About six and a half minutes into the latest episode of My Next Guest Needs No Introduction, host David Letterman asks guest Howard Stern how long they’ve known one another. Viewers are treated to a number talk. The transcript:
David: You know how long you and I have known one another?
Howard: How long?
David: Well, it’s pretty much to the month since 1984.
Howard: Wow. Now I’m gonna do some quick math and figure out how long that is, if you don’t mind. Now math happens to be… I’m good at it. This is how I do it. This is 2018. Right?
David: It’s 34.
Howard: Oh, you gave it away.
David: It’s 34 years.
Howard: Let me check your math.
David: Yeah.
Howard: The way I get to it is, you say 1984 and I add ten immediately.
David: Yeah.
Howard: That brings us to 1994.
David: That’s right.
Howard: That’s ten.
David: Yeah.
Howard: 1994, then 2004 is 20.
David: Yeah.
Howard: Now here’s tricky ’cause I get confused. 2004 to 2014 is another 10. That’s 30. You’re absolutely right. That’s 34 years. Good for you.
David: Now…
Howard: I love to show how I do the math.
David: Speaking of which, you realize that all of that will be subtracted from the show?
Howard: Wow. But really for you… I guess the premise of this show, although who knows what this show is… you know, I don’t even know what I’m doing here, but I thought the premise was that… you’re choosing six people… and I’m way more fun than Obama already, I’m sure. I mean, this is fun.
David: Really?
Howard: Oh, for God’s sake, yeah.
Lucky for us, Letterman didn’t subtract all of this from the show. Some observations…
Despite David giving away the solution, Howard continues to share his strategy. David is not the ultimate authority; Howard is eager to prove this solution. Howard, at least, is interested in Howard’s reasoning. He’s focused on sense-making, not answer-getting; how?, not what? All of this is typical of a classroom number talk.
Howard uses an adding up (or add instead) strategy for 2018 − 1984. He moves forward from 1984 to reach 2018. The context implies distance–not removal–which lends itself to this strategy. Stern’s jumping by tens gives us an opportunity to discuss efficiency, e.g., one jump of thirty rather than three jumps of ten. For what it’s worth, I used an adding up strategy too. First I added 16 to 1984 to get to 2000 (or six and ten to get to 1990 and 2000), then I added 18 to get to 2018.
David, of course, does not record Howard’s thinking. I might use this video clip to have teachers anticipate possible strategies for 2018 − 1984 and consider how they would record them. I chose an open number line to model Howard’s adding up strategy:
Howard is confident: “Now math happens to be… I’m good at it.” He is enthusiastic: “I love to show how I do the math.” He is joyful: “I mean, this is fun.” Over the last two years, it has been my privilege to work alongside Surrey teachers Alex Sabell and Jonathan Vervaet (and others) as they’ve incorporated number talks in their classrooms. These same positive attitudes towards mathematics come through in their students’ interviews (see Alex & Jonathan).
What did you notice in this clip? What did I miss?
Chris Hunter 
I probably would add 40 to 1984 and then subtract 4 and then subtract 2, to get 34…but then, I have been told that I am pretty good at subtracting đŸ™‚
-Suminder
Interesting, Suminder. I think I might have used your strategy if the difference were closer to forty. Ask me again in 2023.
Wow. I never thought I would be impressed by something Howard Stern said. đŸ™‚