Pentominoes have been around as puzzles for over 100 years, although they didn’t get the name “pentominoes” until 1953.
Each pentomino is made of 5 squares that are attached to each other on at least one side. Try to figure out what they must look like, then check to see you have all 12 pentominoes. They are named after the letter they most look like. Here is the set with their names.
And here is a selection of further pursuits, including more tiling puzzles and some mathematical properties you can study using pentominoes
There are lots of variations on the idea, including tetrominoes (four squares) and hexominoes (six), using triangles or hexagons instead of squares. There are computer games and board games based on the same idea (including Soma and Blockout). Tetris is a well-known 3-dimensional variant.