Okay, here's the basic idea:
View attachment 63563
I apologize for the sloppiness--I haven't used EAGLE in a little while
Anyway, the circuitry on the left is the debouncer circuit. S1 is the main switch. This is the switch that will change which LED is on. S2 is the reset switch. After each question, you'll need to "clear" everything. This is why there is no LED on Q0 (first output). Normally, when you reset it, Q0 would switch on. Normally, you wouldn't want an LED on, so by leaving out the LED the entire array will be clear. From then on, every time you would ask your son a question, he'd be able to press the switch and each time a different LED would light up. He could stop at the one corresponding to his answer. After you get the answer, you'd want to reset it using S2, and you're ready for the next time.
It also wouldn't be a bad idea to have an audio indicator that the button is pressed, as I believe someone suggested already. You should be able to attach a buzzer or beeper to the "Q" pin of the 555. Just make sure it's the type with a built-in oscillator.
I realize it looks a little complicated. I'm sure someone who's been using EAGLE recently would be able to do a much better job with the circuit and make it look neater and easier
Good luck!
[EDIT] Please ignore the second attachment under "Attached Thumbnails", below. That is the wrong circuit and I can't seem to figure out how to remove it