Dear Lisa. Thanks for your nice post. So glad to hear that your children enjoy math so much. :)

The reason to enter pairs on the back side of the abacus is so you can easily see the two fives and be able to recognize when to trade for example, 10 ones for 1 ten. If for example you put 7 on one string and then added 4 on the other string you would not be able to visualize quickly that you have 11, however, if you added 7 by using the doubles technique and then added four you could see easily that you have two 5's and one more making it an easy visual to trade.

Does this make sense? It really is all about being able to "see", visualize quantities. The AL abacus and how Dr. Cotter has us use it is set up for us to "see" the numbers the easiest way.

I hope this help answer your question. Please feel free to email, call or post any other questions you have or to continue this conversation.

Sincerely, Rosine