Show your work, the instructions say, in tens and ones.

Okay. Fair enough. What’s the problem?

35 – 18 = ____

When I was a kid learning to do the math,

we were taught to borrow from the tens column

which made a problem like this easier to do; it

made one hard problem with two big numbers

into two easier problems with smaller numbers and

everything worked out nicely.

You ended up, without too many mental gymnastics,

with a neat and tidy correct answer: 17.

But now, you must show your work in tens and ones.

I could not figure it out. I learned, only after

an email to the teacher and specific instructions sent home,

that you create a graphic representation for each number,

say, three slash marks for 30 and next to that, five circles for 5;

underneath that you make one slash mark for 10 and eight circles for 8.

You cross out one 10 from three tens and you get 20, but you know,

you can’t take 8 ones away from 5, so you have to do that borrowing thing

by graphically crossing out another 10 slash mark

and then replacing that by putting 10 more circles over there with the

5 over the 8. Okay, now we’ve got something like 15 circles over 8.

Subtract or cross out 8 from 15 and you’ve got 7! Ad that loner 10 to the 7

and you’ve got 17.

By the end of that first evening, before I got the remedial second grade

math help I needed, the symbolic part, flustering even his double

masters degree dad, gets the boy saying the words every parent,

but especially one who happens to be an educator, dreads,

that homework sucks and math, in particular, is stupid,

and additionally,

the boy is weeping and throwing a tantrum.

I’m doing my best to be encouraging and supportive

but it’s really difficult because I’m having a real

hard time with the new math where the young ones

are expected to make the abstract concrete

by drawing pictures for every move in a problem

they can probably do in their head while they cry

and begin learning to hate school.

I am there to do some cheerleading.

Maybe it helps the boy to see his father

struggling with the problem; maybe the boy

feels validated when his dad says he’ll

write the teacher an email asking to be

taught some second grade math so that

he can help his son; and maybe he learns

the really difficult lesson that so many

of my high schoolers never picked up:

hold to the difficult, Rilke says, learn

to love the questions themselves.

The math will be solved when it’s

ready to be solved and soon, maybe

we’ll live our way into the answers.

So we move the second grader from

addition and subtraction of double digit

numbers to Rilke’s *Letters to a Young Poet *and we see how that flies.

This is brilliant. Thanks, John!

An open number line is an easy way for kids to show their thinking, and might make more sense to him. Try this link:

or do a search for “open number line.”

Not sure if he’s there yet, but for the problem you showed, most of us would think (35-20)+2, I imagine, which could also be demonstrated on an open number line. Maybe you can be efficient and do new math at the same time. 🙂

Thanks, Kirstin. This seems like a pretty nifty strategy. Our little guy eventually mastered the whole graphic representation thing (on that first evening I bet there was more going on than just difficulty with the math), but I could see him latching on to an idea like this. This strategy seems to bypass the whole tens and ones concept–sort of. I wonder if that’s why she’s doing it this way now–and that maybe an open number line is down the road. Maybe I’ll shoot that question out to our second grade teacher!