Definition
Decompose shapes
Decompose shapes means split one shape into smaller shapes that fit together to make exactly the original shape.
What it means
Imagine drawing cut lines inside a shape. The pieces may be different sizes or kinds, but every piece must stay inside the original, and together they must cover all of it—no gaps and no overlaps. You can then use the simpler pieces to reason about area, perimeter, or how the shape is built.
Remember it
A correct decomposition is a perfect jigsaw: every piece is used once, with no gap and no overlap.
Example
Start with an L-shape made from unit squares: five squares across the top and four down the left, with a 3-by-2 corner missing. Draw a vertical cut after the first two columns. The shape becomes a 2-by-4 rectangle and a 3-by-2 rectangle. Their areas are 8 and 6 square units, so together they cover all 14 square units of the L-shape.
Watch for
Cutting off a piece and leaving a gap, placing one piece on top of another, or drawing a part outside the original is not a valid decomposition.
Common mix-up
Decompose does not mean split into equal parts. The smaller shapes may have different sizes and shapes.
Exact meaning
To decompose a shape is to partition it into two or more smaller shapes whose interiors do not overlap and whose union is exactly the original shape.