This is a functional version of the Paper Towel tube rockets I built as a very young child.
 

Materials:
Bounty Paper Towel Tube - main body tube
Charmin Toilet Paper Tube - payload bay
3"x5" Index card - rolled around motor to form motor mount tube
3"x5" Index card - cut in "pacman" shape to form nose-cone.  Left 4 tabs to allow it to be taped to payload tube.
3"x5" Index card - folded in half lengthwise, then curled to form coupler/shoulder of payload bay
3' string - shock cord
5' crepe paper - streamer
USPS 2nd Day Air box - source of cardboard for fins and motor mount centering rings.

Construction notes:

After rolling index card around motor and taping it so it doesn't unwind, then curl the upper end inwards to form a thrust ring.  Use the technique like you were sealing the end of a roll of coins.  Soak the rolled end in glue to help it form a solid stop.
  Assemble motor mount assembly first, then when centering rings are glued to the rolled mmt, apply rings of glue around centering rings, slide assembly in to body tube, then spin tube into the air so centrifugal force will spread rings of glue into fillets.  Make sure to leave mmt exposed enough to tape motor in place.

When attaching fins to body tube, first slit the ends of the fins through the corrogation and spread the outer skins 1/4" so there is more area to glue to.

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