Not “Just Another Brick in the Wall”

This material may not be copied or distributed electronically or in any other format without written permission from NCTM. 84 MATHEMATICS TEACHING IN THE MIDDLE SCHOOL ● Vol. 21, No. 2, September 2015 “l“Low threshold, high ceiling” tasks (McClure 2011) are accessible to diverse learners; invite a wide range of approaches; and hold the potential to further challenge, strengthen, and extend everyone’s mathematical reasoning. We present a family of Brick Pyramid problems (Wittmann 1995; Selter 1997; Muller 2003) as examples of “low threshold, high ceiling” tasks. By eliciting the practices of noticing and describing patterns and then symbolizing and generalizing those patterns, Brick Pyramid problems hold great potential for engaging students in “algebraizing” (Freudenthal 1991). The pyramid in fi gure 1 has fi ve bricks in the bottom row, and each subsequent higher row contains one fewer brick. Numbers are assigned to bricks according to the following rule “Just Anot her Brick in the Wall”