For subtraction, Everyday Mathematics offers five methods. The "trade
first method", the "left to right subtraction method", and the
"counting up method" are already present in the 3rd grade student
reference book, and the "partial differences method" and the "same
change rule" make their first appearance in the 4th grade student
reference. Notice that the traditional right to left subtraction
method is not part of the Everyday Mathematics curriculum. Trade First
Closest to the traditional standard is a method that Everyday
Mathematics calls "trade first". It is the Everyday Math focus
algorithm for subtraction. It is a two stage process, first working
right to left to do all the borrowing (recording the intermediate
results above the top number) and then a second pass, in any order,
doing the subtractions. The intermediate results are twodigit
numbers, so one needs to use wide columns, and it is recommended to
separate the columns with clear vertical lines. In the example at
right, 325  58, we first recognize that the ones column needs
borrowing, so we replace 2*10+5 by 1*10+15. Then we recognize that
the tens column also needs borrowing, so we replace 3*100+1*10 by
2*100+11*10. Then we do the subtraction in each column.


211  115 3 2 5   5 8  2 6 7

Left to Right Subtraction
The second standard method of EM is left to right subtraction, the way
one might well do the problem mentally, but carried out with paper and
pencil. Here "left to right" refers to the decomposition of the
second number. In the example at right, 32558, the 58 is decomposed
as 50+8. The individual subtractions are done mentally.


325  50  275  8  267

Counting Up
The third standard method in EM is the "counting up method". It is
carried out in two stages. In the first pass we count up from the
smaller to the larger number, first by ones, then tens, and so on, and
then the odd remainder, and then in a second pass we add up the
addends. The example at right displays the process on our familiar
example, 325  58.


58 and then + 2 60 2 + 40 + 40 100 + 200 + 200 + 25 300  + 25 267 325

Partial Differences
The fourth standard method of EM, the "partial differences" method, is
again a twostage method. We operate first on each column
individually, keeping track of the sign if a borrow would be needed,
and then we combine the results using mental arithmetic. With this
method, for 325  58 the second stage involves the mental arithmetic
300  30  3 = 267.


325  58  +300  30  3  267

Same Change Rule
The fifth method is the "same change" rule. It is based on the
recognition that a subtraction problem is easier if the smaller number
ends in one or more zeroes. We may bring that about without changing
the answer by changing both terms by the same amount. So, 325
 58 may be changed into 327  60, which we do
mentally to obtain our 267. If the second problem is still difficult
then we might apply the same change rule again, but this is not
discussed in the Everyday Math student reference book.


325 > 327  58  60   267


