Chinese Counting Board and Rods
Counting Board and Rods
This is a virtual version of a counting board with rods. This manipulative was first developed in ancient China and it represents one of the earliest representations of numbers in a base ten place value system. Vertical rods in the rightmost column represent 1. Five of these can be exchanged for a horizontal rod which is worth 5. So all of the digits 1-9 can be represented with 1-5 rods. In the second column from the right a horizontal rod represents 1 group of 10. Five of these can be exchanged for a vertical rod representing 5 groups of ten (i.e. 50). We continue in this manner alternating the role of vertical and horizontal rods for each column (i.e. each place-value, power of 10). Once we get to a value of 10 in one place value the two rods for 5, 5 rods for 1 + 1 rod for 5, or 10 rods of 1 can be exchanged for one singleton rod in the next higher place value. Exchanges can be made in the opposite direction as needed for subtraction. Here are the two forms of arrangement for the rods for the various digits 1-9. We use the bottom representations for place values of 10n where n is an even number, and we use the top representations for place values of 10n where n is an odd number
There are two rows to the board to allow for the representation of two numbers. We can add numbers by just physically moving the rods around.
There are custom tools for creating additional vertical and horizontal rods as needed. There are also tools for creating vertical and horzontal rods that are red in color. These are used to represent negative numbers.
There are two rows to the board to allow for the representation of two numbers. We can add numbers by just physically moving the rods around.
There are custom tools for creating additional vertical and horizontal rods as needed. There are also tools for creating vertical and horzontal rods that are red in color. These are used to represent negative numbers.