At the University of British Columbia, Stanley Coren (canine expert) conducted intelligence tests... The findings revealed that dogs can learn as many as 250 words including signals and gestures... but read on...
The language tests put our canine friends on par with a 2.5 year old child, but it turns out they can trump a 3 or 4 year old in basic arithmetic. Here's how the math test works - the dogs watch as 1 treat and then another is lowered down behind a screen. (1+1=2) When the screen is removed the dog expects to see 2 treats. If one is removed or a third added, the dogs looked surprised and stare longer. This proves that they understand the concept of addition.
Now we are up to about the levels of teens. Dogs, being very social animals, are keen on knowing who is moving up the pack, what the others are doing, who hangs with who and that sort of thing.
Dogs know when they are being treated fairly. In this test one dog is given a treat and the other is ignored. The unrewarded dog avoids making eye contact with the trainer. Interestingly, the dogs do not seem to care about 'equality' - if one dog is given a piece of meat and the other a piece of bread there is no difference in the reaction.
and your dog... of course
If you think dogs can't count, try putting three dog biscuits in your pocket and then giving Fido only two of them. ~Phil Pastoret