How would you answer the question above? How would you teach students to answer it?
What I used to do
When introducing Speed, I previously used a formula triangle much like the one below. Explained what S, D and T stand for. Completed a few examples on the board before setting some questions for students to complete themselves.
As I wander around the room, I notice lots of students have done 72 x 20 (this is incorrect). I pause the class and go through this particular question showing students that minutes and hours are different and how they should have done 72 x 1/3 = 24 miles.
Very quickly, I have hands up. Students haven't fully understood what to do.
Where did 1/3 come from Sir? - Not understanding converting time
Why is it multiply when they are next to each other? What does it mean with the D on top of S? - remembering how to use the triangle effectively
Where does the S go? - forgetting the formula
Teaching using a formula triangle is ineffective. Students aren't being given a deeper understanding of the underlying relationship between distance and time. Having to remember the triangle and how to use it increases cognitive load. Students refer back to the triangle for easier questions where an understanding of the relationship would be much simpler.
What I do now
The learning will start with a focus on the units themselves. Converting time, distance and speed units and understanding the different ways of writing these quantities. After this students are ready to look at the relationship between distance and time. We start with simpler examples and build up as we go but the whole way through it is using a clearly labelled ratio table.
Taking the question above it would look something like the diagram below. We are able to look at the relationship between time and distance vertically (blue) and horizontally (red) to support in answering the question. Whichever relationship we choose, we will still get to the correct answer of 24.
Example 2:
Using a ratio table gives students an understanding of the multiplicative relationship between distance and time. The ratio table allows links to be made with other topics that also have a multiplicative relationship such as Pressure, Density, Proportion etc.
So…the next time you are teaching Speed, use a ratio table!!