What determines how many points I receive when I make a kill?
I've noticed that I don't always receive the same number of points for each kill.
Sometimes I might get 100, other times I might get 200. When my son plays, the information is usually displayed on screen.
How does the game determine how many points to give me when I make a kill?
Modern Warfare uses a system based on performance. In team deathmatch you get awarded bonus points for things like "payback" where you killed the enemy that just killed you, or a "buzz kill" which is you killing someone one kill short of earning a "kill streak".
In Team Deathmatch if you perform a regular kill you get a base score of +50, depending on the settings... and if you save a team mate in the process an additional +50 is rewarded for being the rescuer, if the bullet that kills the oposing player is a head shot, throw on another +50.
That is a +150
So depending on the circumstance of the kill, you can get a variety of tallied points for a single kill.
You are rewarded more points for accuracy, revenge, mission focus and so on. Some of these factors are to motivate you to be positive despite possibly being repeatedly killed while learning.
Others are obvious rewards for just being great at the game.
Sometimes its based on how many you've killed in a row or where you shot them.
If this is MW3 (which it sounds like), I would think if they person you killed was on a spree, you get more points for killing them. If you get a headshot, you get more points.
Here's details on the point system: http://callofduty.wikia.com/wiki/XP
100 Points are awarded per kill (in most game modes, other point amounts are awarded in some game modes) without regard to how they are killed (headshot, legs etc.).
Additional points are awarded based on other factors, for example, a kill with a throwing knife gives you an extra 50 points (for a total of 150) while killing someone who is one kill away from their next kill streak award will give you an extra 100 (for a total of 200).
You can read the list of awards from Modern Warfare 2 HERE. Modern Warfare 3 uses almost the exact same system.