
This one’s interesting. Same kid as last time; he’s actually got it together a little bit more at the moment, most likely because I glued myself to his side the second he got to the board and coached him through when he needed it. The problem in question is 8 5/12 + 11 1/4; note a few things:
1) Correctly adds eight and eleven to get nineteen. This represents progress!
2) Recognizes that 1/4 needs to be converted to twelfths in order to add the two fractions, and– amazingly, to my mind– that he needs to multiply the numerator AND denominator by three to achieve this, and then does so correctly;
3) Successfully adds five twelfths and three twelfths to get eight twelfths.
4) Spells “mark” as “mork.” Can’t win ’em all.
Then an interesting thing happened. I asked him if he needed to do anything with 8/12 and after thinking for a second he came up with the word “reduce.” However, despite having just multiplied three and four to get twelve, he absolutely could not figure out that he needed to divide by four, nor could he successfully divide either eight or twelve by four. Note on the far left of the picture, where he’s tried to divide it, figured out that four goes into eight twice, written the eight underneath the other eight without actually putting a “2” at the top of the problem, subtracted eight from eight to get zero– and then informed me that eight divided by four was zero.
(gets interrupted by customers, promptly makes a subtraction mistake while redeeming tickets)
Harder to read is at the bottom of the picture where he tries to divide twelve by four. He first thinks the answer is two (but doesn’t write it up again) then borrows from the ten digit so that he can make the ones digit… twelve, again, which is where I stopped him and pointed out that he’d already gotten that answer by multiplying.
Note also the rogue seven near the last division part. I don’t know why that’s there, but it’s intentional; he said “seven” when he wrote it.
Clearly we need to work on long division a bit. It’ll be interesting to see how many other issues that ends up clearing up.




