DESCRIPTION OF LEARNING ACTIVITY UNIT

LEARNING UNIT:

Building Bridges

GRADE LEVEL AND SUBJECT AREA:

6 – 9
Mathematics

AUTHOR INFORMATION:

Debbie Curtis and Sue Lehmann

Hamilton Central School
West Kendrick AvenueHamilton, New York 13346
School Phone: (315) 824-3300

E-mail: dcurtis@hamilton.colgate.edu

slehmann@hamilton.colgate.edu

This document was typed on a PC platform using Microsoft Word 97

AUTHORS’ NOTE

This project is based on Dale Seymour Publications, Math Projects Series, Building Toothpick Bridges. We have modified and enhanced it into the unit that follows.

LEARNING CONTEXT

New York State Education Department Learning Standards for Mathematics, Science, and Technology

Standard 1: Analysis, Inquiry, and Design (Commencement)

Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.

Mathematical Analysis

3. Critical thinking skills are used in the solution of mathematical problems. Students apply geometric concepts and skills to the solution of problems.

Standard 2: Information Systems (Commencement)

Students will access, generate, process, and transfer information using appropriate technologies.

1. Information technology is used to retrieve, process, and communicate information and as a tool to enhance learning.

Standard 3: Mathematics (Intermediate)

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

3. Students use mathematical operations and relationships among them to understand mathematics. Students use addition, subtraction, multiplication, division, and exponentiation with real numbers.

4. Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.

5.Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data. Students apply proportions to scale drawings, computer-assisted design blueprints, and direct variation in order to compute indirect measurements. Students use geometric relationships in relevant measurement problems involving geometric concepts.

Standard 5: Technology (Commencement)

Students will apply technological knowledge and skills to design, construct, use, and evaluate products and systems to satisfy human and environmental needs.

7. Project management is essential to ensuring that technological endeavors are profitable and that products and systems are of high quality and built safely, on schedule, and within budget. Students help to manage a group engaged in planning, designing, implementation, and evaluation of a project to gain understanding of the management dynamics.

Standard 7: Interdisciplinary Problem Solving (Commencement)

Students will apply the knowledge and thinking skills of mathematics, science, and technology to address real-life problems and make informed decisions.

1. The knowledge and skills of mathematics, science, and technology are used together to make informed decisions and solve problems, especially those relating to issues of science/technology/society, consumer decision making, design, and inquiry into phenomena.

2. Solving interdisciplinary problems involves a variety of skills and strategies, including effective work habits; gathering and processing information; generating and analyzing ideas; making connections among common themes of mathematics, science, and technology; and presenting results.

New York State Education Department Learning Standards for English Language Arts

Standard 1: Language for Information and Understanding (Intermediate)

Students will read, write, listen, and speak for information and understanding.

1. Listening and reading to acquire information and understanding involves collecting data, facts, and ideas; discovering relationships, concepts, and generalizations; and using knowledge from oral, written, and electronic sources. Students compare and synthesize information from different sources. Students use a wide variety of strategies for selecting, organizing, and categorizing information.
2. Speaking and writing to acquire and transmit information requires asking probing and clarifying questions, interpreting information in one’s own words, applying information from one context to another and presenting the information and interpretation clearly, concisely, and comprehensibly. Students produce oral and written reports on topics related to all school subjects.
   

National Council of Teachers of Mathematics Curriculum and Evaluation Standards for school Mathematics

Standard 1: Mathematics as Problem Solving

In grades 5-8, the mathematics curriculum should include numerous and varied experiences with problem solving as a method of inquiry and application so that students can-

• Use problem-solving approaches to investigate and understand mathematical content;
• Develop and apply a variety of strategies to solve problems, with emphasis on multistep and nonroutine problems;
• Acquire confidence in using mathematics meaningfully.

In grades 9-12, the mathematics curriculum should include the refinement and extension of methods of mathematical problem solving so that all students can-

• Use, with increasing confidence, problem-solving approaches to investigate and understand mathematical content;
• Apply the process of mathematical modeling to real-world problem situations.

Standard 2: Mathematics as Communication

In grades 5-8, the study of mathematics should include opportunities to communicate so that students can-

• Model situations using oral, written, concrete, pictorial, graphical, and algebraic methods;

In grades 9-12, the mathematics curriculum should include the continued development of language and symbolism to communicate mathematical ideas so that all students can-

• Reflect upon and clarify their thinking about mathematical ideas and relationships;
• Express mathematical ideas orally and in writing.

Standard 3: Mathematics as Reasoning

In grades 5-8, reasoning shall permeate the mathematics curriculum so that students can-

• Understand and apply reasoning processes, with special attention to spatial reasoning and reasoning with proportions and graph;
• Validate their own thinking;

Standard 4: Mathematical Connections

In grades 5-8, the mathematics curriculum should include the investigation of mathematical connections so that students can-

• Explore problems and describe results using numerical, physical, and verbal mathematical models or representations;
• Apply mathematical thinking and modeling to solve problems that arise in other disciplines

Standard 5: Number and Number Relationships (Grades 5-8)

In grades 5-8, the mathematics curriculum should include the continued development of number and number relationships so that students can-

• Understand, represent, and use numbers in a variety of equivalent forms in real-world and mathematical problem situations;
• Develop number sense for whole numbers, fractions, decimals, integers, and rational numbers;
• Understand and apply ratios, proportions, and percents in a wide variety of situations.

Standard 6: Number Systems and Number Theory (Grades 5-8)

In grades 5-8, the mathematics curriculum should include the study of number systems and number theory so that students can-

• Understand and appreciate the need for numbers beyond the whole numbers;
• Extend their understanding of whole number operations to fractions, decimals, integers, and rational numbers;
• Develop and apply number theory concepts in real-world and mathematical problem situations.

Standard 7: Computation and Estimation (Grades 5-8)

In grades 5-8, the mathematics curriculum should develop the concepts underlying computation and estimation in various contexts so that students can-

• Use computation, estimation, and proportions to solve problems;
• Use estimation to check the reasonableness of results.

Standard 12: Geometry (Grades 5-8)

In grades 5-8, the mathematics curriculum should include the study of the geometry of one, two, and three dimensions in a variety of situations so that students can-

• Develop an appreciation of geometry as a means of describing the physical world

Standard 13: Measurement (Grades 5-8)

In grades 5-8, the mathematics curriculum should include extensive concrete experience using measurement so that students can-

• Estimate, make, and use measurements to describe and compare phenomena;
• Extend their understanding of the concepts of weight and mass.

CONTENT KNOWLEDGE

ESSENTIAL QUESTIONS

What makes a bridge strong?

How is mathematics used in building a bridge?

What mathematics are used by the different professionals involved in building a bridge?

What role does mathematics play in the construction of the bridge?

PURPOSE

This unit provides the students an opportunity to review their skills in estimation, decimal operations, ratio and proportions, writing checks and maintaining a checkbook register while running a construction company. When used as a project at the beginning of the year, it develops interpersonal skills and rituals for the students within the classroom.

PROCEDURE

Overview: Students work in groups (ideal group size is 4) to simulate a construction company given the job of building a bridge. Each student assumes the role of one of the following: Project Director, Head Architect, Head Carpenter, Head Accountant, and/or Transportation Chief. In addition to this primary role, each student will act as an architect, a carpenter, and an accountant. All group members help design the bridge, the Head Architect is the person ultimately responsible for seeing that the scale drawings are completed accurately and on time. All group members help to build the bridge, the Head Carpenter instructs them what to do and how. It is difficult to finish the construction on time if all group members don’t participate. All group members are required to keep a check register, the Head Accountant will maintain the official register on a spreadsheet while each student will maintain their own register on the page provided. The teacher runs the warehouse from which companies buy supplies. The teacher can assess companies "fines" for violations such as "disturbing the peace", "trespassing", "inappropriate comments", etc (This is a great way to keep control while construction is going on.). The teacher may also give out "awards" for companies that demonstrate creativity, to students who do outstanding at their job, etc. These awards can be considered "company bonuses". Fines and bonuses are given out on post-it notes with the cash amount listed. Following construction of the bridge, each company makes a presentation discussing the process their group went through to complete the task. Strength of the bridge is then determined by how much weight the structure can hold.

INITIATING ACTIVITY: The day before the unit is to begin, take 10 – 15 minutes to explain the project. Students need to know that:

• They will be divided into groups (teacher assigned or student choice), each group will be a company responsible for the building of a bridge.
• Each student will assume the role of accountant, carpenter, architect, project director, and/or transportation chief.
• Each company must stay within a budget to complete their bridge.

• Tomorrow the class will report to the computer lab to research, via the internet, information on types of bridges and methods of construction.
• The homework assignment for tonight is to read the "History of Bridges" copied from the Dale Seymour publication.

The first day of this unit is spent in the computer lab (or any location where the class may access the internet). During this class, students must complete the information guide on bridges. For homework students reflect upon what they learned through the internet: they write their thoughts on "What information did I gather through the internet that would be useful in designing a bridge?"

The second day is started by students sharing ideas from their homework assignment. The teacher leads a discussion in job descriptions for project director, head architect, head carpenter, head accountant, and transportation chief. The class comes up with criteria for each job. For example, the accountant needs to be very good at addition/subtraction of decimals. The project director must be someone whose attendance is excellent and has the ability to work well with others. After establishing the job descriptions, students break into their groups. The task for today is to come up with a company name and design a company logo. Students may design their logo on the computer. While students are creating their logo, they can discuss what job each person would like to have. Most groups can assign these jobs by consensus, occasionally the teacher may need to intervene.

The third day is spent explaining forms and rules. The teacher goes over the "Bridge Building Code" and "Bridge Contest Rules" with the entire class. Students then separate into their companies. The teacher then meets with different groups of students by job category. At these meetings, the teacher explains their roles and the forms. While these meetings are being conducted, companies can finish their logos and discuss what type of bridge they are going to design.

• Project Directors are responsible for keeping the group on task. They must update the "Job Duties and Schedule" sheet, making sure that all members are participating. They are required to keep a "Summary Journal" recording, on a daily basis, progress the company has made, problems they encountered and their solutions. This "Summary Journal" is kept on the computer within a work processing program.They also sign and approve building plans, checks, and order forms. Keeps all records in the company’s folder.
• Head Architect is responsible for the completion of the four scale drawing views required. Supervises other architects and their drawings. Keeps inventory of supplies daily. This inventory is kept on a spreadsheet. Makes sure the carpenters follow the plans accurately. Fills out the order forms to order supplies and has these forms signed by the project director.
• Head Carpenter is responsible for the construction of the bridge. Supervises other carpenters, making sure they are working and building the bridge according to plans. Is responsible for the secure storage of supplies. Consults with the architect as construction progresses.
• Head Accountant is responsible for keeping the checkbook register on the computer using a spreadsheet and writes checks for purchasing materials. Supervises other accountants and helps them to keep accurate records. Consults with the Project Director regarding budget and purchases. Consults with Head Architect to purchase necessary supplies.
• Transportation Chief delivers checks and picks up supplies. They are responsible for making sure the construction sit is left clean and supplies are properly stored. This is the only person permitted to leave their construction site.

At the beginning of the fourth class period, the teacher reviews the grading rubric that will be used for this project. Time should be given for students to ask clarifying questions. The remainder of the period will be spent on designing the bridge plans. Companies may need to purchase "blueprint paper" at this point, so teacher needs to have the warehouse open for business. If facilities are available, this portion of the project can be done on CADD (we recommend this highly). For homework, students complete their "Daily Journal" entry.

The fifth and sixth days are spent finalizing plans and getting them approved. Some companies may be ready to start construction. All plans are due by the end of the sixth day. For homework, students complete their "Daily Journal" entry.

Companies will spend the seventh, eighth, ninth and tenth class periods building their bridges. Stress that all bridges must be completed by the end of this tenth class period. Workers may need to put in overtime hours to complete their bridge by the deadline. For homework, students complete their "Daily Journal" entry.

On day eleven companies prepare their presentation to be given in front of outside panel members. At this point the students are given the grading rubric for their presentation. Time should be given for clarification and questions. Students are required to use a word processing program to type their presentation notes. Students are encouraged to practice their presentations. "Project Debriefing Form for the Bridge Project" is given for homework, to be due following the presentation.

CULMINATING ACTIVITY: The last two days of this unit are devoted to the company presentations and the breaking of the bridges. Students must record on the "Data Sheet" the weight of the bridge, the amount of weight the bridge holds, the number of toothpicks used, and the required ratios and percents. The teacher must invite 3 to 4 outside individuals (parents, teachers, administration, staff ) to assist in evaluating the presentations. Students will also complete the rubric for each other as a peer evaluation. Teacher should arrange to have presentations videotaped to be played for a follow up discussion and reflection with classmates.

INSTRUCTIONAL/ENVIRONMENTAL MODIFICATIONS

• Internet access for the entire class is required during the first day of this unit.
• Students need access to computers on a daily basis in order to maintain their spreadsheets. (3 or 4 computers for the whole class should be fine)
• Optional access to computers with CADD capabilities, if students are to do scale drawings on computer.
• Since students are working cooperatively and choosing jobs according to their ability, little modification is needed for the classified students. Teacher may adjust grading rubrics for students with IEPs.
• Classroom will need to be reorganized to facilitate group work..

MATERIALS

• Building Toothpick Bridges, Math Projects Series, by Jeanne Pollard. Dale Seymour Publications.
• Copies, one per student, "Internet Guide Sheet for Bridge Project"
• Copies, one per student, "Job Descriptions"
• Markers and construction paper for company logos
• Large manila envelopes for company’s to store papers
• Shoe boxes, one per group, to store company supplies securely
• Copies, one per group, "Job Duties and Schedule"
• Copies, one per student, "Bridge Building Code"
• Copies, one per student, "Bridge Building Contest Rules"
• Sign for warehouse, with prices
• Graph paper, cm grid, minimum 4 per group
• Wax paper, one roll will do for four classes
• Toothpicks, bundled into groups of ten (study hall students can be very helpful making bundles) – count on an average of 200 toothpicks per company
• Glue
• Bottle caps, used to sell glue to companies on a daily basis
• Copies, 7 per student, "Daily Journal" form
• Copies, 7 per group, "Summary Journal" form – to be completed by Project Director
• Copies, 10 per group, "Order Form"
• Copies, 1 booklet (10 checks) per group, checks
• Copies, 1 per student, "Balance Sheet"
• Copies, 2, of boat and truck pattern – teacher needs to assemble in advance
• String or thread in case a group decides to build a suspension bridge
• Copies, 1 per student, "Data Sheet"
• Video Camera and blank tape

ASSESSMENT TOOLS & TECHNIQUES

Teacher’s tools:

• Student observation sheets, completed daily by teacher (attached)
• "Quantitative Project Checklist for Bridge Project"
• "Project Debriefing Tool"
• "Oral Presentation Rubric"

Students’ completion of:

• "Daily Journal" entries
• "Balance Sheet"
• Scale Drawings
• Bridge, according to Building Codes
• Presentation
• "Data Sheet"

TIME REQUIRED

Teacher preparation consists of making copies, making the sign for the warehouse (listing prices), setting up checkbooks, bundling toothpicks in groups of 10, and gathering materials. Students in study halls have proved to be a great help in bundling the toothpicks. Estimated prep time: 2 – 3 hours.

Total class time, including research and presentations: 13 class periods (45 – 50 minutes each)

REFLECTION

Between the two of us, we have used this unit with at least 15 classes over a period of 5 years, each time we’ve used it we have made some improvement on it. Next year our goal is to incorporate CADD in the designing of the bridge.

It has been our experience that four days is sufficient time to construct the bridges. If you allow them four days, they will get it finished in four days. If you allow them six days, it will take them six. The first year this project was implemented the students weaseled their way into eight days! Never again!

It would be nice to have a civil engineer or construction worker, a real life "bridge builder", come to speak with the class before and/or after this project. It would give the students more real world connections and perhaps spark more ideas and enthusiasm. It would be great if this person could be there as an introduction to the project and then return for the bridge breaking culminating activity.

This project is a great to use at the beginning of the year, it generates tremendous excitement and enthusiasm. It gives students a wonderful opportunity to learn about group dynamics, learning styles, and classroom rituals. It is a nice opportunity to allow students to participate in a project that they themselves set the criteria. And it’s a fun way to review the basics of decimals, ratio and proportion, and writing checks. It is an excellent way to determine other strengths students may have outside mathematics. Have fun with it!

Project Debriefing Tool

GROUP/TASK TEAM

Directions: Think about how your group worked together to complete this project. Discuss it with your team. In the spaces below please respond to each question. Please give specific examples to support all of your major points.

In your own words, explain your job and the duties you were to fulfill. Give detailed information on how you fullfilled these job each day.

In your own words, do you feel your company was successful? Why or Why not?

In your opinion, did your company work well together to solve problems? How? What things did they excell at? If not, why not? What could they have done better? Think of some specific examples.

What did you like most about this project? Why?

What did you like least about this project? Why?

Describe the process your group went through in designing and building the bridge. Did you discuss the plans before drawing. Did one person draw the plans or did everyone contribute? Who and what? Who was involved in the building and what did they do?

Did anyone in group contribute more than others? Less than others? Did attendance affect the performance of your company? How? Give specific examples.

In your opinion, if you were assigned this project again, what kinds of things need to be done differently next time?

If you were the teacher, what constructive changes would you make in this assignment to make it better?

Describe something you learned about yourself or about working with other people in your group/team during this project.

** Below on this paper please list the names of each member of your group/team. Next to each name please write a brief statement describing your view of that team member's contribution(s) to the quality of this project. Please be very specific!

NAME__________________________ DATA SHEET

COMPANY NAME___________________________________

Project Director:____________________________________

Head Accountant: __________________________________

Head Architect:_____________________________________

Head Carpenter: ____________________________________

Transportation Chief:________________________________

Ending Balance in Account: ________________

Amount of Money Spent Constructing Bridge:___________

Number of Toothpicks: ________________

Weight of Bridge: ______________________ kg

Weight Bridge Held: _______________________

Ratios:=___________kg/$

=______________kg/$

Describe all the math skills used during this project:

Name______________________ Math 8

Mailbox # ___________ Name of Company ________________Cell ____________

DAILY JOURNAL

Date ________________ Teacher's Comments on YOU

Attendance:

Schedule for Today:

What was accomplished?

Any problems? If a problem, what was the group's solution

What did you work on today? - give specific examples in detail!

What did your company members work on today? - give specific examples in detail

Goals for tomorrow?

Schedule determined in the last five minutes of class for tomorrow.

Bridge Internet Information Sheet

Name______________________ Math 8

Mailbox # ___________ Team_______ Bridges – Internet Cell ____________

BRIDGES

I. Kinds of Bridges with their characteristics

II. List the Structural Forms of Bridges and explain the differences

III. Famous Bridges - at least three and give details of each bridge including the history, the design, and the materials

IV. Engineers are problem - solvers. Given the vocabulary of the engineers, explain the term:

A. stress

B. span

C. grider

D. truss

E. strain

F. deck

V. Items I found on the internet that would help me construct my own bridge

"Product" Checklist

Quantitative

Date: ________ Cell: ________

"Product" Rubric

Quantitative

Date: ________ Class Period: ________