I was cutting oranges with one of my nieces for my OTHER niece’s soccer game. She was helping me put them in the bag and she proceeds to tell me:
N: Aunty, you are cutting it in half first and then cutting again and then again
Me: Yes you are right. So when I cut it in half the first time how many pieces does that make?
N: two half pieces.
Me: Right so then you said I cut it in half again? How do you know it is half again?
N: Because it is 2 more equal pieces that you cut it into.
M: Ok, so then what do I do?
N: You cut those pieces in half again. And you do the same thing to the other half of the orange.
M: Are you sure? Watch to make sure I do it exactly like you described. [I proceed to another orange the exact same way as before]
N: Yeah see you did the same thing. So you come out with 8 pieces of oranges.
M: So what does that mean about the “size” of this smallest piece of orange?
N: **thinking** It is the same size as the others.
M: True it probably is very close to being the exact same size. What about what fraction of the orange is it?
N: Oh, it’s one eighth.
M: How do you know that?
N: Because there are eight pieces and this is one of the eight. So this is 1/8 of the orange.
M: Ic, so what is half of half? [I ask this question as I cut the half into fourths]
N: one fourth?
M: How do you know? I don’t see 4 pieces.
N: Because if you did the same thing to the other half you WOULD have 4 pieces. so one of the oranges would be 1/4.
M: Ic, so what is a half of a half of a half? [I ask this question as I cut the fourths into eighths]
N: one eighth?
M: How do you know?
N: Cuz it’s the same as I said before but with more pieces. You are just doing the same thing to both halfs of the orange. So each orange is making eight pieces.
M: Ic, so how many pieces would 2 oranges make?
M: how do you know?
M: Ic, you like doubles yeah?
N: Yeah, doubles are easy.
Orange cutting was completed and we put them in our ziploc bags. I asked her to take pictures of the ziploc bags and our eighths.