I am working with kids who discovered a pattern in squaring numbers and want to know why that is and is there a way of showing it as a formula and visually. The pattern is this: 1 squared is 1, 4 squared is 2, 9 squared is 3, 16 squared is 4, The pattern related to the number being squared and that it increased in a pattern of +3, +5, +7, and continues. Can you explain why?
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1Not squared. "Square-rooted" – David P Sep 03 '21 at 16:00
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Consider $(n+1)^2 - n^2$... The first can expand as $n^2+2n+1$. So... $(n+1)^2-n^2 = (n^2+2n+1)-n^2 = 2n+1$ which is precisely the pattern that you noted. – JMoravitz Sep 03 '21 at 16:01
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Indeed in the reference just given, the graphical explanation by Larry Wang in very understandable by kids. – Jean Marie Sep 03 '21 at 16:51