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Will the Leaning Tower Fall?

Subjects

• Arts & Humanities
--Architecture
--Language Arts
• Educational Technology
• Mathematics
--Algebra
--Geometry
--Measurement
--Probability
--Process Skills
• Science
----Physics
--Process Skills

Grade

• 9-12
• Advanced

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Brief Description

Students research the Tower of Pisa and write a report about its history. Then they examine the physics of why it leans and whether it might fall. Finally, they plan a trip to Italy to see the Tower, develop an itinerary and budget for the trip.

Objectives

Students will:

• Research the Internet to learn about the Tower of Pisa.
• Write a report about the history of the Tower.
• Review the use of a graphing calculator, and then use the calculator to determine the height of the Tower.
• Learn or review how to use Geometer's Sketchpad, and then use the software to explore what might cause the Tower to fall.
• Write a report about their analysis of the Tower.
• Use the Internet to plan a trip to Italy, and then create an itinerary and budget for the trip.

Keywords

Calculator, Tower of Pisa, Italy, geometry, math

Materials Needed[shopmaterials]

• Student Internet access
• TI-83 graphing calculator
• Geometer's Sketchpad software
• TI-83 and Sketchpad "Survival Guides" (provided at the project Web site)
• Planning a Trip worksheet (outline provided at the project Web site)

Lesson Plan

Below is a brief outline of the five parts of this lesson. Specific information, instructions, resources, tips, and recommendations for the entire project can be found at The Leaning Tower of Pisa project Web site at http://teachersnetwork.org/teachnetnyc/fianni/pisa.htm.

Part 1: Students research online the history of the Tower of Pisa and then write a brief essay on the history of the Tower.

Part 2: Students review the mathematical concepts necessary to complete the activity. They then use the Ti-83 graphing calculator to determine the height of the Tower using the Law of Cosine.

Part 3: Students create a program with the TI-83 that allows them to find the missing side in a non right triangle knowing two sides and the angle formed by the two sides. Then they use that program to find the height of the Tower.

Part 4. Students learn or review Geometer's Sketchpad. They use the software to explore what might cause the Leaning Tower to fall, and then write a brief report about the analysis.

Part 5. Students use the Internet to plan a trip to Italy and create an itinerary for their trip.

Assessment

Students will be evaluated on:

• Their participation in classroom activities.
• Their knowledge of the appropriate mathematical concepts and formulas as demonstrated in their class work and written reports.
• Their ability to use the appropriate technology tools competently and effectively.
• The quality of their online research and their ability to effectively evaluate and interpret that research.
• The quality of their written reports.

Lesson Plan Source

Francesco Ianni

Submitted By

Linda Starr

National Standards

LANGUAGE ARTS: English
GRADES K - 12
NL-ENG.K-12.2 Reading for Understanding
NL-ENG.K-12.3 Evaluation Strategies
NL-ENG.K-12.4 Communication Skills
NL-ENG.K-12.5 Communication Strategies
NL-ENG.K-12.6 Applying Knowledge
NL-ENG.K-12.7 Evaluating Data
NL-ENG.K-12.8 Developing Research Skills
NL-ENG.K-12.9 Multicultural Understanding
NL-ENG.K-12.11 Participating in Society

MATHEMATICS: Algebra
GRADES 9 - 12
NM-ALG.9-12.1 Understand Patterns, Relations, and Functions
NM-ALG.9-12.2 Represent and Analyze Mathematical Situations and Structures Using Algebraic Symbols
NM-ALG.9-12.3 Use Mathematical Models to Represent and Understand Quantitative Relationships
NM-ALG.9-12.4 Analyze Change in Various Contexts

MATHEMATICS: Geometry
GRADES 9 - 12
NM-GEO.9-12.1 Analyze Characteristics and Properties of Two- and Three-Dimensional Geometric Shapes and Develop Mathematical Arguments About Geometric Relationships
NM-GEO.9-12.2 Specify Locations and Describe Spatial Relationships Using Coordinate Geometry and Other Representational Systems
NM-GEO.9-12.3 Apply Transformations and Use Symmetry to Analyze Mathematical Situations
NM-GEO.9-12.4 Use Visualization, Spatial Reasoning, and Geometric Modeling to Solve Problems

MATHEMATICS: Measurement
GRADES 9 - 12
NM-MEA.9-12.1 Understand Measurable Attributes of Objects and the Units, Systems, and Processes of Measurement
NM-MEA.9-12.2 Apply Appropriate Techniques, Tools, and Formulas to Determine Measurements

MATHEMATICS: Data Analysis and Probability
GRADES 9 - 12
NM-DATA.9-12.1 Formulate Questions That Can Be Addressed With Data and Collect, Organize, and Display Relevant Data to Answer
NM-DATA.9-12.2 Select and Use Appropriate Statistical Methods to Analyze Data
NM-DATA.9-12.3 Develop and Evaluate Inferences and Predictions That Are Based on Data
NM-DATA.9-12.4 Understand and Apply Basic Concepts of Probability

MATHEMATICS: Problem Solving
GRADES Pre-K - 12
NM-PROB.PK-12.1 Build New Mathematical Knowledge Through Problem Solving
NM-PROB.PK-12.2 Solve Problems That Arise in Mathematics and in Other Contexts
NM-PROB.PK-12.3 Apply and Adapt a Variety of Appropriate Strategies to Solve Problems
NM-PROB.PK-12.4 Monitor and Reflect on the Process of Mathematical Problem Solving

MATHEMATICS: Communications
GRADES Pre-K - 12
NM-COMM.PK-12.1 Organize and Consolidate Their Mathematical Thinking Through Communication
NM-COMM.PK-12.2 Communicate Their Mathematical Thinking Coherently and Clearly to Peers, Teachers, and Others
NM-COMM.PK-12.3 Analyze and Evaluate the Mathematical Thinking and Strategies of Others
NM-COMM.PK-12.4 Use the Language of Mathematics to Express Mathematical Ideas Precisely

MATHEMATICS: Representation
GRADES Pre-K - 12
NM-REP.PK-12.1 Create and Use Representations to Organize, Record, and Communicate Mathematical Ideas
NM-REP.PK-12.2 Select, Apply, and Translate Among Mathematical Representations to Solve Problems
NM-REP.PK-12.3 Use Representations to Model and Interpret Physical, Social, and Mathematical Phenomena

SCIENCE
GRADES 9 - 12
NS.9-12.2 Physical Science
NS.9-12.5 Science and Technology
NS.9-12.6 Science in Personal and Social Perspectives

TECHNOLOGY
GRADES K - 12
NT.K-12.1 Basic Operations and Concepts
NT.K-12.3 Technology Productivity tools
NT.K-12.4 Technology Communications tools
NT.K-12.5 Technology Research tools
NT.K-12.6 Technology Problem-Solving and Decision-Making tools