Author: Jaelyn Quilizapa

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CAMP 2024 Day 5: The Final Day

Welcome to the final day of Bard Math CAMP 2024!

The day kicked off with a memorable moment as all CAMPers gathered in their Bard Math CAMP 2024 T-shirts for a group photo. This snapshot captured the spirit and camaraderie that had built up over the week, creating a lasting memory for everyone involved. The excitement was palpable as everyone beamed with pride, commemorating their week of hard work and learning. After the photo, CAMPers filed upstairs for their final Math Classes of the week.

In Japheth’s Cosine Math Class, CAMPers dove head first into the world of star polygons. They completed their scatter projects, showcasing their understanding of complex mathematical concepts through creative presentations. Once finished, they moved on to creating their own star polygons, some expanding the ideas of what a star polygon could be, honing their creative and geometric boundaries.

The class also delved into the inscribed angles theorem, with a special focus on an isosceles triangle proof guided by Mason. This blend of hands-on activities and theoretical learning made for an enriching final session. The challenge of constructing massive star polygons fostered teamwork and problem-solving skills among CAMPers, leaving them with a profound sense of accomplishment.

Frances’ Sine Math Class began with cube nets, challenging CAMPers to hone their visualization skills and mentally determine which nets could form cubes. This exercise sharpened their spatial reasoning abilities and deepened their understanding of geometric properties. The CAMPers then used Zometools to create Archimedean polyhedra, constructing more complicated 3D models. This activity not only tested their geometric knowledge but also their patience and teamwork. As they built more models, they learned how adding faces impacts the angle degrees, further deepening their understanding of geometric principles.

In the afternoon, CAMPers had lunch provided by Parkhurst Dining, and spent their afternoons in a variety of different electives:

CAMPers continued exploring breadboards in Intro to Circuits, gaining confidence in their ability to explain how they worked to Yulia and Shaylen. This activity reinforced their understanding and comfort with circuitry concepts. They also experimented with more complex circuit designs, learning about the impact of resistance and voltage on their projects.

In Art Class, CAMPers created fun photo booth props for their group photos, adding a playful touch to their final day memories. They designed and decorated props that reflected their individual personalities and experiences from the week, making the photo session even more enjoyable.

Frances guided CAMPers back to the Zometools in her Polyhedra Class to create even more complex polyhedra for the Open House. This session allowed CAMPers to showcase the advanced geometric models they had learned to construct. They marveled at the intricate structures they were able to build, applying their knowledge of Euler’s formula and other geometric principles.

In Shoshi’s Art Class, CAMPers busied themselves with finishing projects from the week. They put the final touches on their circuits, completed the massive magic cube, and crafted intricate origami pieces for the Open House. This creative flurry ensured that all their hard work was ready to be showcased to family and friends. The atmosphere was one of joyful collaboration, as CAMPers shared ideas and techniques, enhancing each other’s projects. Shoshi’s guidance helped them see the connections between art and mathematics, highlighting the beauty of geometric design in their creations.

Yulia’s Computer Science Class saw CAMPers applying all the skills they had learned throughout the week to create intricate tessellations with NetLogo. This final project allowed them to demonstrate their coding prowess and creativity, culminating in beautiful, mathematically complex designs. CAMPers explored the use of sliders and repeat commands to automate the creation of polygons, enhancing the complexity of their tessellations. Yulia’s encouragement and expertise helped them push the boundaries of their coding abilities, resulting in impressive and unique patterns.

At 3:00PM, the Bard Math CAMP team was thrilled to welcome families to the Open House, where they had the opportunity to revel in the CAMPers’ hard work and accomplishments from the week. As families explored the various displays, they were greeted by a vibrant showcase of intricate tessellations, complex polyhedra, slideshows, and creative art projects. The pride and excitement on the CAMPers’ faces were matched by the admiration and amazement of their families. It was a joyous occasion, filled with enthusiastic explanations, demonstrations, and heartfelt moments of recognition. The team was immensely proud to see the CAMPers confidently presenting their projects and sharing the knowledge and skills they had gained.

This celebration of learning and creativity was the perfect culmination of a remarkable week at Bard Math CAMP. From learning complex mathematical theories to creating intricate art projects and building lasting friendships, Bard Math CAMP 2024 was a resounding success. The CAMPers’ enthusiasm, curiosity, and determination made this week truly special. We hope the skills and memories forged here will inspire these young minds for years to come. Thank you for being a part of this extraordinary experience! We look forward to seeing what our CAMPers will achieve in the future, armed with the knowledge and confidence they gained this week.

It was a pleasure to blog for you all – have a great rest of your summer! – Jaelyn Quilizapa

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CAMP 2024 Day 4

Welcome back to another Bard Math CAMP Blog!

Here’s a detailed look at today’s engaging activities and lessons:

The day began with energy as CAMPers engaged in a variety of opening activities, such as games, tessallations, and art projects, including one giant magic cube! These activities set a positive start for the rest of the day, preparing the CAMPers for the lessons and explorations ahead.

In Frances’ Sine class, the day started with a review of the two methods CAMPers used to determine the number of degrees in each angle of a regular polygon. They discovered that, when written in algebraic notation, both methods yielded the same results, reinforcing their understanding of mathematical consistency. Next, they moved on to constructing polyhedra with Magnatiles. This hands-on activity helped them explore the relationships between the number of faces, edges, and vertices in these three-dimensional shapes.

CAMPers then delved into the properties of regular polyhedra. CAMPers began building these fascinating shapes using Zometools, which provided a more precise and intricate method for constructing polyhedra. This activity allowed them to see firsthand how the geometric properties they had been studying came together in complex, three-dimensional forms.

In Japheth’s Cosine class, CAMPers explored the fundamental differences between polyhedra and polygons. They learned about convex shapes and how these relate to Platonic solids, which are the building blocks of many complex geometric forms. The class examined 20 different nets of a cube, challenging CAMPers to mentally determine which ones could form a proper cube without physically assembling them. This exercise significantly improved their mental imagery skills.

Additionally, CAMPers made their own cube nets without lifting their pens, requiring them to plan their moves carefully before executing them. The class also explored polyhedra algebraically using inequalities and discussed the concepts of nets, which provided a deeper understanding of geometric structures.

Today’s lunch was once again provided by Tastebudds, and with the beautiful weather, CAMPers took the opportunity to sit outside and enjoy their midday break.

As the afternoon rolled in, CAMPers eagerly transitioned to their elective activities, where they could explore a variety of interests and hands-on projects. Here’s a look at what each elective had to offer today:

CAMPers were thrilled as they learned new math magic tricks from Frances, which they performed for their peers. This elective, though magical, are solely based on mathematical principles, creating an exciting and educational experience.

Intro to Circuitry was a blend of theory and practical application. CAMPers reviewed circuit symbols and experimented with breadboards, enhancing their understanding of electronic components. Shiven explained electromagnetic fields around magnets and related this to the functionality of a hand-crank flashlight, helping CAMPers grasp the principles of electricity conduction. They continued their projects from previous days, but now conducting electricity through a breadboard in order to make their LED bulbs light up.

In the Origami elective, CAMPers created Lilies and Hummingbirds with Ariella!

Shoshi’s Art Class was a creative haven where CAMPers designed and created 3D cubes using their own dimensions. This hands-on activity allowed them to apply their understanding of geometry in a tangible way. CAMPers personalized their cubes with unique designs, colors, and patterns!

Yulia’s Computer Science class was a hub of activity as CAMPers delved into more advanced programming concepts. They learned about sliders and the repeat command, which allowed them to set the number of sides and the length of each side, making their tessellations more intricate and complex. CAMPers learned to create buttons that could automatically generate polygons, streamlining their coding process and making it more efficient. This, paired with revising their triangle codes from the previous day, taught them valuable coding techniques but also showed them how to apply these skills to create beautiful, mathematically accurate designs.

For closing activities, some CAMPers continued with their tessellations, magic cubes, and origami projects, while others tackled Mason’s Math Challenge!

Along with this, CAMPers were asked, “What made you smile today?”, their answers are as follows:

As Day 4 draws to a close, the excitement and learning at the Bard Math CAMP continues to build. Each activity and lesson contributes to the CAMPers’ growing knowledge and enthusiasm. We can’t wait to see families and CAMPers back for the last day of CAMP!

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CAMP 2024 Day 3

Welcome back to another day at the Bard Math CAMP!

As the day began, CAMPers once again dove into a variety of opening activities, such as games that tested their strategic thinking and teamwork skills, another intriguing Math Challenge presented by Mason, and continuing their art projects from previous classes, refining their designs and adding creative touches to their works. This combination of activities set a dynamic tone for the rest of the day.

Japheth kicked off the day with his Cosine Math Class by reviewing concepts from the previous session. Japheth emphasized the power of simplifying complex problems using algebraic equations, making seemingly difficult tasks much easier. CAMPers then worked in groups to explain to each other how to find the degrees of polygons using these equations, ensuring everyone understood before moving on.

Afterwards, CAMPers moved to drawing a 4X2Y polygon and identifying the X and Y axes. Japheth, building off of Shoshi’s Art Class, touched on the fascinating craft of hexaflexagons, highlighting the importance of precise angles to create a perfect one. Then, CAMPers faced a challenge: figuring out the angular domino effect of Japheth’s hexaflexagon if it had been first folded with a 76-degree angle instead of a 60-degree angle.

CAMPers revisited star polygons, this time focusing on a seven-sided star. CAMPers learned how to use the external angle method to determine the internal angles of each point, adding another layer to their geometric knowledge.

In Frances’ Sine class, CAMPers began with a review from the previous day before diving into more shapes that tessellate. CAMPers explored why these new shapes work in tessellations and hypothesized whether a decagon (10-sided polygon) would also tessellate. This eventually led to a discussion on whether a flat plane could be considered a square.

Using blocks, CAMPers configured different tessellations from previous days, experimenting with various patterns and shapes. They observed the unique properties of each shape and how they fit together seamlessly, enhancing their understanding of geometric relationships.

After lunch and before the rain in the afternoon, CAMPers had the opportunity to participate in various electives!

In Intro to Circuits, CAMPers continued their projects from yesterday. They successfully conducted electricity through their creations, lighting up LED bulbs. They learned about the role of resistance in preventing conduction and how the pressure they applied to their projects affected the outcome. CAMPers also experimented with breadboards, learning how to make their LED lights flash by controlling the flow of electricity through them.

Some CAMPers took a walk to the Parliament of Reality with Yulia, exploring Bard College’s beautiful campus.

Unfortunately, we were unable to get photos of CAMPers here,
but Friday would be another beautiful day to go with your CAMPer!

Others stayed inside and tackled Paper Puzzles with Mason and Gemma, exercising their problem-solving muscles:

And the rest of the CAMPers attended Unit Origami with special guests Milo Pomarico and CAMP alumni Hadley Parum! Milo and Hadley led CAMPers through an exciting art elective, creating a Bird Tetrahedron. All CAMPers worked together to build the base of the structure, and will be able to put it all together by the end of the week, constructing one large Bird Tetrahedron out of everyone’s hard work.

Shoshi’s Art Class was a hit, guiding CAMPers through the intricate process of assembling wooden blocks to create magic cubes that could transform into various shapes. Each CAMPer had the chance to personalize their cubes with unique designs, colors, and patterns, allowing them to express their individuality and artistic flair. The activity not only honed their craftsmanship and attention to detail but also illustrated the intersection of art and geometry.

As the CAMPers worked on their projects, Shoshi played music that added a lively ambiance to the classroom. The combination of creativity, music, and hands-on learning made for an enjoyable art session. The CAMPers left the class with a sense of accomplishment and a deeper appreciation for the artistic potential of geometric shapes.

Yulia’s Computer Science Class continued to build on the fundamentals of turtle graphics. CAMPers reviewed how to draw with turtles, set their colors, and change their shapes. They also learned new commands such as “rt num,” “lt num,” and “fd num,” which allowed them to create more complex drawings.

CAMPers drew regular and isosceles triangles and polygons with their turtles, even managing to draw a human figure! Yulia introduced the concept of X and Y in their world, helping CAMPers understand how these coordinates correspond to their drawings.

Then, they moved on to creating patch mosaics and learned how to use functions in their code to automate the drawing of polygons. This coding exercise sparked creativity and problem-solving skills among the CAMPers.

Finally, CAMPers convened in the art classroom for their final activities, including block tessellations, group games, and more origami. Since CAMP Day 1, there has been considerable debate among the CAMPers about turtles: whether they should be kept “alive” for their value, “dead” to create something new, or if they aren’t living at all, making neither answer correct. The poll results are as follows:

AliveDeadNot Living, Neither
9210
The CAMPers have spoken – turtles are NOT living! However, it seems some could be swayed..

As another day at the Bard Math CAMP comes to an end, we look forward to more adventures and discoveries tomorrow. The teamwork, creativity, and enthusiasm of all the CAMPers continues to inspire us. Stay tuned for more updates!

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CAMP 2024 Day 2

Welcome to Day 2 of the Bard Math CAMP 2024!

CAMPers started the day with some opening activities designed to get minds moving. “Top This!” and “Block by Block”, along with other various games, were not only fun but also great for sharpening problem-solving skills. Everyone enjoyed the variety games, adding a sense of excitement and energy to the morning.

In Japheth’s Math Class, CAMPers began by reviewing yesterday’s lessons and assignments. CAMPers had been tasked with looking up the names of certain polygons, such as 19-sided and 20-sided polygons. Japheth and CAMPers went over these names and used new formulas to figure out the interior angles of these large polygons.

The class also explored 5-pointed star polygons, learning about the internal angles of these stars and discussed the properties that differentiate them from regular polygons. One of the highlights was understanding why tessellations of a flat plane can be reduced to hexagons, triangles, and squares. The CAMPers grasped this concept through an algebraic proof, blending geometric insight with algebraic reasoning.

Frances’ Math Class was guided through the world of regular polygons. Building on yesterday’s lesson on tessellating triangles and discovering that their angles sum up to 180 degrees, the class applied this knowledge to explore the angles in other polygons.

CAMPers reviewed the properties of regular polygons and calculated the measure of each angle in these shapes. Using pattern blocks, they created tessellations and demonstrated the necessity for all angles meeting at a vertex to sum up to 360 degrees.

Following their morning classes, CAMPers were able to sit outside in the sun and enjoy their lunch provided by Tastebudd’s Cafe, located in Red Hook, NY.

After lunch, CAMPers enjoyed a variety of activities!

Some CAMPers played various lawn games outside of Kline Commons with Mason and Gemma:

Frances dazzled others with mathematical card tricks, teaching CAMPers how to execute them on their own:

And Shiven led a session on circuits, where CAMPers created a circuit using copper tape and LED lights, while designing the front of their project to incorporate their respective LED light colors. Tomorrow, they will connect their batteries to their projects to conduct electricity through their circuits, completing their innovative creations!

In the Cosecant and Secant Art Classes, Shoshi introduced CAMPers to the intriguing concept of Origami Hexatetraflexagons. These fascinating geometric shapes added an imaginative twist to the day. CAMPers explored the construction and properties of hexatetraflexagons, learning how to fold and manipulate these paper structures to reveal hidden faces and patterns.

Shoshi encouraged CAMPers to experiment with colors and designs within their hexatetraflexagons. This activity not only honed their origami skills but also provided a deeper appreciation for the geometric principles behind these captivating shapes. The session was filled with creativity and excitement as CAMPers marveled at the beautiful results of their work!

Yulia’s Cosecant and Secant Computer Science Classes continued to explore the exciting world of computer science. CAMPers started by reviewing topics from yesterday on NetLogo, such as creating turtles, setting colors and attributes, and switching from observer mode to turtle mode. Yulia reemphasized that algorithms are like recipes – order matters!

CAMPers then expanded their skills by learning about patches, how to change the color of the world, and making the turtles do various things. Yulia showed CAMPers how to change the turtles directions to draw complex patterns and how to teleport their turtles. These new skills allowed CAMPers to create even more intricate and colorful designs with their turtles.

As the second day came to an end, CAMPers gathered once again in the Art classroom for the final activities of the day. They dove into games, took on another Math Challenge, and socialized with their new friends as they awaited their families’ arrivals.

(P.S., In case your CAMPer is interested in using NetLogo at home, the download link is embedded in the bolded NetLogo phrase under Yulia’s CS Class section. Have fun!)

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CAMP 2024 Day 1

Welcome back to another exciting year of the Bard Math CAMP! This year, CAMPers are going to be learning about polygons, which are any closed shapes consisting of a set of line segments that are connected!

The excitement was palpable as families and CAMPers arrived for the first day of Math CAMP! Each CAMPer had the opportunity to select their elective for the day, with options including Paper Puzzles, Intro to Circuits, or a hike to Bard’s Zabriskie’s Waterfall.

After a warm welcome and some initial games, such as Spot It! and Mason’s Math Challenge, the kids were escorted to their first classes of the day, eagerly anticipating the adventures ahead. 

 

Japheth’s Cosine Group kicked things off with a Polygon Challenge, where the task was to place four points on a plane so that there were only two distinct distances between any two points. Japheth demonstrated this with an example of four points at the corners of a square.

The students worked in groups and discovered three examples of special polygons that met the criteria. This activity introduced the concept of casework, where they broke the problem down into smaller, more manageable parts. Japheth explained that in their example, if X is one length and Y is the other, the square configuration had four X lengths and two Y lengths.

Next, the CAMPers tackled a new challenge: investigating the case of 3 X lengths and 3 Y lengths. They worked collaboratively to explore this scenario, successfully finding one configuration. However, a question lingered: were there more configurations to be discovered? This encouraged further exploration and critical thinking among the CAMPers, while “solemnly swearing not to look up the answer!” This fun promise added an element of challenge and camaraderie. They also began exploring the degrees of angles in various polygons, setting the stage for deeper mathematical thinking.

Meanwhile, Frances’ Sine Group focused on defining polygons. The CAMPers learned about what constitutes a polygon and the characteristics of regular polygons and congruent shapes. They delved into the world of tessellations, which are patterns made by repeating a regular polygon, using triangles to create beautiful, repeating patterns.  After finishing up, the CAMPers were able to walk around and admire each others work before the second class session began.

After the math classes ended, the Cosine and Sine groups split up into Cosecant and Secant groups, where the former went to Art class, while the latter went to Computer Science class!

Throughout the day, Cosecant and Secant CAMPers explored their creative side in Shoshi’s Art Class by making ninja stars, origami birds, and hexaflexagons. Hexaflexagons are fascinating flat models, usually constructed by folding strips of paper, that can be flexed or folded in certain ways to reveal faces besides the two that were originally on the back and front. This hands-on activity demonstrated the real-world application of geometry and symmetry and helped reinforce mathematical principles in a fun and engaging way!

Secant CAMPers, in their Computer Science class with Yulia (or rather, Robot Yulia!), learned about computer algorithms. Each group wrote instructions for “Robot Yulia” to follow in order for her to draw a square on the whiteboard. Despite their efforts, no group was able to have Robot Yulia successfully draw a square. This experience led to an important lesson on the necessity of specificity in algorithms, highlighting how crucial it is to provide clear, detailed instructions in computer programming.

“Why do you like trick questions so much?” 

“They make you ponder!” – Yulia

Everyone enjoyed a delicious and bountiful lunch, recharging their energy for the afternoon’s activities!

After lunch, it was time for the eagerly awaited electives. In the Intro to Circuits class, CAMPers formed groups to create magnetic circuits, gaining a hands-on understanding of how circuits work and what is needed to make them function. The Paper Puzzles elective offered a stimulating session with Sudoku and Tuno Touch puzzles, challenging the kids’ logical thinking and problem-solving skills. Meanwhile, those who chose the hike enjoyed the natural beauty of Bard’s Zabriskie’s Waterfall, a perfect way to combine physical activity with the day’s learning.

 

Both Cosecant and Secant learned about the inner workings of Net Logo, which is a programmable modeling application that simulates different inputted scenarios, creating turtles in their respective “driver/navigator” dynamics. They learned how to make the turtles move around, teleport, draw, and change directions. This activity also included exploring the boundaries and size of their world, providing a hands-on understanding of programming logic and spatial awareness.

As the day drew to a close, CAMPers filed into the Art classroom for some final activities. They engaged in more exciting games, tackled another Math Challenge presented by Mason, and enjoyed the opportunity to unwind and socialize with their new friends. This relaxed yet stimulating environment allowed CAMPers to reflect on their day’s adventures and solidify the concepts they had learned.

While they eagerly awaited pickup from their parents, the room buzzed with chatter and laughter, a testament to the fun and enriching experiences of their first day at Math CAMP.