Cindy (the teacher) introduces the Polygons task where students will work with squares, pentagons and hexagons to find each shape’s perimeter.
As the class discusses the rule t + 2 as a solution to the Triangles task, the teacher, Cindy, asks them to consider where the +2 comes from in the visual representation. After some discussion, Lindsey poses the question, ‘Why isn’t it plus 4?’
Amelia explains how she came up with her equation for Schemel’s Logo from the visual model. Jason tells how he found the equation from the table, and Amber comments that Jason’s table shows that Schemel’s Logo is not linear.
In viewing this discussion of Regina’s Logo, we focus on how the teacher and student assistant manage the discussion as Kiril shares how he found the closed form equation using a table, and Reymond shares his geometric approch.
Siri & Tiffany’s group share how they approached the Pool Border task, decomposing the border into four “side plus corner” pieces, the equation for which they write as n = s4 + 4
After students have worked on the Triangles task, Jackie and Amanda each share their solution methods. Cindy asks the class if the two methods can be connected to each other.
Pascal, Tammy, and Adam to go to the board and show their equation, n = (s + 2)4 – 4, explaining that each of the pool’s 4 sides is s + 2, giving you (s + 2)4. They add that since they counted each of the 4 corners twice, they needed to subtract them out (– 4).
In this class discussion of Regina’s Logo, Kiril shares how he found the closed form equation using a table, and Reymond shares how he obtained the equation from visually exploring the geometric model.
After working on a variation of the Growing Dots task in which the starting point is shifted to several different times, students share what their graphs look like for several different starting points, and the discussion moves on to focus on connections across the graph, table, and equation.