Hi! Still here. Still have an awesome 13 year old here. Last week I bought cookies and dumped them in the cookie jar before J got home. When she noticed them, we had this conversation:

J: How many cookies are in the jar?

What do you think?

J: 50

I see 16 on this side. There's like 3 sections so that would be 48. But I feel like there are more cookies in the middle.

J: 61

I happen to know that they came in three rows, so it's probably a multiple of three.

J: No fair! How do you know that?

I put the cookies in the jar. There were three rows in the package.

J: I get to change my answer then...

Why do you want to change it?

J: 61 isn't a multiple of 3. So... 66.

Okay. Let's see what the package says.

J: (looks at snapchat on her phone while I retrieve the package from the trash) Ha! He said 11. There's 11 right there!

(I figure out that she sent a photo of the cookie jar to her friend and asked him to guess too.) Tell him to try again! So the package says the serving size is two and there are about 27 servings per package.

J: Doesn't it just say how many there are? (Grabs package) It has the weight... How are we supposed to know?

You can do this. So if one serving is two cookies and there are 27 servings, how many cookies is that?

J: I don't know.

One serving is two cookies. How many cookies in two servings?

J: 4

Three servings?

J: 6

Want me to keep going until 27?

J: No... Isn't there a problem we could do?

Sure!

J: What is it?

You tell me!

J: I dunno

Well, how did you get 6 for three servings?

J: I added two... So I keep adding two... Until 27... So we do 27 times two?

Great idea! (She starts opening the calculator app.) What's twenty times two? (She types it in her calculator anyway.)

J: Wait, what's your guess?

(I realized later she meant my estimate for cookies in the jar, not my guess for 27*2.) 54

J: I was way off. I thought it was like twice as many.

No, you were pretty close. Twice as many would be 108. So it says about 54, does that work? Is it a multiple of three?

J: No. (Looking at snapchat again.) Ha. Now he guessed four. He's not even trying!

(I explained too low and too high guesses for Estimation 180 but her friend didn't want to talk math with us.)

J: Wait but what was your guess?

Oh. Um. When I counted the 16 on one side I thought there were more than 48 so I guess I thought it would be over 50.

This conversation was less about me probing J's thoughts on estimating and more about me modeling mine. I'm curious how she got 50 as an initial guess (surprisingly close!) or why she picked 66 as her multiple of 3 when 60 and 63 were closer to her last guess. But I knew that we were going to figure out the number of cookies by serving size and I wanted to keep her interested through to that part of the conversation. I was fascinated by her phrasing "Isn't there a problem we could do?" She didn't think of "How many cookies?" as a problem. She didn't think of "one serving is two cookies and there are 27 servings" as a problem either. She only thinks of "27*2=__" as a problem.

Fun!

ReplyDeleteHere's a follow-up or two that I'd like to have fun with:

How many more cookies are need to fill the jar?

How long will the cookies last?

When will there be too much air in the jar that it makes the cookies go stale even faster?