A Brief Look at Phrasing Descriptions of Functions

During a lesson this morning, students were asked to describe this function rule in their own words:

One student came up with this:

We had a brief group discussion about whether this phrase made sense or not. One student said that they might interpret this phrase differently:

Some students agreed, saying that the wording could possibly suggest that the sum was performed first, and then squared after. I asked them to think of a better way to say what was trying to be said, and they came up with this:

Not terribly different, but the order of the words made a lot of difference. The students agreed that this phrasing was clearer than the original.

Admittedly, this was a pretty simple problem, but the students brought up some good points in our conversation around it. It was a good opportunity to explore the nuances of being precise when talking about mathematics. Even one turn of phrase can be misleading; hopefully the students learned a bit about being careful about their wording while still being succinct.