There is an argument for spending longer on one task and exploring the various methods in which different learners may approach it. Yeap Ban Har says “it is better to solve one problem five ways, than five problems one way”.
This task demonstrates an idea which is commonly found in Japanese classrooms – where learners have to compare various strategies. In Japan the time spent comparing strategies is called Neriage.
Takahashi (2006) states: “One of the most important roles of the teacher during this type of lesson is to facilitate mathematical discussion after each student comes up with a solution. When the teacher presents a problem to students without giving a procedure, it is natural that several different approaches to the solution will come from the students. The goal of the structured problem-solving approach is to develop students’ understanding of mathematical concepts and skills, therefore a teacher is expected to facilitate mathematical discussion for students to achieve this goal.”
Mathilde Warden suggest that as you plan the neriage, remember that its purpose is for students to uncover important mathematical ideas as they analyse and compare solutions, and that “The teacher’s role is not to point out the best solution but to guide the discussion toward an integrated idea” (Shimizu, 1999).
This pedagogical approach has much potential.
Credit for task shown: @mrgraymath