Often the standard introduction to the concept of scalars and vectors in physics is something along the lines of:
A scalar is a quantity that is completely described by a single number (it has no directional dependence). A vector is a quantity that requires both a magnitude (a number) and a direction to be specified in order to completely describe it.
This is then followed up by examples of the two, such as
mass, charge and distance are all examples of scalar quantities, whereas, velocity, displacement and force are all examples of vectors.
I feel what is often missed out is a physically intuitive explanation of why certain quantities are vector quantities whilst others are scalars. I have thought up of a few examples and I'm hoping that people can provide feedback, and/or suggest some intuitive examples/explanations.
An example of a scalar quantity is temperature. Indeed, the temperature at a point is completely specified by a single number. It is rotationally invariant, in the sense that facing northwards, or south-eastwards (or indeed any other direction) at the same point does not affect the temperature at that point. Therefore it has no directional dependence and is a scalar. Another example would be distance. A distance of $n$-meters measured from one point to another remains $n$-meters, regardless of which direction it is measured in and hence it is a scalar quantity.
An example of a vector quantity would be an objects velocity. In order to determine the motion of an object it is clearly not enough to simply provide the speed at which it is travelling. The object will travel in a particular direction, and so two objects travelling at the same speed, but in different directions will end up at completely different locations. Hence, in order to completely specify the motion of an object one must use a vector quantity - the objects velocity.
Finally, the force acting on a object is also a vector quantity, since it acts in a particular direction on the body. Whether the force acts from the top, bottom or sides of the body will have different effects on the body, hence its action is clearly directionally dependent and must be described by a vector (two forces with the same magnitude, but acting in different directions on the same object will have different effects on the object).
Hopefully what I've written is coherent. I'm hoping to convey this information to a person with a fairly minimal background knowledge in physics, so any feedback about it would be much appreciated.
To clear up ambiguity. I am not asking whether I have understood the concept correctly or not. This is more a question about How one should give an elementary introduction to vectors and scalars? I am not currently in education and so don't have a lecturer or fellow students to ask about this. I have been asked by someone to explain it to their teenage son and I wanted to hear the thoughts of others (most likely more capable than I) on how to teach this concept.