partition (something) into (something)
To divide some larger space into multiple smaller spaces. Instead of moving us into a larger office, they're just partitioning the existing space into a bunch of tiny cubicles to fit the new employees. We decided to partition our father's land into three equal sections for each sibling.
partition (something into something)
to divide or separate something into something [smaller]. I will partition this room into two separate spaces. Do you think you can partition this box into four compartments so we can store files by quarter?