What's a multiplayer LAN game?
You can safely give your kids the fun of playing in multiplayer by setting up a game over LAN (Local Area Network). This means that one person shares their world with other players who are nearby in the same house/area, so they can all play together in that world at the same time.
How do I do that?
1. Launch Minecraft and enter Single Player mode
2. Select an existing world (or create a new one) and click Play Selected World
3. Pause the game (press Esc) and select Open to LAN
4. Set the game mode and whether to allow cheats, then click Start LAN World
5. Other players nearby can now join this game - when they select Multiplayer they should see the world in their list of available servers
NOTE: The game will only be available to other players for as long as the person who initially opened the game to LAN is still playing in the world. When they log out the LAN connection will close.