# How to calculate speed using ratio notation

Whenever I teach how to calculate speed as a measure of distance and time I either use the formula or the triangle method.  In my experience most students are know about the triangle method from their science lessons.  For this reason I would have expected speed to appear either within the algebra or shape and measures strands of the new syllabus.   Calculating speed and other compound measures is now in the ratio, proportion and rates of change strand of the key stage 3 syllabus.  So I wondered if there was a different, more conceptual way of teaching how to calculate speed using ratio notation.  I discovered there was.

Using the formula

Using the triangle method

##### Writing speed as a ratio of distance to time

If we think of speed as a measure of distance covered per unit of time the ratio becomes simple and links nicely to writing ratios in the form 1 : n.  In the starter students are asked to match a two part ratio with its equivalent ratio given in the form 1 : n.  As this is prerequisite knowledge for the remainder of the lesson I have the class attempt this on mini-whiteboards with the multipliers clearly shown as part of their working.

##### How to calculate speed using ratio notation

In the development phase we discuss speed as the change in distance for a fixed period of time.  When the distance is given in metres the unit of time is per second and for kilometres or miles it is per hour.  Therefore, speed can be written as the ratio of distance to unit of time.

Once students are able to calculate a speed we move on to finding the time or distance using the same ratio notation.

My motivation for teaching this approach of how to calculate speed using ratio notation was mostly out of interest.  I didn’t really expect it to change my practise but as I watched the students work through the questions it became apparent how comfortable they were using ratio notation compared to rearranging formulae or using the triangle.  Teaching speed in this way gave ratio a practical context and reinforced their understanding of equivalence and proportional reasoning.

##### Is this the preferred method for teaching speed?

As I write this I do wonder whether most teachers have been using this method for a while and I’m preaching to the choir.  Having been a teacher for 15 years I’m always delighted to find new and interesting ways of teaching things especially when they fit so nicely with a conceptual way of learning mathematics.

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