) the experience of going outside with a field guide and looking at their favorite kind of plants/animals and figuring out which kinds there are, seeing how many kinds there are, seeing the detail of them. learn to make distinctions by naming the similar but different organisms.
) how to measure length of everyday things and how to use arithmetic to think about miles, feet, meters, area...
) experience helping an adult take apart, repair, rebuild, maintain the family car! There are so many math and science concepts and skills learned in this concrete way. plus you learn not to just be a helpless consumer of technological tyrrany
) and thus what all that 1/2, 3/8 inch and 14mm is all about!
) stories of the lives of some famous scientists and mathematicians. when they lived.
) the experience of working on an easily stated math puzzle and WANTING to see how it comes out. learning that many easily stated math puzzles have not yet been solved after 300 years of intense work!
) maintain a fishtank. collect pond critters themselves from their favorite spot and watch em in the fishtank. how long can you keep it going before it goes bad and stuff dies off. you can even try maintaining a complete ecosystem and see how long it works with no fishfood!
) look at the pond muck, fishtank muck/algae under a microscope and see there are WORLDS in there. and that there are TINY critters. Absolute requirement is to understand how HOW tiny they are. 20 microns, 1/50th of a millimeter, 1/400th of an inch etc...
) draw, sketch plants, animals, stuff from microscope, mechanisms, buildings, as a way to communicate ideas. as a way to commune with detail.
) play with a chemistry set
) learn to identify some minerals, learn distinctions between color, lustre, hardness, fracture, that the minerals are chemicals.
) grow a garden.
) grow plants for a long while, propagate them.
how's that for a start?
i guess in part this list expresses my own childhood experience. I would be interested to see what others think.