Units of measurement

This post is edited and remixed from a post on my other blog last summer.

Loyal reader Jim Doherty wrote in to report the following conversation with his 4-year old daughter Mo.

They are on a long drive to a hotel.

Mo (4 years old): How far are we?

Jim: We are 20 minutes away.

Later, having arrived safely, the family heads to the pool. Mo is practicing the fine art of jumping from the edge of the pool into her father’s arms. An important part of this art is to increase the risk by jumping greater and greater distances.

Tabitha reconstructs a jump of considerable size for illustrative purposes.

Mo: (four years old) Back up, Daddy!

Jim: This far?

Mo: More!

Jim: Here?

Mo: More! You need to be five minutes away!

Jim: Do you mean five feet away?

Mo: No! Five minutes!

At this point, Papa Doherty is flustered. Is Mo messing with him? Is she confused? Is he at fault for answering Mo’s earlier How far? question with a time rather than a distance? What should he do?

My hunch is that Mo is not messing with her father. Instead, she has taken his cue for talking about how far, and she is playing with it. This is how children learn—they hear something and they try it out.

Here is how we might turn this conversation into a bit more math learning. Imagine Jim’s next response this way:

Jim: OK. Tell me when I’m there. But then don’t jump right away; I want to ask you a question before you do. [Daddy backs up slowly…]

Mo: OK! There!

Jim: Right. Here’s my question: Do you think it will take you five minutes to get to me from where you are?

Mo: Yes.

Jim: Do you know how long five minutes is?

Mo: That far.

Jim: No, no. Can you think of something we do together that takes five minutes?

Mo: No.

Jim: It takes us about five minutes to read [INSERT TITLE OF FAVORITE PICTURE BOOK HERE] together. Do you think it will take that much time for you to get to me?

At this point, I have no idea how Mo will respond (which is what fascinates me so much about talking math with kids). I do know that pretty soon, she is going to want to jump, and that whether that’s right away or after a few more exchanges doesn’t really matter.

What matters is that she’s been asked to think.

This line of discussion lays the foundation for thinking about distances, times and their relationships to each other. It supports Mo’s attempts to participate in the conversation about measurement.

My conversation with Tabitha about the height of our hill last summer was in a similar spirit; we worked on the meaning of height when she asked me to lie down on the hill.

Griffin wanted in on the action. Here is his jump shot.