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Let the number of packages Sam bought be represented by x.
Since each package contains 9 beads, the total number of beads in the packages is 9x.
When Sam's mom bought him 63 more beads, the total number of beads he has is now 9x + 63.
Since Sam has 153 beads in total, we can set up the equation 9x + 63 = 153.
Subtracting 63 from both sides, we get 9x = 90.
Dividing both sides by 9, we find that x = 10.
Therefore, Sam bought 10 packages.