Goal: Think like a mathematician! Looking for repetition in the way you draw or count, then generalize the regularity.
Source: Pattern #75 on www.VisualPatterns.org
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We used this task with a group of 8th graders. They loved it! They thought of at least 8-10 different ways to conceptualize the growth in this sequence, based on the visual pattern rather than just making a table of values. It was really impressive and they were thoroughly engaged. The task has a very low floor and a high ceiling, so it differentiates itself. It also was a rich source for mathematical discourse. Thanks!
Sounds like paying attention to process paid off for your students!
Working on this task with 8th graders, we saw several students come to the board to share their generalizations who rarely participate in class. One of these students came to the board and was the first to point out that the number of rows of 2 dots on each side was one less than the figure number. This led to the class generalizing, and coming up with an expression, from her “chunking”.
Also, this task led to students having lengthy, rich discussions when sharing their repetitions and generalizations.
It is exciting to hear that the routine offered entry points to students who typically do not participate in math class. Do you have a sense of what exactly it is about Recognizing Repetition that hooked those students?