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.

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!

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!)

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.