Let \( x \) be the number of packages Sam bought. Since each package contains 9 beads, the total number of beads Sam has from the packages is \( 9x \).
According to the problem, Sam's mom bought him 63 more beads, so the total number of beads Sam has now can be expressed as:
\[ 9x + 63 = 153 \]
To solve for \( x \), we first subtract 63 from both sides of the equation:
\[ 9x = 153 - 63 \] \[ 9x = 90 \]
Next, we divide both sides by 9:
\[ x = \frac{90}{9} \] \[ x = 10 \]
Thus, the number of packages Sam bought is \( \boxed{10} \).