## Classroom Visits Spring 2020

During the Spring 2020 semester, we continued with our BAMM @ Your School program. We were able to visit three elementary schools in February and March. We had more visits scheduled, but unfortunately, at the moment it seems unlikely that those visits will happen. We are following the appropriate social distancing recommendations to contribute to keep our community healthy.

We visited a 1st grade class at Deer Run Elementary and a 2nd grade class at Wyandot Elementary. On those workshops, students explored polyominoes. They each had a bunch of square tiles, and we started by asking them to take two tiles and put them together so that they share a full side. This was such an easy task that they looked at us intrigued, wondering if that was really all we were asking. Then we asked them to take two more tiles and try to come up with a different way of arranging the tiles, but again so they shared a side. This seemed a more interesting task, but it didn’t take them long to come up with the two different dominoes: vertical and horizontal. They were also able to conclude that a third one cannot be found.

The next task was to repeat the process with 3 tiles and then with 4 too. Some started competing with each other to see who could find more tetrominoes. Some were eager to go to the next step and asked “Can I try with 5 tiles now?”. We gave them a grid paper mat where they drew their findings. The last task was to make rectangles with pentominoes. They could use any they want, but if you’ve ever played tetris, you probably now this task is not as easy as it sounds.

At Glacier Ridge Elementary, we visited a 4th grade classroom and had them play games on graphs. We first talked a little about this other type of graph most of them were not familiar with and explained what a graph coloring is: one where connected vertices are of different colors. Then students chose a partner to play against and were given a board with a graph and some colored chips. To start, the players choose a set of colors to play with. One of the players is the “Maker”, trying to achieve a valid coloring, while the other player is the “Breaker” who is trying to ruin the coloring. However, the Breaker has to respect the coloring rule too, that is, they cannot put a color on a vertex if one of its neighbors already has that color. The players take turns placing a chip on an empty vertex each time.

Students played on different graphs and with different numbers of colors and came up with some winning strategies, sometimes for the Maker and sometimes for the Breaker.

BAMM @ Your School is free and its only subject to time availability. Find more information about the program here. Volunteers are very much welcomed and appreciated. Find out about the upcoming volunteering opportunities, in this and our other programs, and register here.

## BAMM @ the Museum

This Spring we also finally started a couple of partnerships we were looking at since last year. The program is called BAMM @ the Museum and it is a great way for us to extend our programming to other cities in Ohio. Museums are great hubs for interactive learning and they often offer workshops and other programming beyond their permanent exhibits.

In February and March, we visited for the first time two of our state’s great museums: AHA! A Hands-On Adventure, A Children’s Museum, in Lancaster, and The Works, Ohio Center for History, Art and Technology, in Newark.

AHA! is a very special museum for toddlers. There we set a station for three hours, during which a few toddlers stopped to play and experiment with materials such building tiles, rep-tiles puzzles, and Frogs and Toads. One 6-year old girl was very commited in trying all our activities and upon solving a puzzle looked at us like asking “What’s next?”

We crashed The Works on a slow rainy day but enjoyed hosting their Curious Kids program. Curious Kids is a weekly workshop for 2- to 6-year olds that lasts 30 minutes. Bart Snapp led a workshop on tilings and symmetries. The tables were fulled with wood tiles with different equilateral shapes and kids were asked to put them together creating patterns. He showed some examples with different types of symmetries and the little ones, with some help from their parents, were able to come up with examples of their own.

We promised to come back for Curious Kids every month. We will also join another one of their programs: Girls Night In, for teenage girls and their mothers.

We hope to find other museums in cities around Columbus, so that we can extend our math programming to all Ohio.

## BAMM and the AAASCEC

The Department of African American and African Studies has a Community Extension Center (CEC) located on the Near Eastside of Columbus. The CEC strives to provide academic and community education opportunities for its Near Eastside neighbors and the greater Central Ohio community. We were lucky to have come in contact with the AAAS Departament and are now joining their efforts offering math programming at the CEC.

On three consecutive Fridays in February and March, we offered a Mathmagic workshop there. Every session we taught one or two different magic tricks, so people who wanted to come to all would not be seeing repeated content. The workshop was addressed to middle school students, but some parents and other accompanying adults joined to. We were really happy to see adults and children alike very engaged in discovering the math behind the magic tricks.

That is not all, because we will be offering a math exhibit every month on the second Saturday. On those days, which we have called Math Day, from 12:30 to 3 pm everybody is welcomed to stop at the CEC and explore the beauty and richness of mathematics through numerous games, puzzles and crafts.

We also plan to keep on bringing more workshops for the K-12 students in the community, as well as other math programming.

## J-term at Metro Middle School

During the first two weeks of school this year, BAMM had the opportunity of participating on the January term at Metro Early College Middle School. The Metro Early College Schools were born out of a partnership between OSU and Battelle to create a STEM school. At Metro Middle School, J term is time that allows for both extension and remediation, all personalized to the needs of each student. Students who master a subject have an opportunity to take an extension class in J-term. We were invited to teach one of these elective extension class for advanced math students.

We chose a different topic for each week and taught a daily period of 1.5 hours. The first week we talked about tesselations. Students started exploring tesselations with regular shapes, first using a single shapes and then mixing them. They also studied tesselations with nonregular triangles and quadrilaterals. We challenged them to find pentagons that could tesselate and were surprised to see them come up with a couple of families of them.

The second week was about Mathmagic, something the students were really looking forward to. Each day, we performed one or two tricks in front of them and then challenged them to unveil the tricks. At first they would always say that the trick was obvious and really easy, but upon trying to perform it themselves, they would realize that it was not as simple as they first thought. However, sometimes with a hint, most of them were eventually able to uncover it.

Through these engaging magic tricks, students practiced or learned mathematics ranging from multiplication tables to topology, passing through algebra and number systems. We very much enjoyed the experience and were amazed at these students ability with math. I wouldn’t be surprised that some of them ended up going for a career in math.

BAMM @ Your School is one of the outreach projects at the Department of Mathematics. Through this program, we take fun, engaging, and deep mathematics workshops to schools in the Columbus Metropolitan area.

Just on November 21st, we had the opportunity to visit a fourth grade group at Daniel Wright Elementary School. Erika Roldan led a workshop on Mondrian numbers. Students worked in pairs and received an envelope containing red, yellow, blue, and white rectangles of all possible integer dimensions between 1 and 5. “Today you are going to become painters with these pieces”, said Erika.

Their first task was to classify the pieces according to their shape, in other words they had to make groups of congruent rectangles. Then they were asked to find all possible ways of building a 3 by 3 square using non-congruent pieces. When finished, they went on to do the same for a 4 by 4 and a 5 by 5 square.

Their last task was to compute the Mondrian number for all the possible configurations they had found. The Mondrian number of one of these such configurations is the difference between the maximum and the minimum areas of its pieces. To be able to do these, students registered their configurations on their notebooks. Some students made a lot of progress in the task, but even those who weren’t as fast practiced their geometrical skills and had a fun math class.

BAMM @ Your School is free and its only subject to time availability. Volunteers are very much welcomed and appreciated. Contact us, if you would like to visit a school with us.

## The Mathematics of Origami

Last week, the Department of Mathematics, through the outreach initiative, had a guest for the Recreational Mathematics Seminar. Laura Jimenez is a mathematician and a PhD candidate at the Department of Ecology and Evolutionary Biology at the University of Kansas. In college, she began to develop a passion for origami, and she was able to tie it with mathematics. When she was a master’s student, she worked in mathematical outreach and popularization and gave workshops about the mathematics behind origami.

At the Recreational Mathematics Seminar on Friday, November 15, Laura talked about how not only math is used in proving whether something is foldable or not and finding the folding pattern, but also origami can be a powerful tool for solving mathematical problems, such as solving a third-degree equation.

During the talk, the speaker presented the Huzita axioms, the mathematical principles of paper folding. The axioms list the seven operations that can be achieved by folding paper. The first axiom reads “Given two distinct points p1 and p2, there is a unique fold that passes through both of them.” The second one goes about placing a point into another; in this case the fold created turns out to be the perpendicular bisector to the segment joining the two points. Later on, Laura showed how one can trisect an acute angle by folding paper, in other words, by following the Huzita axioms.

The seminar was followed by a workshop where attendants learned how to fold a cube and a 12-pointed star of modular origami. Some would say that this type of origami is the most mathematical one. Modular origami pieces are made up by several sheets of paper. Each sheet is folded in the same manner, creating a unit with flaps and pockets. Then all pieces are put together by inserting flaps into pockets. This type of origami allows us to build geometrical objects such as the platonic solids.

Laura emphasized how origami is a great tool for teaching geometry.

On Saturday, our guest also ran our Girls Exploring Math Monthly workshop. Students explored the properties of buckyballs, polyhedra with regular pentagons and hexagons as faces. They analyzed the number of vertices, edges, and faces of each type, and came up with a relation between them. When building the origami model of a dodecahedron, the girls also looked at its graph representation and found a Hamiltonian path on it. Then, they used it to decide how to assemble the origami modules so that all the edges connected in every vertex had different colors (using modules of three different colors – it’s not as easy as you might think!).

The Recreational Math Seminar is gaining presence within the Department’s community, showing the most entertaining side of math. Recreational Math is a great way of getting undergraduate students interested in research. We will continue to bring more guests next term.

## Building Real Mathematical Surfaces

This week, Buckeye Aha! Math Moments had a series of events around the work of a special guest. Maria Garcia Monera, from the University of Valencia (Spain), is interested in Topology and Geometry and in designing and building paper models of surfaces.

Even from last week we started preparing for Maria’s visit. We built some of her models and displayed them in the Mathematics Tower lobby for everybody to see. Then on Monday, Maria gave the Recreational Mathematics Seminar. She explained that he technique she uses is based on the work of Felix Klein, Alexander Von Brill, and John Sharp. In an era before computers, where one could render the surfaces on a screen, the motivation for creating these models was aiding students in the visualization of the mathematical objects. The idea behind is finding plane curves contained on surfaces that can be cut in paper and used to reproduce the model.

The seminar was well attended by postdocs, graduate and undergraduate students, and lecturers, becoming the most popular Recreational Mathematics Seminar so far.

On Tuesday, Maria gave a workshop at the Columbus Public Library (Northside Branch) were some children built an orange paper sphere and decorated it as a pumpkin. Then on Wednesday, during Teas, those who attended the seminar (and a few others) put in practice what they had learned, building paper surfaces such as paraboloids, water drops, ellipsoids, and hearts.

Finally, on Thursday Maria worked with a 6th and 7th grade math class at Metro Middle School. She talked about surfaces of revolution and then the children worked in teams to craft spherical pumpkins and hearts.

Recreational Mathematics is about fun and entertainment, but that doesn’t mean there aren’t serious mathematics involved. As the Mathematical Association of America writes “Recreational mathematics is inspired by deep ideas that are hidden in puzzles, games, and other forms of play”. With Maria’s visit, the Department’s community had fun and obtained a tool for helping students visualize surfaces. Hopefully, some were so inspired that they will design their own paper model.

## Girls Doing Math

The second session of Girls Exploring Math Monthly took place this last Saturday. This time the attendees explored latin and magic squares. They worked by themselves, challenged each other and naturally ended up working together to solve the problems.

A Latin square is an n by n grid filled with n different colors, each occurring exactly once in each row and exactly once in each column. When counting the number of different 3 by 3 Latin squares, Ella, a 7th grade student, said “If I fix the red, then there are only two possible ways of arranging the other two colors. Since there are 6 different configurations for the red, then there are 12 distinct colorings.”

During lunch, they had fun playing SET. They were competing against each other, but when the group of cards on play was a particularly difficult one, they joined forces. They came up with classification strategies that could help them better tackle the problem.

This event is part of a long term project that includes monthly workshops and a summer camp. The project Girls Exploring Math invites young women to experience mathematics through engaging activities in an nontraditional environment, and seeks to attract women to pursue careers in math.

## Anamorphic Art – Mathematics behind the Illusions

On Saturday the Department of Mathematics received a group of female high school students to learn about using math to create anamorphic art. The workshop was taught by Anna Davis, Ph.D., from Ohio Dominican University.

The word anamorphosis refers to a distorted projection or drawing which appears normal when viewed from a particular point or with a suitable mirror or lens. Anamorphosis has become increasingly popular in art, especially in street art.

Led by Prof. Davis, students drew anamorphic projections aided by a laser and further explored them using GeoGebra. They also wrote functions to create an anamorphic version of a “normal” drawing. Finally, they had time to create their own anamorphic art.

This event is part of a long term project that includes monthly workshops and a summer camp. The project Girls Exploring Math invites young women to experience mathematics through engaging activities in an untraditional environment, and seeks to attract women to pursue careers in math.