Patterns ending in 25...

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?

PLAYING BY THE RULES

Not exactly a math story but...

My 7-yr old grandson was at bat today. The next pitch appeared to graze him and the umpire told him to take 1st base. He turned around and said that the ball hit his bat and not him. The shocked ump told him to get back in. Two pitches later, he walked anyway. There's a moral here somewhere...