MALIA: 25!
TEACHER: So, Malia, even though she didn’t wait for us, thinks she knows
the next square number... is 25...
MALIA:[laughing] No... No...
TEACHER: So, she’s going to have to prove it! Do you agree?
SHARONDA: No, because after 3 is actually 4 instead of 5.
MALIA: After 4 what goes after it?
SHARONDA: 5...
MALIA: And what is 5 5?
SHARONDA: 25! So, if you put... oh, sorry! [laughing]
TEACHER: Sharonda is having a moment there... so 1, 4, 9, 16, 25...I sensed that they were working on some important ideas. The students thought
back to what they knew about squares and how a square figure connects to a square
number—that a square number is a number multiplied by itself. They were very
excited and engaged. I was pleased that they were thinking beyond just answering
the question to being curious about what was actually going on. I constantly encour-
age my students to think like mathematicians—to be curious about why numbers
work the way they do—so to see this happening was quite thrilling for me.
I decided that it was time to review and solidify their understanding, revisit-
ing the array model, but I did not explore what was happening to the array each
time the dimensions increase by 1 (e.g., why the pattern goes from 9 to 16 to 25).
Although Malia seemed ready for this discussion, I knew that Kendrick and
others were not quite ready, and I did not want them to lose focus.
TEACHER: So, is it clear what makes a square number? Think about the
shape of a square—equal sides. So 1 by 1, equals 1, which is a square num-
ber, and 2 by 2 makes 4, a square number. So, let’s look at those numbers
again. Is 25 a square number?
ALL: Yes!
TEACHER: What makes 25 a square number?
ALL: 5 times 5!
TEACHER: Which is the same as 5 squared! Remember that, too?
SHARONDA ANDMALIA: Oh, yeah!
TEACHER: How about 81?
KENDRICK: That’s 9 squared!
TEACHER: Oh, Kendrick, that’s very good!I was pleased with the contribution that Kendrick made during the discussion.
Because he is quiet and soft spoken, he sometimes tends to get lost in the crowd
during our large-group discussions. And because he also has processing problems, I
BUILDINGUNDERSTANDINGTHROUGHTALK