Hola, amigo.
I am not a teacher. Nor am I a native speaker.
I'd like to share my understanding of the difference between can and be able to. I hope this will save teachers some time.
If you use can and be able to in present and future tenses. They basically have the same meaning, i.e. to show someone has the ability to do something.
But, there's a little difference when they're used in past tenses. In this case, we use could instead of can and was or were able to. Here could conveys the meaning that during a period of time in the past, someone had the ability to do something. At the same time, was or were able to shows in a specific past event, someone successfully did something.
An example may help clarify the difference. Let's suppose there were two men on board when the tragedy of Titanic happened. These two miserable figures were Joe Bloggs and John Smith.
Let's take a look at Joe Bloggs' case for a start. Soppose he grew up in Cormwall and started swimming when he was merely three years old. When the tragedy took place, he was 27 years old and already a very good swimmer. He'd once swimmed across the English Channel. Unfortunately, when the ship broke in to two parts, he was at the wrong side of the vessel. However hard he had tried to escape, he was finally pulled down.
When we talk about him now, we can say:
Joe Blogg could swim when the ship went down.
Joe Blogg wasn't able to swim to a lifeboat.
Now, let's consider John Smith. All his life he stayed away from water and never chose vessels as transportation, except for the Titanic, the unsinkable vessel. As he was informed that the ship was going down, he paniced at the first. Then a captain gave him a lifevest. When the ship began to break itself apart, he fell in to the sea. He was lucky for the ship had only just started to sink. Because he had a lifevest, he floated on the water. After seeing a lifeboat not far away from him, he used every bits of his body to get himself move towards it. So he did it and became one of the few suivivors.
When we talk about John Smith now, we can say:
John Smith couldn't swim when the ship went down.
John Smith was able to swim to a lifeboat.
In a word, when talking about a past event, you could do something was no guarantee that you were able to do it. It could be one of those days.
Richard