Definition
Area model
A partitioned rectangle that makes multiplication, division, or fraction relationships visible through area.
What it means
Think of one rectangle built from smaller rectangles. The numbers along the sides tell the lengths. Multiplying the matching side lengths gives each smaller area, and adding those smaller areas gives the whole. The picture makes the structure of the calculation visible.
Remember it
Side × side gives each part; all the parts rebuild the rectangle.
Example
For 14 × 6, split 14 into 10 + 4. One subrectangle has area 10 × 6 = 60 and the other has area 4 × 6 = 24. Add the subareas: 60 + 24 = 84, so 14 × 6 = 84.
Watch for
A rectangle with arbitrary partitions or labels that do not match its side lengths is only a sketch, not a valid area model.
Common mix-up
An array counts objects in rows and columns; an area model uses the areas of rectangular regions. They can look similar, but the represented quantity is different.
Exact meaning
An area model is a rectangle whose side lengths and partitions represent quantities, so the area of each subrectangle represents a partial product or part and the subareas combine exactly to the area of the whole rectangle.