Squishlings

Squishlings are jelly blobs made of little cubes. A 6 can squish into a 2×3, a 3×2, a 1×6 or a 6×1, but never anything else. Stretch them under ceilings, tip tall towers onto ledges, and glue friends together to fill each jar exactly.

Poor 7 can only ever be a noodle. Glue a 2 onto it and it becomes a 9, which can be a perfect square. Factors, primes, squares and area, all felt with your thumbs. 14 levels.