IMPORTANT INFORMATION: For those complaining about champion shard drop rates
Patch 6.10 notes
A lot of people are complaining that champion shards are too hard to get and that it ruins the mastery 6 and 7 system.
At the end of the Patch Notes for 6.10, Riot said this:
ZOINKS!: We’re adding a new mystery champ item to the store for RP or IP in a future patch that’ll help offset the RNG of finding champ shards and permanents in chests
This means that you don't have to worry about getting champion shards as a random drop from chests if you don't want to. Soon there will be a way to use either RP or IP to prove your mastery of a champion.