A child can sort two, four and six counters into pairs, then hesitate when asked about zero. Nothing is on the table, so it may feel as though the usual rule cannot apply. This is a useful moment to return to the definition rather than asking the child to memorise an exception.
Use the same test for every number
An even whole number can be written as two times a whole number. Zero meets that test because two times zero is zero. In a pairing activity, zero counters leave no unpaired counter. It belongs with the even numbers without needing a special rule.
Begin with familiar quantities. Arrange six counters in pairs, then four, then two. Remove the final pair and ask how many counters remain unpaired. The answer is still none. Keep the empty space visible rather than immediately replacing it with another example.
Distinguish no objects from no answer
A blank response and a written zero mean different things. In the activity, zero is the quantity you are describing. Encourage the learner to say or write it explicitly. Two empty circles can represent two equal groups containing zero objects each.
Now compare with one counter. It cannot be paired with another counter because none is available. That contrast helps explain why one is odd while zero is even. Let the learner explain the distinction in their own words before introducing more examples.
Connect the objects to the pattern
Place number cards in order and mark every second number starting at zero: zero, two, four, six. Ask what happens when two is added or removed. Keep the physical activity connected to the numerical relationship rather than treating the pattern as a separate trick.
If confusion remains, return to the question about leftovers. The aim is a reason the learner can reuse, not a quick correct answer that disappears when the counters are put away.