CHRIS: You can double the 25 and get 50 because you’re just adding 5 more
floors. There are 25 rooms when it’s 5 floors so 25 more is 50.
SAVANNAH:[breaking the 10-floor building in half] See, these are the same.
They each have 5 floors, so it’s double.The students also had ideas about why you couldn’t double the rooms in a 6-
story building to figure out the total in a 10-story building. Jessica said, “If you
double the sixth floor then that would tell you how many rooms are on the
twelfth floor. That would be 60.”
Another student demonstrated this with cubes much like Savannah did
earlier. Still another student further elaborated on the idea by saying you
could double the total on the second floor to find the total on the fourth floor,
and you could double the total on the fourth floor to find the total on the
eighth.
These student explanations helped Pam understand that the math in the
activity went beyond counting patterns and doubling. I think it helped her to see
the level of knowledge needed for students to justify the doubling strategy. When
the students left for music class, we debriefed.
PAM: I can see why using the buildings helps.
MICHAEL: Absolutely. That’s why I make everyone build them even if they
notice that they can double to solve for the tenth floor. Do you feel like
Steven was making the connection?
PAM: Not at first. I had to introduce the whole process all over again. He
forgot about the rooms and floors. He really didn’t know what he was doing.
But it was good because I had Robert work with him and sort of teach him
how to make the buildings.
MICHAEL: That was good idea. How was the pacing with both of them?
PAM: It was actually fairly balanced. Steven needed a lot of support con-
structing the building and Robert needed help with the table so they were
able to help each other.I understood why Pam wanted to push Steven’s strengths to help him with
the activity. If all the activities were like the first ones, he would have aced all of
them. However, once she understood the bigger picture, she knew he needed
much more.
Reflections
As Pam became more proficient at observing and analyzing students while they
worked, she began thinking like a teacher. For example, she made better decisions
WORKINGCOLLABORATIVELY