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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.

 

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CAMP Reunion 2024

Today was a very special day in Bard Math CAMP history – the very first CAMP reunion! CAMP alumni/ae, staff members, parents, and friends gathered in the lobby of the Reem-Kayden Center once again for a selection of math games and puzzles – old favorites like Ghost Blitz and the Towers of Hanoi, along with some fun new challenges like Tantrix (How can you use all the hexagonal tiles to make a blue loop? A red loop? What about a yellow loop?).

A table full of math puzzles was the perfect place for former CAMPers to reunite with old friends and to hear about what everyone’s been up – from aerospace research and a hackathon for data science to full-time jobs in tech.

Next, everyone trekked over to the dilapidated dodecahedron – a mysterious, nearly invisible sculpture in front of the math building – to try and make it pop out while discussing what its mathematical structure might be – a stellated dodecahedron? The dual of a truncated icosahedron?

Finally, the former CAMPers & co. retired from the heat into the musty shade of Preston Theater for a math movie night of sorts – we all piled into the velvet folding seats to watch Secrets of the Surface: The Mathematical Vision of Maryam Mirzakhani on the big screen.

The day was full of sunshine, laughs, and healthy dose of CAMP nostalgia. Just like math puzzles and do-decorating, the reunion is sure to become a new CAMP tradition – where past, present, and future CAMPers can come together and celebrate their shared love of all things mathematical.

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CAMP 2023 – Questions to Ponder

Calling all CAMPers, parents, and curious readers – CAMP math instructors Japheth and Frances have a few fun problems for you to think about for the rest of the summer:

Cookies and Kids: Kids A, B, C share a certain number of cookies (some might get zero). Find a systematic way to represent each way to share. Then arrange all the ways to share in a triangle. Hint: This problem has a hidden relationship involving the numbers 2 and 5. Can you find it? Bonus Question: Can you find a pattern for different numbers of kids, and/or different numbers of cookies?

Grid Paths: Point B is two blocks East and some number of blocks South from point A. How many paths are there from point A to point B that are of the shortest possible length? Find a systematic way to represent each possible path. Then arrange all the paths in a triangle. Bonus Question: We also looked at shortest walking paths in a square grid with walks North and East. Is there a pattern to the number of possible shortest walking paths when walking 2 blocks North and b blocks East? What about when walking 3 blocks North and b blocks East?  

Spot It! : Seven was the largest number of symbols and cards we found if there are 3 symbols per card. Is 7 the largest possible number of cards that could be made with 3 symbols per card? Prove (or disprove) this statement. Hint: How can we know when something is impossible or possible but not yet figured out?

Spot It! – Bonus Question 1: Is the largest number of cards that can be made always equal to the number of symbols? Bonus Question 2: Can decks of Spot It! Cards be made for any number of symbols per card or are there numbers for which cards cannot be created? Bonus Question 3: The decks sold have missing cards. Are there efficient ways to find which cards were omitted? Bonus Question 4: How many cards and symbols are there in a deck of 7 Spot It? Then design a deck of 7-Spot It, which some people claim does not exist.

Fractions: 2/3 x 5/7 can be thought of as “2/3 of 5/7”. If we use a circle to represent the number one, what can be drawn in the circle to demonstrate the meaning of and answer to 2 ⁄ 3 x 5/7 ? 

Pascal’s Triangle: Pascal’s Triangle is full of interesting relationships. Keep looking at it and write the ones you discover. What other questions do you have about these topics?

Have fun, and keep exploring!

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CAMP 2023 Day 5

It’s the 5th and final day of the 10th year of CAMP. This morning, while they puzzled out Slitherlink challenges, magic tricks, and Set – games that many of them had never seen before the beginning of the week – the CAMPers recieved their ocean blue T-shirts, just in time for a big group photo on the stairs inside RKC.

After that, the CAMPers split into SINE and COS for math class, where both groups were working on ice cream bowl problems (and their variations). The SINE group game together to discuss their solutions to the problems they worked on yesterday: the ice cream problem, the handshake problem, the shortest-paths problem, and the sharing-cookies problem. Next, Frances introduced them to Pascal’s Triangle, a triangle of numbers where the middle entry below two numbers is always the sum of those two numbers. The CAMPers constructed the triangle from scratch, then looked along its diagonals, finding the counting numbers (1, 2, 3, 4, 5, etc) and the triangular numbers.

“In France, there are actually streets named after mathematicians and schools named after mathematicians… There’s a street named after Pascal.”

– Frances

Meanwhile, COS continued working on their table from Day 4, which showed the number of ice cream flavors and the number of ice cream bowl (ICB) combinations for a 2-scoop ICB. The CAMPers observed that the number of ICB combinations was always a triangular number (a number made from summing up counting numbers): 1 + 2 = 3, 1 + 2 + 3 = 6, 1 + 2 + 3 + 4 = 10, 1 + 2+ 3 + 4 + 5 = 15, etc … . Japheth then handed out individual problems for each of the smaller groups to investigate. Their goal was to find an isomorphism between them – to figure out what made the problems the same. They found that the handshake problem was isomorphic to (the same as) the ice cream bowl problem… the two remaining problems – shortest paths and cookies – were left to the CAMPers as puzzles to think about for the rest of the summer.

In Art class, the CSC group wrapped up their Spot It! decks, origami cranes, and doodles for the end-of-CAMP photo booth.

Meanwhile, in CS class, the SEC group worked on drawing a ball, making it move, and controlling all the aspects of its motion on the canvas – for example, speed in a certain direction, with ballspeed_x and ballspeed_y. Next, they learned about void draw(), void setup(), and void keyPressed(), which helps to organize the code, making it look less messy on the screen by grouping pieces of code together. At the end of class, Arnav showed the CAMPers some of the mesmerizing creations that use Java processing – for example, https://bleuje.com/gifanimationsite/2023_1/ .

“You should all be proud of yourselves… in, like, 5 hours of study, you’ve already covered more in processing than a lot of people have in their college classes.”

– Arnav

After class, CAMPers grouped together for Friday electives – AMC contest problems, decorating the photo booth, and more tic-tac-toe variations with sidewalk chalk.

In Computer Science, the CSC group learned more about the inner workings of a computer. They talked about input – the information that the computer receives, from buttons on a keyboard or a microphone – and output, which appears on the screen or from the speakers. The input is stored as the computer’s memory, either volatile (temporary) or non-volatile (permanent, unless you delete it). They talked about the CPU (Central Processing Unit) before switching gears to talk about text binary – the CAMPers wrote “hello” notes to each other in 0’s and 1’s as their last activity before the open house…

… where, at the end of the day, the CAMPers were given the chance to showcase the puzzles, games, and code they had been working on all week.

(A Tip for Parents: If you want a first-hand account of what your child has been learning this week, be sure to take a peek at their notebook! )

The 10th year of CAMP was an absolute blast – an explosion of creativity, where everyone jumped in to ask questions, try ideas out, and work as a team on a quest for the answer. This week, the CAMPers dove right into new concepts, exploring areas of math, CS, and art that most of them had never touched before – from magic tricks to juggling to coding in Java, to the intricacies of ice cream scoops and Spot It! and computers. Wherever they go next, they’ll be able to tap into the new kind of thinking they learned at CAMP – a mindset of questioning, exploration, and discovery.

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CAMP 2023 Day 4

The sun is shining over RKC – setting the stage for lots of summer fun at CAMP! This morning, CAMPers got together in the auditorium to solve more math puzzles – the Towers of Hanoi, Rush Hour, and shape-matching challenges. The problem of the day: Completely fill a 3×3 grid with X’s and O’s. How many of these configurations have three X’s or O’s in a row?

In math class today, SINE broke into four smaller groups to work on four different but similar problems: finding the number of possible handshakes between 5 people, then taking 3-way handshakes into account; finding the number of 2-scoop ice cream bowls you can make with 5 different flavors, then doing the same for 3-scoop bowls; figuring out the shortest path out of all the different ways to move by 2 blocks north and 3 blocks east, then generalizing to b blocks in any direction; and finally, determining the number of ways for 3 kids to share 3 cookies – or more than 3 cookies.

“The ice cream bowls are shaking hands!”

Meanwhile, the COS group started analyzing 8-Spot-It! – the classic version. They started with existing Spot It! decks, putting cards in piles based on the symbols they found on a randomly-drawn card C. Next, they chose one pile (A) to put back in the box, laying out the remaining cards in columns and rows that matched the top card of the pile, and discussed the observations and questions they had.

After that, they switched gears to solving the same ice cream bowl problem that the SINE group was working on – How many unique 3-scoop ice cream bowls can we get with 5 different flavors of ice cream? The first scoop gave them 5 choices, the second 4 choices, and the third 3 choices, which multiplied together to give 60 choices. However, the CAMPers found that in counting combinations they had actually over-counted by a factor of 6, since there were 6 ways to get the same ice cream bowl with each combination of 3 flavors.

After math class, CAMPers in the CSC group walked over to the art room, where they worked on origami, highly ambitious 7-symbol Spot It! decks, and beaded Fibonacci necklaces.

In Computer Science, the SEC group learned about using booleans (true or false) and comparators (>, <, greater than or equal to, less than or equal to) to write conditionals: “if” statements with conditions on variables x and y. They also learned about “if else” statements, which tell the computer what to do if the variable does not satisfy the condition. Breaking off into their usual groups, the CAMPers used these concepts to make their drawings bounce in different directions – up and down, side to side, and diagonally.

The CAMPers had lots of fun outdoor electives to choose from – a hike to the Sawkill waterfall, more magic tricks with Frances, variations on tic-tac-toe with sidewalk chalk outside the building, and, drumroll please: Break-Your-Brain Rhythm Games!

After lunch, the CSC group learned about bits and bytes, which are used to store data in a computer – a bit takes a value of 1 or 0, while a byte is an 8-bit (binary) number. The instructors explained why kilobytes, megabytes, gigabytes, and terabytes aren’t “clean” numbers ending in a bunch of 0’s: All of them are powers of 2.

The CAMPers were treated to a special investigation – opening up an actual computer and taking it apart! This allowed them to search for the basic parts of the computer and answer questions: Where does it hold its power? Where does the memory live?

The CAMPers were able to find….

  • The Central Processing Unit (CPU) …
  • The transistors, little switches that flip between 0 and 1 …
  • The motherboard, the most important circuit board, which basically holds everything together …
  • The RAM (Random Access Memory) chips, which store the computer’s volatile memory …
  • The capacitors, which are like little battery tanks that hold small amounts of energy …
  • The hard drive, which is made up of spinning magnetic disks that encode 0’s and 1’s …
  • … and the fans (to keep the CPU from overheating).

At the end of a long and eventful day, the CAMPers wound down by playing math games and working on their magic tricks.

Day 4 was full of new adventures, breathtaking views, and mathematical magic. We can’t wait to find out what tomorrow will bring!

Photo Credit: Kateri Doran (images 1-11, 13-19, 24-28), Julianne Louie (image 12), Japheth Wood (Featured Image, images 20-23).

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CAMP 2023 Day 3

This morning, the CAMPers gathered in the auditorium for a collection of math puzzles and the new problem of the day: How many Tower of Hanoi board states are there? The CAMPers had fun trying to work it out, rewriting the problem on the board – in the Greek alphabet. Right before breaking up into their usual Math groups, Japheth led them all in the International Math Salute.

Following up on the argument they made yesterday, the COS group worked together to prove that there couldn’t be an 8th symbol in a 3-Spot-It! deck. They then drew up a graph that brings to mind the “Deathly Hallows” from Harry Potter, showing the 7 cards as nodes and the symbol in common between two cards as edges. Next, they broke up into smaller groups to work on designing a 4-Spot-It! deck – What’s the greatest number of cards we can get with 4 symbols on each card? Some of the CAMPers observed that for the 2- , 3- , and 4-Spot-It! cases, the number of symbols was the same as the number of cards. To look for more patterns, they took the difference between the number of cards in n-Spot-It! and (n-1)-Spot-It! , then took the difference between the differences – getting 2 every time. Leaving this conjecture as a cliffhanger for a later date, the CAMPers embarked on a final investigation – to make one pile for each symbol using existing Spot It! decks.

Meanwhile, the SINE group used tree diagrams to explore the main concepts of combinatorics. Taking the letters S, T, R, and E, they mapped out all the possibilities of what letter could come after each letter in a word, branches branching off into other branches. They followed different branches to make different words like SET, REST, STREET, TEETERS, and – appropriately – TREES. The CAMPers continued their discussion by breaking into two smaller groups to work on these examples: choosing ice cream flavors for a multi-scoop cone, and choosing paths to take when going from Point A to Point B. How many combinations are there? How many choices do we have?

In Computer Science class, the SEC group learned about the random() function, void setup() and void() , variable assignment – how to turn x into (x+1) in order to move a shape somewhere else on the canvas. Their challenge for today: Rather than just moving your drawing around, can you make your drawing move in an animation?

After class, the students joined their elective groups: more magic tricks, more paper puzzles (AKA the Harry Potter debate club), as well as origami.

During lunch, the rain started pouring outside Kline, and the CAMPers had to break out their umbrellas to make it to their next classes – Art and Computer Science.

CSC went to Computer Science, where they continued to learn about truth tables. Then they broke into small groups, using logical operators to write out a combination of A and B that was equivalent to the XOR (exclusive or) operator. Then they took out Little Bits (batteries, cables, and LEDs) to make an XOR statement in real life.

In the Art room, music was blasting while the SEC group continued working on their Spot It! cards, then dove into a variety of artistic and mathematical endeavors – Fibonacci challenges, 4×4 tic-tac-toe, pink paper airplanes, and optical illusions.

Afterwards, the two groups converged in the auditorium – finally dry and ready for some math games.

New ideas, new methods, new questions and answers filled Day 3 with color, excitement, and fun! The CAMPers made so many new discoveries today, leading to even more unanswered questions – perfect to tackle with zeal on Day 4.