ANCIENT GAMES & PUZZLES AROUND THE WORLD LESSON PLAN 3-6 GAME CARDS 7 WORLD MAP 8 ENGINEERING & CONSTRUCTION: BUILD A RUBIK S CUBE (2X2)

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2 ANCIENT GAMES & PUZZLES AROUND THE WORLD LESSON PLAN 3-6 GAME CARDS 7 WORLD MAP 8 ENGINEERING & CONSTRUCTION: BUILD A RUBIK S CUBE (2X2) LESSON PLAN 9-13 CUBE TEMPLATE 14 FIBONACCI S PERFECT SPIRAL LESSON PLAN EXAMPLES GAME VARIATIONS: ULTIMATE TIC TAC TOE LESSON PLAN ULTIMATE TIC TAC TOE GAME BOARD 26 ENGINEERING DESIGN PROCESS 27 MIXED UP MATH LESSON PLAN PIXEL ART: DESIGN A RUBIK S CUBE MOSAIC LESSON PLAN MOSAIC TEMPLATES FOR 3X3 CUBES RATIO & REASONING: EXAMINING 2X2 AND 3X3 RUBIK S CUBES LESSON PLAN STUDENT PAGES SAMPLE MOSAIC TEMPLATES MOSAIC TEMPLATE FOR 2X2 CUBES 47 CODON CRITTERS LESSON PLAN STUDENT PAGES 52-62

3 Ancient Games & Puzzles Around the World Middle School In this lesson, students will examine the history of certain games, including the Rubik s Cube. Common Core Standards: CCSS.RST Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts. CCSS.WHST Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration. CCSS.WHST Gather relevant information from multiple print and digital sources, using search terms effectively; assess t he credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation. Objectives: Students will gain a cross-cultural understanding of the history of gaming. Materials: Variety of games, suggestions include: Mancala, Chinese checkers, traditional checkers, wooden brain teasers, dominoes, Rubik s Cubes, parcheesi, Monopoly, Scrabble, etc Optional reading: Mistakes That Worked, 40 Familiar Inventions and How They Came to Be, by Charlotte Foltz Jones

4 Procedure: Procedure: Before class: Familiarize yourself with how to play the various games you have available for the students. Make copies & cut apart the game cards and mix up the dates, games, and countries of origin. Can have 1 copy per student, per pair, or small group. Part 1: The History of Games (30 minutes +) 1. Distribute game cards to individual students, partners, or small groups. Instruct students to match the dates with the games the country of origin, and arrange the dates in a timeline order. 2. You can give clues as the students are matching the dates-countries-games, or let students know which ones they have correct when they ask you to check their work. As a clue, you may consider showing pictures of the lesson common games to students. Historical photos may give clues regarding the country of origin and timeline. 3. After you reveal the correct dates and countries, students can create a timeline of the games and their origins and identify their origins on the world map. 4. As time allows, students may play as many of the games mentioned in the matching game as you have available in your classroom. Part 2: Rubik s Cube History 1. Look closely at the history of one or more of the games, such as the Rubik s Cube. Students can research to develop a timeline specific to one game, write a summary, or prepare a presentation for classmates. 2. Make resources available to students to use for research purposes or review the materials 4

5 together as a class. Potential sources of information for the Rubik s Cube include: a. History of the Rubik s Cube (article from Rubiks.com): b. Stuff of Genius, Erno Rubik (video from HowStuffWorks): ubiks-cube-video.htm c. Rubik s Cube Inventor, Mysteries at the Museum (video from Travel Channel): Students can develop a timeline specific to events in the history of the Rubik s Cube or researched game of their choosing. Technology Connection: Many of the games have online versions that can be played online: Senet - Ur - h ttps:// Mah Jong - Backgammon - Checkers - Optional Follow Up / Extend the Lesson: Examine the maps in which students marked the games from the matching activity. Ask: What continents did we not identify games from? (South America, Australia, Antarctica) Research to find games popular in countries that are part of these continents. (Exception- you probably won t find anything from Antarctica.) Students can learn about other familiar inventions from reading short excerpts from the book Mistakes That Worked, 40 Familiar Inventions and How They Came to Be, by Charlotte Foltz Jones 5

6 Notes to Teacher: Many of the modern games are adaptations of ancient versions, so you may find alternate countries of origin and dates depending on which sources you reference. If you want to make additional game cards, you may consider adding: 3000 BCE - Egypt - Ur 1100 s - China - Dominoes United States - Parcheesi United States - Monopoly This lesson is an adaptation of Introduction: Ancient Games and Puzzles Around the World, originally developed by STEM.org for You CAN Do the Rubik s Cube. References:

7 Ancient Games & Puzzles Around the World Game Cards 3100 BCE Egypt Senet 500 Ethiopia Mancala 600 India Chess 1535 France Checkers 1880 China Maj Jong 1892 Germany Chinese Checkers 1948 United States Scrabble 1974 Hungary Rubik s Cube Make copies and cut apart cards for each student or group of students. 7

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9 Engineering & Construction: Build a Rubik s Cube (2x2) Middle School In this lesson, students will build a functional 2x2 Rubik s Cube out of paper. Common Core Standards: CCSS.MATH.CONTENT.5.MD.C.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. CCSS.MATH.CONTENT.5.MD.C.4 Measure volumes by nd counting unit cubes, using cubic cm, cubic in, cubic ft, a improvised units. CCSS.MATH.CONTENT.6.G.A.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. CCSS.MATH.CONTENT.7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three- dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. CCSS.Math P ractice 5 U se appropriate tools strategically. RST F ollow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks. Next Generation Science Standards: MS-ETS1-1 D efine the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions.

10 MS-ETS1-2 Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem. Objectives: Students will plan, measure, and follow directions to build a 2x2 model of a Rubik s Cube. Materials: 2x2 Rubik s Cubes (1 per student) Colored paper - red, blue, yellow, green, orange String (18 per student) Heavy duty tape (packing tape) Scissors (1 per student) Glue sticks Background Knowledge: Helpful, but not essential: Students should understand how a net can be folded to create three-dimensional polyhedron. Students should understand that the template net is not the only configuration of a net that will create a cube. Procedure: Before class: Copy cube template page- each student will need 4 sheets (2 cube templates per sheet) Cut strings about 4.5 inches long - each student will need 4 strings Make a sample of the project to show the students. Part 1: What is Engineering? 1. Discuss engineering with students. What is engineering? What is the purpose of engineering? While some people have stumbled upon great ideas, others set about trying to solve real-world problems. 10

11 2. Define the main branches of engineering: electrical, mechanical, chemical, and civil. Work with the class to come up with examples of things each type of engineer might build. 3. Students can learn about accidental inventions through the short stories in the book, Mistakes That Worked, by Charlotte Hone, et.al. Share a few of the stories with students. Part 2: Examine the 2x2x2 Rubik s Cube 1. Give students exploration time with the 2x2 Rubik s Cube. Ask: What are the similarities and differences between the 3x3 and 2x2 Rubik s Cube? Why are they called 3x3 (three-by-three) and 2x2 (two-by-two)? 2. Determine the perimeter and area of each face and the surface area and volume of the 2x2 cube with students. 3. Identify the shapes and angles that make up the cube. 4. Define net in mathematics. (a two-dimensional figure that can be folded into a three-dimensional object) 5. Work through the interactive problems on the Illuminations website where students will identify which 2D nets can be folded into cubes. Part 3: Build a 2x2x2 Rubik s Cube 1. Now, students will follow directions to make a functional paper model of a 2x2x2 Rubik s Cube. Show students the sample 2x2 cube they will be making. 2. Students will measure and cut 4 squares 1.25 inches on each side of each color. 3. Glue colored squares onto the appropriate spaces for each corner piece. You may want to show 11

12 students where the colors should go, or have them examine the 2x2 cubes to determine the placement. 4. Cut out each cube template and fold on solid lines to create 8 cubes. *Students could also create their own cube nets, but the template will help expedite the activity 5. Students can use glue sticks or tape on the tabs to create the cubes. Covering the cubes in clear packing tape will help make the pieces more durable. 6. Attach strings (with clear packing tape) diagonally on pairs of cubes in the upper and lower layers of the cube. *See photo 7. Twist the cube to tangle the strings creating a working 2x2 Rubik s Cube model! 12

13 Technology Connection: Online resources for learning to solve the 2x2 Rubik s Cube: it/2 x 2 solution Activity where students determine which nets will create cubes: If you choose to make the pieces out of origami cubes, demonstrations are available online: Modular cube using 6 pieces of paper per cube, easy to fold, but will require 48 modules: Cube made from single piece of paper, more difficult fold: Optional Follow Up / Extend the Lesson Using the You Can Do the Rubik s Cube Rubik s Cube Solution Guide or online videos, students can learn to solve the 2x2 cube. Notes to Teacher: Depending on the class time you have available, and skill level of your students, you can increase the difficulty on the project by having the students make origami cubes rather than using the cube templates. You can also make the project a bit quicker by having the colored squares precut for the students. 2x2 Rubik s Cubes are available to borrow from the You CAN Do the Rubik s Cube Lending Program at no cost other than return shipping. library This lesson is an adaptation of Engineering & Construction: Solving Real World Problems, developed by STEM.org for You CAN Do the Rubik s Cube. 13

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15 Middle School Fibonacci's Perfect Spiral This lesson was created to combine math history, math, critical thinking, and art. Students will learn about Fibonacci, the code he created, and how the Fibonacci sequence relates to real life and the perfect spiral. Students will practice drawing perfect spirals and learn how patterns are a mathematical concept that surrounds us in real life. This lesson is designed to take 3 to 4 class periods of 45 minutes each, depending on the students focus and depth of detail in the assignments. Common Core CCSS.MATH.CONTENT.HSF.IF.A.3 Recognize that Standards: sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n 1) for n 1. CCSS.MATH.CONTENT.7.EE.B.4 Use variables to represent quantities in a real world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. CCSS.MATH.CONTENT.7.G.A.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

16 CCSS.MATH.CONTENT.7.G.A.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. CCSS.MATH.CONTENT.8.G.A.2 Understand that a two dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations given two congruent figures, describe a sequence that exhibits the congruence between them. CCSS.MATH.CONTENT.8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two dimensional figures using coordinates. Objectives: Students will review the Fibonacci sequence learn how to draw a perfect spiral use art to learn about math and how it relates to real life have fun learning math Materials: Samples pictures of perfect spirals in nature Sample of a perfect spiral on paper (included in lesson) Grid Paper (about 0.75 squares) Color pencils (blue, orange, red, green and yellow) Background Knowledge: Knowledge of Fibonacci, good but not required How to solve one face of a Rubik s Cube (edges and corners) 16

17 Procedure: Before class: Ensure all materials are available. Make copies of handouts for students. With students: 1) Introduce or review Fibonacci sequence. (0,1,1,2,3,5,8,13,21,43 ) 2) Explain that this sequence is a part of everyday life in the form of what is known as the perfect spiral. 3) Show examples of real life perfect spirals, pointing out the sequence in each. 4) Explain the steps for drawing a perfect spiral by demonstrating on the dry erase board 1. In the center of the graph paper outline a single square. See purple square on perfect spiral example sheet (included) 2. Go to the square to the right of the 1. Outline that little square to represent the next number in the pattern, another 1! (outlined in light blue) 3. Use the line above the two 1 squares to outline a square that is 2 little squares long and 2 little squares high. This represents the next number in the sequence 2. (Outlined in brown) 4. Now move to the right of the 1 and 2 squares. Use the right side of the 2 square and the right side of the second 1 square to draw a square that is 3 little squares high and 3 little squares long. 3 is the next number in Fibonacci s pattern. (Outlined in light purple) 5. Use the bottom of both 1 squares and the bottom 17

18 of the 3 square to make the next number in the pattern a big square that is 5 little squares long and five little squares high. (outlined in orange) 6. Move to the left of the 2 square, the 1 square, and the 5 square. Use their left edges to make the 8 square. (Outlined in green) 7. Continue this way until you run out of room or have enough spirals to work with. 5) The next step is to draw Fibonacci's spiral. All you have to do is connect one corner of each square with the opposite corner of that square with a sweeping curve. You may need to practice a few times to get it right. Examples on the Perfect Spiral example sheet. This is the biggest that is really needed for art project. 6) Once the spiral is drawn then boxes could be erased or used to create an abstract piece of art. 7) Show examples of what can be drawn out of the perfect spiral and have students create a picture with their spiral that can be pixelated using the colors of the Rubik s Cube. 8) Once the picture is complete have the students create their masterpiece using Rubik s Cubes. Technology Connection: Information about perfect spirals and spirals in nature can be found at Notes to Teacher: The more examples you have, the better idea it gives the students. 18

19 For students that need a challenge, have them draw a double spiral or create a pattern using multiple spirals (have examples available). Drawing a large example on the board is helpful and compasses make drawing the spiral easier. 3x3 Rubik s Cubes are available to borrow from the You CAN Do the Rubik s Cube Lending Library at no cost other than return shipping. library This lesson was written by Kim Hyde. Use this as an example to follow. 19

20 Example of a double spiral abstract 20

21 Perfect Spiral Example page: 21

22 Examples of Rubik s Cube mosaics of perfect spirals: 22

23 Game Variations: Ultimate Tic Tac Toe Middle School In this lesson, students will experience the engineering process when creating modifications to a familiar game. Next Generation Science Standards MS-ETS1-1 Engineering Design Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution. MS-ETS1-2 Engineering Design Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem. MS-ETS1-3 Engineering Design Analyze data from tests to determine similarities and differences among several design solutions to identify the best characteristics of each that can be combined into a new solution to better meet the criteria for success. Materials: Copies of Ultimate Tic Tac Toe game boards, or blank white paper Pens/ Pencils Computer w/ Internet connection & projector 3x3 Rubik s Cubes Background Knowledge: Students should know how to play the traditional tic tac toe. If not, they can certainly be taught very quickly. Procedure: Before class: Learn how to play Ultimate Tic Tac Toe. Make copies of Ultimate Tic Tac Toe game board, or have blank paper ready for students.

24 Part 1 Learn a New Game 1. Teach Ultimate Tic Tac Toe to students. a. Project game board for Ultimate Tic Tac Toe from website onto white board (ultimatetictactoe.creativitygames.net) or draw a few tic tac toe grids on chart paper b. Challenge a few students (one at a time) to traditional tic tac toe. c. Explain that if both players are paying attention and reasonably intelligent most games will end in a draw/ tie. d. Challenge the computer player to Ultimate Tic Tac Toe and have students observe. Talk through some of your moves, discussing the strategy of why you would or would not choose certain squares. 2. Pair students up and have them challenge each other. If you have an odd number of students, the teacher can play against them, or let them play against the computer. They can draw the grids on blank paper or you can make copies of the supplied game board. Part 2 Analyze Traditional / New Game 1. Discuss: a. How does the new version ultimate tic tac toe change the difficulty of the game? b. Which version do you prefer? c. How else could tic tac toe be modified? Part 3 Modify a Game Further, Analyze Again 1. Discuss: a. How could you use Rubik s Cubes to play tic tac toe? b. What rules need to be created? 2. Have students write up their game modifications and teach their new versions to another student / small group. 24

25 3. Discuss as a class some of the problems encountered when using Rubik s Cubes to play tic tac toe. (Example: How to make a move without undoing your opponent s move, or maybe this is a strategy and part of the game.) 4. Discuss how could these problems could be solved, and how some students may have taken these issues into account in their own game versions. 5. Allow students to share their various modifications for the game. 6. Send students back to the drawing board to make adjustments to their game and try out their revised versions with a partner or small group. Technology Connection: Ultimate Tic Tac Toe can be played online here: This site could be used when demonstrating how to play the game, or the students can challenge the computer or play 2 players online. Notes to Teacher: 3x3 Rubik s Cubes are available to borrow from the You CAN Do the Rubik s Cube Lending Program at no cost other than return shipping. library Ultimate Tic Tac Toe rules/ description can be found online here: tic tac toe/ or search ultimate tic tac toe online for many variations. 25

26 Ultimate Tic Tac Toe Image is screenshot from 26

27 Engineering Design Process When working on an problem that involves designing, building, and testing something, engineers often use the Engineering Design Process. The steps are listed in the graphic below. Describe how you used the Engineering Design Process while creating your version of tic tac toe using Rubik s Cubes. 27

28 Middle School Mixed Up Math This lesson can be adapted for younger students to practice other computational math concepts. In addition to the content math standards, students will strengthen logical thinking skills and time management. Common Core Standards: CCSS.MATH.CONTENT.6.NS.B.3 Fluently add, subtract, multiply, and divide multi digit decimals using the standard algorithm for each operation. CCSS.Math Practice 6 Attend to precision. Objectives: Students will practice adding, subtracting, and multiplying multi digit numbers with decimals. Materials: 3x3 Rubik s Cubes Pencils & paper for math calculations Background Knowledge: Students should already know the procedures and rules for adding, subtracting, or multiplying multi digit numbers with decimals. Procedure: With students: 1. Assign a numerical value to each color on the Rubik s Cube. For the first activity, these will be single digit numerals. (Example: Yellow = 1, Red = 3, Blue = 5, Green = 7, Orange = 9, and White =0) Record these assignments on the board where students can reference them, and where they can be changed if desired. 2. Explain that the center tile on each face will be used to i dentify the face ( green face means the face with the green tile in the center) and will also be the decimal point in the number. 3. Show students how to read the face of the cube, by starting at the top row, reading from left to right (see example).

29 4. Create problems for the students and challenge them to be the student with the largest (or smallest) answer. 5. Students can also be challenged to create the largest (or smallest) answer by being allowed a few seconds to manipulate (twist) the cube after the problem is announced. Technology Connection: If you do not have a Rubik s Cube for each student, or want all students to use the same scramble, you can use an online Rubik s Cube that can be scrambled: 3x3x3/ Or Variations Depending on the ability levels of your students, you can choose the operations to be used, the value of the colors, and the number of tiles to be included. You can use single digit numbers and practice problem solving across just one row of the cube. Start with + + and just one row of the cube, increase to + x, and then beyond. You could also focus on the four corners and use all four operations. Recommended order is + x 29

30 Require that all students make at least three twists to their cube before announcing the next sequence. Allow students to make twists to create the best scenario (largest sum/product), or just to search the six sides to find their best outcome. Notes to Teacher: 3x3 Rubik s Cubes are available to borrow from the You CAN Do the Rubik s Cube Lending Program at no cost other than return shipping. library 30

31 Pixel Art: Design a Rubik's Cube Mosaic All grades Designing a Rubik s Cube mosaic involves creativity, collaboration, pattern recognition, and computer skills. Common Core CCSS.Math Practice 1 Make sense of problems and persevere in s olving them. Standards: CCSS.Math Practice 2 Reason abstractly and quantitatively. CCSS.Math Practice 5 Use appropriate tools strategically. CCSS.Math Practice 6 Attend to precision. CCSS.MATH.CONTENT.HS.G-MG.A.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Next Generation Science Standards MS-ETS1-1 Engineering Design Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution. MS-ETS1-2 Engineering Design Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.

32 Objectives: Students will design their own pixelated picture or pattern and then replicate it using Rubik s Cubes. Materials: 3x3 Rubik s Cubes Colored Pencils Graph paper or use included student page(s) Mosaics can also be made with the help of online programs, in which case you will also need: Computers with Internet access Color printer Background Knowledge: It is helpful if students know how to solve one face of the Rubik s Cube (manipulate edges and corners), but students can also learn that skill while working on this lesson. Procedure: Before class: Copy mosaic templates based on the number of students and cubes you have available. If you are going to use the Google Sheets option, save a copy of the file found at for yourself. If students have their own Google drives, share a view only copy with them before they do part 2 of this lesson. Watch the video at for instructions on part 2 of this lesson (using Google Sheets to create a mosaic template). Part 1: Design a mosaic template by hand. 1. Using only the colors yellow, blue, orange, red, and green, students draw a pattern or picture onto the template sheet, or grid paper, using one color per box. 2. After templates are designed, students can use 9, 16, or 25 Rubik s Cubes to create their mosaic. 32

33 Technology Connection: Part 2: Design a template using Google Sheets. Instructions for this part of the lesson can also be found in this video: 1. Make a copy of the Google Sheets file found at (The file has View Only restrictions, so you need to make a copy before you will be able to edit it.) 2. After sharing a View Only version of the file with your students, have them save a personal copy of the file. (Or send them to the original file to make their own copies.) 3. Students will use the Fill Color tool to color the pixels in the template grids to make their own images and designs. 33

34 Pixel art images can be found online to assist students. The number of squares of the image and the given space for each student is often not the same and they will need to adapt the image to fit the grid space they have. An internet image search of pixel art will give ample results, and be narrowed by adding a subject such as pixel art unicorns Extend the Activity: Students can also examine how adding more cubes / more pixels to their design affects the area of the mosaic. Notes to Teacher: 3x3 and 2x2 Rubik s Cubes are available to borrow from the You CAN Do the Rubik s Cube Lending Program at no cost other than return shipping. library Teachers and youth leaders can borrow Mosaic Builder Sets sets of Rubik s Cubes from You CAN Do the Rubik s Cube at no cost other than return shipping. a set/ 34

35 Design Your Own Rubik s Cube Mosaic: 9 cubes Create a template to make a pattern or picture using only Rubik s Cube colors: white, yellow, green, blue, red, and orange. Each individual square may consist of only one color. 35

36 Design Your Own Rubik s Cube Mosaic: 16 cubes Create a template to make a pattern or picture using only Rubik s Cube colors: white, yellow, green, blue, red, and orange. Each individual square may consist of only one color. 36

37 Design Your Own Rubik s Cube Mosaic: 25 cubes Create a template to make a pattern or picture using only Rubik s Cube colors: white, yellow, green, blue, red, and orange. Each individual square may consist of only one color. 37

38 Ratio & Reasoning: Middle School Examining the 2x2 & 3x3 Rubik's Cubes In this lesson, students will compare the 2x2 and 3x3 Rubik s Cube and examine the ratio between the cubes. Common Core CCSS.MATH.CONTENT.6.RPA.3 Use ratio and rate reasoning to solve real-world and mathematical Standards: problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. CCSS.MATH.CONTENT.7.RPA.2 Recognize and represent proportional relationships between quantities. CCSS.MATH.CONTENT.7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three- dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Objectives: Materials: Background Knowledge: Students will compare the ratio for measurable aspects of the 2x2 and 3x3 Rubik s cubes and their respective mosaics. 2x2 Rubik s Cubes 3x3 Rubik s Cubes Rulers Mosaic template (provided) Graph paper, or use provided page Template for mosaic using 36 2x2 cubes Students should know what a ratio represents, different ways to write ratios, and how to read ratios. This lesson does not teach them the fundamental knowledge they ll need, but allows them to apply their learning with a hands-on problem.

39 Procedure: Before class: Copy the student page for each student. Copy the mosaic template for each student. They do not have to have color copies of the mosaic, black and white will work fine. Copy graph paper and blank template pages for each student. Part 1- Comparing Cubes 1. Using the student page as guide, have students use rulers to measure different aspects of the 2x2 and 3x3 Rubik s Cubes. 2. Students will also list the ratio between the cubes for each aspect. Discuss with your class how you would like the ratio written. What format would best represent the data? 3. Have students analyze the ratios of the different cube measurements. Are the ratios the same? Why or why not? Part 2- Comparing Mosaics 1. Show students the template for a Rubik s Cube mosaic that is made from 36 3x3 Rubik s Cubes. (You may want to project one for the whole class to view, and also hand out copies of the mosaic for each student.) 2. Examine how the mosaic is set-up. 36 cubes, 6 rows of 6 cubes. 3. ASK: If you wanted to create this mosaic, but had 2x2 cubes instead of 3x3 cubes, how many cubes would you need? (Allow students to wrestle with this question. You may also want them to explain their answer in writing, or prove it with a drawing.) A mosaic of 36 3x3 cubes will take 81 2x2 cubes. 4. Discuss with students how they arrived at their answer. Is there a formula that can be used? ( Students may count the cubes by sectioning the 39

40 mosaic template into 2x2 cubes. Alternately, they could multiply the number of cubes in a row by 3, for the number of pixels in each cube, to determine the number of pixels needed for each row, then divide by 2- the number of pixels in each 2x2 cube.) 5. Show students other mosaic templates available at Examine how the number of cubes needed for each mosaic compares as a ratio. a. The 100 cube mosaics are made with 10 rows of 10 3x3 cubes. How many 2x2 cubes would be required for this mosaic? ( 225 2x2 cubes ) b. The 225 cube mosaics are made with 15 rows of 15 3x3 cubes. How many 2x2 cubes would you need to make these mosaics? ( Not possible - ask students why not.) c. The 400 cube mosaics are made with 20 rows of 20 3x3 cubes. How many 2x2 cubes would you need to make these mosaics? ( 900 2x2 cubes ) d. The 600 cube mosaics are made with 30 rows of 20 3x3 cubes, or 20 rows of 30 cubes, depending on if they are horizontally or vertically aligned. How many 2x2 cubes would you need to make these mosaics? ( 1,350 2x2 cubes ) 6. Using the findings from Part 1, what size frame would you need for each mosaic? How would the area of the 3x3 mosaic compare to the 2x2 mosaic? Part 3- Make a new template 1. Have students redraw the 36 3x3 cube mosaic template for 81 2x2 cubes on graph paper. 2. Ask: Could the same pattern be made using just 36 2x2 cubes? 40

41 3. Have students resize the pattern and color in the template for 36 2x2 cubes. Technology Connection: Students can modify and use the Google Sheets program used for the previous lesson for redrawing the 2x2 mosaics. Optional Follow Up / Extend the Lesson Students could also measure the paper 2x2 cubes they made in the previous lesson and analyze those ratios as well. (Ratio to a 3x3 cube, ratio to the Rubik s brand 2x2 cube, etc) Notes to Teacher: 2x2 and 3 x3 R ubik s C ubes are available t o borrow from the Y ou CAN Do the Rubik s Cube Lending Program at no cost other than return shipping. 41

42 Ratio & Reasoning: Examining the 2x2 & 3x3 Rubik s Cubes Student page Part 1: Using a ruler, measure the 2x2 and 3x3 Rubik s Cubes. Record your findings in the chart below. 2x2 Rubik s Cube 3x3 Rubik s Cube Ratio Length of 1 cubie (cm) Length of 1 edge (cm) Area of 1 face (cm 2 ) Surface area of cube (cm 2 ) Volume of cube (cm 3 ) 1. What formula is used to find the area of one face of the Rubik s cube? 2. What formula is used to find the surface area of the Rubik s cube? 42

43 3. What formula is used to find the volume of the Rubik s cube? 4. Is the ratio between the measurements the same for all aspects of the 2x2 and 3x3 cubes? Explain. Part 2: Examine the Rubik s Cube mosaic templates that are currently designed for building mosaics out of 3x3 Rubik s Cubes. How would these templates be adapted if you have 2x2 cubes instead? x rows of y 3x3 Rubik s Cubes x rows of y cubes - if 2x2 Rubik s Cubes Total number of 2x2 cubes needed Ratio of total cubes needed 36 cube template 100 cube template 225 cube template 400 cube template 600 cube template 43

44 5. Using your data from Part 1, what size frame would you need for a mosaic with 36 3x3 Rubik s Cubes? 6. What is the area of a mosaic with 36 3x3 Rubik s Cubes? 7. What size frame would you need for a mosaic with 36 2x2 Rubik s Cubes? 8. What is the area of a mosaic with 36 2x2 Rubik s Cubes? 44

45 Mosaic Template for 3x3 Rubik s Cubes 45

46 Mosaic Template for 3x3 Rubik s Cubes 46

47 Mosaic Template for 2x2 Rubik s Cubes: 36 cubes Do your best to recreate the 3x3 Rubik s Cube mosaic template using the same number of 2x2 Rubik s Cubes. 47

48 Middle/High School Codon Critters This activity can be done as an example of deciphering a complicated code, or as part of a in-depth study of DNA. The cube demonstrates RNA s role in transcription and translation by acting as a string of mrna carrying the 18 traits for an imaginary creature the students will make. Each row on the cube will code for a single amino acid and to simplify things, traits are determined by just one amino acid. This activity can be done individually or in pairs, and can be simplified by working in groups where each student is responsible for only a fraction of the whole cube (1 side only, 2 sides, etc) and then the group can collaborate on the drawing, or each student can draw their own creature. Common Core Standards: RST Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks. Next Generation Science Standards: MS-LS3-1 Develop and use a model to describe why structural changes to genes (mutations) located on chromosomes may affect proteins and may result in harmful, beneficial, or neutral effects to the structure and function of the organism. MS-LS3-2 Develop and use a model to describe why asexual reproduction results in offspring with identical genetic information and sexual reproduction results in offspring with genetic variation. Objectives: Students will use Rubik s Cubes to model RNA s role in transcription and translation. The cube acts as a string of mrna carrying the 18 traits for an imaginary creature the students will make.

49 Developing and Using Models: Modeling in 6 8 builds on K 5 experiences and progresses to developing, using, and revising models to describe, test, and predict more abstract phenomena and design systems. Materials: 1 Rubik s Cube per group Cube Critter handout (1 per student) Codon Table (1 per student/group) Table of Traits (can be shared) Unlined paper Colored pencils or markers Background Knowledge: Students should have understanding that: Hereditary information is contained in genes, located in the chromosomes of each cell. An inherited trait of an individual can be determined by one or by many genes and a single gene can influence more than one trait. The characteristics of an organism can be described in terms of a combination of traits. Although different species might look dissimilar, the unity among organisms becomes apparent from an analysis of internal structures and the similarity of their chemical processes. Vocabulary : adenine DNA transcription amino acid guanine translation codon thymine cytosine traits 49

50 Procedure: Before class: Make copies of handouts for students/ groups. (Codon Critters, Codon Table, Table of Traits) With students: 1. Explain how to use a codon table. Left side is the first base, top is the second base, right side shows the last base. 2. Explain some details necessary for this activity: a. Point out to students that the center square on each face of the Rubik s Cube is fixed, so that s how the faces are named. When referring to the yellow face. this means the face of the cube with a yellow center tile. b. The diagram at the bottom of the handout shows a way to look at the cube so everyone is using the same row for the same trait. It s not absolutely necessary that everyone does this, but it helps illustrate that even when reading everything the same way, odds are you re going to have different traits. 3. Distribute Cube Critters handouts to students. Read through instructions together. 4. Give each student (if working individually) or group a Rubik s Cube. The cubes can be already scrambled, or if the start with solved cubes, instruct the students to mix up the cube by performing at least 10 random turns. 5. Be available to help students as they work through the activity. Technology Connection Students can practice transcription and translation with this online activity: 50

51 A teacher s answer key is available for download at The file is called Codon Cube C ritters Checker.xls and a how to use video is online: Optional follow-up/ Extend the lesson The creatures can also be sorted into into classes, orders, families, etc based on characteristics of the student s choosing. Students should explain and justify their classifications. Notes to Teacher: 3x3 Rubik s Cubes are available to borrow from the You CAN Do the Rubik s Cube Lending Program at no cost other than return shipping. Thank you to Adam Raymond, math and physics teacher at Rockdale Magnet School for Science and Technology (Georgia), for the teacher s answer key for this lesson. 51

52 Cube Critters: Student Page All of life as we know it is based off of DNA. Everything from the smallest and simplest organisms to the biggest and most complex creatures ever to live all begin with guanine, cytosine, adenine and thymine. To better understand the universal nature of DNA and to show how four things can create an almost infinite combination of traits, we are going to work with something most (if not all) of you are familiar with: the Rubik s Cube. Despite being composed of only six colors and 20 moveable pieces, there are 43,252,003,274,489,856,000 unique combinations that can be made on a Rubik s Cube. To put that into perspective, all 7 billion people alive on Earth today would need over 600 million cubes each to make all of the combinations. For this reason alone, the Rubik s Cube is perfect for our study of transcription and translation. In DNA, a codon is 3 bases read together and on your Rubik s Cube, a codon will be three squares in one row of the cube. Each codon will code for an amino acid and in our simplified version, each amino acid will determine a trait. By the time you finish, you will have determined 18 individual traits for your organism and will then illustrate your newly designed critter. 52

53 Activity Instructions: The center square on each face will never change its place. When a side is mentioned by color (for example: the green side), it is referring to the side with a green square in the center spot. Each side of the cube will code for 3 specific traits, all fitting a common theme. To insure that everyone reads their code the same way, the traits will be named in the following manner: Note the order of the colors of the cube when solved: The traits will be read in this order for each side: 1 signifies the first trait for that color s face, 2 the second, and 3 the third. The letters a, b, and c refer to the first, second, and third base respectively for each given trait. Each color face will determine 3 different traits. 53

54 Procedure: 1) Scramble your Rubik s Cube thoroughly. Make at least 10 random turns. 2) Place the cube on your desk with the yellow face on the top and the orange face towards you. 3) Beginning with the top left corner of the yellow face, record the arrangement of your cube in Data Table 1 (It may be helpful to write down both the color on the cube and the base in the area provided.) 4) For each set of three bases, find the corresponding amino acid on the Codon Table. 5) Repeat steps 3 and 4 for the orange and blue faces. 6) After recording the information for the yellow, orange and blue faces, flip your cube over so the white face is on top now and the green face is towards you. 7) Repeat steps 3 and 4 for the three remaining faces. 8) After filling in the amino acids for all traits, complete Data Table 2 by writing the amino acid for each trait from Data Table 1 into the appropriate box and matching the amino acid to the trait description. 9) Once all trait descriptions are written, draw a quick sketch of what each trait will look like in your finished critter. 10) Carefully Draw and color a detailed image of your newly created critter on a separate sheet of paper, making sure to include all 18 of the traits in your drawing. Codon Table *In a real codon table, the codons UAA, UAG, and UGA are considered stop codons where translation would end. For this activity, they are replaced with two imaginary amino acids fakeinine and pretendisine, and translation should continue. 54

55 Green (G) = Guanine (G) Yellow (Y) = Adenine (A) White (W) = Uracil (U) Blue (B) = Cytosine (C ) Red (R) (on face with Yellow, Orange or Blue center) = Guanine (G) Red (R) (on face with White, Green, or Red center) = Adenine (A) Orange (O) (on face with Yellow, Orange or Blue center) = Uracil (U) Orange (O) (on face with White, Green, or Red center) = Cytosine (C ) 55 Data Table 1 Face Row EXAMPLE Base 1 Base 2 Base 3 Amino Acid Color = Base Color = Base Color = Base G = G Y = A W = U Aspartic Acid Yellow Orange Trait 1 = = = Trait 2 = = = Trait 3 = = = Trait 1 = = = Trait 2 = = = Trait 3 = = = Trait 1 = = = Blue Trait 2 = = = Trait 3 = = = White Green Trait 1 = = = Trait 2 = = = Trait 3 = = = Trait 1 = = = Trait 2 = = = Trait 3 = = = Trait 1 = = = Red Trait 2 = = = Trait 3 = = =

56 Data Table 2. Face Row Amino Acid Description Y E L L O W O R A N G E B L U E W H I T E G R E E N R E D Trait 1- General Appearance Trait 2- Body Size Trait 3- Body Type Trait 1- Base Color Trait 2- Pattern Color Trait 3- Pattern Trait 1- Leg Length Trait 2- Tail Type Trait 3- Foot Type Trait 1- Muzzle Trait 2- Ears Trait 3- Eye Color Trait 1- Wings Trait 2- Fire Color Trait 3- Horns Trait 1- Biome Trait 2- Time of Activity Trait 3- Egg Type 56

57 Trait 1: Coverings YELLOW Face = Appearance Fur Feathers Scales Smooth Asparagine Glutamine Histidine Leucine Lysine Phenylalanine Tyrosine Methionine Proline Serine Tryptophan Valine Aspartic Acid Cysteine Fakeinine Glutamic Acid Isoleucine Threonine Alanine Arginine Glycine Pretendisine Trait 2: Body Size Dog-Sized Horse-Sized Bear-Sized Elephant-Sized Arginine Aspartic Acid Cysteine Fakeinine Glutamic Acid Lysine Methionine Alanine Pretendisine Serine Threonine Asparagine Leucine Proline Tryptophan Valine Glutamine Glycine Histidine Isoleucine Phenylalanine Tyrosine Trait 3: Body Type Skinny Medium Large Chunky Asparagine Aspartic Acid Glutamine Histidine Leucine Lysine Pretendisine Arginine Proline Tryptophan Valine Glutamic Acid Glycine Methionine Serine Threonine Alanine Cysteine Fakeinine Isoleucine Phenylalanine Tyrosine 57

58 Trait 1: Base Color ORANGE Face = Colorations White Black Brown Orange Yellow Isoleucine Phenylalanine Tryptophan Valine Cysteine Fakeinine Methionine Tyrosine Alanine Glutamic Acid Lysine Glutamine Pretendisine Serine Blue Green Purple Red Arginine Asparagine Glycine Proline Aspartic Acid Threonine Histidine Leucine Trait 2: Pattern Color White Black Brown Orange Yellow Isoleucine Phenylalanine Tryptophan Valine Cysteine Fakeinine Methionine Tyrosine Alanine Glutamic Acid Lysine Glutamine Pretendisine Serine Blue Green Purple Red Arginine Asparagine Glycine Proline Aspartic Acid Threonine Histidine Leucine Trait 3: Pattern Stripes Dots Rings Blotches Hearts Arginine Fakeinine Glutamic Acid Phenylalanine Aspartic Acid Cysteine Histidine Serine Tyrosine Asparagine Glutamine Leucine Lysine Methionine Tryptophan Glycine Isoleucine Pretendisine Valine Alanine Proline Threonine 58

59 WHITE Face = Head Structure Trait 1: Muzzle Short Long Short Beak Long Beak Curved Beak Arginine Fakeinine Glutamic Acid Phenylalanine Aspartic Acid Cysteine Histidine Serine Tyrosine Asparagine Glutamine Leucine Lysine Methionine Tryptophan Glycine Isoleucine Pretendisine Valine Alanine Proline Threonine Trait 2: Ears Short Pointed Long Pointed Short Floppy Long Floppy Dumbo Isoleucine Pretendisine Proline Threonine Glutamic Acid Histidine Leucine Lysine Tryptophan Alanine Fakeinine Glycine Valine Asparagine Aspartic Acid Cysteine Serine Arginine Glutamine Methionine Phenylalanine Tyrosine Trait 3: Eye Color Blue Green Black Red Arginine Aspartic Acid Cysteine Fakeinine Glutamine Phenylalanine Glycine Pretendisine Proline Serine Tryptophan Alanine Glutamic Acid Leucine Methionine Threonine Asparagine Histidine Isoleucine Lysine Tyrosine Valine 59

60 Trait 1: Leg Length BLUE Face = Extremities Very Short Short Medium Long Very Long Alanine Glycine Threonine Glutamine Histidine Leucine Pretendisine Tryptophan Tyrosine Cysteine Fakeinine Phenylalanine Serine Arginine Asparagine Aspartic Acid Glutamic Acid Lysine Isoleucine Methionine Proline Valine Trait 2: Tail Type None Nub Medium Long Two Tails Fakeinine Glutamic Acid Histidine Lysine Methionine Valine Leucine Phenylalanine Threonine Tyrosine Alanine Cysteine Serine Arginine Glutamine Glycine Pretendisine Asparagine Aspartic Acid Isoleucine Proline Tryptophan Trait 3: Foot Type Hoof 3-Toed No Claws Short Claws Long Claws Arginine Asparagine Glutamic Acid Phenylalanine Pretendisine Histidine Lysine Serine Tyrosine Glycine Proline Valine Alanine Isoleucine Methionine Threonine Tryptophan Aspartic Acid Cysteine Fakeinine Glutamine Leucine 60

61 Trait 1: Wings GREEN Face = Fantastic Add-Ons None Bird Insect Dragon Fairy Isoleucine Pretendisine Proline Threonine Glutamic Acid Histidine Leucine Lysine Tryptophan Alanine Fakeinine Glycine Valine Asparagine Aspartic Acid Cysteine Serine Arginine Glutamine Methionine Phenylalanine Tyrosine Trait 2: Fire Color Red Orange Yellow White Blue Green Glycine Lysine Serine Fakeinine Histidine Phenylalanine Threonine Cysteine Glutamic Acid Proline Tyrosine Leucine Tryptophan Valine Arginine Isoleucine Methionine Pretendisine Alanine Asparagine Aspartic Acid Glutamine Trait 3: Horns Antlers Small Pointy Big Pointy Curly None Arginine Fakeinine Glutamic Acid Phenylalanine Aspartic Acid Cysteine Histidine Serine Tyrosine Asparagine Glutamine Leucine Lysine Methionine Tryptophan Glycine Isoleucine Pretendisine Valine Alanine Proline Threonine 61

62 Trait 1: Biome RED Face = Environment Desert Forest Plains Arctic Arginine Glutamic Acid Histidine Lysine Phenylalanine Tyrosine Fakeinine Glycine Leucine Tryptophan Valine Alanine Methionine Pretendisine Proline Serine Asparagine Aspartic Acid Cysteine Glutamine Isoleucine Threonine Trait 2: Time of Activity Day (Diurnal) Night (Nocturnal) Dusk/Dawn (Crepuscular) Leucine Threonine Valine Fakenine Lysine Tyrosine Pretendisine Tryptophan Serine Glycine Proline Cysteine Glutamic Acid Glutamine Histidine Arginine Alanine Isoleucine Aspartic Acid Asparagine Phenylalanine Methionine Trait 3: Egg Type Blue Speckled Red Speckled Striped Solid White Solid Brown Alanine Glycine Threonine Glutamine Histidine Leucine Pretendisine Tryptophan Tyrosine Cysteine Fakeinine Phenylalanine Serine Arginine Asparagine Aspartic Acid Glutamic Acid Lysine Isoleucine Methionine Proline Valine 62