I think that the following story is quite illuminating for introduction. Naturally, one can/should adapt/change it to better fit the audience, I just wanted to sketch the general idea.

Suppose you came here by bus. Which bus was that? You say it was the 42, which is the line that goes from the main station to the university. However, was it really the 42? Is there only a single bus carrying this number?

No, there are multiple buses marked 42, but you don't care which one you rode, because they all take the same route. You abstracted the differences between particular cars, because they were equivalent for your purposes. You have just used the concept of equivalence classes.

After that, I try to explain the intuition using graphs (informally), like here.

I hope this helps $\ddot\smile$

I think that the following story is quite illuminating for introduction. Naturally, one can/should adapt/change it to better fit the audience, I just wanted to sketch the general idea.

Suppose you came here by bus. Which bus was that? You say it was the 42, which is the line that goes from the main station to the university. However, was it really the 42? Is there only a single bus carrying this number?

No, there are multiple buses marked 42, but you don't care which one you rode, because they all take the same route. You abstracted the differences between particular cars, because they were equivalent for your purposes. You have just used the concept of equivalence classes.

After that, I try to explain the intuition using graphs (informally), like here.

I hope this helps $\ddot\smile$

I think that the following story is quite illuminating for introduction. Naturally, one can/should adapt/change it to better fit the audience, I just wanted to sketch the general idea.

Suppose you came here by a bus. Which bus was that? Suppose you say 42, because it is the line which goes from the main station to the university. However, was it really 42? Is there only a single bus which carries this number?

No, there are multiple buses marked 42, only you didn't cared which one, because any of those would do. You abstracted the differences between particular cars, because those were equivalent to you. You have just used the concept of equivalence classes.

After that, I try to explain the intuition using graphs (informally), like here.

I hope this helps $\ddot\smile$

I think that the following story is quite illuminating for introduction. Naturally, one can/should adapt/change it to better fit the audience, I just wanted to sketch the general idea.

Suppose you came here by bus. Which bus was that? You say it was the 42, which is the line that goes from the main station to the university. However, was it really the 42? Is there only a single bus carrying this number?

No, there are multiple buses marked 42, but you don't care which one you rode, because they all take the same route. You abstracted the differences between particular cars, because they were equivalent for your purposes. You have just used the concept of equivalence classes.

After that, I try to explain the intuition using graphs (informally), like here.

I hope this helps $\ddot\smile$