How many triangles?

 I took this lovely activity from Nolan Fossum's tweet. 

Next One?

 

Math Pics 15: Van Eck's Sequence

Problem 114: Factorial Sequence

Problem 98: What Comes Next?

Rich Tasks 11: Making Sequence Competition

Rules and Explanations
-Students can change the order of the numbers to make sequences,
-When there is a team challenge, I give the points to the first two teams who produce a sequence with a reasonable description.
-Using two dice may be better in order to emphasize term to term rule or the nth rule.

Here is another version as a worksheet.

Rich Tasks 9: Sequence Making using the die

Problem 19: Next Number in the Sequence

1, 1, 2, 3, 3, 5, 4, 6, 5, 9, 6, 9, 7, 13, 8, 12, 9, 17, 10, 15, 11, 21, 12, 18, 13, 25, 14, ?