Eiffel Tower Challenge! Print out Notes Pages before presenting project. Teaching notes and student questions included within. SC Math Curriculum Standards addressed: Applies content of geometry and measurement strands with a strong emphasis on process standards of problem solving (design & construct), reasoning (use photos to describe math ideas), connecting (apply math ideas in design), communicating (create a Math flag) and representing (construct a model). A Middle-Grades Math Project By: Karey M. Santos, NBCT

The Eiffel Tower, designed by Gustave Eiffel, was an incomparable engineering feat when it was erected in preparation for the Universal Exposition of 1889. Introductory slides 1-4 give brief history of the Eiffel Tower.

Historical photos source: http://www.tour-eiffel.fr/teiffel/uk/ It only took five months to build the foundations and twenty-one to finish assembling the metal pieces of the Tower. March 15, 1888  September 15, 1888  December 26, 1888  March 12, 1889 The assembly of the 300 meter tower was a marvel of precision, as all chroniclers of the period agree. (Imagine a tower taller than 3 football fields, end to end.) The construction work began in January 1887 and was finished on March 31, 1889. Historical photos source: http://www.tour-eiffel.fr/teiffel/uk/ The finished tower was 300 meters. Use this data to estimate its height in each of the progressive photos shown. Historical note: In 1956 a fire in the radio room caused excessive damage to the Tower. The renovation modified its height to 324 meters (including the flagpole).

- a tower firmly attached atop. Tower is basically composed of two parts: - a base, which is a sort of sturdy stool, standing on 4 main pillars, and - a tower firmly attached atop. The pillar base allows the Tower to withstand the swaying wind forces. Emphasize the 2 part structure and the purpose of the stool-like base. Students may wish to include this idea in their designs.

Use your Math terms to describe what you see… Because the basic structure composed of laminated iron is visible, the Geometry is clear. Let’s explore this marvel, looking for the MATH! Use your Math terms to describe what you see… View from elevator – bridge (Pont D’Iena) crosses the Seine, leading to Palais De Chaillot If Smartboard technology is available, have students use writing tools on the following slides 6-13 to show what they are describing mathematically.

Parallel Equidistant Congruent These stairs lead you to the first level observation deck. Where is the Math? Parallel Equidistant Trivia: There are 1665 steps in the Tower. If a typical home staircase consists of 15 steps, how many times would you have to climb a home staircase to model the stairs of the Eiffel Tower? (111 times) Assuming that you did NOT tire and slow down, how long would it take you? How could you find out? Congruent

Looks for examples of congruent circles, arcs, parallel, perpendicular, rhombi, and tessellations. Can you find a cone? (Look at the base of the cylinder/pole – middle, right)

Cool shot beneath the Tower: symmetry, square, rectangles, right angles, intersecting lines, vertices, etc…

Intersecting line segments Triangles Intersecting line segments Congruent shapes Background – view of Paris Perpendicular

Pulley system for elevators Pulley system for elevators. Look for examples of perpendicular, radii, circumference, etc…

rays

At the base, the footing rests on a truncated stone prism, cut at a precise angle to support the Tower. How could you estimate the tilt angle? What would you measure?

Teacher supplied materials Your Challenge! You will work with a Design and Construction Crew to create a new Tower, using only the materials provided by your teacher. Teacher supplied materials Option 1 (for smaller towers): grid paper (for designs), plastic coffee stirrers (or drinking straws), masking tape, 8” X 8” mat boards (1/team), construction paper for flag Option 2 (large towers): have students collect old newspapers to make their own rebar*, grid paper (for designs), masking tape, 1m X 1m mats cut from bulletin board paper (1/team), construction paper for flag *newspaper rebar: lay out 6 sheets of newsprint, roll tightly into tube shape, masking tape to secure – THESE ARE VERY STRONG AND TOWERS MAY NEED TO BE ERECTED OUTSIDE AS THEY MAY EXCEED CEILING HEIGHT. Too cool…

Your Tower base may not have more than 4 supports at the base. Your Tower base must be set on the mat provided. Your Tower must be structurally able to support a tennis ball at the top. Your Tower must reach minimum height requirements. Remind students that their design must include a feature to support a tennis ball. Set the height requirements based on your materials (e.g.: coffee stirrers = 0.5 m, drinking straws = 1 m, newsprint rebar = 2.5 m)

Your completed Tower will compete with other Towers for maximum height – so build it tall! Your team must design an original flag that expresses a Mathematical Theme which will be placed on the top of your Tower. Discuss symbolism and set flag criteria. To receive full credit for flag, each team must write an explanation of the symbolism represented on their flag on a 3 X 5 card which will be set at the base of the Tower.

Product Scoring Rubric: Completed on Time 20 pts. Follows Design Plan 10 pts. Meets size specs. 10 pts. Meets support specs. 10 pts. Original flag 10 pts. Creativity 10 pts. Neatness 10 pts. Teamwork 20 pts. 10 EXTRA CREDIT POINTS WILL BE ALLOTTED TO THE TALLEST TOWER!!! At the completion of the project, ask each student to individually score their team using this rubric and calculate the mean average for a self/peer review score.

Start designing and good luck! Homework: Have each student sketch his/her own design plan on grid paper, showing Tower footprint, front and side views. Assign design crews at the beginning of the following class. Students compare designs and may choose to construct 1 of the plans or generate a new plan, combining the best features of all plans. Remind them that the final design plan must be submitted with the finished product.

Photographs taken by Karey & Joe Santos, 6/06. Sources: Eiffel Tower historical information/photos http://www.tour-eiffel.fr/teiffel/uk/ Flag of France http://education.yahoo.com/reference/factbook/fr/flag.html Photographs taken by Karey & Joe Santos, 6/06. Go to Eiffel Tower link for more historical information.

SC Grade 4 MATH Curriculum Standards Addressed: 4-1.3 Explain and justify answers to problems on the basis of mathematical properties, structures, and relationships on mathematical properties, structures, and relationships. 4-1.4 Generate descriptions and mathematical statements about relationships between and among classes of objects. 4-4.1 Analyze the quadrilaterals squares, rectangles, trapezoids, rhombuses, and parallelograms according to their properties. 4-4.5 Use transformation(s) to prove congruency. 4-4.6 Represent points, lines, line segments, rays, angles, and polygons. 4-5.1 Use appropriate tools to measure objects to the nearest unit: measuring length in quarter inches, centimeters, and millimeters; measuring liquid volume in cups, quarts, and liters; and measuring weight and mass in pounds, milligrams, and kilograms. 4-5.2 Compare angle measures with referent angles of 45 degrees, 90 degrees, and 180 degrees to estimate angle measures.