.25, y= (approx.) 21
4. The point on the graph that lies on the y-axis (vertical axis) is called the y-intercept. Whatdoes the
y-intercept tell you about the runner?
Their starting point, as the y intercept has the x value of zero. Therefore, the runner has notran at all.
5. In the Gizmo, set the Number of points to 3. Then create a
graph of a runner who starts at the 20-meter line, runs to the
40-meter line, and finishes at the 30-meter line.
A. Sketch your graph to the right.
2019
Student Exploration: Distance-Time Graphs
Vocabulary: speed, y-intercept
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)Max
ran 50 meters in 10 seconds. Molly ran 30 meters in 5 seconds.
1. Who ran farther, Max or Molly? Max
2. Who ran faster? Molly. Explain: Molly had covered the distance at a higher rate of work than max.
This is as 30m/5 seconds = 6m/s, whilst 50m/10 seconds = 5m/s. 6m/s > 5m/s
Gizmo Warm-up
The Distance-Time Graphs Gizmo shows a graph and a runner
on a track. You can control the motion of the runnerby
manipulating the graph (drag the red dots).
Check that Number of points is 2, and that under Runner1 both
Show graph and Show animation are turned on.
The graph should look like the one shown to the right –one
point at (0, 0) and the other point at (4, 40).
1. Click the green Start button on the stopwatch.
What happens? Runner 1 (red) starts running, with the
graph displaying the distance he covered relative to the time.
2. Click the red Reset button on the stopwatch. The vertical green probe on the graph allows you to
see a snapshot of the runner at any point in time. Drag it back and forth. As you do, watch the
runner and the stopwatch.
A. What was the position of the runner at 1 second? 10 meters.
B. What are the coordinates of the point on the graph that tells you this? (1, 10)
C. When was the runner on the 30-meter line? 3 seconds.
D. What are the coordinates of the point on the graph that tells you this? (3,30)
2019
, Get the Gizmo ready:
Activity A:
• Click the red Reset button on the stopwatch.
Runner position
• Be sure the Number of points is 2.
In the Gizmo, run the “race” many times with a variety of different graphs. (The red points on thegraph can
be dragged vertically.) Pay attention to what the graph tells you about the runner.
1. If a distance-time graph contains the point (4, 15), what does that tell you about the runner?(Be
specific, and answer in a complete sentence.) As the x coordinate represents the time spent running
and the y coordinate represents the meters ran, this shows that in 4 seconds(x=4) the runner ran 15
meters (y=15). This gives us a speed of 15m/4s = 3.75m/s.
2. Look at the graph to the right. Notice where the green probeis. If
you could see the runner and the stopwatch at this moment, what
would you see?
The runner would be running backwards, and would
currently be at the 20 meter mark.
3. Look at the image below, from the Gizmo. What must be true about this runner’s graph?
X= 3.25, y= (approx.) 21
4. The point on the graph that lies on the y-axis (vertical axis) is called the y-intercept. Whatdoes the
y-intercept tell you about the runner?
Their starting point, as the y intercept has the x value of zero. Therefore, the runner has notran at all.
5. In the Gizmo, set the Number of points to 3. Then create a
graph of a runner who starts at the 20-meter line, runs to the
40-meter line, and finishes at the 30-meter line.
A. Sketch your graph to the right.
2019
