## Thursday, February 16, 2012

### Perfect Squares and Perfect Cubes

My algebra 2 students are starting their unit on radicals.  This unit includes a review of square root arithmetic, the quadratic formula, higher order roots and fractional exponents.  It's kind of a dry unit.  I was trying to think of a way to spice it up and also, I was thinking about how in years past, my high school students have not been able to recognize perfect squares or perfect cubes at all because elementary schools around here don't emphasize the multiplication tables.  Then I remembered a comment on a blog (I think it was f(t) but I can't find the actual comment) from a guy who said he got students to recognize perfect squares by coding the alphabet with perfect squares from 1^2 through 26^2 and putting messages up on his board in code.  I thought this was a pretty awesome idea, so I went through and coded messages for my students for each day of the unit.  Because they're in algebra 2 though, I went beyond perfect squares and made more interesting codes.  I'm just awarding candy to those who solve the codes, but I'm also thinking about making it a competition.  The person who decodes the most messages correctly gets some prize.  I did my first one yesterday and my second today and so far, my students are really into it.  I thought I'd share the coded messages here for anyone who was interested.  I got all the messages by googling around for math jokes or math quotes.

Day 1:

“169-1-400-64  81-361  324-1-16-81-9-1-144”

Day 2:

81-400  81-361  196-225-400  400-64-25  100-225-4  225-36  169-1-400-64-25-169-1-400-81-9-1-196-361  400-225  16-225
9-225-324-324-25-9-400  1-324-81-400-64-169-25-400-81-9.   81-400  81-361  400-64-25  100-225-4  225-36  4-1-196-121
1-9-9-225-441-196-400-1-196-400-361

Day 3:

676  196-676-49-361-484-196-676-49-324-676-169 324-64 676 529-484-25-324-576-484 441-144-81  49-36-81-169-324-169-400  576-144-441-441-484-484  324-169-49-144  49-361-484-144-81-484-196-64

Day 4:

676-289-64-361-49-144-16-361-64-4  64-324  1-16-64-169-36  676-1-121-16  361-196  4-196-400-169-361  400-225  361-196  361-484-16-169-361-576  484-64-361-49-196-400-361  361-676-100-64-169-36  196-25-25  576-196-400-289  324-49-196-16-324

Day 5:

4-144-1-9-121  64-225-144-25-361  324-25-361-441-144-400  36-324-225-169  49-225-16  16-81-484-81-16-81-196-49  400-64-25  441-196-81-484-25-324-361-25  4-625  676-25-324-225

Day 6:

441-324-25-484  144-36-49  144-441  441-144-36-81  121-484-144-121-225-484  361-676-25-484  49-81-144-36-625-225-484  16-324-49-361  441-81-676-576-49-324-144-169-64

Day 7:

3375-1728-64  2197-1-8000-512-125-2197-1-8000-729-27-729-1-2744-6859  2477-125-10648-125-5832  64-729-125  8000-512-125-15625  1000-9261-6859-8000  1728-3375-6859-125  6859-3375-2197-125  3375-216  8000-512-125-729-5832  216-9261-2744-27-8000-729-3375-2744-6859

Day 8:

8191-2-2187-256-32-8192-2-2187-512-8-729  512-729  27-243-9-19683-512-3-128  2187-256-32  8192-9-729-2187  9-4-19683-512-9-6561-729  2187-256-512-3-128  512-3  2197-256-32  4096-32-2-729-2187  9-4-19683-512-9-3561-729  59049-2-531441

Day 9:

3  1296-7776-3-7776-256-7776-256-27-256-3-625  27-3-625  64-3-49-243  64-256-1296  64-243-3-81  256-625  3-625  3125-49-243-625  3-625-81  64-256-1296  4-243-243-7776  256-625  256-27-243  3-625-81  64-243  343-256-25-25  1296-3-16807   7776-64-3-7776 3125-625  3-49-243-216-3-16-243  64-243  4-243-243-25-1296   4-256-625-243

I hope my students learn to recognize perfect squares and perfect cubes after doing these codes.  At the very least they're fun and they don't take away any class time because I'll pass them out on slips of paper at the end of class and students will have to decode in their own time.

If you want an answer key, just leave me a comment.

1. Hello!

I got given the following number sequence to solve:

1-324-81-400-64-169-25-400-...-...

You list the answers as 81 and 9 - which is correct, but I have no idea why.

Would you mind being so kind as to why 81 and 0 logically follow in this sequence?

Thanks for any help. Good blog!

2. I was going back through my starred items in GReader and found this. Would you be so kind to email me the answer key? lmhenry9 at gmail dot com. Thank you!