Apparently sometimes $1/2 < 1/4$? My son brought this home today from his 3rd-grade class. It is from an official Montgomery County, Maryland mathematics assessment test:
True or false? $1/2$ is always greater than $1/4$.
Official answer: false
Where has he gone wrong?


Addendum, at the risk of making the post no longer appropriate for this forum:
Questions about context are fair. This seems to have been a one-page (front and back) assessment. Here is the front, notice the date and title:

Based on the title, it seems to me that this is an assessment about the number line in which case my son's picture and written proof are inappropriate and better would have been to locate $1/2$ and $1/4$ on the line and state something like "No matter how many times you check, 1/2 is always to the right of 1/4." However, based on the teacher's response it seems the class has entered into a quagmire and is mixing up numbers with portions.

'What about this?' is ABSURD. Fractions are real numbers and $1/2$ is NOT smaller than $1/4$. Period.
If the dumb teacher wants to compare a half of biscuit to a quarter of pizza, then they are no longer numbers, but physical quantities (masses or volumes), which have their units, and the stupid needs to consider bringing them to appropriate common unit of measure to compare. One should also consider the correspondence of the quantity type (say, not to compare a half of hour to a quarter of mile!)
