is it strong? will it squish down if a child stands on it?

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Yes, it will squish down.  It is almost like air.  It is an 'open cell' meaning it will absorb water.  A closed cell foam is firmer because the cells are sealed in thousands of little bubbles.
If you put 5 pounds on it in a 9" bowl, it sinks to the bottom.  Not much good for anything.
I use it exactly like the other answer - No weight on it, but as a separator for small items.  It's very good and light-weight and won't damage delicate things.  
The 1" is very soft and little support for weight on top of it.  It is best used to separate things.  It's great to put between anything that has about 1/4" space between it and the next item and it gives a little cushion to keep the items from rubbing each other.
While it may stop rattling of cans with a huge flat surface, if a person would step on it it would be difficult to feel because it will probably compress to about 1/16".  I squeezed it between my thumb and forefinger for you and it cannot possibly be thicker than 1mm to 1/16".  
I put small items in boxes, and use this vertically, like the other answer, to keep things that probably weigh on average less than 2-3 ounces from bumping around in the boxes.

Brand	Amylove
Model Number	SSU-220908-D
Color	black
Product Dimensions	41 x 30.5 x 8 cm; 222 Grams
Material	Foam
Item Weight	222 g

polyurethane Foam Sheet Foam Pad for Case Packing Toolbox Storage and Crafts(16" x 12" x 1", 4 Pcs)

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