# Assessment Teacher Directed

## Bridge Construction

### Topic - Algebra - Patterns and Functions

*Teacher Directions:*

- Students work alone using Cuisenaire rods to construct bridges and discover a patterns.
- Give each person an assortment of rods and the following work sheet.
- Explain that they are to build different kinds of bridges and answer some questions about them.
- Tell them when they are finished to ... and when all are done or after 40 minutes they will discuss the results as a class.

Student work sheet:

## Bridge Construction

### Topic - Patterns and Functions

Directions:

Part 1

You are an engineer who wants to build different kinds of bridges. The first bridge is a one span bridge. An example can be made with one yellow rod and two red.

Build a bridge with a yellow rod as a span and red rods as piers.

The bridge is 5 cm

To make the bridge longer a second span can be added with another yellow rod and two red rods.

This makes the bridge with a 10 cm span:

As you build the bridge longer think of a way to keep track of the number of spans (yellow rods) and piers (red rods) needed to make bridges of different lengths.

Your goal is to find a pattern for the number of spans and piers (rods of each color) needed to build a bridge of any size. You can use the following sequence as a guide.

Build a three-span bridge.

- How many spans (yellow rods) did you use? _____
- How long is your bridge? _____
- How many piers (red rods) did you use? _____
- How many spans and piers (rods) did you use altogether? _____

Try to answer these questions without building a five-span bridge. Later, if you want, you can build a five-span bridge to check your answers.

- How many spans (yellow rods) would you need for a five-span bridge? _____
- How long would your bridge be? _____
- cHow many piers (red rods) would you need? _____
- How many spans and piers (rods) would you need altogether? _____

3. Without building a twelve-span bridge, answer the following questions.

- How many spans (yellow rods) would you need for a twelve-span bridge? _____
- How long would your bridge be? _____
- How many piers (red rods) would you need? _____
- How many spans and piers (rods) would you need altogether? _____

4. How many spans (yellow rods) and piers (red rods) would you need to build a twenty-eight-span bridge?

_____ spans (yellow rods) and _____ piers (red rods).

Explain your answer.

5. Write a rule for figuring the total number of spans and piers (rods) you would need to build a bridge if you knew how many spans the bridge had.

6. How many spans (yellow rods) and piers (red rods) would you need to build a bridge that is 185 cm long? _____ spans (yellow rods) and _____ piers (red rods).

Explain your answer.

Part 2

The bridges for this part are built like this 2 - span bridge:

The black rods are 7 cm long, and the light green rods are 3 cm long. Notice that the supports are shared between spans, except at the ends.

1. Build a three-span bridge of this same kind, with black and light green.

a. How many spans (black rods) did you use? _____

b. How long is your bridge? _____

c. How many piers (light green rods) did you use? _____

d. How many spans and piers (rods) did you use all together? _____

2. Try to answer these questions without building a five-span bridge. If you want, build a five-span bridge to check your answers.

a. How many spans (black rods) would you need for a five-span bridge? _____

b. How long would your bridge be? _____

c. How many piers (light green rods) would you need? _____

d. How many spans and piers (rods) would you need altogether? _____

3. Without building a thirteen-span bridge, answer the following questions.

a. How many spans (black rods) would you need for a thirteen-span bridge? _____

b. How long would your bridge be? _____

c. How many piers (light green rods) would you need? _____

d. How many spans and piers (rods) would you need altogether? _____

4. How many spans (black rods) and piers (light green rods) would you need to build a fifty-six-span bridge? _____ spans (black rods) and _____ piers (light green rods). Explain your answer.

5. Write a rule for figuring how many spans and piers (rods) you would need to build a bridge if you know how many spans the bridge had.

6. How many spans (black rods) and piers (light green rods) would you need to build a bridge that is at least 429 cm long? _____ spans (black rods) and _____ piers (light green rods). Explaining your answer.