Preschoolers can count the number of weights they use, to see how much weight their bridge can hold. By this age, most children can count to at least 10 on their own.
Preschoolers can also try using a ruler to find out how wide their "valley" is. Many preschoolers will need help from a grownup to learn about how to measure something with a ruler. While most preschoolers can recognize the numbers on a tape measure or ruler, when they go to "measure" they usually place an object on a number and call it a "5" or "7", rather than actually measuring. Grownups can help by showing kids that "measuring" starts with placing one end of the thing they are measuring at the zero-end of the ruler.
Preschoolers can find and identify different shapes found in real bridges, by looking at pictures or 3-dimensional models. Grownups can help children at this age notice how many bridges use triangles or half circles. Preschoolers can trace the shapes in pictures of bridges with a marker or crayon.
Preschoolers can observe other children's bridges and notice what works, and what doesn’t, in paper bridge design.
Using a balance scale can help preschoolers observe what happens when you add weight to something.
Preschoolers may be able to design their own paper bridge (without a paper bridge example right in front of them) after looking at pictures, models, or other children's paper bridges.