We carefully chose the problem 26 x 4 for this number talk (mental math) in order to apply the bar model to student thinking.
I think a key element to this lesson is a deep understanding of division. For this particular class at this time, I might try inserting a lesson before the division bar model problem, that asks students a multiplication bar model problem. Once we tried out both, students might clarify for themselves similarities and differences between the two types of stories and the two opposite operations.
BECCA SHERMAN: Okay. Show me you’re ready for mental math. Put your hands on your head. Show me you’re ready for mental math, put your hands on your shoulders! Switch your hands on your shoulders. Switch ‘em again. Switch ‘em again. Put your hands on your… cheeks! Put your hands on your… chin! Who’d I get? Nobody. I got one. Put your hands on your… cheeks! Okay.
BECCA SHERMAN: Here we go. You’re gonna try it in your head, we want you to think about, a multiplication problem. 26…Here we go. Here we go. Show me you’re ready with your hands on your head. You guys were ready …and then I wasn’t ready. Gosh, Ms. Sherman. Here we go. Here’s the problem: 26 x 4. Thank you, ma’am. Just think about it. When you have an answer, how do you show me? Thumb at your.. chin.
STUDENT: No, chest.
BECCA SHERMAN: At your chest. If you have two ways to solve it, how do you show me? Two fingers. 26 times 4. I’m gonna put the… remember, don’t stop anyone else from thinking. Don’t say anything out loud.! That’s another one. Just think to yourself. You’re gonna share in just a minute. Okay. We’re gonna go with one minute. Talk to your neighbor. How did you do it? What did you get? How did you do it?
STUDENT: Um, I did… 4 times 12 equals,
STUDENT: First, I did 6 times 4 is 10, carry the 1 up. 1 times 2 is 3, 4,5,6,7. So it’s 70.
STUDENT: equals 96.
STUDENT: 100, then 100 plus..
STUDENT: 26 times 4, 6 and 4 equals 24, carry the 6,
STUDENT: I would maybe go down, and that would be 4 times 6, equals 24, so I put the 4 down,
STUDENT: Put the 2 up there, 2 times 4 equals 8, plus 2, equals 10, so, uh, 104.
STUDENT: 6 times 4 on the, like equals, like…
STUDENT: 24, and but the
STUDENT: put the 2 on top of the 2, that makes 4.
BECCA SHERMAN: Could you do it another way, where you break it apart into equal groups?
STUDENT: What is the answer? What’s the answer? I forgot.
STUDENT: 104, yeah.
BECCA SHERMAN: Okay, lots, lots of good ideas. Let’s see if we can get different ideas up here. You can share your idea or your neighbor’s. Can we start with answers first? Let’s just see, what did you guys get for answers. What’d you get.
BECCA SHERMAN: Okay, a different answer.
BECCA SHERMAN: What’d you guys get?
STUDENT: Um, 30.
STUDENT: I got 170.
BECCA SHERMAN: What?
STUDENT: No! Not 100! Not 170, just 70.
BECCA SHERMAN: Okay, thank you.
BECCA SHERMAN: So, okay. Is this an answer that there’s gonna be more than one correct answer to? Or a question that there’s gonna be more than one correct answer to?
BECCA SHERMAN: Sometimes there are, sometimes there aren’t. This one, if we’re multiplying groups, there’s gonna be one correct answer. So we’re gonna learn from these. And we’re gonna see how we thought about it. Okay?
Students first respond with the common strategy of using a traditional U.S. algorithm and making traditional errors.