Presented by Dan Van der Vieren, Ambassador/Educator, You Can Do The Rubik's Cube
When the Rubik's Cube was invented by Erno Rubik in 1974, it was a wooden prototype with rubber bands for its twisting mechanism. Since then, the Rubik's Cube has caught the attention of many. This puzzle can be integrated in any curriculum to create mosaics, qteach problem-solving skills, encourage teamwork, and spark students' curiosity. Dan Van der Vieren, who spoke about this topic at TEDxBoulder in 2018, will share his successes in the classroom and ideas to take the Cube to the next level.
Hi, I’m Dan Van der Vieren and I’m a math educator and a Rubiks Cube ambassador. Today, I'm here to answer the question, "Is the sky even the limit with the Rubik's Cube?"
Your first encounter with the Rubik's Cube may have been like this one (referencing image): You found a Rubik's Cube or received one as a gift from a friend or family member; you turn the faces a few times, got frustrated and either peeled the stickers off--before they made the tile version of the Rubik's Cube--or you took a hammer to the Rubik's Cube, blowing it into several thousand pieces, or you may have been like me, who is very inquisitive and really interested in what the puzzle had the offer. I was able to learn more about the Rubik's Cube in college and also figure out how I could utilize the Rubik's Cube as a cipher system.
But who is Erno Rubik and why does he have a Cube?
From this point forward if there are any links below images, please type those into your browser [and] investigate them on your own. There are awesome resources at the end of the presentation. I'll have a page of these resources so you can look at them later if you so desire.
So I wrote a thesis called Arm-twisting vs Cube Twisting. This was for a project that I did when I was at the University of Colorado Denver. In the program, I was able to study how the Rubik's Cube was able to motivate and incentivize students to learn more about math and also build teamwork and camaraderie within their school. I had this math elective in the 2017 fall semester as well as the 2018 fall semester and [in] the spring of 2019 [as well]. Some of the questions I asked my students in a survey involved, "Do you believe that this course will help you with your problem solving skills?" Another one was, "Has this class built up your self-confidence and self-esteem? The names of the electives were "Art and Problem Solving with the Rubik's Cube: Diversity" and "Art and Problem Solving with the Rubik's Cube: Nature and Science."
The 5-week courses were split into two sections across 10 weeks. The first five weeks, I completed 18 mosaics: two of them were 36 Cubes, seven of them were 100 Cubes, eight were 225 Cubes and there was one a very special one that one of our staff members was able to see for his birthday: 625 Rubik's Cubes! A total of 3,197 Cubes "solved." Now they don't have to be solved entirely, just one face that shows the image needs to be facing upwards.
In the second five weeks, I completed six mosaics with my students. One was a 225 Cube mosaic, another was 400 Cubes, [and] four were 600 Cube mosaics for a total of 3,025 Cubes "solved" by one face facing up. The mosaics completed include some of these as you can see here (about to show images).
I'm going to show you images of the Rubik's Cube mosaics that we completed. If you have a camera phone, I highly recommend that you take it out and look at the screen through the phone. You're able to see the pixels pop out at you and they provide a very clear image compared to what you might see close up.
Chinook West Alternative High School is the name of the school that I worked with students with the Rubik's Cube mosaics. In the image shown you can see several students putting Rubik's Cubes in trays of 25 Cubes. The students would then combine these trays to have a completed mosaic. But how did this happen?
STEM, which stands for science, technology, engineering, and math, was given an "A" to produce "STEAM". The "A" stands for "ART" It is very important in a lot of the projects that we do with the Rubik's Cube program but also in science, technology, engineering and math in general.
I was able to speak on this in a talk that I gave that TEDxBoulder in 2018 in an 8-minute video that you can watch at your leisure. Another contribution that I made with this program as an article submitted to the UKEd Magazine. You can read that by following that link (referenced on slide). I was able to participate in the World Council for Gifted and Talented Children which was held in Nashville, Tennessee in 2019.
**The scavenger hunt word at this point in the presentation you can access by going to that link there, do a little digging, and you'll find it in the comment section.**
What can you do with this program if you're an educator? You can help students with teamwork, critical-thinking skills, and also motivate them through an exercise building mosaics together in class. Here are several that we've done that are marked with stars. The ones that we did not do are not marked with stars in the corner there's a heart and a pattern; a smiley face and a hummingbird; a butterfly and an eye; circles, gradients, stripes, and another pattern; a baseball, ducks, flowers, a spider and T-Rex; a symmetrical pattern and a rendition of Starry Night by Vincent van Gogh; Mona Lisa and Vincent van Gogh; Anne Frank, Sitting Bull; Rosa Parks and Nelson Mandela; a hockey player and a Tibetan shrine; Marilyn Monroe and Amelia Earhart; Martin Luther King, Jackie Robinson; Mahatma Gandhi and Cesar Chavez; Harriet Tubman and Katherine Johnson; Sally Ride and Nikola Tesla; Abraham Lincoln and John F Kennedy; Terry Fox; a chimp and Jane Goodall; Marie Curie and Maya Angelou; the Golden Gate Bridge and Bill Nye the Science Guy; John Glenn and another astronaut; former First Lady Michelle Obama and former President Barack Obama; a dolphin scene; desert scene; Eleanor Roosevelt and Winston Churchill; Malala and Neil deGrasse Tyson; an eagle, Statue of Liberty, and a wolf.
There are a lot of mosaics that are currently being added to the You CAN Do the Rubik's Cube program. Several of these are on the next couple slides. (Referencing slide) These are the 2x2 Rubik's Cube mosaics. Here are several more three-by-three mosaics that have been added within the last year. There are materials online that you can access by going to YouCanDoTheCube.com. Mosaics themselves were made out of stones or tiles or rice or other tesserae but now we have Rubik's Cubes that we can make mosaics out of. There is a website that you can use to customize mosaics. It is called Mosaic.TwistTheWeb.com. It will step through how to customize mosaics there and you can investigate on your own and upload images that you have personally and create mosaics out of them.
I picked my alma mater from University of Northern Colorado. I'm in a master's program right now and this image I was able to take through the Creative Commons and use and upload to the Mosaic.TwistTheWeb.com website. One of the questions asked when you are going to the portal is how many Cubes you have. If you enter 225, it'll provide a decent picture if you have any more [Cubes] the details will be greater. You can change the mosaic by adjusting the color threshold. You'll notice the image right here (referencing image) that there are not all the correct colors; some greens in there, orange and yellow, or not exactly the color of the image. If you're able to adjust those manually that would help you when you share that with your students.
"Set the Number of Cubes Per Page" and the "Title of Mosaic" is if you're making a manual to print out for your students to create the mosaic together. Here's an example of the assembly guide. You'll notice A-1, B-1, and C1 are the pages that correspond to the sections of the mosaic. A2, B2, and C2 is the letter corresponding to the column and the number corresponds to the row. A3, B3, [and] C3 are the last three sections of this mosaic. Other mosaics that you can make with the Cubes: when I was teaching at my last school, we were able to create mosaics for the graduating class and present them at graduation. (Referencing slide). Here is an example with the actual mosaic created from the University of Northern Colorado logo.
You can also make creative mosaics with the Rubik's Cube! Here on the left, I used 2x2 Rubik's Cubes to play a game of Battleship. What I was doing on the right was utilizing 3x3 Rubik's Cubes to demonstrate the Pythagorean Theorem: "a squared plus b squared equals c squared."
There's also a mosaic contest that students can participate in and that is on Facebook. Students can submit their mosaics at different sizes and there's a competition and [voting] that can occur and whoever wins gets pride and a prize. This video here (referencing link on slide) is a short clip that describes how some teachers were able to integrate Black History Month using several of the templates on the You CAN Do The Cube website.
If you're not doing actual mosaics there [are] also patterns that students can try out that are very interesting designs and can provide an extra extension to activities.
There are World Records with the Rubik's Cube. On the left is a mural mosaic made up of over 85,000 Rubik's Cubes and this is located in China. On the right is not a Rubik's Cube mosaic but if you click on the link you can find an image of the actual mosaic of Prince Harry. This was completed in England last year in October of 2019. It was made of 1,620 Rubik's Cubes.
There are sample lessons to download if you go to the You CAN Do The Cube website. You can teach students how to solve as well as download other resources there. There are units and lessons that can supplement any curriculum, and teachers in the United States and Canada can borrow [and] use Rubik's Cubes--up to 600 Cubes for up to six weeks at a time! You're just responsible for return shipping.
The solution manuals, which I was actually able to participate with editing this last year-- have been updated for 2020. Previously, the additions had some different images and were updated this year to provide a very clear solution. (Referencing slide) This is the back of one of the older editions of the 4x4 manual that I was able to contribute to as a Rubik's Cube ambassador several years ago.
"Teaching students to solve": If you're able to, give students free exploration time and establish rules for handling the Cubes. It will help with the instructional process. It also is helpful if the teacher learns how to solve the Rubik's Cube himself or herself prior to sharing it with students so he/she can help the students and guide them in addition to several peers that might be able to assist. Also, working in small groups, playing Rubik's Cube videos, using checklists and practicing one step at a time are all strategies that can help with the problem solving process.
The algorithm for solving 2x2 Cubes: "R-i", "D-i", "R", and "D" are abbreviations to represent the face of the Cube. "R" represents "Right Face"; "D" represents the "Down [Face]" and "i" is denoting counterclockwise turning so just four steps for the 2x2? Yes indeed!
The algorithms for solving the 3x3 Cubes to flip the color or an edge tile: you can follow that algorithm there (referencing slide). To place a corner correctly, you can follow the algorithm listed on the screen. Eight steps for the 3x3? Pretty much!
A few quotes from Einstein are here:
"If you can't explain it simply, you don't understand it well enough." " The important thing is not to stop questioning." "Curiosity has its own reason for existing." "I have no special talents, I am only passionately curious," and "Imagination is everything [and] is the preview of life's coming attractions."
So where is the future headed? You can watch this short video. If you imagine the awesomest thing you can, there [are] a few other ideas out there that are really interesting and thought-provoking. Go give it a shot and be the change you want to see.
One way you can do this is to borrow a set! Borrow a set for up to six weeks at a time and share this with your students. The link you can go to and it'll bring you to a "Borrowing the Rubik's Cube" form. There [are] even more resources: some of the pictures following are a variety of other Rubik's Cube-like puzzles and games.
Did you know that these existed? (Referencing pictures on slide). The first one's actually a "Rubik's Cube Tower." The middle is called "Rubik's Magic" and the one on the right is a spherical version called the "Rubik's 360." Some of these other puzzles are not all Rubik's Brand. The one you see labeled is the Rubik's Pyramid; it's an interesting puzzle. I've yet to try that one. The other images: the one that's really scrambled and looks a little intimidating is a "Mirror Cube" which is not a Rubik's Brand and this here is called the "GO Cube." It's a programmable Rubik's Cube that has an app attached too. [A] little expensive online but if you're interested you can purchase them and have competitions and track progress for students if they have the app.
There [are] other engineering activities that you can share with your students, one being a very primitive--yet fun--activity: creating a 2x2 Rubik's Cube out of just paper. The image on the right is one of the "Build-It-Solve-It" 3x3 kits for students who are interested in taking apart Rubik's Cubes and putting them back together. There [are] additional instructions in there.
Robots and artificial intelligence have been touching and playing with the Rubik's Cube recently as well. This image is one of a robotic arm that can actually solve the Rubik's Cube. There's been a couple of drops but for the most part it does a really good job. There's a self-solving robot that's actually a Rubik's Cube with a robot inside of it. You can watch that video. It's very fun. And a speed-solving robot that can solve the Rubik's Cube in less than a second.
Rubik's Cubes come in all shapes and sizes as well. The world's largest Rubik's Cube is in Knoxville, Tennessee and the world's smallest Rubik's Cube you can find in the store. Very tiny! Rubik's Cube competitive games: the "Rubik's Race" is a fun game that two players can compete with; the goal or object of the game is to complete the pattern in the inside nine squares before your opponent. The "Rubik's Cage" on the right is kind of a pattern-based game and the goal is to get a certain pattern in a row and variations of the game are within the instructions.
Please go out there and get more information! The two links here, (referencing slide), "Rubik's More Info" will bring you to a page where you can enter some information and be entered into a prize drawing and then also the "Rubik's Cube Links" link will be providing all the links from this presentation that you can access all in one spot.
Thank you so much again for attending the Brainstorm 2020: Limitless Learning Conference. I really appreciate that you were able to watch and learn and hopefully you can take some of this to your classroom. Thank you.