So there are 10 10 10 5 35 silver cars. Then there is another part.
They are going to need to subtract to find out how many cars are not silver.
There are 280 cars left.
JOHN: So now we are back to visualizing 3 black cars for every 2 white cars.
We want to continue that representation using an array model. The array
model of division would work well in determining how many groups of 5 are
in 280 (the number of nonsilver cars) [see Figure 23–2].
MARTA: So the students have to visualize these groups of 5, with 2 white
and 3 black like we did before until they get to 280 cars.
JOHN: And hopefully instead of counting each car, they will look at them
in groups of 5. So, you might ask, “If we had 10 groups of 5, how many of
each color would you have?”
MARTA: And they should be able to say, well, there are 20 groups of 5 in- Twenty in another 100, which would be 40. Another 10 would be 50,
and then you would need 6 more. That would be 56 groups of 5 in 280.
KAREN: So, what we are trying to do is get them to see 280 in groups of 5.
MARTA: Right, once they get that there are 56 groups, they should think
that in each of those 56 groups of 5, there are 3 black cars and 2 white cars.
JOHN: So, they are going to have to multiply the number of groups by the
number of cars of each color in each group.
KAREN: So, 56 3 black cars and 56 2 white cars.
MARTA: And 56 2 would be 112 white cars and 56 3 would be 168
black cars.
JOHN: Which would you give you the 280.
Preparing for Points of Confusion
Throughout our discussion, we all noted places that might be difficult for the chil-
dren, and we developed strategies to help them work through those challenges.
We knew that keeping track of what the problem was asking—figuring out how
many cars were silver and then splitting up the remaining cars proportionately to
figure out the totals—would all be areas of challenge for these students. We saw
the KWC chart as a tool to help them organize the information and understand
Planning Guided Math GroupsFigure 23–2.
20 20 10 65 100 100 50 30