Mathematical Proof
Mathematical Proof is a step-by-step argument that shows why something in math must always be true.
Think of it this way
A recipe has numbered steps. Each step follows from the one before it. If you follow every step correctly, you always get the same result. A math proof works the same way — each line follows from the last, so the final result must be true.
Explaining mathematical proof by grade level
Think about a game where you take turns picking up sticks. You can figure out a trick to win every time. When you test your trick over and over and it always works, that is good. But a proof shows WHY it works, not just that it works.