One goal here is to access prior knowledge and formatively assess student understanding and confidence levels about multiplication. Additionally, we have planned to organically introduce the bar model and to highlight the importance of "equal groups" in multiplication.
BECCA SHERMAN: While she’s doing that, let’s think about our groups. The groups are all of 3. Is it still multiplication if we have a group of 3 and a group of 4 and a group of 5? Could we use multiplication for a group of 3 and a group of 4 and a group of 5. Add them all up. Could we do multiplication? What do you think.
STUDENT: It would be 15.
BECCA SHERMAN: So you added those, how did—3 plus 4,
STUDENT: ‘Cause, um, there’s 3 groups of um, I mean, there’s, um. There’s 5 groups of 3, and 3 plus 3 equals 6, and with another 6, 12, and one more 6 it would equal 15.
BECCA SHERMAN: Okay. So we just had an explanation of… 3 groups of 5? 5 groups of 3. Okay, we’ll come see in just a minute. We just had an explanation of 5 groups of 3 that we’re gonna look at in just a minute. Can you show us… we were looking for 3 groups of 3 in our picture. What’d you come up with?
STUDENT: Groups of 3.
BECCA SHERMAN: Can you show us? What’d you do. Tell us what you did.
STUDENT: Um, in this other 3 I put the box here.
BECCA SHERMAN: One more box? Okay. Thank you! What do you guys think about, if we add 1 more box, What do you think, Derek?
STUDENT: Then it would be .. then it would be 3 times 3.
BECCA SHERMAN: Okay. So that was my funny little design there. I can put another 3 in there. If it’s the same size box, we can maybe guess that it’s 3 still? Okay. Then we said all together that would be
I love the chatter in the background. It reminds me what an engaging math classroom sounds like… kids sharing ideas. The connection between multiplication and addition is brought to the forefront for exploration and justification. The culture of investigation seems alive with students safely questioning each other’s thinking: Given the statement that 6+3=9 is connected to 3x3=9, a student questions where the “6” cam from. I see now that this was an opportunity to capitalize on the student language of “groups” and further the idea that they must be equal groups.