During preparation for my class with the idea that a p^2-1 (where p is prime > 3) is divisible by 24 I was trying to find a way to explain p^2-1 = (p+1)x(p-1).
I found the following way with the place value kit. Say you have 13^2. You have 13 rows of 13 each. When you remove one. You get 13 rows of 12 and one additional column of 12. Moving the column to a row you get 14 rows of 12. i.e. 13^-1 = 12x14. It can be seen from the picture that this would always hold.
In fact this is a nice way to see that any a^2-b^2 (where b
I didn't get a chance to use it in class, but i thought it was cute anyway.
I found the following way with the place value kit. Say you have 13^2. You have 13 rows of 13 each. When you remove one. You get 13 rows of 12 and one additional column of 12. Moving the column to a row you get 14 rows of 12. i.e. 13^-1 = 12x14. It can be seen from the picture that this would always hold.
In fact this is a nice way to see that any a^2-b^2 (where b
I didn't get a chance to use it in class, but i thought it was cute anyway.
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