Build a catapult or trebuchet

What can I substitute for the plastic spoon, popsicle sticks, or rubber bands if I can't find them?

If you don't have a plastic spoon to tape to the overhanging arm (step: Tape the plastic spoon...), use a bottle cap or small paper cup taped or glued to the arm, replace popsicle sticks with cut cardboard strips or wooden paint stirrers for the base and arm, and swap rubber bands for elastic hair ties or a short length of strong string tied with a knot to hold the stack together.

The arm won't swing or the launch is weak—what should I check or fix?

If the arm doesn't pivot smoothly after you loop the rubber band around the base stack and the arm (step: Loop a rubber band...), make sure the rubber band isn't too tight around the arm, move the loop slightly away from the base so the arm has room to move, and add a short drinking-straw segment as a low-friction axle between the arm and stack.

How can I change the activity for younger kids or make it more challenging for older kids?

For younger children have an adult pre-stack the six popsicle sticks and pre-wrap the rubber bands and tape the spoon so the child only loads and releases the cotton ball, while older kids can add more popsicle sticks to the arm, attach a counterweight to convert it toward a trebuchet, and systematically record distances when they 'Change only one thing' to investigate levers and angles.

How can we extend or personalize the catapult/trebuchet experiment after the first launches?

To extend the project decorate the base and arm, use a ruler and protractor to record launch angles and distances for multiple trials (step: Measure the distance...), try different projectile types and arm lengths, and then share a photo and your data-driven conclusions about force and angles on DIY.org.