Can 1/3 and 1/3 = 2/6? It seemed so
The units are missing, and I think that's a key factor here.Both of the equations up on the board at the end are correct because they are counting different things. This is a huge miss if you use a numeric only approach to fractions.The student came up and wrote 1/3 + 1/3 = 2/6.What they meant by that is 1/3 (of the students at a table) + 1/3 (of the students at a different table) = 2/6 (of the students at those tables).The teacher then demonstrates an entirely different formula:
1/3 (of the students at a table + 1/3 (of the students at a table) = 2/3 (of the students at a table).The confusion comes because no one calls out that they're talking about fractions of different things.Edit: There are a whole range of exploratory questions you can follow on from here as well.Imagine if the tables have different numbers of students or if there are more than two tables. Helping students navigate these types of ratio transformations is why keeping track of units is so important. Otherwise, things can get hairy for the students very quickly.