Patterns are one of the beautiful aspects of mathematics. This activity offers my favorite one-pager that I gave to students at the beginning of each school term. It went into their Mathematician’s Notebook and on the first day – when we have all the “stuff” to do – students determined the next THREE patterns because if they just find the next pattern, they might have made a lucky guess.
I would have linking cubes available if students wanted to use the manipulative to support their investigation. Throughout the term, we revisit this sheet as we encounter different function types and sequence types. Studying the multiple representations of the sequences – the table, the set of ordered pairs, investigating for a common difference, the abstraction of the symbolic function, the graph, pictorial vs. numeric….all of this helps support students’ developing functional fluency.