"The sum of two odd numbers is even." Is that always true — and how would you show it? These free printable worksheets make a claim about numbers and ask a child to prove it or break it, which is where mathematical proof begins.
If they get stuck
The answer key prints on a separate page.
The asymmetry at the heart of proof is the thing to learn here, and it is not obvious. One counterexample is enough to sink a claim forever, while no number of examples is ever enough to establish one — checking that it works for three, five, and nine says nothing about the tenth. A child who feels that difference has understood something no amount of arithmetic teaches.
The claims are chosen so a real reason is within reach. Two odd numbers are each one more than an even number, so their sum is two more than an even number, which is even — that is an argument, not a list of cases, and building it is the work. Where a claim is false, the counterexample is usually hiding among zero, one, and the negatives.
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Is it always true?, step by step