Fractions apply to sets of objects, not just wholes. 1/4 of 8 counters = 2 counters. This connects fractions to division.
Use concrete objects like counters. Divide the set into equal groups and count one group.
Not dividing into equal groups; confusing the fraction with the count.
You already know two things that come together here: equal groups (making sure every group has the same amount) and unit fractions like 1/2, 1/3, and 1/4 (which describe one piece of a whole). Fractions of a set extends that idea from shapes to collections of objects.
When you found 1/4 of a rectangle, you split the whole shape into 4 equal parts and shaded 1 part. Fractions of a set work the same way — you just split a group of objects instead of a shape. To find 1/4 of 8 counters, split the 8 counters into 4 equal groups and count one group. Each group has 2, so 1/4 of 8 = 2. The denominator (4) tells you how many equal groups to make; the numerator (1) tells you how many groups to count.
What makes this powerful is the connection to division: finding 1/4 of 8 is the same calculation as 8 ÷ 4. The fraction bar is, in fact, a division symbol. This is not a coincidence — dividing into equal groups is exactly what the denominator of a fraction asks you to do. Every time you find a unit fraction of a set, you are performing a division.
You can extend this to fractions with numerators greater than 1. To find 3/4 of 8, split into 4 equal groups (2 in each), then count 3 of those groups: 2 × 3 = 6. So 3/4 of 8 = 6. The pattern is always: divide by the denominator first (to find the size of one group), then multiply by the numerator (to count the right number of groups). This two-step process — divide then multiply — is the foundation of fraction multiplication you'll use in later grades.