One definition of a force So I know there are many questions on this subject here and I know them all but this question is a bit more concrete. So, knowing that it is hard to rigorously define a force, I will quote a definition of a force in a primary school textbook: 
A force is a physical quantity which we use to describe interaction.
So, I am finding it hard to understand why is this written in this way? For me, we can see that a body moves when some other body is near it. It can move or change shape. We can say that there is some interaction going on betwen bodies i.e. we can see that two bodies act on each other because when we remove either one of them there is no more movement. I can see that this interaction has a direction or I can assigne a direction to it by observing the direction of change of velocity. Also, I can quantify it. So, in a way I can say that interaction is measurable and I can call it a force. I dont see the need for distinguishing betwen force and interaction, they seem to be almost the same. Couldnt we just say that force is a cause of change in objects velocity or shape whoes source is some other object? 
 A: Interaction is semantically embodying the idea of action between (inter) two systems. In a way, it is a more general concept than force in contemporary physics.
A way to see the difference is to recall that interactions may change velocities, but they may also change energies. Well, in classical mechanics, potential energy is directly related to forces (force is the gradient of the potential energy). However, in quantum mechanics, the concept of force as a cause of velocity changes disappears, while interaction as a way to control the energy of a  system remains.
There are examples of interaction in classical physics where no force is implied.
A couple of examples could be:

*

*thermal interaction between a cube of ice and its environment. The process of heating and eventual melting of the ice can be described as an interaction where no force appears. Still, two subsystems (ice and environment) interact.

*notwithstanding the interaction of light and solid bodies can hardly be reduced to the introduction of forces (do we introduce forces for describing refraction or diffraction?), there is no doubt that some effect on the light propagation due to the solid body is present.

This is to clarify that, in physics, force and interaction are not always synonyms.
Whether it is worthwhile to pinpoint such a difference with kids 12 o 13 years old is left to who is directly involved with such a teaching.
About a reasonable definition of force for that age, I think starting from the basic properties of forces in mechanics, i.e., as a possible source of deformation or change of velocity, characterized by magnitude and direction, could be enough. In any case, the choice of the definition should be consistent with the planned use of that concept in the teaching.
A: "I dont see the need for distinguishing betwen force and interaction"
When there is an interaction (involving forces!) between two bodies each experiences a force. The forces are  equal in magnitude but opposite in direction. It is clear that in my last sentence we could not sensibly substitute 'interactions' for 'forces'. There is one interaction but two forces. It is the way we use the words. It's a little bit like having the general term 'human being' to cover both male and female. [I did say a little bit ...]
Another aspect of the way we use the words is that although interactions are quantifiable, the actual quantification is done using forces, potentials etc. It's rather like saying that when you connect a battery to a bulb and the bulb lights up, it's because of electricity. When it comes to quantifying, we need the concepts of current and pd.
If we're talking pedagogy, it's usual (in the UK at least) to tell children that a force is a push or a pull. Although this may be derided as empty, circular etc, it points them in the right direction so they tend no longer to make vague statements like "electricity is a force". We then investigate combining forces, and some of the things that forces, and in particular the resultants of forces, do. This takes them beyond push and pull [though I don't think that $\Sigma F=d(mv)/dt$ is adequate by itself as a definition of force. That's another story.] Then, at some stage, comes Newton's third law about forces between body A and body B (perhaps restricted to local interactions) and the idea that this is not a co-incidence but that the two forces are part of the same interaction.
A: Force is a basic concept in physics. You should not expect to be able to define it in a single sentence. The value of your proposed definition depends upon its intended purpose- if you mean it as a way to give a loose idea of force, then it is ok. However, you should bear in mind the following:
1)A force doesn't always result in a change to an object's velocity or shape. if you press against a brick wall neither its velocity or shape need be affected. 
2)The source of a force doesn't have to be 'an object'. In the a petrol engine, for example, the piston in a cylinder is forced down by the expansion of the ignited fuel-air mixture, which you wouldn't normally describe as an object. 
3) A definition of force ought to cover the fact that forces are vector quantities, that a net force results in an acceleration proportional to the mass of the body upon which the force operates, and that forces are a means of transferring energy.
A: Length is what you measure with a ruler, time is what you measure with a clock, and a force is what you measure with a spring scale.  Mass is a more subtle entity.
