iphone 5S using way too much data?

I bought my daughter an iphone 5S and since getting it, she has had connectivity issues with wifi and now I just noticed a high data usage on our Telus bill. Any ideas on how to fix this?

I noticed on other forums that the iphone 5 might revert to cellular usage when in lock screen.

This is an issue as we have never seen data usage like this before... and of course the costs associated are crazy.