Promoting primary students to reason about grams and kilograms conversions using a number line

Teacher: OK, I've got some little cards for you and I want us to put them on our number line ((pointing to number line on whiteboard)). This number line says 0 kilograms and 1 kilogram. So we're going to come up and stick them on our number line where we think they go. So my first one is 300 grams ((holding up card)). Who thinks they know where that might go on my number line? ((Several hands raised)) Aria. Come and explain why you've put it where you've put it.

Aria: ((Moves to front of class)) I think, erm, 300 grams should go here ((places card on number line)) because I think that halfway between 0 kilograms and 1 kilogram would be 500 grams, and I think that 300 grams would be closer to 500 grams. So I think that's where it should be.

Teacher: Would it be helpful to mark on halfway? ((Hands Aria the whiteboard pen))

Aria: Yes

Teacher: Pop on halfway then. ((To class)) How else could we be really specific about where 300 grams could go? ((Aria marks 500 grams on number line, on whiteboard)) Matthew.

Matthew: If you looked at it, 300 grams would be a lot closer to 500, as Aria said, than it would be to 0 kilograms. So it would be-, I think it would be further along.

Teacher: So you're disagreeing with where it's going at the moment. You'd like it moved closer to 500?

Aria: I think I agree with Matthew.

Teacher: You agree with Matthew. Go on then, move it if you want to. ((Aria moves card along number line)).

TURNS LATER

Teacher: OK. Dillis.

Dillis: I might think it will be-, because 0's bigger than 0.-, is 0 bigger than 0.9? Would it be before the 0 kilograms? ((Teacher writes 0 and 0.9 on the board))

Teacher: OK, good question, Dillis. I like your questions this morning. What do we think? Which one is bigger - 0 or 0.9? ((Some hands raised)) Cody.

Cody: 0.9.

Teacher: Because?

Cody: Because 0 would also be 0 grams, but 0.9 kilograms would be 90 grams-, 900 grams, and 900 grams is bigger than 0 grams.

Teacher: OK. Dillis, in this number ((pointing to 0 on whiteboard)) there is 0. There is no units. If I put a decimal point here, there'd be no tenths. This number is bigger ((pointing to 0.9 on whiteboard)) because I've got a 9 in the tenths. Michael.

Michael: I also got confused with what Dillis did, but the only reason it confuses you, it won't be confusing if you converted to grams.

Teacher: OK.

Michael: Cos right now it looks like it would actually be smaller, way smaller than 1 kilogram. It actually looks like it would be closer to 0 kilograms.

Teacher: I agree, and the problem we've got is we've got this one recorded in grams ((pointing to first card on whiteboard)) and this one recorded in kilograms ((pointing to second card on whiteboard)), which is why it could be confusing. Which is why it was really good that Ashton said this is 900 grams ((pointing to second card on whiteboard)). So, if this is 300 grams ((pointing to first card on whiteboard)), halfway is 500 grams ((pointing to number line)), I know 900 grams ((pointing to second card on whiteboard)) is nearly 1,000 grams. It's a really good tactic, Michael. Thank you for spotting that. Really good tactic to convert them to the same unit. So this is 300 grams ((pointing to whiteboard)), this is 500 grams or halfway, this is 900 grams. I'm going to write '900 grams' underneath it ((writes on second card on whiteboard)), and that, Dillis, might help you spot it.