For every 80,000 points you earn on the regular map, you will get a chance to play a matching game. These appear as a grey spade with some little symbol. In the game, you try to pick two cards that match. If you do that, you get the item on the matching cards. Use the following guide to get all of the items. Just find the board that matches the one on the game.
Below are the symbols I'll type and what they mean.

& = Fire Flower X = Starman ! = 1up
1 = 10 coins 2 = 20 coins @ = Super Mushroom

Boards-

& X ! & 2 @ ! @ 1 @ & X & 1 ! & ! @
1 @ 2 ! @ 1 @ 1 X 2 2 & X @ 2 X @ 1
X & X @ & X X ! & @ & X X & 2 @ & X

@ & 2 @ 1 X & 2 @ X ! & @ & ! & X X
& ! @ 1 ! 2 ! & 1 @ 2 X 2 X @ 1 ! &
X & X @ & X @ 1 X @ & X 2 @ 1 @ & X

& X ! & ! @ @ & 2 & 1 X
1 @ & X @ 1 2 ! @ 1 ! &
X 2 2 @ & X X @ X @ & X

The board is chosen at random every time.