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Speedy Sidney

Two trains set off at the same time from each end of a single straight railway line. A very fast bee starts off in front of the first train and flies continuously back and forth between the two trains. How far does Sidney fly before he is squashed between the two trains?

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A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?

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Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

Up and Across

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The problem provides a visual context in which to consider how graphs can represent horizontal and vertical movement over time.

A possible start to using the interactivity in a classroom could involve asking students to sketch the graphs in advance, before seeing the polygon(s) roll. Their suggestions could be displayed for all to see and discuss.

The pause button could be used to focus discussion on the different stages of the "journeys" and to make conjectures about what will follow.

Possible follow up questions:
  • Some graphs start at the origin and others don't. Can you explain why?
  • Some graphs have sections that are horizontal and others don't. Can you explain why?
  • Why is the horizontal speed not constant during each stage of the "journey"?

This problem is the third of three related problems.
The first two problems are How far does it move? and Speeding up, slowing down .