Here's another set of polyominoes (sizes 4,5,6,7,8,9,10) that you can print and cut out. As before, the two smallest (same pieces as previous version) make a 3x3. The rest of the pieces are different. Also as before, add a piece at a time to make a 3x5, 11x2, 5x6, 3x13 and 7x7.
There's only one way to make each rectangle. You are allowed to flip pieces over.
If I feel energetic I might extend this by adding an 11-omino (6x10) and 12-omino (8*9).
The reason the first two are the same... those are the only two that work.