MP8: Look for and express regularity in repeated reasoning.

This task aligns with math practice 8 - look for and express regularity in repeated reasoning - because it requires the student to identify patterns in reasoning and determine a general rule for any number of tables. The math practice states, "notice if calculations are repeated and look both for general methods and for shortcuts." A shortcut is achieved by finding the rule in part b of the task so that the student does not need to draw several tables to determine the number of guests.

Students may struggle with the abstraction of the physical tables (or squares drawn on a piece of paper) to the variable n. I would address this difficulty with my 6th graders by using a "table symbol" of some kind for a while, until they demonstrate proficiency with variables as representations of values.

This task could be made more engaging by making the scenario relevant to the students, perhaps talking about the lunch tables at school or the tables or desks in the classroom.

The floor of this task could be lowered by using the tables or desks in the classroom, starting with just a few and adding 1 desk at a time. A teacher could then transition to pictures to represent the tables and people, again adding 1 table at a time. This would help demonstrate that 2 people are being added each time a table is added. This task could be extended for students with higher skill sets by increasing the number of rows for the tables, or introducing a second table-type that is of another shape and number of guests. This task could also be reversed for students to determine the number of tables they would need to seat n number of guests.