Your IP is assigned to you by your ISP (Internet Service Provider). You can have a fixed one (usually more expensive) or a dynamic one, meaning you might get a different one every time you connect.
The thing is, your modem or router is receiving its IP from a DHCP (Dynamic Host configuration Protocol) server and this server will have grant you a lease of, lets say, 24 h.
So, during those 24h your router's MAC address will always get the same IP.
But you can try to change it, just open a command prompt and type:
C:\ipconfig /release (This will clear clear your configuration)
C:\ipconfig /renew (This will ask your server for a new IP)
Of course, there are other techniques including ways to spoof your real IP but I believe those are far too complex for someone asking the kind of questions you ask... Good luck!