Alexis said the area of 1/3 of the trapezoid is greater than the area of 1/6 of the hexagon because 1/3 > 1/6. does her statement make sense?

While Alexis is right in saying that 1/3 is greater than 1/6, she is NOT RIGHT in saying that the area of 1/3 of the trapezoid is greater than 1/6 of the hexagon.

We do not know the size (area) of these shapes. It could be that the trapezoid is terribly tiny and the hexagon is huge. The only way we can compare 1/3 of this to 1/5 of that is if the sizes of this and that are the same.

As an example, is eating 1/2 a pizza a lot? Well, whatever you believe about how much one should eat, the answer also has a lot to do with the size of the pizza. 1/2 of a personal pizza meant for one person is quite different that 1/2 of a large 8-slice restaurant-style pizza. What this means is that we cannot simply compare the fractions (1/3 and 1/6 or with the pizza 1/2 to 1/2), we have to keep in mind the areas (the size) of the figures (hexagon, trapezoid or whatever the pizza is...usually round) involved.