About Multi-digit Work
Subtitled: Please don’t teach your child to “carry the one!”
Around this time of year, a lot of parents notice that we are working with 2-digit numbers and
wonder when the children will be learning, for addition, “carrying the 1”, and for subtraction,
“borrowing,” those terms we remember from our own childhood experiences with 2 nd grade
math.
The answer is multi-faceted. Math today has not totally abandoned these algorithms, rather,
they have moved residency to fourth grade. The reason is that these strategies represent
memorized shortcuts. For typically developing second grade math students, these methods
teach only the memorized steps. Students do not gain a sense of place value, what the digits
mean, and efficiency of operation. They don’t get a chance to “muck around” with digits and
place value and build their growing number sense.
So what do we do instead? The focus this year is on finding the efficient strategies for the
presented problem. For example, the “partial sums” method would be an efficient strategy for
37+46, and that strategy looks like this:
37+46
add the tens first: 30+40=70
then add the ones: 7+6=13
then combine the subtotals: 70+13=83
The student first adds the tens, then the ones, and then combines the two subtotals. Note
that when using this strategy, the student is required to understand that the 3 in 37
represents 30, and the 4 in 46 represents 40. This is the kind of place value knowledge that is
NOT required to do the traditional “carry the one.” Though it is implicit in carry the one that
the 1 means a 10, many students do not internalize that. This can lead to math difficulties later
on, long after it seemed the student was proficient in 2-digit adding because they showed
themselves able “carry the one.” Quite often student just memorized the steps. Think of it as
building a house with holes in the foundation. It might still get built, but there will be
structural problems later on!
Let’s take another problem, 98+44. Partial sums would not be the most efficient strategy for
this problem. We are encouraging students to use a strategy called “compensating.” For this
strategy, the student recognized that 98 is close to the landmark number 100, takes 2 from 44
to make 98 into 100, and turns the problem into 100+42. Much easier to do this problem
mentally now, and even shorter than partial sums! Throughout math, students are encouraged to
us landmark numbers, multiples of 10, to help them compute. We call them, for obvious reasons,
“friendly numbers” because 100+42 is a much friendlier problem than 98+44.
In another example, we had a former math coach tell our staff of the problem 100-99, and how
children crossed out the zeros and “borrowed” but didn’t see it was just ONE LESS! Kids get so
wrapped up in the “right way” that they fail to see easier paths and more efficient strategies.
Another tool students use today that may seem new to parents is the “open number line,” simply
a straight line without numbers, which children use to show their work, for example, a student
using the open number line to solve 98+44 might show their work in a number of ways. Please
note the use of friendly landmark numbers to make the computation easier:
40
2
2
98
100
140
142
40
Or:
4
98
102
142
40
Or:
4
98
138
142
So why do we ask parents not to teach the “old” strategies? Firstly, the students will learn
them anyway, just later on. Secondly, in our experience, once children know these algorithms,
they perceive them as “the right way,” and resist any other method. And it is the other
methods which better develop students’ math understanding, skills and number sense.
Hopefully, this letter offered a better understanding of what your second grader is learning,
and will help if any questions come up on the math calendar!
Thank You,
The Second Grade Team