This can be adopted to an activity with the young children.

Make this shape out of paper 24 small matchs or tooth picks or slips of paper.
How many square do U C ? There are more then 9.  Get an ahha.  Answer_____________

Now start taking some out in a regular way, so that there will be no lines sticking out and no rectangles.

This is Not allowed soince the line sticks out. 

This one is allowed.  Write by it the number taken out (=out) and the number of squares left(=Left)
Out=1 Left=10

Out=2 Left=11

Out=2 Left=7

Continue exploring and summarize your finding in a Table

Out     1     2    2

Left     10  11   7

Make up questions that will work for young kids and also older kids.   Most of the young kids will probably only be able to count the 1X1 small squares.