Decomposing shapes means breaking larger shapes into smaller pieces. This develops understanding that shapes can be divided in different ways and builds flexible spatial thinking.
You already know the basic 2D shapes — squares, rectangles, triangles, circles — and their attributes: how many sides, how many corners, whether the sides are straight or curved. Decomposing shapes uses that knowledge in a new direction. Instead of just recognizing a shape, you ask: what smaller shapes could fit together to make this one? And working the other way: if I split this shape with a line, what do I get?
Start with the simplest example. A square can be cut in half with a straight line from corner to corner, making two triangles. That same square can be cut with a straight line through the middle (top to bottom or side to side), making two rectangles. The square didn't change; the line you drew just revealed the smaller shapes hiding inside it. This is what decomposing means — taking apart, or finding the pieces.
Try a rectangle. Cut it from corner to corner and you get two triangles — just like the square, but the triangles are longer and thinner. Cut it down the middle and you might get two smaller rectangles or two squares, depending on the rectangle's proportions. Already you can see that the same shape can be decomposed in more than one way, and the pieces you get depend on *where* you draw the line.
Now think about putting shapes back together, which is called composing. Two triangles can come together to make a square or rectangle. Two squares can make a rectangle. Composing and decomposing are reverse operations, like addition and subtraction. When you know that a rectangle is made of two triangles, it helps you understand both shapes better — their relationship, their sizes, how area is shared between them. This two-way thinking (taking apart and putting together) is one of the most important ideas in geometry and will come back when you study fractions, area, and more advanced shapes later on.