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_vOnGGByM_6hL_wojWDeddOXsczDPPMtsnNhhIA-KUl6kb0v1_OAx1Y8r-bf83jr4dHKi91frQGiQJ7OkNUHvkDmCk0bhMdOkvl0iyJiGvizFZ6kkdy=s0-d)
. I get a variety of answers:
* I don't know
* 4 times
![\sqrt{3}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_t_H_g2a1NhOV45c7gDcL7F08MV-ZcXi0wA4_5Nll4QWaEEaiknIzyH4z7PU19NkAE-9rvAlHVwUDVIM0q5X2rUb6PkGozlpf3DCcm8S-mY6MZLJQs=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_t_H_g2a1NhOV45c7gDcL7F08MV-ZcXi0wA4_5Nll4QWaEEaiknIzyH4z7PU19NkAE-9rvAlHVwUDVIM0q5X2rUb6PkGozlpf3DCcm8S-mY6MZLJQs=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_vOnGGByM_6hL_wojWDeddOXsczDPPMtsnNhhIA-KUl6kb0v1_OAx1Y8r-bf83jr4dHKi91frQGiQJ7OkNUHvkDmCk0bhMdOkvl0iyJiGvizFZ6kkdy=s0-d)
+
![8\sqrt{3}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_u7HyaUWEhAWbwa-s19qSMUUgrPTbzJ60SF1SDGx-DsAA-90ohPgWiY3QFZMPUTbVN_RWdf1EQ3aPEakK6ebagkbSrFcSmsYfwNrr3mVoyOAa7wvQh6aQ=s0-d)
, I expand the story: "... and over by the door, 8 more sexy
![\sqrt{3}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_t_H_g2a1NhOV45c7gDcL7F08MV-ZcXi0wA4_5Nll4QWaEEaiknIzyH4z7PU19NkAE-9rvAlHVwUDVIM0q5X2rUb6PkGozlpf3DCcm8S-mY6MZLJQs=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_tcKsJfhLyuF4AyH6l-eQfp0Tk6BIi-jxV3X9zmJa1pYKWIpr3g-iChY116czAvT7tK_OL72U-gfzK_MjRWiQ0ChzEcpMbplwj_dgKUyRRMYzOEmVyKGg=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_tcKsJfhLyuF4AyH6l-eQfp0Tk6BIi-jxV3X9zmJa1pYKWIpr3g-iChY116czAvT7tK_OL72U-gfzK_MjRWiQ0ChzEcpMbplwj_dgKUyRRMYzOEmVyKGg=s0-d)
mean?". Pretty quickly someone answered: you have 12 little
![\sqrt{3}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_t_H_g2a1NhOV45c7gDcL7F08MV-ZcXi0wA4_5Nll4QWaEEaiknIzyH4z7PU19NkAE-9rvAlHVwUDVIM0q5X2rUb6PkGozlpf3DCcm8S-mY6MZLJQs=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_s7dgH5isXmdP8ousuQn0MylutpSkraZlPUk8tQEEoUJbG89WBHMiLBilnVOXpOeCXlSXjh0W-ScQU_cDk5MJk_D1BqlSra_1EUVi8kATJ9dQTbWDs=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 ....