The partial sums algorithm is fairly straightforward, implicitly uses and enhances place value understanding, and doesn’t require carrying. It’s biggest problem, actually, is that after using it students don’t want to learn the standard algorithm.

Basically you add the ones to the ones, record them, add the tens to the tens, record them, and add these two partial sums. An example probably explains it best (ones and tens are colour coded to help show partial sums).

Addition Question |
Add the tens and record. |
Add the ones and record. |
Add the two partial sums. |

Some teachers prefer to add and record the ones first, as it’s then just a small step away from the standard carrying algorithm.

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