How to Make a Flying Carpet — Lois June Wickstrom

The frog magnet on the refrigerator fell and broke. Alex likes to make fun stuff from old broken things. She does a variety of experiments with the magnet, and finds things they stick to and things they don't. She finds a box full of magnets on the workbench in the garage. She discovers that magnets can both repel and attract each other. She decides to use the repelling properties to make a flying carpet. That leads to more experiments.