The Partial-SumsAlgorithm

The Partial-SumsAlgorithm

Used for adding multi-digit numbers.

Used for adding multi-digit numbers.

Created by Paula Cantera Elk Neck Elementary

Children should be encouraged to check their answers to see whether they make sense.

Children should be encouraged to check their answers to see whether they make sense. Whether done in advance or as a final check, it is desirable to make a “ballpark estimate” of the answer.

Whether done in advance or as a final check, it is desirable to make a “ballpark estimate” of the answer.

One way to make a “ballpark estimate” is to round each addend to the nearest ten or hundred, depending on thenumbers being added.

One way to make a “ballpark estimate” is to round each addend to the nearest ten or hundred, depending on thenumbers being added.

For example:For example:

63 + 24 is close to 60 + 20.63 + 24 is close to 60 + 20.

Students can easily add 60 + 20 to get 80.

Any answer not close to 80 would not be a reasonable answer and should be checked for accuracy.

When using the partial-sums algorithm, the partial sums may be calculated in any order - it does not matter whether you add the tens first or the ones first.

When using the partial-sums algorithm, the partial sums may be calculated in any order - it does not matter whether you add the tens first or the ones first.

Think of each addend in its expanded form:Think of each addend in its expanded form:

6324

60 + 320 + 4+

Now add the tensNow add the tens

80

6324

60 + 320 + 4

60 + 20

Next add the onesNext add the ones

80

6324

60 + 320 + 4

60 + 203 + 4

7

+

+

Finally, add the partial sums.Finally, add the partial sums.

80

6324

60 + 320 + 4

60 + 203 + 4

7

+

+87

Of course this can be expanded to work with 3-digit numbers, and 4-digit…….

Of course this can be expanded to work with 3-digit numbers, and 4-digit…….

342145+

300 + 40 + 2100 + 40 + 5400

807+

487

Partial-Sums Algorithm Partial-Sums AlgorithmJust one way to add multi-digit numbers.

Try some at home today!

Just one way to add multi-digit numbers.

Try some at home today!