What important physics idea is this question targeting?
This task targets if students can use the profile of a hill to determine the distance traveled while on that hill. (I)
This task informs the teacher about whether the student can interpret a position–time graph to determine displacement. (C)
This task examines reasoning about kinematics in real-world contexts through data interpretation. (V)
Which answer best describes what student A's response indicates about their physics understanding?
While the student is able to identify key points of the graph (the starting position and the ending position), they fail to take into account that the cyclist is moving away from the start and then moving towards it. (I)
They are clearly reasoning about this as a position time graph, but seem to confuse "how far they traveled" with displacement. (C)
This student is starting to connect graphical features with a story of motion over time. (V)
Which of the following options would best support Student A in being able to correctly respond to this question?
I would give different groups different 5-minute sections of the graph, and have each group re-create the shape of their section using a toy car on a ruler. We would then put them all together and discuss how far the car travels, which direction it is going, and if it is relatively fast or slow and find patterns to summarize our ideas. We could then revisit these questions maybe as an exit ticket. (C)
I would have lab groups each examine a different vocabulary term: speed, velocity, distance and displacement. We would then discuss the difference between speed and velocity, and the difference between distance and displacement before revisiting the graph and illustrating each of those ideas. (I)
I’d have each student annotate the graph in their own words and explain what they think is happening in each section.(V)
Which answer best describes what student B's response indicates about their physics understanding?
This student is applying the Pythagorean theorem to find the total distance traveled, which shows they understand that determining how far the cyclist went involves both time and distance. (I)
The student misunderstands what a position–time graph represents — they find total distance by treating segments as physical paths. (C)
This student is engaging in rich mathematical modeling and quantifying the graph through geometric reasoning. They take a unique approach, but they’re clearly interpreting visual trends in the graph and using them to construct a physical narrative.(V)
Which of the following options would best support Student B in being able to correctly respond to this question?
I would create four different cycling "stories" (like: "a bike starts from rest and slowly and steadily climbs a hill and then accelerates on the way down") and have groups create a height/distance graph and a distance/time graph for their story. We would then compare the two kinds of graphs and discuss what "up" and "down" indicate in each graph. (C)
I would tell them the cyclist is going downhill during the last section and ask them to find the elevation change and compare that to the total distance traveled. Then we would compare total distance to displacement. (I)
I’d have the student write a summary of what the graph shows in their own words and then share with a partner. (V)