Here are two examples of subtracting in parts, working from left to right:

• Consider taking away 139 from 458 and try doing it in parts,

since 139 = 100 + 30 + 9.

First subtract the 100s

458 – 100 = 358

Then the tens

358 -30 = 328

Then the ones

328 – 9 = 319

• Other students apply their understanding of negative numbers to subtract

458

- 139

They find the differences and add them

300

20

-1

319

(300 + 20 + -1 = 319)

When teaching the standard algorithm, teachers have to be sure the students thoroughly understand place value. As John Van de Walle, a prominent teacher of teachers explained in his book Elementary and Middle School Mathematics: Teaching Developmentally :

The traditional algorithms require an understanding of regrouping, exchanging 10 in one place-value position for 1 in the position to the left – or the reverse, exchanging 1 for 10 in the position to the right. The corresponding terms carrying and borrowing are obsolete and conceptually misleading. The word regroup also has little meaning for young children. A preferable term is trade. Ten ones are traded for a ten. A hundred is traded for 10 tens.

In reviewing the trade first algorithm, students first work with models using place-value mats and base ten blocks. If you have never seen this and your children are using this algorithm, be sure to have them explain it to you by demonstrating their process with the blocks. (They can borrow some from their classroom) It might be the first time you ever made sense of a procedure you have applied for years! We will demonstrate the modeling of Trade First Subtraction in the next Math Corner.