"Where there's History, Invention, Chance, Curiosity and Purpose... and there's a compelling Math Connection."
Field Trips
The details that follow describe some trips and include links to the Program Guides.
M athHappens has created field trips! We develop the topic, content and logistics to ensure that students have rich mathematical content to accompany their field experience. We have three trips to describe in detail. One to the Texas State History Museum for high school students can be adapted for middle school math students, another to Ransom Center Archive for high school students, and one to the Austin Nature and Science Center customizable for elementary, middle or high school students.
Texas State History Museum La Belle Exhibit
The Texas State History Museum is located in Austin and is the permanent home of La Belle a sailing vessel which was part of La Salle's last excursion in 1685. La Belle was recovered in Matagora Bay in 1995 and brought to Austin for permanent exhibit at the Museum. The story of her voyage, its connection to the Age of Exploration, and to Texas History is told through the exhibit of the ship remains and a dramatic film. As a math field trip destination, the exhibit offers an ideal way to highlight the contributions of mathematicians to this excursion and to exploration through a study of the tools of navigation. The Museum hosted a field trip for 75 gifted 7th graders and we provided an hour of activities so students could learn about the Mercator Map, the Quadrant, the Nocturnal, and the Parallel ruler. They actually assembled mini parallel rulers to take home with them as a "making" portion of the program. This field trip has been in our portfolio since 2017. After multiple experiences with middle and high school students we feel confident that it provides an experience and understanding of math that supplements their school work. The Thank You notes we've received confirm this observation.
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- UTeach Intern Ashley Cauich explains the parallel ruler to a student who will shortly be assembling one for himself.
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- The Dippers can rotate around the North Star. Setting the Nocturnal directly on the disk is the best simulation since light from the stars hits earth in parallel lines. The dippers change location in the sky depending on the date and rise and set according to the time (of night)
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- Quadrant, North Star, Tape and set of Triangles. Find latitude by pointing Quadrant at North Star. If you know the height of a lighthouse you can also use the Quadrant to find your distance from it at night which the triangles demonstrate.
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- These two maps show the difference between the Mercator Map with longitude lines parallel to each other and a traditional map. The Mercator Map allows navigators to draw a straight line and plot a direct course. The 3d printed shells demonstrate the distortion of northern continents. When you shine a light a the top of the shell, translating to a flat surface the shadow is a perfect 6×6 square grid.
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- Learning to use the Quadrant with UTeach Intern Quan Vuong
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- Figuring out the Nocturnal with UTeach Intern Ayesha Quadri
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- UTeach Intern Viyang Shah demonstrates map distortions.
Ransom Center Field Trip
The Ransom Center is a document and collection archive on the UT Campus. They recently mounted an exhibit of Lewis Carroll papers to celebrate the 150th anniversary of Alice in Wonderland. MathHappens helped create activities for a math alcove for this exhibit and we were able to page some of these materials for a special viewing for this group of high school students. The Lewis Carroll collection offers a wonderful variety of math concepts to explore.
Challenge: With the archive rules in force we could only give the students yellow lined paper and only pencils for writing. We were able to page original materials to display in glass cases, and we had a chalk board and chalk. Otherwise we could read text (from yellow paper). The center made some special allowances and were were allowed to bring in some iPads, and some leather and wood models to accompany the different elements of the program. The program took place in a beautiful conference room.
The Program Guide is here. Students arrived at the center ground floor for an orientation on the mission and function of the archive and then proceeded to the second floor conference room. After viewing the materials we proceeded through the program. At the end students took time to view the permanent exhibits on the first floor including a Gutenberg Bible and the very first photograph.
Austin Science and Nature Center Field Trip Outline
The Austin Science and Nature Center is free and open to the public. Since 1960, the Austin Nature & Science Center (ANSC) has provided hands-on nature exhibits, educational programs and recreational activities for countless visitors, teachers, and children of all ages that increases awareness and appreciation of the natural environment.
In working at and designing math activities for the Austin Nature and Science Center, the MathHappens team visited over several months through the summer and fall of 2016. We explored the current exhibits and gained an understanding of the visitor population. Informed by these visits we decided to focus on Fibonacci Numbers, the Golden Ratio and Fractals. We created prototypes and tried them out with visitors. These included golden ratio calipers, an adjustable forearm, wrist, fingertip measure arm measurement, a hurricane Sandy/Golden Spiral puzzle, a Fibonacci Rabbit Problem model, a golden ratio grid mirror and a Sierpinski fractal puzzle.
The PROGRAM GUIDES for the Field Trip
The Measurement Activities (Mr. Morales/ Mr. Ahrens). In the planetarium we had the giant calipers, the arm - wrist - hand proportional measurement tool, some pictures of various animals, the Hurricane Sandy Puzzle with its golden spiral, the Golden Ratio Hand Mirrors, and the calipers to give to each student. Students also visited the specimen room in the next building to explore, use their calipers and chat with Mr. Ahrens about some of the specimens in the collection.
There are two proofs to think about in this packet. The first is to do with the design of the calipers and the second is the appearance of the golden ratio in a 5 pointed star. Students may not have time to tackle the proofs, but they can provide opportunities to extend this experience after the field trip, or can be considered if there is extra time.
Link to the Guide for Measuring Proportions (includes caliper proof):
Link to the Pentagon Proof Challenge:
Comparing Sequences (Mrs. Siegel). In the breezeway, we had a very non-traditional outdoor environment for working on a mathematical calculation. This is intentional and it was very successful. One photograph of students leaning on walls, sitting on benches or standing arms crossed faces focused on the patterns and calculations is particularly encouraging. With groups passing by the the visitor center, a cold breeze and some noisy wind we were very well out of a normal math learning environment. We compared two sequences and derived the Golden Ratio. We looked at “sequences” a little differently by setting up our stepping stone mats and playing the Fibonacci Stepping Stone Game.
Guide for Comparing Sequences- we are using the quadratic formula!
Stepping Stone Game- Fibonacci numbers manifested a different way.
Fibonacci Trees, Blocks and Bunnies (Mrs Lay)
Mrs. Lay, a teacher of both art and math was in the small room in the visitors center opposite the cave.
She guided the students in drawing some trees based on human and bee ancestry. With these models constructed students can compare the two and see the Fibonacci pattern in the Bee Ancestry. We will have the Fibonacci block puzzle and the Fibonacci Bunny Rabbit Problem models in this room as well. You can access the Program Guides for those components here:
Fractals
The Fibonacci Trees, Hurricane Sandy, the Nautilus shell, and the Human and Bee Ancestry, all share characteristics with fractal forms. The fractal sheet guides a pair of students - one to read the other to do through a couple of patterns and asks them to consider what is a fractal. There will be some Fractal puzzles available in the Planetarium Room.