0@Loc: CarlaJim/garden1.cha1@PID: 11312/t-00001780-12@Begin3@Languages: eng4@Participants: T Teacher, G Student, H Student, S Student, N Student, D5Student6@ID: eng|CarlaJim|T|||||Teacher|||7@ID: eng|CarlaJim|G|||||Student|||8@ID: eng|CarlaJim|H|||||Student|||9@ID: eng|CarlaJim|S|||||Student|||10@ID: eng|CarlaJim|N|||||Student|||11@ID: eng|CarlaJim|D|||||Student|||12@Media: garden1, video13@Date: 15-MAY-200314@Comment: Transcript from Greeno & van de Sande, Garden Lap Problem15Perspective, 8th grade algebra16*T: &=standing_up_front okay, Ladies and Gentlemen. ▶17*T: What I would like (.) &=looking_around18for us to do right now +... ▶19*T: We spent a lot of time, ▶20almost like a whole class period setting up ▶21the prob ▶22the picture of the flower xxx problem. ▶23*T: and Jason had proposed one possible uhm +/. ▶24*S: solution . ▶25*T: solution . ▶26*T: &=drawing_on_board ▶27and you guys decided on +... ▶28*T: I'm drawing it backwards ▶29from how you guys drew it ▶30&=drawing_rectangle_and_labeling_the_length_and_width_dimensions . ▶31*T: you guys decided that Jason's was incorrect because? ▶32*T: &=rising_intonation_and_standing_to_side_of_drawing ▶33Do you guys remember that? ▶34*T: why was Jason's not right? ▶35*T: &=drawing_the_left_vertical_portion_of_the_inner_rectangle . ▶36*S: &=say_dimensions_are wrong ▶37&=tell_her_correct_dimensions . ▶38*T: &=makes_changes . ▶39*T: Why was Jason's +... ▶40*T: Do you guys remember that? ▶41*T: Why was Jason's not right? ▶42*S: Because xxx . ▶43*T: It was (.) right. ▶44*T: It wasn't an even border ▶45&=continuing_to_draw_the_inner_rectangle . ▶46*T: We needed to have an even border. ▶47*T: &=finishes_drawing_the_inner_rectangle . ▶48*T: and, you guys found that this area of this part +... ▶49*T: &=shading_in_the_border_region_blue . ▶50*T: You guys found that this area was equal to: ▶51&=writing_in_the_border_area ▶52twelve thousand, ▶53I mean twelve hundred, sorry ▶54twelve hundred, feet squared. ▶55*T: Is that true? ▶56*T: &=turning_and_looking_briefly_at_the_s's . ▶57*T: And then the area inside of here ▶58&=indicating_the_inner_rectangle . ▶59*T: you guys found ▶60&=shading_the_inner_rectangle_red ▶61was equal to: ▶62like sixteen (.) what was it? ▶63*T: sixteen: eighty or something? ▶64*T: Is that right? ▶65*T: Feet squared. ▶66*T: okay. ▶67*T: &=walking_to_the_back_of_the_classroom . ▶68*T: &=standing_toward_the_back_of_the_classroom ▶69so, you guys had found umm (.) ummm. ▶70*T: So, what I wanted to do ▶71you guys could go ahead and keep on guessing and checking ▶72I think actually this group ▶73&=H's ▶74&=walking_forward_and_pointing_out_one_group_of_s's ▶75went ahead and guessed and checked and found ▶76you guys found the even border ▶77&=walking_up_to_the_board_and_indicating_parts_of_the_diagram . ▶78*T: You guys found what the answer would be for these two borders . ▶79*T: what would have had to have been cut into this court ▶80&=pointing_to_vertical_border_and_horizontal_border ▶81&=motioning_in_the_air ▶82to make that be an even border. ▶83*T: &=erasing_some_of_the_border_shading . ▶84*T: So, this is my ▶85&=moving_to_side_of_classroom . ▶86*T: What Jason had proposed didn't work, ▶87so what I wanna know is what in this problem +... ▶88*T: Let's xxx work guess and check +... ▶89*T: We want xxx guess and check . ▶90*T: we want to also be able to write ▶91equations that will hopefully help us be able to solve ▶92problems like this. ▶93*T: So, to have an equation, ▶94we need to have a variable to write the equation. ▶95*T: So, in this problem +... ▶96*T: I kind of gave it away. ▶97*T: what I wrote, oh, well ▶98ummm. ▶99*T: what would my variable be? ▶100*T: xxx ▶101(.) . ▶102*T: Oh, not all at once. ▶103*T: What would my variable be in this? ▶104*T: What am I trying to figure out here? ▶105*T: &=calling_on_G okay, G? ▶106*G: You're trying to figure out the two lengths of the inside square. ▶107*T: I'm sorry. ▶108*T: I couldn't concentrate on what you were saying. ▶109*G: You're trying to find out the two lengths of the inside ▶110or the +... ▶111*T: the two lengths? ▶112*T: What do you mean 'the two lengths'? ▶113*G: of the inside square, like ▶114&=points_up_at_board . ▶115*T: &=indicates_length_and_width_of_inner_rectangle_on_board ▶116This? ▶117*G: yeah. ▶118*G: You could put them as x@l and y. ▶119*T: &=labeling_the_vertical_length_x_and_horizontal_length_y ▶120x and y. ▶121*T: okay ▶122&=standing_to_side_of_picture . ▶123*T: so, is there any way I can write an equation for this? ▶124*G: &=raising_hand_and_beginning_to_speak_when_T_looks_at_her ▶125Umm ▶126I came up with ▶127ummm ▶128x@l divided by ▶129or, forty minus x@l ▶130divided by two . ▶131*T: &=leaning_forward_and_looking_back_at_the_diagram ▶132forty ▶133minus x@l ▶134divided by two. ▶135*T: where'd you get that from? ▶136*G: can I go up and show you xxx ▶137&=G_goes_up_to_board_and_T_walks_toward_back_of_classroom ? ▶138@Comment: In her explanation below , G has the x@l and y@l dimensions139reversed, so she refers to 40-x as the vertical border width and14072-y as the horizontal border width instead of the way it is141depicted. Recall, however, that T mentioned earlier that she was142drawing the diagram backwards, so it is possible that his confusion143resulted from that transposition rather than a misunderstanding of144the relationships.145*G: &=up_at_board ▶146this length is forty ▶147&=indicating_the_vertical_length_of_the_outer_rectangle . ▶148*G: This length right here is forty. ▶149*G: And this is um x@l ▶150&=indicating_a_vertical_length . ▶151*G: So, if you do forty minus x@l ▶152divided by two, you'll get the two ▶153&=indicating_the_two_vertical_borders ▶154widths, I think. ▶155*G: That's what I came up with. ▶156*G: I don't ▶157think it's right I don't know if it's right. ▶158*G: And then seventy two minus y@l ▶159&=indicating_the_y_on_the_diagram divided by two will get those ▶160&=indicating_the_horizontal_border's_dimensions . ▶161*G: I don't know. ▶162*G: I tried ▶163(.) . ▶164*G: Does it work? ▶165*S: You could make it into, like +... ▶166*G: Cause xxx &=and_indicating_parts_of_the_diagram . ▶167*T: Could you write out what you're saying? ▶168*T: I'm having a hard timehearing it. ▶169*G: &=writing_on_board so, if you do seventy two minus y. ▶170*T: uh huh. ▶171*G: &=writing_and_speaking ▶172and, like, forty minus x@l ▶173&=attending_to_the_diagram . ▶174*G: And then you'll get the ▶175and then divide ▶176cause you're trying to get this here, rightâ†‘ ▶177&=indicating_the_horizontal_top_and_bottom_border's dimensions . ▶178*G: So, then you'd divide it by two. ▶179*T: You're trying to get what? ▶180*G: Cause remember how you said that we were trying to get what this is181▶182&=indicating_the_top_border's_dimension . ▶183*T: uh huh. ▶184*G: So, then if you divide it ▶185&=pointing_to_seventy_two_y ▶186by two you should get ▶187this and this ▶188&=the_top_border's_dimensions . ▶189*T: Yeah, but I don't have enough numbers to get it, though, do I? ▶190*G: 0191[% turning seventy two y@l and forty x@l into 72-y/two and 40-x/2]192. ▶193*S: Well, you do if you know what x@l and y@l are. ▶194*G: Yeah. ▶195*G: That's what I'm trying to say ▶196&=stepping_back_from_work ▶197Cause you said that we need a variable, and so ▶198&=shrugs . ▶199*T: Ok, and, so then how would I write an equation with those things? ▶200*G: ummm ▶201I don't know. ▶202*T: does anybody have . ▶203*G: I wrote this yesterday. ▶204*G: I just +... ▶205*T: Ok. ▶206*T: No. ▶207*T: So, do you guys understand what ▶208Can you point out where ▶209the seventy two minus y@l is going to be that question mark? ▶210*G: &=walks_toward_seat . ▶211*T: one of the question marks? ▶212*T: Which question mark is it going to be? ▶213*G: &=walking_back_up_to_the_board . ▶214*G: Oh. ▶215*G: It would be the ▶216this one ▶217&=indicating_the_right_border_dimension . ▶218*T: Ok. ▶219*H: Couldn't you use substitution since you have two equations? ▶220*H: I mean, you could make another equation x@l times y@l equals one221thousand six hundred and eighty? ▶222*G: Yeah, ▶223I had that last time &=night ? ▶224*G: I just didn't write that down. ▶225%com: writing on board above 72-y/ two and forty - x/ two . ▶226*G: So, ▶227you have x@l times y@l equals &=writing:1680 . ▶228*H: So, now you have two ▶229two equations and two variables. ▶230*H: So, ▶231you could, ▶232like, ▶233do substitution for the other one? ▶234*H: (.) and then you can +... ▶235*T: Ok, so I see one equa(l) ▶236do you guys agree with what she has right ▶237there? ▶238*T: x times y@l equals one thousand, six hundred and eighty. ▶239*S: uhh. ▶240*S: well +... ▶241*T: Do you have a question ▶242any questions for her ▶243for what she's ▶244written so far? ▶245*T: Cause you ▶246I want you to understand what she has there. ▶247*S: &=raises_hand . ▶248*T: Yeah, N. ▶249*N: Why do you divide by two? ▶250*G: Cause you're trying to figure out this ▶251&=indicating_border_region_dimensions_on_board . ▶252*S: oh, yeah. ▶253*G: I think it's because you're trying to figure out this and this. ▶254*G: I [/] I [/] I wrote this yesterday ▶255and you just asked ▶256so I thought ▶257I'd show and see if it was right. ▶258*S: Yeah, that is. ▶259*S: It's ▶260&=students_raise_hands +... ▶261*G: Yeah, so, and I also put this was equal to each other . ▶262%com: indicating the - 72-y over two and the- 40-x over two ▶263*G: but I don't think that's right, so ▶264&=calling_on_student ? ▶265*D: Umm. ▶266*D: Is seventy two minus ▶267like seventy two minus y. ▶268*D: &=motioning_horizontally_with_her_hand ▶269Is that xxx the length of y@l or x@l times y. ▶270*G: Yeah. ▶271*G: Cause it's seventy ▶272it's seventy two minus y@l cause you're trying to ▶273find. ▶274*D: &=motioning_again_with_hands find . ▶275*G: these two ▶276&=indicating_the_vertical_left/right_border_dimensions ▶277right here. ▶278*G: So, if you get seventy two minus y, you're going to get ▶279the ▶280&=indicating_the_left_right_border_dimensions_separately . ▶281*H: And they're both going to equal the same number. ▶282*G: Yeah. ▶283*G: The reason you divide it by two is so that you can find the ▶284two separate sides ▶285&=framing_the_inner_rectangle_vertically ▶286&=Capping_the_marker_and_stepping_back . ▶287*G: Yeah. ▶288*T: So ▶289you said that they're going to equal the same number? ▶290*T: How could you ▶291Do you guys agree that those are going ▶292to equal the same. ▶293*T: what [//] ▶294what's going to equal the same number? ▶295*T: X and y@l are going to equal the same number? ▶296*S: No ▶297the question marks . ▶298*G: yeah. ▶299*H: seventy two ▶300seventy two minus y@l divided by two and forty minus x@l divided by301two. ▶302*H: They're both going to equal the same number. ▶303*T: okay. ▶304*T: &=pointing_to_board can you show that up there? ▶305*T: Can you change what's written up there so that you know ▶306so that it ▶307shows that those are equal? ▶308*H: Like, make another variable? ▶309*T: Do we need to have another variable? ▶310*T: (.) I think we've got plenty ▶311two variables is ▶312more than enough. ▶313*H: Well, all I'm ▶314saying is that +/. ▶315*T: &=getting_up_from_seat_and_walking_toward_board so, she's saying ▶316that okay yeah . ▶317*G: They shouldn't be equal to each other, right? ▶318*T: What shouldn't be equal to each other? ▶319*H: Oh! ▶320*H: I get it! ▶321*G: The seventy two minus y@l divided by two and the forty minus x@l322+/. ▶323*T: &=writing_on_board xxx an equal sign right here . ▶324*G: Yeah. ▶325*G: I put one there. ▶326*G: I just didn't know if it was right. ▶327*T: &=turning_to_class_and_pointing_at_the_equation ▶328Do you guys agree with that? ▶329*H: Yeah. ▶330*H: Uhhuh. ▶331*S: Yeah. ▶332*T: &=Standing_in_front_of_diagram okay. ▶333*T: This is very interesting. ▶334*T: This is a completely different way than I looked at it. ▶335*T: I only had one ▶336&=holding_up_one_finger ▶337variable when I wrote this, ▶338so this is very ▶339this is hard for me to think about. ▶340*T: &=moving_to_side_of_board . ▶341*T: So, you guys are going to get ▶342so that you should get the same answer, cause I don't see ▶343I mean, do you guys see anything wrong with what's going on here ▶344&=looking_back_at_G's_solution_on_the_board ? ▶345*T: These two equations (.) ? ▶346*T: You guys agree with everything that's written there? ▶347*H: Yeah. ▶348*S: &=students_raise_hand I've got a question. ▶349*S: So, are we looking for the question mark or the x@l and y, or are350we ▶351looking for both? ▶352*H: Both. ▶353*T: &=walking_over_and_pointing_to_questions_marks_on_diagram ▶354Well, she's saying [//] she's saying that [//] ▶355she's using the knowledge that the question marks are equal ▶356to be able to write these two equations &=pointing_to_equations . ▶357*T: So, she kind of found the question marks ▶358&=encircling_72_minus_y_two_with_her_hand just so she could set359those two ▶360&=indicating_the_sides_of_the_equation equal to each other361&=looks_at_class . ▶362*T: So, what we ▶363&=pointing_at_inner_rectangle. ▶364*T: what's the question of this problem? ▶365*T: What's the big question that it's asking ▶366&=walking_away_from_board ? ▶367*T: Usually, you just look at the last sentence +... ▶368*S: xxx. ▶369*T: How many huh? ▶370*S: How many laps did she have to do to walk ▶371at least one quarter of a mile? ▶372*T: How many laps ▶373&=back_at_board_pointing_to_x_and_y_on_diagram . ▶374@End