(This may be a stupid question, but I've only learnt about hybridization yesterday.)
I will take the example of methane. The valence shell electron configuration of ground state of carbon is $2s^2 2p^2$. There are 2 unpaired electrons, both in the $2p$ orbitals. But we need 4 unpaired electrons to form 4 bonds. So one of the electrons from the $1s$ orbital is excited to the 3rd $2p$ orbital. So, there is an $s$ orbital with an unpaired electron, and 3 $p$ orbitals with unpaired electrons, which can all participate in bonding, so now we can form 4 bonds. In the end, there will be 4 $sp^3$ hybridized orbitals.
My question is, why are there going to be 4 hybridized orbitals? I imagine the hybridization as "there is an $s$ orbital and 3 $p$ orbitals, hence $sp^3$." I thought a single $sp^3$ hybridized orbital is the combination of a single $s$ orbital and 3 $p$ orbitals. So how can there be 4 $sp^3$ orbitals in the end if the valence shell of carbon only has a single $s$ orbital and three $p$ orbitals? Intuitively it seems to me that 4 $sp^3$ orbitals would require 4 $s$ orbitals and 12 $p$ orbitals.