And finally, graphs

Step 8

I do think that graphs, perhaps best seen as more-or-less as frozen accumulations, might well be introduced rather late on, with some simple algebraic relationships preceding those.

These can be constructed from the available materials. Still, you’ll have to decide rather carefully how to map the components onto the vertical axes of the graphs, assuming the horizontal axis, as is conventional, remains duration. This is particularly true if you want to build this bridge to graphs early on in the sequence: here you might restrict the quantities represented on the vertical axes to scalar quantities, so avoiding the formal complexities of vectors, once you stop thinking of them as arrow-like objects.

For some, now might be the time to formalise the vector representation as an extension to their understanding of kinematics, as an ordered set of numbers. Or you might relate the predicted movements and vector representations to graphs of the components of vectors. The next step depends on the direction of travel and the desired destination.