A fraction of a set describes part of a group of objects rather than part of a single shape. For example, 2/3 of 12 counters means dividing 12 into 3 equal groups and taking 2 of them — which equals 8. The denominator indicates how many equal groups to make; the numerator says how many to count.
Use counters or cubes that students physically divide into equal groups. Start with unit fractions (1/2, 1/3, 1/4 of a set), then extend to non-unit fractions. Connect to division: 1/4 of 20 = 20 ÷ 4.
You already know how to name fractions of a shape — like shading 2/3 of a rectangle. Fractions of a set work the same way, but instead of a shape, you have a group of objects: counters, apples, or students. The fraction still means "part of a whole," but now the whole is the total number of objects in the set.
The denominator is your dividing number: it tells you how many equal groups to split the set into. If you want 1/4 of 12 counters, divide the 12 into 4 equal groups. Each group has 12 ÷ 4 = 3 counters. That one group is 1/4 of the set.
The numerator then tells you how many of those groups to take. For 3/4 of 12, you already found that each group has 3 counters. You need 3 of those groups: 3 × 3 = 9. So 3/4 of 12 is 9. The pattern is always the same: divide by the denominator, then multiply by the numerator.
This is actually your first look at multiplying a whole number by a fraction — 3/4 × 12 = (12 ÷ 4) × 3 = 9 — a connection you'll formalize later. For now, the physical story of "split into groups, then count some groups" is what matters.
One important constraint: this works cleanly only when the set size is divisible by the denominator. Finding 1/3 of 10 requires dividing 10 into 3 equal groups, but 10 ÷ 3 doesn't come out evenly. Either the problem is poorly designed, or the answer is a fraction — a situation you'll handle in later grades.