This list of activities came from the card packaged with the abacus Aidan got for Christmas. I'm putting them here because it seems to be oddly difficult to find beginner-level activities to do with the abacus. What's below seems to be enough to get a good start anyway.
Match My Move
Move any number of beads to one side of the frame. Ask the child to match your "move" on the wire below yours. This can also be done with a repetitive pattern--- arrange the 10 beads in different groupings (eg 3 beads, 1 bead, 2 beads) for the child to mimic on the wire below.
Move a certain number of beads to one side and ask the child to count how many beads you moved and how many remain on the other side. Or have the child count from one to one hundred as they move that number of beads on each of the ten wires.
Beat the Clock
Quickly move a certain number of beads to one side and have the child say how many were moved and what color they are as fast as he can (eg 7 yellow beads, 4 red beads, etc). See if he can get all 10 wires correct, or how many in a row can be answered correctly.
Make A Shape
Have the child try to make simple shapes using beads on multiple wires -- a square, triangle, rectangle, diamonds, or a perfect straight or diagonal line.
Simple Addition Games
Choose a number and determine how many different combinations you can find to achieve that sum. Combinations of ten would be 1+9, 2+8 etc.
Complex addition games.
Create larger numbers by assigning different numbers to the colors -- blues are ones, reds are tens, whites are 100s, green are thousands, etc. Line up any number of beads below each other (eg 1st wire -- 3 blue, 2nd wire 2 red etc) and have the child add the totals together to determine the sum.
Do addition, subtraction and even simple multiplication and division problems by using the first wire for the first number, the second for the second, and have the child answer it on the third wire (eg 7-4= 3.). After putting a certain number of beads on the first and second wires, yell out the type of problem (addition) and have them race to get the answer.
Match a Letter
Draw or say a capital letter, and have the child create its shape on the abacus (eg letters A, I, E, L are good for starters).