Definition
Set model
A set model represents a fraction using a whole made of separate, countable objects.
Continue from this idea into connected AXIO math.
Boundary check: Five selected objects mean 5/20 only because the whole set is fixed at 20.
What it means
First point to the entire set—that is the whole. Then count how many objects are in the whole and how many are selected. For basic fraction-of-a-set tasks, every object counts equally. The same selected objects can be named with an equivalent fraction after the counts are simplified.
Remember it
Count the whole set, then count the chosen part.
Example
A set has 20 counters, and 5 are blue. The blue part is 5/20 of the set. Dividing both counts by 5 shows the same part is 1/4 of the whole set.
Watch for
The whole set must be stated clearly; five selected objects can represent different fractions when the total set changes.
Common mix-up
A set model uses separate objects; an area model uses regions of one continuous shape.
Exact meaning
A set model for fractions represents the whole as a defined collection of separate objects. The denominator describes how the whole is partitioned into equal-count groups or names the total equal objects, and the numerator identifies the selected groups or objects according to the task.