If I have a mixture of sand and marbles in a dish, what can I use to separate the two solids?

There are couple of ways to do the separation. We can separate the sand and marbles based on their size or density.

Size:

Marbles are generally bigger in size than the sand and hence can be separated by the process of filtration. We can use fine sieves and filter the mixture through them. Sand, being finer, will be able to pass through the sieves, while the marbles would be collected on the sieves.

Density:

Sand has a lower density (1.4 - 1.6 g/cm^3) as compared to marbles (2.6 - 2.8 g/cm^3) and hence the separation can be on the basis on differences in the density. We can simply shake the mixture vigorously for some time, this will cause denser particles to settle, while lighter particles will rise up. This way we can separate sand and marbles.

Hope this helps.