This exercise practices something that is often overlooked: every note with a dot sounds exactly the same as a pair of tied notes of the same pitch (with a double dot, three tied notes instead of two). More precisely, with a tie, the kind of curve that adds up the lengths of the notes instead of only joining them expressively. A dot is just a shortened way of writing that tie. You have to recognize the equivalence in both directions: given the dotted note, find the tied pair, and the other way around.
Why a dot is a tie
A dot adds to a note half of its value. And that half, in the series of note values, is always the next note down (half of a half note is a quarter note; half of a quarter note is an eighth note, and so on). That is why:
| With a dot | Sounds the same as |
|---|---|
| Dotted whole note | Whole note tied to a half note |
| Dotted half note | Half note tied to a quarter note |
| Dotted quarter note | Quarter note tied to an eighth note |
| Dotted eighth note | Eighth note tied to a sixteenth note |
With a double dot the reasoning repeats once more: the second dot adds half of what the first one adds, so a double-dotted quarter note sounds the same as a quarter note tied to an eighth note tied to a sixteenth note. This equivalence does not depend on the time signature: it is always the same proportion, unlike how many beats the note lasts, which does change with the time signature (that is practiced in note values in each time signature).
How it differs from "note value equivalences"
It is not the same exercise as note value equivalences, although both use the dot. Equivalences asks how many equal notes fit in another (how many eighth notes in a dotted quarter note: three). Here the question is different: which pair of different notes, tied together, replaces the dotted note exactly. One counts; the other recognizes the tie.
You can practice one direction at a time or both mixed. Each test has 10 questions and the same one never comes up twice in a row.