This is a post describing some ideas for introducing 2D and 3D vectors that I used with my students this week. Each of the tasks contain an element of physical construction. It is my conjecture that the time constraints at A-level and Higher lead to teachers feeling as though they do not have enough time to spend working with vectors in a physical way. In my experience, this leads to learners having difficulties visualising vectors problems, particularly those in three dimensions.
There are some lovely moments in this video, particularly when the students start posing their own problems, and explaining what they are doing and why.
After the video, the students were working on some problems (see below), for which the cube proved useful. During this, I decided to ask one of the students whether he could find two points on the cube with a length sqrt(7). He replied: "For that you would need 1 ,2 and 4 [as the squared components of the vector], but that's not possible because of the 2."