Definition
Mathematical reasoning
Mathematical reasoning uses facts and logical steps to decide what is true and explain why.
What it means
It is the “because” part of maths. You connect what you already know to the claim you are making, one sensible step at a time. Trying examples can help you notice a pattern, but reasoning explains why the pattern works or why a method must give the right result.
Remember it
Build a bridge from what you know to what you claim; every plank is a reason.
Example
Why is the sum of two odd numbers even? Each odd number can be split into pairs with one item left over. When the two odd numbers are joined, the two leftover items make one more pair. Nothing is left over, so the total is even.
Watch for
Several examples can support a guess, but examples alone do not prove that a claim is always true.
Common mix-up
Reasoning is not the same as giving an answer; it shows the steps that make the answer believable or certain.
Exact meaning
Mathematical reasoning is the process of using definitions, known facts, relationships, evidence, and valid logical steps to reach, test, or justify a mathematical conclusion.