Yesterday's opener question:
Count the circles.
Several students tallied the left half of the pyramid, doubled it, and then added the middle column. One student not only counted the circles one-by-freaking-one but kept a current tally inside each circle.
There are 324.
He was somewhere in the low hundreds when I drew his attention to the numbers at the end of each row: 1, 4, 9, 16 ….
"What do you notice? How can we use that to save ourselves time?"
The tedium of busy work can motivate student invention.