anticipate difficulties the students might have but they also help the paraprofes-
sionals understand the mathematics in the lesson. If they understand the math,
then they can offer appropriate support in the lesson.
The lessons we discussed required students to construct buildings using cubes.
In this series of activities called Cube Buildings, each cube represents a room and
each row of cubes represents a floor in the building (Russell et al. 2008e). A build-
ing might start off as a row of 3 cubes. This would be a 1-story building with 3
rooms. Each time a new floor is added, the total number of rooms increases by 3.
Therefore, this same building with 5 floors will have a total of 15 rooms.
In the lesson I describe here, I took the process a step further by introducing
tables. After the students constructed each floor of their buildings, they tallied
the total number of rooms they had to that point and entered this data in their
two-column tables (the first column listed the “Total Number of Floors” and the
second column was labeled “Total Number of Rooms”). They continued these
steps, working floor by floor, until they constructed the building 5 floors high. At
that point the table jumped to 10 floors (see Figure 21–1).
As Pam and I were going over the activity during our planning process, the
following exchange took place.
PAM: So they just have to double the fifth floor to get the tenth.
MICHAEL: Well that’s what we’d like to see, but most kids won’t be ready to
make that jump right away. They’ll have to build to the tenth floor a few
times so they can get a sense of what a 10-story building looks like.
PAM: But wouldn’t doubling be quicker?
WORKINGCOLLABORATIVELY
Total Number of
Floors
Total Number of
Rooms
1
2
3
4
5
10
Figure 21–1.