Middle schooler playing on calculator observes

25²=625=6|25,2•3=6

35²=1225=12|25,3•4=12

45²=2025=20|25,4•5=20

COREFLECTIONS...

1) What can we do to make this a teachable moment?

2) To which of the Mathematical Practices does this relate?

3) Do you think it's important for students to describe the pattern both verbally and symbolically?

3) Algebraic derivation?

(10t+5)²=100t²+100t+25

=100t(t+1)+25

4) Extensions? Does the pattern continue into 3 digits e.g., 105²=11025=110|25, 235²=55225=552|25, 23•24=552

Does the pattern eventually break down?

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