Definition
Diagram
A diagram is a purposeful drawing that shows mathematical objects, quantities, or relationships.
What it means
A good diagram keeps the parts that matter and leaves out the rest. It might show a shape with marked equal sides, a bar split into known and unknown amounts, or arrows connecting steps. Read its labels and marks carefully: the drawing is a thinking tool, not a photograph.
Remember it
Keep the structure; skip the scenery.
Example
A bar is labelled 18 and split into parts labelled 7 and ?. The diagram shows the relationship 7 + ? = 18, so the missing part is 11. The bar does not need to be a real object; its job is to preserve the part–whole structure.
Watch for
A diagram may suggest a shape or size, but only labels, measurements, and agreed marks can guarantee those facts.
Common mix-up
A diagram shows mathematical structure; an illustration may only decorate a story.
Exact meaning
A mathematical diagram is a drawing that represents selected objects, quantities, positions, or relationships so they can be reasoned about. Labels, measurements, conventional marks, and connections carry the meaning; unmarked appearance alone does not prove a fact.