#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.