My kids can : making math accessible to all learners, K–5

Karen was glad that we had discussed possible computation strategies prior to
the lesson. She was able to support the students as they computed 315 divided by
9, using their strategy of breaking up 315 into groups of 9 with “friendly numbers,”
such as 10 9 and 15 9. From her schooling, Karen was only familiar with the
long division algorithm, but she was beginning to see that methods such as
“chunking” foster a deeper conceptual understanding.

KAREN: It looks like all of you got 35. So we know we have 35 silver cars.

What do you think we need to do next?

NINA: We need to figure out the black and white. The and.

KAREN: Do we know what number we are going to take and from?

SALLY: Not yet.

TASHIA: We have to find how many are left after we take out the silver. So

we can find out about the black and the white.

KAREN: OK, so let’s find that out.

The students worked to find out the difference between 315 and 35. This
group of students was fairly proficient with basic operations, so Karen didn’t need
to give them much support to be successful with this step.

SETH: We have 280 cars left.

TASHIA: And some of those are black.

SALLY: And the rest are white.

JULIO: Let’s make a chart. [Other students add rows to Nina’s row of 3 black

and 2 white cubes.]

KAREN: OK, let’s look at the groups of 5 cubes we have started. How could

they help us make a chart or to solve the problem? To make the problem

easier? [see Figure 23–3].

JAY: We can go 5, 5, 5, 5 times a number.

KAREN: It might take a long time to count by 5s.

JULIO: We could divide 280 by 5.

JAY: It might have a remainder.

NINA: I don’t think so.

The students worked to find the number of groups of 5 in 280. Karen was re-
ally impressed with the way the students split apart the 280 into 100, 100, and 80
and found how many groups of 5 there were in the total by adding 20, 20, and 16.

KAREN: So now we know there are 56 groups of 5.

JAY: We could take of 56.

KAREN: OK. So let’s look at the cubes. There are 56 groups like this.

JULIO: We will divide them.

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WORKINGCOLLABORATIVELY