*Relearning to Teach Arithmetic, Susan Jo Russell. 1999.

Everett Public Schools, 2005

Addition Strategies

Adding left to right

(expanded notation)

256 + 687

200 + 600 = 800

50 + 80 = 130

6 + 7 = 13

800 + 130 + 13 = 943

This algorithm is related to the traditional “carrying” algorithm, which is also a form of adding

by place, except that traditionally we were taught to start with the ones rather than the largest

place.*

Starting with ones of the numbers, then adding on the other number in parts, often (but not

always) starting with the largest place.*

256 + 687

256 + 600 = 856

856 + 80 = 936

936 + 7 = 943

Round one or more of the addends to numbers that are easier to work with, then compensate.*

256 + 687

256 + 700 = 956

956 – 13 = 943

Transform the entire problem to an equivalent problem that is easier to solve.*

256 + 687

256 + 687 = (256 – 13) + (687 + 13)

243 + 700 = 943

Please note that students may use larger numbers or chunks once they are more confident with

their understanding with number. Also, the recording of the numbers is to

explain

how they

solved the problem and can look tedious. Many of the steps can be done

mentally

with some

keeping track on paper if necessary.

It is important that students eventually learn to read all common notations, including both

vertical and horizontal notations for addition, subtraction, and multiplication, as well as the

various notations for division. However, they need to be secure enough to interpret these

notations correctly while still relying on their own mathematically sound procedures to solve

problems notated in any of these ways.*

2 + 4 = 6

32 – 27 = 5

5 = 32 - 27

2

32

12

12 x 7 = 84

+4

- 27

x 7

6

5

84

6

24 ÷ 4 = 6

24/4 = 6