Lesson Plan on Rubik s Cube Mosaics: An Intermediate guide for use in the classroom

Transcription

1 Lesson Plan on Rubik s Cube Mosaics: An Intermediate guide for use in the classroom By Suzanne Kubik Middleborough High School Middleborough MA Grades 9-12 Algebra 2, Geometry, and Statistics Learning to solve the Rubik s Cube is a great warm-up activity. In many classes I teach (Algebra 2, Geometry, and post Exam AP Statistics), students come into class during a specified time period (about 3 weeks) and grab a cube. Each day they learn a new algorithm for solving. It takes three days for me to teach students to solve the first two layers and then 3 or 4 more days to solve the entire cube. In an 84- minute block, we devote about minutes to cubing. Students enjoy hands on problem solving. They rise to the challenge and feel smart and accomplished when they can solve a cube without any assistance. Many students have seen the movie, The Pursuit of Happyness, where Will Smith solves the cube in the taxicab and captures the attention of a potential employer. In keeping with that theme, my students say that they have potential to the exponential when they earn their certificate for solving Rubik s Used under license Rubik's Brand Ltd. All rights reserved.

2 To make mosaics with Rubik s Cubes, students engage in problem solving, visual and spatial awareness, reasoning, communication, and representation. Students persevere in problem solving and must find entry points into problems. They reason abstractly and must use tools of technology for making a pixel template. Texas Essential Knowledge & Skills (TEKS) K-12 - Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:. (A) apply mathematics to problems arising in everyday life, society, and the workplace; (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution; (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems; (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; (E) create and use representations to organize, record, and communicate mathematical ideas; (F) analyze mathematical relationships to connect and communicate mathematical ideas; and (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication 1974 Rubik s Used under license Rubik's Brand Ltd. All rights reserved.

3 Now for the fun! I would recommend that classes start with a 6x6 mosaic and then try the larger ones on sequential days. My students were left craving the bigger patterns. To begin, project the template and then assign students to solve a specific row or column. Groups of 3-6 students can typically solve a 36-cube mosaic in about 15 minutes. They do not always achieve perfection as seen below. It is helpful to have a team leader. Not all members of the team have to be able to solve the cube to be part of the fun. We assigned nonsolvers to be project leaders for the 15x15 mosaics. They organized the 9 (25) cube sections based on the template Rubik s Used under license Rubik's Brand Ltd. All rights reserved.

4 Van Gogh s Starry Night was built during a visit to a Geometry Honors Class. This 100-cube mosaic was a simple start for a room full of beginners. Many students had no formal training but could intuitively solve a side for green. They loved to be part of the action. Four proficient solvers built Einstein using 225 cubes on my desk in one hour. Five students built Abe Lincoln in the cafe. They attracted many interested onlookers. All of these templates are available online through You Can Do the Rubik's Cube. cube-mosaics/ 1974 Rubik s Used under license Rubik's Brand Ltd. All rights reserved.

5 Now that a 15x15 cube mosaic was easy for us we wanted to design our own template. Two students asked our Principal for permission to take his photo. They promised a surprise in a few days. There were two options for us to use to design our own computer generated pixel template: GIMP and Photoshop. As luck would have it, a Photoshop 2 class was running during the same block and the teacher was willing to try a cross-curricular project with me. Mrs. Sharon Sangeleer wrote step-by-step instructions for her students to follow so that we could assign cube colors to all 2025 pixels. Her students taught my students how to use Photoshop and my students taught her students how to solve the cube. This shows the top left section of the designed mosaic. Each square represents one tile on one cube. We worked together for 3 days and then unveiled the following mosaic for the school to enjoy Rubik s Used under license Rubik's Brand Ltd. All rights reserved.

6 The white frame was designed and built by a student. The display board allowed us to explain the process of building a mosaic to other students in our school. After many rewrites of the Photoshop directions (attached) anyone can create a mosaic. We tested the directions with several students who had never used Photoshop and they were able to create templates in under an hour. We worked with the Rubik s Cubes for one month. Only 5 full class blocks were used and they were during the last week of school. Students responded very positively to the project. Students were completely engaged in the project. They could not wait to come to class and were slow to leave when the bell rang. They were featured in our local newspaper and their work was highlighted at the Underclassman Awards Night. We hope to share our excitement with your school and encourage you to try a mosaic of your own Rubik s Used under license Rubik's Brand Ltd. All rights reserved.

7 How to convert a picture into a Rubik s Cube Mosaic with Adobe Photoshop Creative Suite 6.0 (These instructions are specific for a 15 X 15 cube mosaic) Cross Curriculum Lesson: Math & Photoshop Preface: The following instructions were created in Adobe Creative Suite 6.0 for the PC. It is my experience that you may use these instructions with a MAC some of the short cut keys are different but essentially all the menus are the same. In the past when I have used MAC instructions in my classroom I have encountered very few problems. Step: 1 We will begin by creating a 45 X45 Centimeter Canvas Go to File > New Refer to the dialog box for exact settings. Click OK If you don t have Photoshop installed you may download a free one-month trial at Adobe. This is the Creative Cloud version. Enjoy Special Note: If using 100 cubes: Change STEP 1 to represent an area of 30 X 30 cm canvas. STEP 18 will end at 30 cm. If using 36 cubes: Change STEP 1 to represent an area of 18 X 18 cm canvas. STEP 18 will end at 18 cm. Created by: Sharon Sangeleer, Middleborough High School, Middleborough, MA Page: Rubik s Used under license Rubik's Brand Ltd. All rights reserved.

8 Step: 2 We are going to set the grid preferences so that each square on your screen will represent an individual square on your Rubik s cube. 1. Go to Edit > Preferences > Guide, Grid, and Slices 2. Grid Line Every = 3 cm Subdivisions = 3 3. Choose Unit and Rulers 4. Change the Units > Rulers to Centimeters, type pixels. 5. Change the Column Size Width = 1 Centimeter Gutter = 1 Centimeter1 Created by: Sharon Sangeleer, Middleborough High School, Middleborough, MA Page: 2

9 Step: 3 We now want to view the graph paper we have created. Go to View > Show Make sure <Grid> is selected Special Note: Your canvas should take up the entire screen like the image shown. If your screen is too big or small use the following method to adjust your screen. Adjust the percentage in the bottom left hand corner of your screen. Your screen should now look like this. Step: 4 While still in Photoshop open the picture you want to convert into the mosaic. File > Open Created by: Sharon Sangeleer, Middleborough High School, Middleborough, MA Page: 3

10 Step: 5 Special Note: I found my image on Go to Window> Arrange > Tile All Vertically (This is the technique I have found easiest for my students to move the picture onto a canvas.) Drag your image onto your canvas. You do this by dragging the background layer to your preset canvas. Step: 6 Close your original image so that we now only view the picture on our preset canvas. Created by: Sharon Sangeleer, Middleborough High School, Middleborough, MA Page: 4

11 Step: 7 We now see that the image does not fit exactly on the canvas. This is where we can transform it to fit. Go to Edit > Transform > Scale Adjust the scale so it now fits on the canvas. Click the check mark when you get the size adjusted the way you want it. Note: When I ran this particular picture I did not have enough contrast so I made a minor adjustment. When I ran the original filter the eyes disappeared. This will not happen with every image. The Fix: Go to Image > Adjustments > Brightness and Contrast Step: 8 At this time we are going to start to simplify the colors in our picture. Go to Filter>Filter Gallery > Artistic > Cutout Number of Levels = 5 Edge Simplicity = 1 Edge Fidelity = 3 When I ran the filter the first time I was not happy with the results. I tweaked the image and I made a note in the next column. Created by: Sharon Sangeleer, Middleborough High School, Middleborough, MA Page: 5

12 We should get something like the following image. Step: 9 More image prep. Now go to Image > Adjustments> Hue/Saturation Change the saturation to 100% Created by: Sharon Sangeleer, Middleborough High School, Middleborough, MA Page: 6

13 Step: 10 Now we are going to change the image to represent the SIX colors available on the rubik s cube Attention: When working with my students I found this was the most difficult set of steps in the tutorial. Please read carefully and pay attention to the coresponding screen shots. Step: 11 IMPORTANT: Don t click OK until I tell you to. Pallet = Local (selective) Go to Image > Mode > Indexed Color Flatten the layers Choose 9 colors (this is the smallest amount you can have we will deal with the problem momentarily) Created by: Sharon Sangeleer, Middleborough High School, Middleborough, MA Page: 7

14 Step: 12 At this time we are going to add the colors we will need for the mosaic. Select Forced > Custom Custom Dialog box will appear with 2 colors (Black and White) Step: 14 Now we will create Six boxes and assign colors. The below table represents the colors of the Rubik s Cube that you will need to assign. (If you note in the dialog box below has extra white boxes. We assigned nine colors and the cube only has six colors.) White Yellow Orange Red Blue Green FFFFFF FFFF00 FF9C00 F B3 00D900 With the color Picker type in each color number: Step: 13 We will click on each square until we have assigned the colors of the Rubik s cube. Step: 15 Now you can Click OK. Created by: Sharon Sangeleer, Middleborough High School, Middleborough, MA Page: 8

15 This is what we now have Step: 17 OPTIONAL You can change the colors around if you want. Coloring in Photoshop Instructions 1. Go to Image > Mode > RGB 2. Change the colors in the color swatches Step: 16 OPTIONAL Tweaking I was not completely happy with the color separation. I went to Image > Adjustments > Brightness / Contrast and moved the sliders around. 3. Use the quick selection tool / Magic Wand to select an area. 4. With the paint brush paint 5. CTRL + D will get rid of walking ants Created by: Sharon Sangeleer, Middleborough High School, Middleborough, MA Page: 9

16 Step: 18 We are now going to add guide lines which will allow us to see our mosaic in NINE squares to a box. Go to View > New Guide lines Select Vertical and add 15 guidelines. Step: 19 Position: 3 CM 6 CM 9 CM 12 CM 15 CM 18 CM 21 CM 24 CM 27 CM 30 CM 33 CM 36 CM 39 CM 42 CM 45 CM Now we are going to add the Horizontal guide lines. Place the horizontal guide lines in the same positions previously mentioned. Created by: Sharon Sangeleer, Middleborough High School, Middleborough, MA Page: 10

17 How do I now break out sections to build my mosaic? Office 2010 comes with a program called Snipping Tool. This program can be found in the Accessories Folder. This program allows you to Snip sections of you picture and place them into Microsoft Word or Excel. If Snipping Tool not available don t panic, you can complete this by using the PrtScn button your key board. Paste it in word and crop out what you don t want. Created by: Sharon Sangeleer, Middleborough High School, Middleborough, MA Page: 11