# Counting by fives

The time I spend doing the dishes is frequently productive. Tabitha (6 years old) or Griffin (9 years old) will often linger nearby playing and talking. Sometimes they talk to me. Sometimes they talk about math, as on a recent evening.

Tabitha (6 years old): 5, 10, 15, 20, 25, 30…

She continues until 170, at which point she becomes bored.

T: Dad! I can count by hundreds. Want to hear?

Me: Yes. Yes I do.

T: One hundred, two hundred, …

She continues to nine hundred, when she pauses. I wait a few beats to see what will happen. When nothing does, I ask.

Me: What comes next?

T: Ten hundred.

Then…

T: Hey Dad, when do you get to one thousand?

Me: Awesome. Ten hundred is one thousand. That’s the word for ten hundreds.

T: What comes next?

Me: One thousand one hundred.

T: One thousand two hundred, one thousand three hundred,…

She continues. She reaches one thousand nine hundred.

Long pause.

T: Two thousand. [She smiles broadly.]

Later that evening, she is doing her weekly homework, which involves counting by fives. It is not clear from the directions whether she is to start over for each kind of five, or whether she is to continue counting all the way down the page.

Tabitha decides to continue the counting, and this seems the more appropriate challenge for her.

She gets to 95.

T: How do you write one hundred?

Me: A one and two zeroes.

T: How do you write one hundred five?

Me: You tell me. You try, and I’ll tell you whether it’s right.

T: One-zero-five.

Me: How did you know that?

T: Replace the zero with a five. How do you write one hundred ten?

Me: What do you think?

T: One-one-zero.

# So What Do We Learn?

The first activity was about number language. Tabitha was following the patterns in number language and puzzling over the places where the patterns break down. One hundred, two hundred, three hundred…how does one thousand pop out of this sequence?

The second activity was about writing numbers (or numeration). Tabitha had no trouble counting through one hundred five, but she wasn’t sure how to write it.

A common error is to write this: 1005. The thinking goes like this: One hundred is 100, so I’ll write that, then put a 5 at the end.

# Starting the conversation

Any time a child asks if you want to hear her count, the correct answer is yes. Then listen. Listen for the challenging bits (the teens are difficult, as is anything following a ‘9’—such as 19 to 20, or 49 to 50). Be ready to help if they get stuck but also to let them think it through and try for themselves. Then talk about how they knew to do what they did. Talk about their thinking.