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