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
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.
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.
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.
When learning how to simplify surds students need to understand the difference between a rational and irrational number. Rational numbers include integers and terminating and repeating decimals. They can be written as a fraction with both the numerator and denominator as integers. An irrational number is a number which, in its decimal form does not […]
There are three common methods for sharing an amount to a given ratio. Depending on the age group and ability range I am teaching I would choose one approach over the other two. The three methods are: Using fractions Unitary method Using a table In this blog I will demonstrate each of the three methods […]
To introduce plotting scatter graphs and understanding correlation I ask students to think about the relationships between different variables and to describe how they might be related. Here’s my starter activity which students discuss in pairs then present to me on mini-whiteboards. When the students have had time to discuss the matching pairs we talk […]