## Flashback Friday: “Sharing” in Sums

When my own kids were VERY young, we used to play “finger math.” Hold up some fingers on each hand and ask “How much is 2 and 3?” Of course, in time it changed, bit by bit so that “2 and 3” became “2 + 3,” holding up the fingers became their job, and then there were no fingers at all. The specific memory involves asking my daughter “How much is 3 and 5?” Right away she said “Eight!” Since we had been playing for a little while, I teased her, saying “No, it can’t be eight. You told me 4 and 4 was eight!” She replies with “Look, Mama, you give one from the five over to the three and then it’s four and four!”

Why don’t students automatically think that way more often?

I know, some do, but it seems that addition is so often accomplished one of three ways:

-It is a “known fact” they are able to recall immediately.

-They “stack the numbers” (either on paper or mentally) and add using the algorithm.

-Ummm, I’m too lazy so I’ll use a calculator.

Now, occasionally students will use alternative mental strategies, but often only IF the numbers are “compatible” to begin with, such as 25 + 75. Why don’t we encourage them to MAKE the numbers “more compatible,” if they can? Who wouldn’t rather add 40 + 63 than 39 + 64? What about 50 + 75 instead of 48 + 77? How can we improve our students’ “computational FLEXibility” instead of just focusing on their “computational ABility?”

Enduring Mathematical Understanding doesn’t come from knowing how to apply an algorithm, it comes from looking for alternatives, strategies, and shortcuts that arise from a deeper sense of number!