# #AskYourChildWhy: Why does the addition algorithm work?

Suppose that we have to add 47 and 89. From grade-1 onward, children can solve such problems by arranging the numbers vertically, and following the addition algorithm, which is shown below for this particular case:

However, children do not have an inkling of why this algorithm works. They can do all the addition and carry-over steps fluently, but have no idea why they are doing what they are doing. In this article, we explore the **Cuemath approach to the addition algorithm**.

Let’s represent 47 and 89 on the Abacus and think about adding them. Note that each bead on the ones wire represents 1 unit (let’s call any such bead a **one-bead**), while each bead on the tens wire represents 10 units (let’s call such a bead a **ten-bead**):

Now, if we add the one-beads from both the models, we get 7 + 9 = 16 one-beads. 10 of these one-beads can be combined to form a ten-bead, while the remaining 6 can be placed on the ones wire:

We already had 4 + 8 = 12 ten-beads, which combined with this additional ten-bead gives us 13 ten-beads. Now, 10 of these 13 ten-beads can combined to form a hundred-bead, while the remaining 3 ten-beads can be placed on the tens wire:

Final, the hundred-bead goes on the hundreds wire, and we have the resulting number as 136:

Compare this sequence of steps with each sequence of the addition algorithm:

The first carryover is simply 10 one-beads combining to give a ten-bead. The second carryover is simply 10 ten-beads combining to give a hundred-bead.

That’s the why behind the addition algorithm. In math, learning the why is more important than learning the what. That’s the foundation of the **Cuemath approach** to math learning.

Great!!!

I want to become a cuemath teacher.

I am currently working for synchrony, but wold like to join in cue math, please let me know if it is applicable for me