Make a bouncing polymer ball. Examine how the properties of the ball are affected by changing the chemical composition of the ball (altering the proportion of ingredients in the recipe).
Make gelatin plastic. Examine the properties of the plastic as it goes from fully hydrated with water to fully dried out.
Compare the tensile strength of trash bags. How much weight can a bag hold before it tears? Does the thickness of the bag make a difference? How does the type of plastic matter? Do bags with fragrance or colors have different elasticity (stretchiness) or strength compared with white or black trash bags?
Examine wrinkling of clothes. Is there any chemical you can put on fabric to cause it to resist wrinkling? Which fabrics wrinkle the most/least? Can you explain why?
Examine the mechanical properties of spider silk. Are the properties the same for the different types of silk produced by a single spider (dragline silk, sticky silk for trapping prey, silk used to support a web, etc.)? Is silk different from one type of spider to another? Does temperature affect the properties of the silk produced by a spider?
Are sodium polyacrylate 'beads' in disposable diapers the same or are there observable differences between them? In other words, are some diapers meant to resist leaking by resisting pressure on the diapers (from a baby sitting or falling on it) as opposed to resisting leaking by holding maximum fluid? Are there differences between diapers meant for babies in different age groups?
Which type of polymer is better suited for use in swimsuits? You could examine differences between nylon and polyester with respect to stretchiness, durability, and colorfastness in chlorinated water (like in a swimming pool) or seawater.
Do different plastic covers protect against fading better than others? You can test the fading of construction paper in sunlight with different types of plastic overlaying the paper.
What can you do to fake snow to make it as realistic as possible?
Make natural plastic from dairy. Do the properties of the polymer change depending on what you used for the dairy source (percent of milk fat in milk or sour cream, etc.)? Does it matter what you use for an acid source (lemon juice versus vinegar)?
How is the tensile strength of polyethylene plastic affected by its thickness?
How does temperature affect the elasticity of a rubber band (or other plastic)? How does temperature affect other properties?