Time intervals and distances

Differences and values

Wrong Track: Speed is just distancetime, and that's all there is to it.

Right Lines: Distance is the difference between two locations along your track. To find your speed you also need a time interval, the difference between two times on the clock (when you were at the locations). So speed is calculated from difference in location along the track and difference in time (of day).

Speed is always from someone's point of view

Thinking about the learning

Where am I now? is a question that requires a position for an answer (5 kilometre north east of Worcester).

What time is it now? is a question that requires a time for an answer (12:24 on Thursday).

Repeat these questions after a journey and you'll get another position and a different time.

To find a speed you need to combine the two positions, and maybe some more information to find the distance covered on your journey, as well as combine the two clock readings to find the duration of your journey.

Thinking about the teaching

Trying to cut corners to make things simpler often stores up difficulties for the future. This is a place to take care. We'd suggest that you avoid using just time, unless you mean time of day. Avoid What's the time for that journey?, replacing it with something more natural:

Teacher: How long did the journey take?

This kind of phrasing implies a duration, an interval of time. Distance is less of an issue, as we're less likely to use the word to mean many things, as we do for time (which is often used to mean interval of time as well as time on the clock).

We'd suggest that you guide conversations with the following precisely-worded calculations in mind (although this is private, probably not to be shared explicitly with pupils).

distance = position_end − position_begin

duration = time_end − time_begin

speed_average = distanceduration

Then, and perhaps only then, can you use relationships like these with some confidence that you'll be communicating clearly:

speed = distancetime

Or, perhaps, more helpfully:

speed = distanceduration