What Is the Question?
Once we had worked on the visualization and representations, we returned to the
“unpacking part.”
KAREN: So, now we are down to where we are actually computing numbers
to answer the question. We actually need to know how many of each color
they produced. We talked about the constraints, that there have to be 2
white for every 3 black, and there has to be silver.
JOHN: Instead of saying of the cars are silver, another way you could think
about it is 1 out of 9 is silver. Then they have to figure out how many groups
of 9 are in 315.
MARTA: You might even want to model that with cubes. 9 cubes, 1 of
which is silver. So, you could ask, “If you have 18, how many silver would
you have? If you had 27, how many silver would you have?”
JOHN: So continuing the pattern, they will need to figure out, how many
groups of 9 are in 315.Working Through the Computation
At this point, we discussed how to best support students’ computational strategies.
This discussion would also support Karen, who was not as cognizant of the strate-
gies that the students had at their disposal. When Karen worked with students in
math class before, she often found herself asking the students to explain how they
were approaching a computation simply because she didn’t understand their strat-
egy. Although the articulation of their strategies reinforced students’ understand-
ing of their own thinking, Karen knew that it was useful for her to be aware of
how to support students as they applied their computation strategies to a particu-
lar problem, so we discussed possible strategies in some detail.
KAREN: Are they going to want to divide 315 by 9?
MARTA: A lot of them might chunk it, something like this: 10 9s 90; 10
9s90, 10 9s 90. That’s 30 9s 270. Five more 9s 45. 270 45 315.1
91
9WORKINGCOLLABORATIVELYBlack
Cars369121518White 2 4 6 8 10 12
CarsFigure 23–1.