Math Conversation

Using a sample count from field trip, estimated the number of plants in the whole field .

JPM: Marjorie and some children went back to the small cornfield. They counted 34 rows of corn. They counted 112 plants in each row. What would we do to find out how many plants are in the whole field?

CAZ: Count them. You would count really high!

JA: Count how many rows, then count by tens in each row.

AG: You could count by 10’s.

DK: If you counted it would go to infinity!

CAZ: One of my friends said there would be such thing as "infinity-one."

DK: No, because infinity is too high. But if you knew how many were in a cornfield, you could fly over in an airplane and count. You would count more and more.

JPM: What’s you guess about how many are in the field? Your estimates 34 rows, 112 in each row

DK: Infinity.

CAZ: 850.

AG: 25.

JPM: Just to remind you, 34 rows, 112 plants in a row. JA?

JA: 40.

JPM: So our estimates were infinity for DK...

DK: I changed my mind. 1,005.

JPM: DK estimates 1005 corn plants in the corn field.

AG: I changed mine, too. 90.

JPM: 90 corn plants for AG.

JA: Now I think it would be 99.

JPM: JA thinks 99 corn plants in the corn field.

(No record of discussion of how they arrived at their answers; not much evidence of strategy beyond

thinking of a big number.)

JPM: Any ideas for how we could check to see how close our estimates were?

JA: We could go there right now and count them. I was already there about four times with Marjorie.

JPM: Today we haven’t time. Can we represent the corn some way and use that?

(Someone suggested tally marks. No other ideas. JPM made 34 tally marks, one for each row.)

DK: Too bad you don’t have a square for each one.

JPM: You mean like graph paper? The paper with lots of squares all over it?

CAZ: Yeah, like graph paper. We don’t have any.

JPM: Actually we do. I will get some if you have an idea for using it.

(They concur. On graph paper, JPM makes tallymarks while the children count, one for each square. Ran out

of room.)

JPM: What do we do now? There’s not enough room for all the marks we need.

AG: Tape some more to it.

(We do. On the long axis, they help by counting to 112 while teacher makes tallymarks. Again, ran out of

room and taped more paper on.)

JPM: Okay, we made out 34 rows and are 112 in each row. What next?

CAZ: Counting will take a long time.

JPM: Is there a faster way we could use?

AG: You could count by 100’s. There’s 100 and something in the rows.

JPM: Everyone willing to try that with AG and me?

(They are. They all sound a bit hesitant at 1,100 etc., but catch on and keep going all the way to 3,400. Every

one is impressed).

JPM: We counted the hundreds. Remember there were more than 100 in a row. What do we do about the

leftovers? How do we count them?

AG: I think by 2’s.

(We started, but JPM’s sub arrived.)