I threw out a goofy story one day a few weeks ago to get the kids to manipulate radicals properly, and it seemed to help some kids, so I thought I'd share ... and I guess I'll share in building up order instead of the order in which it happened.
I make sure to ask a student (or class) what this means:
![4\sqrt{3}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vB2wrrLHADdO_rdGDgtSElLXKO0mbzIUWPgGbo0ouXldo7DUTUDGWnTzavrqepDsVEreWfBQlWXRdEPBuex9f16Fu3CoWluBvCsU0v0LdJyQxgY61S=s0-d)
. I get a variety of answers:
* I don't know
* 4 times
![\sqrt{3}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_ttA6poVS4rHCncFN71lBBWmW9kaeVRD0Bj2xMYiUAluJe3M9Cu207m4lUtmn9LgLeJA_Spu_kqUJ4n6fycNy26KZMqM7UUCoZ57btnokqdA9FZSbk=s0-d)
?
* are you asking me?
* what?
So then I look suddenly across the room, "Look over there! What's that?". They look. "Just see those 4 cute little
![\sqrt{3}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_ttA6poVS4rHCncFN71lBBWmW9kaeVRD0Bj2xMYiUAluJe3M9Cu207m4lUtmn9LgLeJA_Spu_kqUJ4n6fycNy26KZMqM7UUCoZ57btnokqdA9FZSbk=s0-d)
s running around!" And I go on to describe that you're just counting in shorthand how many there are.
And then if there's a problem like
![4\sqrt{3}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vB2wrrLHADdO_rdGDgtSElLXKO0mbzIUWPgGbo0ouXldo7DUTUDGWnTzavrqepDsVEreWfBQlWXRdEPBuex9f16Fu3CoWluBvCsU0v0LdJyQxgY61S=s0-d)
+
![8\sqrt{3}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tcXlkRxyesMWIzBsLO4_KhSozmi42vM45fBQh-tuE5j8ONMo2tdBQWaT8TWjpVQSaemUnRa0gFiuNk1fDB3QCWo32locHmpctB6cJ6QXsYFfxxSMsd7Q=s0-d)
, I expand the story: "... and over by the door, 8 more sexy
![\sqrt{3}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_ttA6poVS4rHCncFN71lBBWmW9kaeVRD0Bj2xMYiUAluJe3M9Cu207m4lUtmn9LgLeJA_Spu_kqUJ4n6fycNy26KZMqM7UUCoZ57btnokqdA9FZSbk=s0-d)
s just joined the party! How many are in the room now?"
I guess it sticks with SOME of the students because today we had a problem like: (12)(
![12\sqrt{3}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_t6Nz9NDnNbB4mE_zceqEcrXk34zD9a2yWnm3laflT91IZ5pYuO62EtwiPvlEudz57RXOf4mdh495u9QCiVbJfd9R7dfjn9NFkIC8dYGoEvmf7IfBcJyw=s0-d)
) and someone was wondering how to multiply it. So I asked: "what does
![12\sqrt{3}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_t6Nz9NDnNbB4mE_zceqEcrXk34zD9a2yWnm3laflT91IZ5pYuO62EtwiPvlEudz57RXOf4mdh495u9QCiVbJfd9R7dfjn9NFkIC8dYGoEvmf7IfBcJyw=s0-d)
mean?". Pretty quickly someone answered: you have 12 little
![\sqrt{3}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_ttA6poVS4rHCncFN71lBBWmW9kaeVRD0Bj2xMYiUAluJe3M9Cu207m4lUtmn9LgLeJA_Spu_kqUJ4n6fycNy26KZMqM7UUCoZ57btnokqdA9FZSbk=s0-d)
s running around. And then we were able to finish the problem (and you have 12 sets of those 12, so .....
My next goal (someday) is to have them do a dramatic interpretation or story or SOMETHING emotional about
![\sqrt{a}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vmXT1EoP_tqBkGKhpGrIjThwYloxT6hcuOEZ_yy6bRqYkyvLFyo2f1w7Npdyndn63TukI3bd6_Fw1ywWw4px-94St6NGVm7rvXk8W92KkbV2FhjAA=s0-d)
+
![\sqrt{b}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_v3TX6o0x1MpkGCVyvj9AR7CYbup85UOp7GYSxJP7lhLQrWtS4YOqvMICL3OAiV8HWOLisltD6_8LsxX5P8okKO00QuMCF3s5UwT__Gfyv83DkfBIm5=s0-d)
. I've read that things that pack an emotional punch in some way stick better in your head. Or maybe it's just the punching part ....
I was searching for such a thing for a very long time.
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