All bead chains up to cube number. Each set has 10 bead chains.
For example,
bead chain 1 only has 1 bead bar. 1 bead in total (cube number of 1 is 1*1*1=1)
....

Each set has 10 bead chains. We designed this set to be a visual tool for the times table. Times table is up to 10*10. We also have another modified version up to 12 bead bars, so children can work their times table up to *12.
Each number has 10 bead bars.
I made this design when my own daughter was working on times table, and she didn't like the Montessori multiplication board. She was 7 at that time. She didn't like number tiles and found that's too challenging. Therefore, I made these bead chains to help her visualize the times table. Also, that's convenient tool to be around her workplace. She just took a bead chain and count the beads whenever she has doubt about the times table.
I designed these ten bead chains and that is not in the Montessori standard album by Maria Montessori. There are different companies including those well-known Montessori manufactories started to make these ten bead chains after us. It gives people impression that is Montessori standard, but it is not. I was inspired by Maria Montessori's idea and use the bead bars but that's not the Montessori long bead chains.

No. I found we need to wait TOO LONG to do it. A child needs to master 1-1000 before they can work on long bead chains. (Bead bar 9 has 729 beads in total. A child knows how to 3 digits addition before starting it)
For short bead chains, a child only needs to master 1-100 before he/she can start short bead chains.
Also it requires a lot of patience for the working of long bead chains. For bead bar 9, there are 81 bead bars and only 9 bead bars for short bead chain.

It depends.
For counting, they both requires a child mastering 1-100.

-show how to make square number and why we call it 'square' number
-can be used with bead squares together
-use polygon cards for geometry