Abacus Math Program – Lesson 15 – Forward Double Rod

Here we will explore the final bead movement in our basic skill training program that looks at executing the 10 pair addition rule twice across two adjacent rods, called the Forward Double Rod. We discussed in Lesson 13 and Lesson 14 the idea of repeatedly using the same basic bead movements over and over again to solve more complex problems. We can extend this idea across as many rods as necessary to complete the addition operation. For instructional purposes we will show this interaction across two adjacent rods.

If we consider the example 95 + 5, we know we must use the 10 pair addition rule. The first step in the addition rule is to add 1 to the next rod left. In this case, 9 is on the next rod so there are no available beads to add the 1. So to add 1 to 9 we must repeat the use of the 10 pair addition rule on the second rod. We are now incorporating the 10 pair addition rule twice across two rods which is the reason this movement is called the Forward Double Rod.

To complete the problem we need to add 1 to the rod left of the 9 and then subtract 9, the 10 pair of 1, from 9. Please note the 1 we are adding to the 9 is the 1 from the first use of the 10 pair addition rule. We complete the problem by subtracting 5, the 10 pair of 5, from 5 on the first rod. Using the 10 pair addition rule twice leaves us with 100 on the abacus.

In a first example we start by adding 29 to the abacus. Next we add 75 to 29 by first adding 7 to 2 on rod B. Then we add the 5 to the 9 on rod C using the 10 pair addition rule. But here we notice that when we try to add 1 to the 9 on rod B we will again need to use a second 10 pair addition rule which is the Forward Double Rod movement. Add 1 to 9 on rod B we use a second 10 pair addition by adding 1 to 0 on rod A. Next we subtract 9, the 10 pair of 1, from 9 on rod B leaving 0 on rod B. Completing the first 10 pair addition we subtract 5, the 10 pair of 5, from 9 on rod C leaving 4 on rod C. The interim sum is now 104. Next we add 58 to 104 by first adding 5 to 0 on rod B. Then we add 8 to 4 on rod C using a 10 pair addition by adding 1 to 5 on rod B leaving 6 on rod B and subtracting 2, the 10 pair of 8, from 4 on rod C leaving 2 on rod C. The final answer is 162.

In the next example we start by adding 26 to the abacus. Next we add 11 to 26 by adding 1 to 2 on rod B leaving 3 on rod B and adding 1 to 6 on rod C leaving 7 on rod C. The interim sum is 37. Next we add 66 to 37 by first adding 6 to 3 on rod B leaving 9 on rod B. Then we add 6 to 7 on rod C using the 10 pair addition rule. So first we add 1 to 9 on rod B by using another 10 pair addition. This is the Forward Double Rod movement. Add 1 to 9 on rod B we first add 1 to 0 on rod C and then subtract 9, the 10 pair of 1, from 9 on rod B. We finish the movement by subtracting 4, the 10 pair complement of 6, from 7 with a 5 pair by adding 1 and subtracting 5 for a final answer of 103.

Next up the last lesson in our basic skill training series, Lesson 16 Reverse Double Rod.