Profile Sheet for PBL Lesson Plan
Kristi Denery-Page
Teacher: Mrs. Denery-Page
Primary Subject Area: Mathmatics
Outside Subject Area: Language Arts
Class: Geometry
Class Level: General Math Class
Grade Level: 10th Grade
PBL Title: Bay County engineers meet to determine best design and structure for new bridge.
Description of Student Roles and Problem Situation: Students will become engineers employed by Bay County. They will have to analyze shapes and structures in order to determine the best structural design for the new bridge. They must then analyze the existing city map and plan the bridge in accordance with the existing bridges and roads.
Adaptations for a student from a non-Western culture:
I will first place this individual in a group with strong academic students so they would be able to assist if I am helping another student. I will set time aside before we begin this unit to explain and guide the student through the process and what we will be doing. I will completely explain to them what their roles are in the group and as an individual. I would take all necessary precautions to make sure we do not offend detour the student from the assignment. I will give the student step-by-step instructions to follow in advance so they can look over them and ask any questions they may have before they are put into groups. I feel this would be a great opportunity for students to collaborate and maybe even design one of their bridges from a non-western culture to analyze the differences in construction.
Adaptations for ESOL student:
Depending on the ESOL student communication skills I may translate the PBL so that they can have it in their current speaking language. I do not want hinder the student my making him first translate the assignment and then begin. I will also place him in a group of educationally sound and patient students. I feel the environment plays a huge role. If at all possible depending on the language barrier I may have translating dictionaries for all students in the group to make sure that full communications is taking place. I will be readily available for all questions either by the ESOL student or his team mates in order to make the educational process a success.
Title, Learner Characteristics, SSS
Teacher : Mrs. Kristi Denery-Page
Primary Subject Area: Mathematics
Outside Subject Area: Language Arts
Class: Geometry
Class Level: General Math Class
Grade: 10th grade
PBL Title: Bay County engineers meet to determine best design and structure for new bridge.
Primary Sunshine State Standards
Math - Strand C
Standard 1
The student describes, draws, identifies, and analyzes two- and three-dimensional shapes
Benchmark MA.C.1.4.1
The student uses properties and relationships of geometric shapes to construct formal and informal proofs.
Standard 2
The students visualize and illustrate ways in which shapes can be combined, subdivided, and changed.
Benchmark MA.C.2.4.1
The student understands geometric concepts such as perpendicularity, parallelism, tangency, congruency, similarity, reflections, symmetry, and transformations including flips, slides, turns, enlargements, rotations and fractals.
Standard 3
The student uses coordinate geometry to locate objects in both two and three dimensions and to describe objects algebraically.
Benchmark MA.C.3.4.2
The student uses a rectangle coordinate system (graph), applies and algebraically verifies properties of two- and three-dimensional figures, including distance, midpoint, slope, parallelism, and perpendicularity. (Includes MA.D.2.4.1 Represents real-world problems.)
Outside Subject Area Sunshine State Standards
Language Arts - Strand B
Standard 2
The student writes to communicate ideas and information effectively.
Benchmark LA.B.2.4.2
Organizes information using appropriate systems.
Learner Characteristics of High School Students:
Physical: Most students reach physical maturity, and virtually all attain puberty.
Justification: It is important for the teacher to select groups with common characteristics and same levels of puberty. You want the students working on the same page in each group. Putting them in like groups will help insure each member is feeling needed.
Social: Girls seem to experience greater anxiety about friendships than boys do.
Justification: In placing different students in different groups they are forced to speak to students they may not necessarily speak to. Grouping takes the pressure away from walking across the room and introducing themselves to an unfamiliar person. Placing in groups helps break the ice.
Social: Parents and other adults are likely to influence long-range plans; peers are likely to influence immediate status.
Justification: It is important for the teacher to identify the “slackers” to the “motivators”. You do not want a group of students who are going to encourage each other to just fail the project and put forth no effort. Instead you want a majority of the group to want to succeed in order to pull up the individual who would rather slack off.
Cognitive: High school students become increasingly capable of engaging in formal thought, but they may not use this capability.
Justification: In this PBL the students will be required to use previous mathematical knowledge as well as contemplate and investigate different levels of mathematical understanding when evaluating the situation at hand.
Emotional: The most common type of emotional disorder during adolescence is depression.
Justification: Depression is a very touchy area. The PBL will require a lot of time and can cause some stress if not managed in the correct fashion. Teacher should personally identify these students and place in a setting that would eliminate or control the amount of stress that could be caused by the project. Teacher should also make sure students are placed in a group with very socially positive students in order to keep student in an upbeat environment.
Learning Outcomes, Student Role and Problem Situation, Meet the Problem Method PBL Lesson Plan for Diverse Learners
Original Title: Bay County engineers meet to determine best design and structure for new bridge.
Teacher: Kristi Denery-Page
Primary Sunshine State Standards with Learning Outcomes: Math: Standard 1 (MA.C.1.4.1)
1. Given six objects, the student/group will list three characteristics observed by sight with 80% accuracy. (Knowledge)
2. Given the same six objects, student/group will compare each object explain similarities and differences, strengths and weaknesses accurately. (Comprehension)
3. Given building material, the student/group will then build three models of their own choice, making sure to construct each object illustrating all properties of the chosen figure with 80% accuracy.(Application)
4. Given the original six objects and their constructed objects, the student/group needs to categorize each object and form conclusions about the strengths and characteristics of each object with 90% accuracy. (Analysis)
Math: Standard 2 (MA.C.2.4.1)
5. Given a sheet of construction paper, the student/group is to accurately compose a rough drawing of his/her bridge, including all support structures. (Synthesis)
6. Using the three dimensional bridge the student/group constructed and a calculator, the student must calculate square footage of the bridge, surface area, and dimensions of the bridge including roads leading to bridge with 90% accuracy. (Evaluation)
7. Using their diagram and calculations from above, each student/group will compare their design to three bridges they researched online, evaluating the square feet, surface area, and dimensions with 100% accuracy. (Evaluation)
Math: Standard 3 (MA.C.3.4.2)
8. Using the city map, the student/group must create a coordinate system of the bridge and label each joining roadway with 100% accuracy. (Synthesis)
9. Using the map with the plotted locations, the student must connect all three locations forming a right triangle. If they do not form a right triangle the student will use the distance formula instead of the Pythagorean formula. Using either formula the student will find the distance from one location to the next, and then calculate the midpoint between each location with 80% accuracy. (Synthesis)
10. Using the map and calculations, the student/group must evaluate the best size and location for the bridge in accordance with the existing bridge with 90% accuracy. (Evaluation)
Language Arts: Standard 2 (LA.B.2.4.2)
11. Given construction paper and previous directions from Math Strand 1 exercise, the student needs to accurately construct a chart with all the shapes, characteristic, similarities, and differences. It should be easy to look at and determine which shape is being described. (Application)
12. Given formulas and material from Math Strand 2 exercise, the student needs to describe each detail and formula they used in assessing the measurements for their bridge with 90% accuracy. (Evaluation)
13. Given feedback from all assignments, the student/group must accurately summarize how each of these lessons helped or did not help engage their understanding to determine the best design and structure for the bridge. (Comprehension)
Description of Student Roles and Problem Situation: Students will become engineers employed by Bay County. They will have to analyze shapes and structures in order to determine the best structural design for the new bridge. They must then analyze the existing city map and plan the bridge in accordance with the existing bridges and roads.
Meet the Problem Documents: A memo from the County Executive board to the engineers and the original specifications of the existing bridge. They are both used as “meet the problem” documents.
TO: Bay County Engineers, LLC
From: Bay County Executive Board
Mayor Bill Gates
Date: January 25, 2009
Re: Design and Structure of New Bridge
______
As you know the local tax payers have petitioned for a new bridge to be built across the international waterway. The existing bridge is in diminishing form. Not yet a safety hazard we would like to begin design of new bridge to replace current structure.
We would like for your group of engineers to begin research for a new bridge. We would like it to be visually pleasing as well as structurally secure. We would like you to come up with three, three-dimensional models as well as a two dimensional grid system so we can see how it will play with our existing roadways.
The Executive Board will meet on February 28, 2009 at 6:30pm in the County Press Room. We would like for you to attend our television broadcasted meeting to present your proposed models to the public.
Bridge Design and Construction Statistics
Bridge Length, Width, Height, Weight
Bridge Deflection, Load Capacity
Main Tower Stats
Main Cable Stats
Suspender Rope (vertical ones) Stats
Concrete Quantities
Structural Steel Quantities
Total length of Bridge including approaches: 1.7 miles = 8,981 ft = 2,737 m
Length of suspension span including main span and side spans: 1.2 miles = 6,450 ft = 1,966 m
Length of main span portion of suspended structure (distance between towers): 4,200 ft = 1,280 m
Length of one side span: 1,125 ft = 343 m
Width of Bridge: 90 ft = 27 m
Width of roadway between curbs: 62 ft = 19 m
Width of sidewalk: 10 ft = 3 m
Clearance above mean higher high water: 220 ft = 67 m
Total weight of each anchorage: 60,000 tons = 54,400,000 kg
Original combined weight of Bridge, anchorages, and approaches: 894,500 tons = 811,500,000 kg
Total weight of Bridge, anchorages, and approaches (1937): 894,500 tons = 811,500,000 kg
Total weight of Bridge, anchorages, and approaches (1986)*: 887,000 tons = 804,700,00 kg*
Weight of Bridge, excluding anchorages and approaches, and including the suspended structure, main towers, piers and fenders, bottom lateral system and orthotropic redecking (1986): 419,800 tons = 380,800,000 kg*
* The total bridge weight listed for 1986 includes the reduction in weight due to the redecking in 1986. The weight of the original reinforced concrete deck and its supporting stringers was 166,397 tons (150,952,000 kg). The weight of the new orthotropic steel plate deck, its two inches of epoxy asphalt surfacing, and its supporting pedestals is now 154,093 tons (139,790,700 kg). This is a total reduction in weight of the deck of 12,300 tons (11,158,400 kg), or 1.37 tons (1133 kg) per lineal foot of deck.
Bridge Deflection, Load Capacity*
Maximum transverse deflection, at center span: 27.7 ft = 8.4 m
Maximum downward deflection, at center span: 10.8 ft = 3.3 m
Maximum upward deflection, at center span: 5.8 ft = 1.77 m
Live load capacity per lineal foot: 4,000 lbs. = 1,814.4 kg
As an example of how the Bridge is built to move, during the winter storms in 1982, the main span bowed approximately 6 to 7 feet
The three maximum deflections noted above at the center of the suspension bridge are due to the following loading conditions:
1. The transverse deflection is due to a sustained transverse wind load. The maximum transverse movement of 27.7 ft is based on the maximum allowable longitudinal movement of the wind locks at the support towers;
2. The maximum downward deflection is due to a condition with maximum live load on the center span, no live load on the side spans and maximum design temperature to elongate the main cables; and
3. The maximum upward deflection is due to a condition opposite to condition 2 above, with maximum live load on side spans, no live load on center span and minimum design temperature to shorten the cable length.
Main Tower Stats
The Golden Gate Bridge has two main towers that support the two main cables.
Height of tower above water: 746 ft = 227 m
Height of tower above roadway: 500 ft = 152 m
Tower base dimension (each leg): 33 x 54 ft = 10 x 16 m
Load on each tower from main cables: 61,500 tons = 56,000,000 kg
Weight of both main towers: 44,000 tons = 40,200,000 kg
Transverse deflection of towers: 12.5 inches = 0.32 m
Longitudinal deflection of towers: shoreward: 22 in = 0.56 m and channelward: 18 in = 0.46 m
The south tower foundation depth below mean low water is: 110 ft = 34m
To build south tower pier to support the south tower, construction workers pumped 9.41 million gallons or 35.6 million liters of water out of the fender that was constructed first.
Main Cable Stats
The Golden Gate Bridge has two main cables which pass over the tops of the two main towers and are secured at either end in giant anchorages.
The main cables rest on top of the 746-foot main towers in huge steel castings called saddles.
Diameter of one main cable including the exterior wrapping: 36 3/8 in. = .92 m
Length of one main cable: 7,650 ft = 2,332 m
Total length of galvanized steel wire used in both main cables: 80,000 mi = 129,000 km
Number of galvanized steel wires in one main cable that are 0.192 inches in diameter: 27,572
Number of bundles or strands of galvanized steel wire in one main cable: 61
Weight of both main cables, suspender cables and accessories: 24,500 tons = 22,200,000 kg
The galvanized steel wire comprising each main cable was laid by spinning the wire using a loom-type shuttle that moved back and forth as it laid the wire in place to form the cables. The spinning of the main cable wires was completed in 6 months and 9 days.
The galvanized steel wire used for the main cables is carbon steel with the following average chemical composition and physical properties:
Ladle test results (specified)
C: / 0.81% (0.85)
Mn: / 0.66% (---)
P: / 0.026% (0.04)
S: / 0.028% (0.04)
Si: / 0.24% (---)
Tested properties (specified)
Tensile Str, / Fu = 235,600 psi (220,000 psi min)
Yield Str, / Fy = 182,600 psi (160,000 psi min)
Elongation in 10" at rupture = 6.3% (4.0% min)
Suspender Rope (vertical ones) Stats
The Golden Gate Bridge has a total of 250 pairs of vertical suspender ropes. Each suspender rope is 2 11/16 in. in diameter. All of the ropes were replaced between 1972 and 1976, with the last rope replacement completed on May 4, 1976.
Concrete Quantities
Cu. yd. / Cu. m.
San Francisco Pier and Fender / 130,000 / 99,400
Marin Pier / 23,500 / 18,000
Anchorages, Pylons, and Cable Housing / 182,000 / 139,160
Approaches / 28,500 / 21,800
Paving / 25,000 / 19,115
Structural Steel Quantities
Tons / Kg.
Main Towers / 44,400 / 40,280,000
Suspended Structure / 24,000 / 21,772,000
Anchorages / 4,400 / 3,991,000
Approaches / 10,200 / 9,250,000
Problem Statement, Know/Need to Know Board and Possible Resources