In the blog “Standard Algorithm of Addition: Part 1,” we learned how to set up addition problems in a vertical format so that we can manually calculate their sum. We also learned the mathematical terms for the components of arithmetic **expressions** of additions. In the blog “Standard Algorithm of Addition: Part 2,” I used a **{visual model}** to explain the concept behind this fundamental algorithm using green square blocks and blue rods to represent the addends. In this blog, I will show you how the standard algorithm works **{number model}**.

First we set up the arithmetic expression in a vertical format **(A)**. Now we will first focus on the ones column and work our way from right to left **(B)**. We mentally add the **digits** in the ones (9+7=16). Note the sum is greater than 9. This sum is equivalent to 1 unit of ten (blue rod) and 6 units of ones (green squares) **(C)**. I write the digit for the 6 units of one in the ones column under the underline **(D)**. I place the 1 digit of ten at the top of the tens column **(E)**.

Working our way from right to left, we move to the tens column **(F)**. We add the digits in this column noting that we are actually adding multiples of ten **(G)**. Since the sum is not greater than 99, we simply write the sum of the digits in the tens column underneath the **underline** **(H)**. Therefore, the **sum** of the addends, 29 and 47, is 76 **(I)**. It is the most common technique of addition taught to math students, but it is not the only one. We’ll look at some other addition algorithms in future blogs.