# Bridges: Human links and innovations

## CONTENTS OF CURRICULUM UNIT 01.05.02

- Narrative
- Background on Bridge Type
- Different Types of Beam Bridges
- Background on Physical Forces and Bridge Design
- Engineering Vocabulary:
- Mathematical Vocabulary
- Experiment 1: Understanding Force7 (1 Day)
- Experiment 2: Name that Load8 (1 Day)
- Experiment 3: Feel the Pressure (1 Day)
- Experiment 4: Tension (1 Day)
- Experiment 5: Sponge Beam (1 Day)
- Experiment 6: Toothpick Truss (1-2 Days)
- Experiment 7: Straw Shape (1-2 Days)
- Experiment 8: Paper Bridge (1-2 Days)
- Use of math in bridge designs
- Using math to make a scale model bridge.
- The Problem: (10-15 Days)
- Web Site
- Bibliography

### Unit Guide

## Bridging the Math Gap

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## The Problem: (10-15 Days)

Actual bridge dimensions have a width maximum of 15 meters and height minimum of 15 meters. The bridge must have one vehicle travel span, break down/bicycle lane, and a pedestrian walkway in each direction. There is to be exactly two pylons, piers and abutments for construction.

The local city ordinance, regarding sidewalks states it must be within these dimensions, a minimum of 1 meter and a maximum of 2 meters in width. Any new road constructed must have a break down lane in each direction measuring 1.5 meters, and travel lane is a minimum of 3 meters. Bridge design must consider the community's needs and the local ordnances for construction.

The minimum model size is 25 centimeter with 40 centimeters as the maximum length. The town has submitted the contract for bids. The bid requirement calls for the solution to their problem, blueprint and model. You must make a model to represent your solution, state the selection and reasons for your design choice.

Refer back to your notes regarding bridge types and the class engineering experiments. For the task at hand, which bridge type would be your solution to this problem? Draw blueprint on centimeter square graph paper. Once the blueprint is completed it should be used to make the bridge. There should be a minimum of two blueprints, one of the structural side view with all indications to scale and the other that shows the front and top views. The blueprint showing the structural view is using isometric paper, this drawing is not required to be a scale drawing.

You must maintain a notebook that shows all preliminary work, calculations, sketches of bridge designs, and a daily log of your activities to complete project. Your logbook, blueprints and model are required as the final report for the problem/solution. This should also help to organize the work and workload.

To make a scale drawing you must first determine a relationship between the actual bridge and the model. This relation is proportional, meaning there is a direct relationship between two units of measure. Remember the relationship of the model is smaller than the actual size. Your conversion must be to a unit smaller than feet. Use centimeters for the scale unit of measure. If the actual length is 500 ft what could the smaller unit ratio be? One way to determine this is to find all the factors of 500. The factors of 500 are: 500, 250, 125, 100, 50, 25, 20, 10, 5, 4, 2, and 1. Determine which of these numbers is the largest, which will divide into each design dimensional number and use that factor and unit measure as the value for one centimeter. In this case the scale should be 1 centimeter equals 20 feet.

Another method is to divide the scale numbers into the actual numbers and determine if this will be sufficient. Since the units are not the same this is considered a rate and not a ratio, a comparison of different units (feet verses centimeter). A ratio is the same idea however the units are the same, a comparison of the same thing.

Using these calculations put each dimensional unit to scale. Draw a straight 25-centimeter line and label the ends 0 and 25 cm. Using the number line theory begin to make the markings for all-important information that relates to the bridge deck, supports and boat clearance. Mark and label all information on the line. Each marking must be measured. Does the marking satisfy the requirements of the community? Check the information before you proceed.

For this project the consideration is for a grade. There are certain aspects that are required in order to validate the contract. A scoring rubric will be used to assess the company's work. Explain rubric and assign numerical point values before project is started. This is the contract for payment/ grade in this assignment.

These conditions are: Scoring Rubric for Project:

Percentage of Project | Description | Numerical Score |

_________________ | Math Calculations | ______________ | |||

_________________ | Scale Indicator | ______________ | |||

_________________ | Blueprint to Scale | ______________ | |||

_________________ | Isometric Blueprint | ______________ | |||

_________________ | 3 Dimensional Model | ______________ | |||

_________________ | Project Journal | ______________ | |||

_________________ | Self Assessment Sheet | ______________ | |||

_________________ | Parent Comment | ______________ | |||

_________________ | Neatness | ______________ | |||

_________________ | Presentation | ______________ | |||

_________________ | 3-4 Paragraphs using | ______________ | |||

journal and assessment sheet | |||||

as evidence for bridge choice |

I will determine specific items and assign values, and then the class is given some input into the other items. The parental comment is always a part of my projects, they are always extra credit and the stipulation is that I do not need to agree with the comment, but it must be signed and include a phone number. Usually the value is 10% of the points required to earn an A. I have found this often encourages the parent to offer help to their child and a way for the child to share their schoolwork.

"Bridging the Math Gap" was written with a specific type of math person in mind. Yet, any type of math student could enjoy the lessons. Why do I think so? I think so because if you enjoy doing something then it is not work, tedious. How often are students assessed on things they build? What is the true test of building any structure? When my students are given opportunities to learn as this unit is put together they forget the long-range task until the little ones begin to connect. What I see is an excitement to get to the next part of the lessons. The reason is the hands on approach to learning. The students view this type of learning as fun. I often must remind them it is math they are working on, the focus is math.

This unit is easily adapted to algebra, geometry, and basic engineering principles by changing the expectations of the student. Where I discussed the number system, in geometry the focus may be triangles, in algebra students can derive equations and write in terms of variables. If engineering is the focus there are many variations such as types of engineers who design bridges, some history of bridges and a point of resource information. The experiments can be written in the scientific method. Students can incorporate all aspects of bridge building, as a complete bridge unit.

"Bridging the Math Gap" was meant to be a rich, enjoyable unit for the math student.

*(chart available in print form)*