55 – triangular numbers and then sum

Today is a Monday so, as usual, we do our daily math warm-up of What’s Next?

 
The “extra challenge” question on this warm-up asks for the formula for finding the sum of the numbers in the nth row of this array: 55-1
My students do a lot of pattern problems, and this group wanted to whiteboard this extra challenge, extending the warm-up into an in-class PS. I randomly paired up the students, and two groups found the formula!
 
What Gabe said during this activity made my day. He scratched his already tousled mess of wavy blond hair and said, “These patterns just blow me away! Just when I think I have it, there’s something else to it…” 
 55-2

 

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