Besides allowing for a greater number of ip addressed, Classless Interdomain Routing (CIDR) was also intended to slowdown routing table growth in core routers. I may understand how it expands the range of possible Internet Protocol (IP) addresses, but how it helped to slowing down routing table growth? 
Following I describe my understanding of IP, Core Routers, and routing tables:
IP address: a logical non-geographic address which is unique for each devidce coonnected to the Internet. It is composed by a netid (identifying the network) and a hostid (identifying the host in a given network) parts.
Core routers: a device for linking network devices. These routers need to keep a routing table with all netids they have heard of, and the identifier for appropriate outgoing link for each of the netids.
Routing table: is a table that shows the next hop ID for each Netid. If there is 900,000 netids assigned to networks around the world, there will be 900,000 entries in the routing table.
Maybe I'm getting those terms wrong, and because of it I can't understand the effects of CIDR on table growth.
I would really appreciate if someone could clear that up for me.