With a tip o' the hat to Martin Gardner, I thought I'd share one of my favorite birthday-card making techniques. This makes a cool four-sided card with some sides hidden, in a way you can reveal by folding and unfolding properly. (Gardner calls this a "flexagon").
The front of the card starts like this: Happy birthday!
Fold the card "closed" in the way you normally do . . .
. . . but when you open the card up, you open from the back, not the front. (Notice that folding closed meant moving the purple heart down, but opening meant moving the rainbow up). When you unfold from the back like this, a new side is revealed!
How do you make one of these?
Trim a piece of paper so it's as tall as (actually, a tiny bit less tall than) the envelope you want to put it in. It should be less than twice as wide as the envelope. If you're just doing this for your own fun, you don't need to trim the paper at all.
Fold the paper exactly in half (so that it could fit in the envelope) and exactly in half again, to get it folded into fourths.
Fold in the other direction, roughly in thirds (doesn't have to be exact in this direction). It's important that the folds be perfectly horizontal --- I use the vertical fold lines to make sure things are aligned properly.
Following the fold lines exactly, cut out a "tongue" on three sides -- but not the fourth -- from the middle of the paper.
Fold the tongue back over and then under the side of the paper.
Then fold the paper opposite the tongue up and over twice. Tape the tongue -- not the folds on top of the tongue, but just the tongue itself --- to the paper it meets up with. In the top photos, this would be the join between the dog and the cherries.
Decorate the paper, and start flexing to reveal the hidden sides!