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