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Sample Dialogue from
Math for the Real World
Image © Knowledge Adventure. Used with permission.
Puzzle: Stopping for Gas at Sparky's
As you and your band drive across the country in your van, you need to keep an eye on your gas gauge. You need to stop by Sparky's gas station to fill 'er up before you run out of gas (and have to start the game over). In order for Sparky to fill your tank you must use color-coded road pieces to build a road from the van, through various intersections with traffic lights, to the gas tank. The colors of the connecting pieces must match the signals. You can rotate a traffic signal by clicking on it, and rotate a road piece by clicking on its arrow (from the Math for the Real World manual).
The following is a transcript of three teenage playing this game for the first time. The play session was audiotaped, so the individual speakers are not distinguishable.
Dialogue
Game: Howdy there! I like your rig, but before I can fill your tank, you'll need to get to my gas station by building a road just like you see above. Start from your van and end at the gas pump. Use only one road piece between each traffic signal and be sure to use all road pieces. The color of each road piece needs to connect to the same color on the traffic signal. Oh and by the way, you can rotate the traffic signals and road pieces. Now you're ready to build your road. See ya at my gas station!
After the game provides the directions, the girls spend time figuring out the mechanics of this puzzle. They must consider questions such as, How do we move a piece? Turn it? Change a color on the traffic lights? and Which color might go here? They also consider strategies for accomplishing the task. ("Go through the first light." "Get the blue." "No the red down to here, no there is no red." "I just flipped it so a different color.") Much of their talk involves planning and geometric ideas, such as flips and rotations:
--"I wanna know which path we're gonna take... 'cos if we are gonna go up..
--We are going to have to go up eventually. No, no wait. If we flip this...
--No we can't flip that one. 'Cos if we go up here, do we have to go to every one?
Once they make sense of what the puzzle is asking, and learn how to manipulate the pieces, their discussion becomes more mathematical. They think and talk together, using geometric language and spatial thinking to make decisions (do we need to flip, rotate, or turn it?). They think ahead and plan a route through the puzzle ("I want to know which path we're going to take because if we are going to go up, then...") and are using if/then thought processes (if we use red, then what will we do next?)
--If we used green up to this one... no yellow from here to here... hold up... We can always change it, right? It won't give me another space.
--It only flips those two ways.
--That would work if the yellow was there.
--Now we need green... gree... and we need to change this.
--Here give me the blue.
--Here flip the blue, I've got an idea.
--Here can I see it?
--Yeah and then green would go there
--Can I see it!?
--She actually knows... that might work.
--Let's try the other one
--Yeah yeah that'll work
--If you stick it like that... then yellow will fit in here like it is
--Bingo
--...and then from here you need green.
--It won't fit.
--It will 'cos it'll flip, see? No wait flip it again, yeah, see?
--Bingo.
--Done.
--Whew.
Game: Boy oh boy, you did a great job. Your tank's full.
--Thank you.
--Yay!
Puzzle: The Ferry Ride
The following is a transcript of the same three girls working on the ferry ride problem for the first time. The total time of this clip represents 9 minutes and 55 seconds.
Dialogue
The girls seem excited and engaged by the math ("goodie, another one") and invested in the story, even if somewhat sarcastically. As they make sense of the problem, they also relate it to real world data that is important to them -- how much they (and others they know) weigh.
Game: Hey, help us figure this out.
--All right, goodie, another one. ...
--(sarcastically) Hey, I'm psyched, more money (Laughter.)
--We need to take a ferry to our next gig...
--The weight of everybody?
--Listen! (Sorry.)
--(reading) ...we get all six of us across the river... reach...
--That one weights as much as me. (120?) Yeah.
--None of them weighs as much as me.
--This one weighs as much as S. (a sister, not present)
--This one weighs a LOT.
Now the girls begin thinking about the actual problem. They think about familiar numbers that might help them with finding combinations of 325, such as 300. When they realize they don't have a 25 pound bag, they think about a more general strategy for solving the puzzle: start with the heaviest guy and then work from there.
--Ok so 325.
--325, so... if we put two 125 people on, that's 300 pounds, so...
--That's these two and then one 25 pound bag.
--Wait, let's think this, so these two are gone, with this little thingy...
--No the 125.
--Wait, this guy... this lady... let's see...
--60... 260... plus 40 which is 300...
--But you don't have a 25 thing to put on.
--But we can put this.
--But we want to make it in the least amount of trips, so ... get rid of the heaviest guy first. ...
--No, wait.. why?
Clearly these girls are invested in solving this problem. They spend a lot of time playing with different combinations of numbers, and with different strategies for finding them (start with the heaviest guy, try two people and some bags, try one with just all bags). You can see a lot of mental computation, the use of the calculator as a tool, the desire to check their answer (in order to not lose any money), as well as an impressive level of persistence.
...later in the same puzzle...
--So 165 and a guy, and all the luggage and him.
--Oh wait, if 125 and 120 go together, then they can take a 30 bag with them. (Mmhmm.)
--OK so that gets rid of the 30.
--Mmhmm but then we have one 35.
--125 and something? 125?
--No we just did that.
--Ok I got it, I got it so we can make...
--Make 120 go with 140
--That's 260.
--Plus a 40 bag.
--Then we have.... (whispering)
--Oh. wait. you guys. 35 and 15 is 50
--Do you wanna use the calculator? (Yes.)
--35 and 15... I mean 120 plus 35 plus 35 (hurry up) (she's doing it as fast as she can) plus 15
--170. That's not enough she needs more
--OK but then we can put another person on
--How much do we have left?
--Put this 120 person on
--No that's the one we did
--Oh wait 120 do that again plus 35 (is 170) I know just do this .. then 15 right plus 15 plus 125= (I hope I didn't break it) 295. how much we have left?
--30. We have a 30 pound bag...
--140 and 130, what's that?
--270. Wait, 270 plus this guy...
--I think it's gonna be too much. (Way too much.)
--Maybe 130 and 120 pound guy.
--Is this guy 130 too? (Yes. also.)
--Wait I got another idea (What? 140) Plus 1...
--But can't we use the girl, the 130? (Yeah we can.)
--We can send the 30 and the 25 that's 50.
--OK, wait, that's 325, that's perfect (claps)...
--You sure that's the least amount of trips we can take?...
--OK wait, let me see something. there are two.. people weigh 130 correct? and there's 2 that weigh 125, correct? (Check)
--Wait wait wait
--But we lose money if we
--Exactly
--No no no not yet!
-- I don't think if we can stuff any more people in here
--I'm checking ... I'm just doing it all over again
They hit check my answer, and the ferry honks its horn, signaling a correct answer.
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