On a geoboard, to find the perimeter of a rectangle you can count the number of spaces between pins along the path of the elastic. To find the area you multiply the number of spaces between pins on two adjacent sides of the rectangle. 
The smallest rectangle you can make is actually a square with area of 1 and perimeter of 4. 
See if you can find each of the following: 

Find two rectangles with the same perimeter, but different areas. 
 
Can you find another pair with the same perimeter, but different areas? 

Find two rectangles with the same area, but different perimeters. 

How many figures (squares and rectangles) can you create that have a perimeter equal to their area? 
How many different sized squares and rectangles can be made on the geoboard (no diagonals!). 