One square, a few folds, and a cicada with two matching wings
Fold the square corner to corner and turn it so the 90° corner points up and the long folded edge is at the bottom. This is an isosceles right triangle: two equal sides and two 45° angles. The long edge is the square's diagonal, about 1.41 times as long as a side.
Fold each lower corner up onto the top point. Each crease runs exactly half way between the corner and the point it lands on, at a right angle to the line joining them. The paper becomes a diamond, a square half as wide standing on a corner. Then fold the two side points of the diamond behind, along lines parallel to the middle line, to make the body narrower.
Fold the top of each flap down and out along a slanting crease: these are the wings. They are mirror images, because the middle line from head to tail is the line of symmetry. Finally fold the top point of the front layer down, and the point of the next layer down a little higher up, so the head shows two stripes. Both head folds run straight across, at 90° to the line of symmetry.
Pause on any fold and ask the tutor which angles are equal, why the wings match, or how many triangles you can find.