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## Teachers talking about elementary mathematics

This is a transcript of a group of beginning teachers discussing the mathematics of a lesson presented in a published curriculum. The lesson, which was written for fifth graders, asks students to make place value (or magnitude) estimates before multiplying. In other words, students look at a problem and then decide if the answer is in the tens, hundreds or thousands before solving it. One of the teachers was not happy with this idea, however.

 Lara: You know what? I want to share a problem that I have with this lesson. It's asking them to find a magnitude estimate, like tens, hundreds, thousands. Is that what we want? Let's say you have a number like 9.7 and 9.8 and you multiply these. Well, the answer is going to be, if you round it, it's going to be 100. If you don't round it, the actual answer is not in the hundreds. It's less than a hundred. Mike: Did it always want to round like that or was it looking for high rounds, low rounds? Because if you round down, your lower estimate is going to be 81. So it's somewhere between 81 and 100. Lara: But this particular activity, see, is asking you to round. And then multiply and you figure out, well, 200. It's in the hundreds. But it's not all the time. That's the thing. Mike: You have to show them that if we're circling the hundreds it doesn't mean that it's going to be 100. It's going to be near a 100. Or say we're rounding up. This is the highest it could possibly be. So that's our upper limit. The highest it could possibly be is in the hundreds. Lara : So we should show an upper and lower limit? Gillian: Some people may push a button when they're using their calculator and they'll be like “Oh, 12,150,” when it's really supposed to be a little above 100 or a little below. So I think that's the main objective. Lara: That is the main objective. I just really feel like there's a huge difference between a number like 200 and 900. They're both in the hundreds; but, if a kid's getting 200 on the calculator and it's supposed to be 900, I don't see how saying ‘hundreds' in the estimate is going to help.

Discussion questions:

• Do you agree with the problems Lara raises with this lesson?
• Should this lesson be taught as is, revised or scrapped?
How does this sort of conversation differ from one about how to make estimation interesting to children?