In Algebra 2, the topic today was an overview of functions. Some students were having difficulty understanding the "each input has exactly one output" condition, and the previous example (percent score --> letter grade) just wasn't cutting it.

The follow-up example was much better. The domain was a set of boys' names, the range was a set of girls names, and the mapping was "dating". And, of course, one of the boys had an arrow pointing to three different girls. We discussed why this was not a function, and one student said, "So to be a function, they have to be faithful!". Exactly! I took her up on this, and had them add to their notes: Functions are Faithful! This instantly made sense to them, and this language carried forth through the rest of the lesson. I then added another boy pointing to one of the girls that was already in the list, and asked if everyone was still faithful. They said no, and we clarified things; our new "taken-as-shared" idea was that only the boys (the inputs) have to be faithful for it to be a function. (I mentioned that if all the girls were faithful too, then it is called a one-to-one function, and we'd look at that later.)

It was really amazing - even when we did examples involving decontextualized numbers, they were still very comfortable using the analogy: i.e., that set of ordered pairs is not a function because the 4 is being unfaithful! It even made the vertical line test a breeze to teach.

It's always nice to find something new to add to the bag of tricks.

A beautiful combinatorics argument

11 hours ago

## 4 comments:

great example. i shared it with our math teachers....

Totally different, but sounds the same:

To be a function, each x can get mapped only to one y, right?

So I make the x's the questions and the y's the answers and what happens when you ask the same question but get two different answers?

jonathan

Today we reviewed the chapter on functions for the Finals, and a number of students still did not understand the difference between a relation and a function. I projected up this post, magnifying the text, and told the students that those worksheets they'd been working on the past weeks? They were made by this math teacher in San Jose, and here is his blog. Had a student read the text aloud, and we made a table of boys and girls, and also placed the boys along an x-axis and the girls along a y-axis to show that a vertical line test would pick out any cheaters. The students cheered and clapped for the example, so here's passing that on. Thanks!

Cool. I hope your students do well on the final!

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