Two-Digit Addition – When Do I Show Them the “Real” Way?

Last week, I attended Carole Fullerton‘s parent presentation. She discussed strategies students have for adding two-digit numbers. Carole’s timing was great since I’ve been having similar discussions with teachers in recent weeks.

How many ways can you add 59 + 37?

The most common strategy that I see students use is to add the tens, add the ones, and then combine. Students working with ten frames naturally begin by grouping the 10’s, not the 1’s, together.

Students find other strategies. For example,

  • Add 1 to 59 to make 60. Take 1 away from 37 to make 36. 60 and 36 is 96. (make ten)
  • Add 1 to 59 to make 60. Add 3 to 37 to make 40. 60 and 40 is 100. Take the extra 4 away. (friendly numbers and compensation)
  • 30 more than 59 is 89. 7 more than 89 is 96. (add on)

These are the strategies I use to compute mentally. On paper, I fall back to the traditional right-to-left digit algorithm. It’s the result of performing thousands of such calculations in elementary school.

Students should be encouraged to write their mental math strategies down on paper. Some students will have to.

Teachers and parents appreciate these strategies. They make sense. Teachers and parents want mathematics to make sense to their kids. But at some point they always ask the question: “When should they learn the traditional/regular/real way?” They ask this because they are concerned their kids will not be prepared. “But do these strategies work for three-digit addition?” Yes.

“Relax. This will look familiar,” Carole joked. The same natural left-to-right strategy described above can be written vertically. We start with 50 and 30 is 80. Already, we know the sum is greater than 80.

Compare that with the traditional algorithm. We start with 9 and 7 is 16. We know the sum will have a 6 in the one’s place.

Which piece of information is more important? Carole made the point that accuracy is important. Always was, always will be. But it’s not where we should start. Strategies should be built on conceptual understanding. The emphasis of a left-to-right strategy is on number whereas the emphasis of a right-to-left strategy is on digits.

In her new blog, Amy Newman also writes about this. As well, she shares Carole’s key messages for parents helping children at home.