Page: 1 of 6 [T/R 1 takes one red rod away.] If I had to give another name, a number name for the red rod, if I called the dark green rod one, what would I call the red rod? What number name would I give to it? If I called the dark green rod one, what number name would I give to the red rod? [Most of the students have their hands raised.] How many of you think you know a number name, for the red rod? Why don t you talk to your partner a little bit and see what you think? [T/R 1 speaks to students off camera] You did already? [Most hands are still raised.] Beth, you want to tell us? 1.0.110 Beth: One third. 1.0.111 T/R 1: Nice and loud Beth. 1.0.112 Beth: One third. 1.0.113 T/R 1: How many think one third? You all agree. Can you tell me why you would give it the number name one third? 1.0.114 Beth: Because if you put three of them, it makes one whole. 1.0.115 T/R 1: Okay, so if it makes, three of them would make one whole. Do you agree with that? So we give it the number name one third. Okay, very good. Someone told me that light green is one third as long as blue. What do you think? 1.0.116 Erik: It s right, right, right. 1.0.117 Alan: Hmm? 1.0.118 Erik: It s right. 1.0.119 Alan: Mmm-hmm. Yep, one third. 1.0.120 T/R 1: Someone told me that light green is one third as long as blue. What do you think? What do you think, Jessica?
Page: 2 of 6 1.0.121 Jessica: It is. 1.0.122 T/R 1: Jessica thinks it is. And how would you convince me, Jessica? 1.0.123 Jessica: Because you could, if you have, you have three of these you could put it up to the blue, and it s one whole. 1.0.124 T/R 1: So if I call the blue rod one, what number name would I give to light green, everybody? 1.0.125 Students: One third. 1.0.126 T/R 1: I would give it the number name one third. Now notice, if I called the dark green rod one what number name would I give to the red? 1.0.127 Students: One third. 1.0.128 T/R 1: So are the number names always the same? 1.0.129 Students: [Tentatively] No 1.0.130 T/R 1: Are the color names always the same? 1.0.131 Students: No. 1.0.132 T/R 1: Does this have another name other than blue? Am I ever going to call this something else other than blue? 1.0.133 Student: No, oh yeah. 1.0.134 T/R 1: What am I going to call it? 1.0.135 Student: Dark blue. 1.0.136 T/R 1: Well, dark blue. So are the number names same, do they change? I mean the color names. 1.0.137 Erik: Color names, no.
Page: 3 of 6 1.0.138 T/R 1: Erik thinks that the color names don t change. Right, do we agree that the color names are always the same? 1.0.139 Alan: Mmm-hmm. 1.0.140 T/R 1: Do the number names change? 1.0.141 Students: Yes. 1.0.142 T/R 1: Okay, tell me why the number names change. Give me an example of why the number names change. Erik. 1.0.143 Erik: You could think, you could say that, you could take an orange block and a blue block and that would be, that would be three, three thirds of it. Wait, no. Wait, hold on. Well, no I mean, if you take, if you take a blue rod and you could call it one whole then you would take a diff, a smaller rod and that would be something 1.0.144 T/R 1: Which one? 1.0.145 Erik: Um, well, oh, you take a light green, and that ll be a third of it. 1.0.146 T/R 1: Okay, so I called the light green one third and I called the red one third. Why could the light green be a third and why could the red be a third? How is that possible for both of these to be a third? 1.0.147 Erik: [Raising his hand] Oh, oh, I know. 1.0.148 T/R 1: Michael? 1.0.149 Michael: Because there is a different size whole. 1.0.150 T/R 1: Because there is a different size whole. There is a different number name I gave for what I called one, okay? So when the blue is one, can you see that the light green becomes a third? But can you see
Page: 4 of 6 1.0.151 Students: No. when the dark green is one, then you see that the red becomes a third? So do we have permanent number names? 1.0.152 T/R 1: No the number names change, that's very important when using these rods. Do the color names change? 1.0.153 Students: No. 1.0.154 T/R 1: No the color names don't change. Every one of these rods has a permanent color name, but the number name changes with the problem. So let s be sure we re familiar with the color names so that we can call them the same thing, um, for the rods, we have a color name for this one, we re calling this one blue or dark blue, right, we agree with that? And we re calling this one light green, why don t you make sure you pull out all of them and see if it is true that there are ten of them, and see if we can come up with the different color names and then we ll do some problems with number names. [Many students build staircases.] 1.0.155 Alan: Six [Alan and Erik count out loud as they line up the rods as a staircase] Seven so far, seven, eight, nine 1.0.156 Erik: I got nine, but where is the ten? 1.0.157 Alan: Let s get them in lengths [Both continue to count out loud] 1.0.158 Erik: Eight, nine, ten there we go, I got them. [Alan continues to count his rods] 1.0.159 T/R 1: How many think there are ten? [long pause, students raise their hands] Okay. Okay, as I look around the room I see that you arranged them all, some of you did the same thing, some of you did
Page: 5 of 6 them differently. Kelly, your arrangement, you want to say something about your arrangement? Nice and loud Kelly. 1.0.160 Kelly: [Describing the staircase that she built] I put the tallest, then the second to tallest, third 1.0.161 T/R 1: Which is the longest rod? 1.0.162 Kelly: Um, the orange. 1.0.163 T/R 1: The orange, do all agree? 1.0.164 Students: Mmm-hmm. 1.0.165 T/R 1: And then, tell me what to do. 1.0.166 Kelly: And then I put down the blue 1.0.167 T/R 1: Blue. 1.0.168 Kelly: Then the brown 1.0.169 T/R 1: Brown. 1.0.170 Kelly: Then the black 1.0.171 T/R 1: I can t find the brown, brown. 1.0.172 Kelly: Then black, then dark green, then yellow, then like the pinkish-red. 1.0.173 T/R 1: We call this purple. 1.0.174 Kelly: Purple. 1.0.175 T/R 1: I know it looks sort of pink, doesn t it? Okay. 1.0.176 Kelly: Um, light green, then red, and white.
Page: 6 of 6 1.0.177 T/R 1: And then white. How many of you agree? Ten rods? Ten color names? You agree.