I know I know…I SAID I was going to post about the magic tricks…Which I AM blogging about “magic tricks” but it is not the post you have all been waiting for. Sorry! When I blog about the magic tricks I want to have this whole line up that leads to all these things that I am testing right now in my class. With that said I wanted to share about this idea I had for magic tricks….I am really making this up as I go along (aren’t we all) so I decided to trick my students (I do this all the time) into thinking that some “other” student came to me and gave me an equation that “he said he used” for magic tricks. I told them I couldn’t figure it out and I wanted to know if they could help me. They instantly knew that they had to “Find a (number guessed)” but they were not really sure what to do. They squirmed a little bit, ok wait I’m lying, they squirmed A LOT! But I had my bag of questions ready for them….”So what do you notice about this equation? What do you KNOW how to do with magic trick equations?” With those two first questions said they were able to at least set up the subtract 5 to make 0. Then came their next dilemma: where does the -5 go on the “other side” of the equal sign? The next question from my bag “Well what do you think? Which number do you think it belongs with? The 4a or the 10?” They naturally went for the 10 (YES!) and of course I asked them why? “Because they both are just regular numbers without a variable. Now we are at 3a=4a+5. So here is the tricky part because only NOW at this exact moment in the lesson and class do I realize that their next step HAS NOTHING TO DO WITH MAGIC TRICKS AND OPPOSITE! So I instantly mentally prepare for this one: “So now what do we do?” <–how many times have we heard this one? I play it cool: “I don’t know, what do you think?” Student response: “Well since you put the numbers together then you gotta put the ones with variables together??” Students nod and agree with her…with that figured out I ask them “So what do you want the 4a to BE?” *silence* (this is a hard one) “Well, do you want it there? What do you want it to BE if you don’t want it there?” response: “ZERO!” (YES!!) “So how do you MAKE IT A ZERO?!” That gets the ball rolling again and they are off…..The rest of the equation is easy peasy for them because they are using their opposite strategy from our magic tricks.
At this point my students look up and ask me “So was his number -5?” My response “I don’t know I didn’t ask him that. I was so intrigued by his equation that I didn’t ask him what his number was.” They slump over…looking defeated….and then a student responds: “NO WAIT! we can check it!” She’s off again….doing some calculations in her notebook….and she’s back…”YES IT IS RIGHT!!” everyone is staring at her like what?? how do you know this? She shares with us that she plugged it in to the equation and it created a true statement (-10=-10).
From her idea I get an idea…”Ok so Katieanna showed us her way of proving it and we can agree that it makes a true statement but even without that confirmation are there any ‘moves’ or steps that we might have performed that were ‘illegal’ or untrue statements?” We go through our statements “is -5=-5?, is -4a=-4a?, is -1=-1?” We figure out (with many questions from my bag) that all our moves are “legal” and we don’t see how anyone can disprove our moves (divide by -1 because we must do the opposite according to our magic tricks, subtract 5 for the same reason, subtract 4a because we WANT a zero). So I ask the last questions before our homework: “So we don’t really KNOW if we did it correctly but without knowing, could anyone PROVE US WRONG?! Could any one accuse us of doing something that we did not justify with reason?” Students: “NO!” My response: “So are we right?” Student: “We have to be! There is no way to show that we are wrong.” They get their homework and everything/one is out the door but not without one student stating: “this is a tricky way to do a magic trick…this student who gave you this is smart and tricky…its good!”
We are back after last night’s homework. And of course they ask if I asked the student…I tell them I did (there really is no student I just made this up…I know I am evil) and yes his number was -5. But I had this idea and I wanted to talk to them about it. I told them how the student got his equation….I told them that the student took a number he guessed and did different magic trick steps to get the same result with two different equations. Then he realized that since both equations were equal to -10 then he thought that he would just let the two equations be equal to each other (3a+5=-10 and 4a+10=-10 are the two original magic tricks). They could understand that and it helped them see how “this student” got his equation. For some reason this kept them engaged because I gave them one more different type of magic trick and we practiced it together. I did pose the question about doing the opposite of add 2 or sub 10. Some students did add 2 some did sub 10 and we compared answers. In the end we realized it doesn’t matter which one we did first because we got the same answer (more than one way?! my fav).
In conclusion, why am I writing about all these questions and responses from students? Because I feel like I just made this up (I did actually) and for some reason they went along with it. It perplexed them, they really wanted to know the answer they really wanted to figure it out. Truth be told I was really worried when I first posed the scenario with the fake student and it went a little rough but it had to go that way for them to squirm. But I also feel like it WORKED!! Now don’t get me wrong we are not done but I just used magic tricks to fake them out with math AGAIN!!
p.s. I will do a final post that pulls together all the ways I used magic tricks to make students successful.