IPhone 5 always uses LTE when on standby. Why?

My iPhone 5 is connected to the Wi-Fi in my house, but every time I pick it up to use it after its been doing nothing for a minute or more, it has the LTE symbol in the top right instead of Wi-Fi. Then after I start to use it again the Wi-Fi symbol comes back. Why is this? Is it using the data plan when it does this? If so, any way to stop it? I'd like to switch to the lower data plan, so I'm trying to use it lightly.

All iPhones do that. It doesn't use the Wi-Fi antenna when it doesn't need to. Once it does it comes back on