How to explain to a child why can acceleration be positive or negative? I want to find out how can acceleration  be negative? I have an answer and this answer is: 
$$a=\frac{v_f-v_i}{t_f-t_i} < 0$$ because $v_f < v_i$ where $v_f$ is final velocity and $v_i$ is initial velocity; $t_f$ is final time and $t_i$ initial time. 
But I want a more intuitive explanation - an explanation for a child who does not know very much about Mathematics or Physics. 
Thanks!
 A: Positive means speeding up, negative means slowing down.  Now this is assuming you are traveling in the positive direction but through an axial change you could always guarantee this.  I think this would be a good starting point for a child.
A: Reusing your car example: use the fact that acceleration is "change in velocity". This can be positive (acceleration in the usual/common sense), but everyone knows that velocity can also be decreasing. This is what phsicists call negative acceleration.
A: I would explain that we can feel acceleration in a car. 
As our speed increases we are pushed back into the car seats. This is positive acceleration. 
As we slow down we are pulled back by the edge of the seat/seat bell. 
If the child is happy that acceleration is a change of speed then they should be able to tell with their eyes closed if the acceleration in a car is positive or negative with the car speeding up or slowing down. 
In reality acceleration is in three dimensions and positive and and negative only have meaning with respect to acceleration in one direction - children can also close their eyes and feel the acceleration as a car goes around a corner due to centripetal/centrifugal force.
A: Forget all ideas about vectors and velocity and relate it to a car which is travelling at a speed of 70 mph slowing down to a speed of 50 mph.  So the idea is negative means slowing down and positive means speeding up.  This would be a reasonable start and all the subtleties can come later. 
