These monsters work by air from a plastic milk carton.

Squeezing the carton compresses the air inside and forces it to move along a tube into a balloon.

As the balloon inflates it pushes on the inside of the top jaw of the creature and makes the mouth open.

A balloon (especially a brand new one) can be very difficult to inflate for young children as they have to push quite hard on the milk carton but there is a simpler way!

By using a finger from a latex glove (of the type decorators or doctors use) instead of a balloon it is a lot easier to blow up since the thin latex stretches more easily.

This picture shows the milk carton detached from the creature.
You can see the green milk carton screw cap and tube sticking out from it.
Making the hole in the screw cap to fit the tube is done with a bradawl or fine crosspoint screwdriver to begin with and then the hole is gradually enlarged a little at a time using successively thicker screwdrivers or even pencils until the correct size to make a tight fit on the tube is achieved.

Push one of the short foam pieces into the hole in the base by holding firmly near the bottom and squashing and pushing into position. Make sure the sides of the short upright piece line up squarely with the sides of the base.

Sharpen a wooden dowel - or use the short dowel - to make a piercing tool and pierce a hole near the top of the upright using a slow pushing and twisting action making sure to pierce in a straight line as shown.

Push and twist the pointed end of the short dowel through the long foam lever near one end and into hole in the upright piece. This joins the two pieces together but allows the lever to move up and down.

Use masking tape to join another small foam strip to the lever - making sure there is a gap between the two small pieces to allow movement of the lever. The lever will stick if they are too close to one another.

Place one end of the tube a little way into the glove finger or water bomb balloon.
Use an elastic band doubled around the finger as many times as possible to secure the finger and make it airtight.

Pierce another hole near the bottom of the upright strip to allow passage of the tube so that the balloon rests under the lever (the additional short piece which has been taped in place gives a larger area of contact for the balloon on the lever).
A pencil can be used to make this hole. Make sure to push and twist as before but repeat several times to make sure the hole is big enough.
Place an elastic band around the base and lever near to the point where the lever attaches to the upright. This will pull the lever back down after it has been raised by the balloon. If this elastic band is too tight or in the wrong position the lever may be difficult to raise or unable to return after raising.

Pierce a hole in the centre of a plastic milk bottle cap using a fine crosspoint screwdriver or bradawl.
Gradually enlarge the hole with a twisting action using a bigger screwdriver and finally a standard pencil.
The hole should now be wide enough to take the plastic tube - it must be held firmly and pushed and twisted into the hole to make a tight fit.

Draw and cut out a card body shape.
The creature must be in two parts -
1. The body which stays still and attaches by paper fasteners to the base.
2. The moving jaw which is deliberately cut out longer than the lower jaw so that it helps conceal the lever. It is attached by paper fasteners also.

Take care not to push a fastener through the body and on into the moving jaw - children sometimes do this!

All sorts of monster designs are possible and you can even make a blinking eye by cutting an eye hole in the body then drawing an eye on the moving jaw in a suitable position. You can also add a moving tail or horns by adding pieces to various parts of the lever behind the body.