This class discussion highights how two students, James and Danielle, interpret x differently. Another student, Matt, uses money (quarters) to explain the distinction between the two interpretations.
Support Productive Struggle in Learning Mathematics
As students discuss a variation of the Growing Dots task in which the starting point is shifted, one student shares that when the first dot is at time 0, the rule is 4x – 3. Another student, Angel, asks, “Where is the –3 in the picture?”
This video focuses on the Polygons task and the interactions between Cindy (the teacher) and Stuart (a student) and his work. Cindy poses questions to Stuart to help understand his approach.
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).
Maryann introduced the Cubes in a Line task by showing her students two cubes and asking the question, “If I put two cubes together, how many faces are there showing?” We drop in as several students explain how they arrived at their totals.