Simple activity (also works well as a demonstration with discussion):
Give students two paper plates. Ask them to drop them at the same time. They should hit the ground at about the same time. Repeat the drop several times, so that students are convinced they fall at the same rate.
Then ask students to crumple one of the plates, then drop them side by side again. The crumpled plate will hit the ground much faster.
The plates are the same weight, so the downwards force on them from gravity is the same.
The difference is the air pushing upwards on the plate - with the greater surface area of the flat plate, more air is pushing up on it. This greater upwards force negates a lot of the downwards force. The crumpled plate has a smaller surface area, so less air is pushing up on it, so it is not slowed down as fast, so hits the ground faster than the flat plate.
More complex activity:
Drop pairs of objects from the same height, and record which hits the ground first (do three trials for each).
In a group discussion compare the objects of the same shape (e.g. chopstick, pipe cleaner and straw e.g. square of wood, cardboard and paper of the same size) - which will likely fall fastest to slowest in that order.
Ask why one falls faster than the other - students will think of weight. Weigh and record the items weights (we had chopstick 3g, pipcelaner 1g and straw 1/2g of one shape, then a wood tile 37g, cardboard square 3g and paper square 1/2g).
Compare objects of the same weight, but different shapes (e.g. chopstick and square of cardboard, or paper and straw). They all have the same force of gravity acting on them. Ask students why they fall at different rates - their shapes: the cardboard/paper is flatter, so hits more air molecules as they fall which push back up on the object to slow it down. This is called the force of air resistance (a kind of friction). The narrower chopstick or straw have less air resistance.
[This paragraph needs editing and cleaning up conceptually] Compare objects of the same shape, but different weights. The heavier objects will have a greater force of gravity pulling down on them, but surprisingly, this is not the full explanation, because on the Moon a heavy and light object fall at the same speed (see the Apollo 15 video of a hammer and feather being dropped: https://www.youtube.com/watch?v=KDp1tiUsZw8). There is no air on the Moon - it is the air on Earth, pushing upwards as air resistance, explains why the lighter object falls slower. The air resistance (pushing up) very quickly balances the pull of gravity (pulling down) on a lighter object, so it quickly stops speeding up. A heavy object has to speed up a lot more before air resistance balances out with the force of gravity, and in a relatively short drop height (as in our experiment) the heavier object is still getting faster before it hits the ground.
Summary: as an object falls, the force of gravity on the mass (called weight) and the force of air resistance pushing up (which depends on the shape and speed of the object) are both acting on a falling object. The speed that it falls is determined by how those forces balance out.
Objects keep speeding up as they fall, until they are moving so fast that the air resistance is large enough to balance the force of gravity. Then they have reached terminal velocity. This happens much faster with a lighter object.
In many sports, we design equipment and shape our bodies keep air resistance, also called "drag", to a minimum e.g. bike racers bend down to reduce air resistance and bike one behind the other to be sheltered from air resistance e.g. a bobsled is shaped to be as streamlined as possible, so reducing air resistance. e.g. skiiers and speed skaters wear suits that are very smooth, so reducing air resistance.
In some sports e.g. parachuting, we use air resistance to our benefit so that we do not land on the ground too fast.
Addditional surprising activity:
Drop the paper on top of the heavier wood tile (or a small book).
The paper will stay with the book and fall faster than on it's own.
The paper experiences no air resistance because it is on the book, so falls as fast as the book. The book falls faster than paper because it is heavier - the weight of the book overcomes air resistance.