Counting board for young learners
This counting board was inspired by the "Inca abacus". The Incas recorded numbers by tying knots on strings, called quipus. They used a base-ten system, putting one to nine knots next to each other to represent the digits 1 to 9, and they left an empty space for 0. They performed computations with beans on some form of counting board. But how they did it is not known anymore. Only one picture supposedly showing such a board is preserved. And part of this picture is used here as our counting board.
(Picture taken from Ascher, M. & Ascher, R. (1997). Mathematics of the Incas: Code of the Quipu. Mineola, NY: Dover Publications.)
Our board:
On this board we have 5 locations that have the value 1, 3 locations that have the value 5, 2 locations that have the value 15, and 1 location that has the value 50. For tokens we use colored non-rolling glass beads. When all eleven locations are occupied by beads, their total value is 100. Counting is done by adding beads to the boards and regrouping: 5*1 = 1*5, 3*5 = 1*15, and 5*1 + 3*5 + 2*15 = 50.
Example of a task
Children work in pairs. Each pair has two containers, one of them empty, and the other filled with up to 100 small objects, and one counting board and at least 11 beads.
One child hands to the other a small number of objects (one to five) at a time. The other updates the position on the counting board and puts the objects into the second jar. They both should "read' the current count from the board.
This is a task for early grades when children learn addition facts.