Exploring perfect squares and irrational roots. Thanks Mathalicious. I couldn't show their terrific video about Pythagoras ( and his belief that when you fart a little piece of your soul escapes) because my district's web filter marked their website as "adult content." Perhaps it was the "-licious" part?
With the seventh graders, I used a gem I found at MathMunch's website: a link to Abraham Lincoln's homework. I cut out a problem about "if a footman can walk" so far in so many days, if the days are so long...how long will it take ..." We're beginning the section on unit rates, so this was a great way to talk about units. They could intuit it, sort of, but we got to talk about how it's not just miles per day, since "day" had different meanings in the statement and in the question.
We also got questions like:
"why could he walk longer on different days?"
"Is that a reasonable distance to walk in a day?"
"Would you really walk for that many hours without stopping?"
"what's a foot man?"
"Is that a 1 or a 7?" (handwriting was different then)
"Did he get it right? I don't see my answer in his work..."
Perhaps my FAVORITE part was emails I got from 2 parents saying how cool it was. I loved the fact that they loved the problem enough to take it home and show it to their parents!
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