Me: Can you show me where 1/2 is on a number line?
Student 1: It's half way between 0 and 1.
Me: Where would 1.2 be on a number line?
Student 2: It's after the 1. Between the 1 and the 2.
Me: So, can 1.2 be equal to 1/2?
S2: Oh yeah, if it was 1.2, there would be a 1 in front of the fraction, so it has to be 0 point something.
Me: So, what do you think 1/2 is as a decimal?
S2: Because it has to be a 0 before the decimal and there's a 2.
All right...back to the number line...
Me: Can you show me what that would look like on the number line?
S2: If I split this in to 4 equal pieces, 1/2 is at the second line, so that would be 0.2
S2: (Points to the 1st mark) This would be 0.1.
(Points to the 3rd mark) This would be 0.3.
(Points to the 4th mark) This would be 0.4
(At this point, I've basically sat back and let the girls go...hoping for a glimmer of light.)
S2: Yeah, 0.4 is not 1.....Wait....we need to split this in to 10 pieces.
(Oh, thank goodness...)
Me: Can you explain why?
S2: Because that's what the decimal place means. That's the tenths place.
Me: Ok, so try that.
Me: Does that make sense?
S2: Yeah, because it's like 50 cents is half of a dollar.
S1: Oh yeah.
What would you do?