Slowing down at the end of a long, active spring day. Stormy clouds are rolling in. Tabitha and I watch them together for a couple of minutes from the west-facing window at the top of our stairs.

I ask Tabitha if I can ask her a quick math question.

She consents.

Me:How many tens are in 32?

Tabitha(7 years old): Three.

Me:So quick! How do you know that?

T: 10, 20, 30. Easy.

A silent moment elapses.

T: And there’s 10 tens in a hundred.

Me:Yes. Lovely. So true.How many tens are in 200, though?

T: Twenty.

Me:Whoa!

T: Yeah.

Another silent moment elapses.

T: Asking “How many tens are in 30?” is like asking “How many ones are in 2?”

Me:Wow. I had never thought of it like that. And is it also like asking “How many hundreds in 300?”

T: Except I don’t know that one.

Me:You don’t know how many hundreds are in 300?

T: No.

Me:Three.

T: Oh. I thought it wastensin 300.

## So what do we learn?

The power of silence and of conversations in quiet moments. Both times a silent moment elapsed in this conversation, Tabitha continued with an idea of her own. And both are gems.

**And there’s 10 tens in a hundred. **Many grade school worksheets have attested that *there are 0 tens in 100*, when what they really mean is that *there is a 0 in the tens place in 100*. We can do a lot more mathematics with the *ten tens in 100* conception than we can with the *0 tens in 100* one.

**Asking “How many tens are in 30?” is like asking “How many ones are in 2?”** This right here is powerful stuff. For Tabitha, *ten* is such an important part of the structure of numbers that it behaves like *one*. Ten, for Tabitha, is a unit—a thing that you count.

If you are new to this blog (and many of you are—Welcome!), you may not have spent four minutes with video. Do so now, please. Consider it your Talking Math with Your Kids homework. It’ll be fun. Promise.

## Starting the conversation

Wait for a quiet moment. Ask for consent. Ask *How many tens are in 32? *Listen, follow up and allow a few moments of silence.

One of the problems with numbers is that there is confusion between the number and the representation of the number. 10 is not a number, it is how we write the number whose name is “ten” in symbolic form.

10 is one ten and no ones (or units, which I think is better). Poor kids who are led to believe that there are no tens in 100 when what is intended is that there are no tens in the symbolic representation of one hundred.

have a look at my 12 page diatribe on the subject of number in elementary math:

http://www.mathcomesalive.com/savingschoolmath.doc

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