## Building Bridges

## Opening

**Work Time**

# Building Bridges

The diagrams in this table represent a series of bridges. The bars are the segments that make up a bridge. *n* represents the number of triangles. *b* represents the number of bars.

The following algebraic expressions show different ways to calculate the number of bars based on the number of triangles.

*b* = 3 + 4(*n* – 1)

*b* = 3*n* + (*n* – 1)

*b* = 4*n* – 1

Each expression was found based on a different method for constructing the bridges. These methods are explained and illustrated here.

Method A: At each stage add a triangle at the end and then add a bar across the top.

Method B: At each stage (after the first stage) add a triangle with a bar at the top that points to the left.

Method C: At each stage add a triangle with a bar at the top that points to the right. At the end subtract the last bar pointing to the right.

- Determine which expression matches which method/diagram.

- Evaluate each expression for
*n*= 10.