Algebra and geometry both had concept tests today. I spent half the period reviewing a few concepts for a school wide diagnostic test they are taking on Monday. After they finished the test I gave ’em this pattern.
A lot of students were randomly guessing what the next three terms would be. In response, I asked them what the pattern was. They are still used to yes/no answers to questions, which doesn’t encourage any critical sort of thinking.
This is a fun problem because each term is independent of the rest. Students are wired to try and find a common difference/ratio and when that doesn’t work they look for extended versions of those patterns like +1, +0, +2, +0, +3, ect.