Two rules: both means both

Two gates, one decision

A number dock has two gates. A number must be even, and it must be greater than ten. Passing only one gate is not enough. The word and connects the conditions. Our pretend cargo inspector needs both checks, not a lucky guess.

Check the first gate

Eight is even because it can be split into two equal whole-number groups. But eight is not greater than ten. It passes the first gate and fails the second. That is enough to reject it under this stated rule, even though one check succeeded.

Check a different failure

Fifteen is greater than ten, but it is odd. This time the second gate passes and the first fails. Eight and fifteen reach the same decision for different reasons. A useful explanation names the failed condition instead of simply saying the number is wrong.

Find the accepted cargo

Twelve and eighteen are both even and greater than ten. They pass both conditions and enter the accepted group. Exactly ten would not pass, even though ten is even. Greater than excludes the boundary itself. Read that tiny phrase before opening the gate.

Pause: a new pair of gates

Try a new rule: odd and less than ten. Your numbers are five, eight and eleven. Pause and decide which single number passes both conditions. Check odd or even first, then check the size. Explain why each rejected number fails.

Check the new cargo

Five is odd and less than ten. Eight is small enough but even. Eleven is odd but too large. Only five passes both conditions. Notice that the accepted numbers changed when the rule changed. The rule, not a favorite number, decides the group.

Two reasons can say no

Fun fact: two different reasons can produce the same rejection. In the first dock, eight was too small while fifteen was odd. That is why a yes or no answer tells only part of the story. Explaining the reason shows how you used the rule.

Keep the gates honest

Continue to the worksheet below. Sort the original numbers, explain each rejection and test the exact boundary. Then try Rule Patrol from the games page for a fresh collection. Take your time: careful comparisons matter more than rushing past either of the two gates.