What actually is aggregate demand? I have been tasked with teaching some students macroeconomics, and will shortly need to introduce them to the concept of 'aggregate demand'. Usually, this is defined by the following sort of equation:

$AD$ = $C + I + G + X - M$

where the symbols have the usual interpretations.

My question is whether aggregate demand is supposed to refer to the quantity that is demanded or rather the value of total demand.

Both options would seem to present difficulties:

On the one hand, if we say that aggregate demand is a quantity, one needs to ask 'of what?' Naturally, if there were just one good in the economy, answering this would be easy. But in reality, there are many different goods. Are we supposed to just add up the quantities demanded of all these different goods (e.g. if people demand 5 laptops, 3 apples and nothing else, aggregate demand is 8)?

On the other hand, we might say that aggregate demand is the value of total demand, i.e. $p_{1}q_{1} + ... + p_{n}q_{n}$ where $p_{i}$ and $q_{i}$ are the quantity demanded and price of good $i$. That seems a bit more meaningful, but then it is far from intuitive that aggregate demand falls when the 'overall price level' (whatever that is) rises. For one might have thought that if prices rise, the value of total demand would (sometimes) rise, just as a firm's total revenue can increase when the price increases (if demand is inelastic).

My apologies if the answer is obvious; I am simply not very familiar with macroeconomics.
We measure these in values.

Also, this is a macroeconomic identity, it holds always by design.

You need an economic model that will make specific behavioral and other assumptions, in order to discuss movements when the price level change.

For example, you write


  it is far from intuitive that aggregate demand falls when the 'overall
  price level' (whatever that is) rises


Even in introductory economics courses beware of "intuitive" thinking.  

And indeed, where is the model and its assumptions based on which one would argue that as price level rises aggregate demand falls? It is certainly not embedded in the macroeconomic identity.  

Find the model that predicts so, understand its assumptions, and then discuss whether these assumptions are "intuitive".