Teaching Tips

#AskYourChildWhy: Why does the addition algorithm work?

Reading Time: 1 minutes

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:

why

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):

why

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:

why

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:

why

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

why

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

why

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.

Would you like your child to learn concepts this way and never forget them? Cuemath is the right choice.

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Manan Khurma

Manan is the founder, lead program designer and CEO of Cuemath. He is a graduate from IIT Delhi and is also an acclaimed mathematics author with Pearson and McGraw Hill. His mission is to make every child in India love math the way he does.