ANCIENT GAMES & PUZZLES AROUND THE WORLDlghttp.60951.nexcesscdn.net/80487FB/Downloads/... ·...

ANCIENT GAMES & PUZZLES AROUND THE WORLD

LESSON PLAN 3-6GAME CARDS 7WORLD MAP 8

ENGINEERING & CONSTRUCTION: BUILD A RUBIK’S CUBE (2X2)

LESSON PLAN 9-13CUBE TEMPLATE 14

FIBONACCI’S PERFECT SPIRAL

LESSON PLAN 15-19EXAMPLES 20-22

GAME VARIATIONS: ULTIMATE TIC TAC TOE

LESSON PLAN 23-25ULTIMATE TIC TAC TOE GAME BOARD 26ENGINEERING DESIGN PROCESS 27

MIXED UP MATH

LESSON PLAN 28-30

PIXEL ART: DESIGN A RUBIK’S CUBE MOSAIC

LESSON PLAN 31-34MOSAIC TEMPLATES FOR 3X3 CUBES 35-37

RATIO & REASONING: EXAMINING 2X2 AND 3X3 RUBIK’S CUBES

LESSON PLAN 38-41STUDENT PAGES 42-44SAMPLE MOSAIC TEMPLATES 45-46MOSAIC TEMPLATE FOR 2X2 CUBES 47

CODON CRITTERS

LESSON PLAN 48-51STUDENT PAGES 52-62

Ancient Games & Puzzles Around the World

In this lesson, students will examine the history of certain games, including the Rubik’s Cube.

Common CoreStandards:

Objectives:

Materials:

CCSS.RST.6-8.7 Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts.

CCSS.WHST.6-8.7 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.6-8.8 Gather relevant information from multiple print and digital sources, using search terms effectively; assess the 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.

Students will gain a cross-cultural understanding of the history of gaming.

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

Middle School

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. Canhave 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 tomatch the dates with the games the country oforigin, and arrange the dates in a timeline order.

2. You can give clues as the students are matchingthe dates-countries-games, or let students knowwhich ones they have correct when they ask youto check their work. As a clue, you may considershowing pictures of the lesson common games tostudents. Historical photos may give cluesregarding the country of origin and timeline.

3. After you reveal the correct dates and countries,students can create a timeline of the games andtheir origins and identify their origins on the worldmap.

4. As time allows, students may play as many of thegames mentioned in the matching game as youhave 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 canresearch to develop a timeline specific to onegame, write a summary, or prepare a presentationfor classmates.

2. Make resources available to students to use forresearch purposes or review the materials

Procedure:

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together as a class. Potential sources of information for the Rubik’s Cube include:

a. History of the Rubik’s Cube (article fromRubiks.com):https://www.rubiks.com/about/the-history-of-the-rubiks-cube

b. Stuff of Genius, Erno Rubik (video fromHowStuffWorks):http://www.geniusstuff.com/videos/40367-the-stuff-of-genius-rubiks-cube-video.htm

c. Rubik’s Cube Inventor, Mysteries at theMuseum (video from Travel Channel):http://www.travelchannel.com/videos/rubiks-cube-inventor-0235646

3. Students can develop a timeline specific to eventsin the history of the Rubik’s Cube or researchedgame of their choosing.

Technology Connection:

Optional Follow Up / Extend the Lesson:

Many of the games have online versions that can be played online:

Senet - https://www.mindgames.com/game/SenetUr - https://www.yourturnmyturn.com/java/ur/index.phpMah Jong - https://www.mahjonggames.com/Backgammon - https://www.classicgame.com/game/BackgammonCheckers - https://www.classicgame.com/game/Checkers

Examine the maps in which students marked the games from the matching activity.

Ask: What continents did we not identify gamesfrom? (South America, Australia, Antarctica)

Research to find games popular in countries thatare part of these continents. (Exception- youprobably 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

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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 1869 - United States - Parcheesi 1933 - 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: https://en.wikipedia.org/wiki/History_of_games http://www.checkershistory.com/ http://www.domino-games.com/domino-history.html http://www.tradgames.org.uk/games/Mah-Jong.htm http://www.sweetoothdesign.com/games-mancala http://www.playchinesecheckers.com/CCHistory.html http://originalpeople.org/senet-and-the-history-of-chess/

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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

Ancient Games & Puzzles Around the WorldGame Cards

Make copies and cut apart cards for each student or group of students.

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8

Engineering & Construction: Build a Rubik’s Cube (2x2)

In this lesson, students will build a functional 2x2 Rubik’s Cube out of paper.

Common Core Standards:

Next Generation Science 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 counting unit cubes, using cubic cm, cubic in, cubic ft, and 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 Practice 5 Use appropriate tools strategically.

RST.6-8.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

MS-ETS1-1 Define 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.

Middle School

Objectives:

Materials:

Background Knowledge:

Procedure:

MS-ETS1-2 Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.

Students will plan, measure, and follow directions to build a 2x2 model of a Rubik’s Cube.

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

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.

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.

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2. Define the main branches of engineering:electrical, mechanical, chemical, and civil. Workwith the class to come up with examples of thingseach type of engineer might build.

3. Students can learn about accidental inventionsthrough the short stories in the book, MistakesThat Worked, by Charlotte Hone, et.al. Share afew 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 anddifferences between the 3x3 and 2x2 Rubik’sCube? Why are they called “3x3” (three-by-three)and “2x2” (two-by-two)?

2. Determine the perimeter and area of each faceand the surface area and volume of the 2x2 cubewith students.

3. Identify the shapes and angles that make up thecube.

4. Define net in mathematics. (a two-dimensionalfigure that can be folded into a three-dimensionalobject)

5. Work through the interactive problems on theIlluminations website where students will identifywhich 2D nets can be folded into cubes.https://illuminations.nctm.org/activity.aspx?id=3544

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 bemaking.

2. Students will measure and cut 4 squares 1.25inches on each side of each color.

3. Glue colored squares onto the appropriate spacesfor each corner piece. You may want to show

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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 l inesto create 8 cubes. *Students could also createtheir own cube nets, but the template will helpexpedite the activity

5. Students can use glue sticks or tape on the tabs tocreate the cubes. Covering the cubes i n clearpacking tape will help make the pieces moredurable.

6. Attach strings (with clear packing tape) diagonallyon pairs of cubes i n the upper and l ower l ayers ofthe cube. *See photo

7. Twist the cube to‘tangle’ the strings creating a working2x2 Rubik’s Cubemodel!

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Online resources for learning to solve the 2x2 Rubik’s Cube: https://www.youcandothecube.com/solveit/2x2solution

Activity where students determine which nets will create cubes: https://illuminations.nctm.org/activity.aspx?id=3544

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:https://www.youtube.com/watch?v=6qktujAMcV8&t=2s

Cube made from single piece of paper, moredifficult fold:https://www.youtube.com/watch?v=cDvHp_hg25Q&t=10s=

Optional Follow Up / Extend the Lesson

Notes to Teacher:

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.

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. www.youcandothecube.com/lendinglibrary

This lesson is an adaptation of Engineering & Construction: Solving RealWorld Problems , developed by STEM.org for You CAN Do the Rubik’s Cube.

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14

Fibonacci's Perfect Spiral

This l esson was created to combine math history, math, critical thinking, and art. Students will l earn about Fibonacci, the code he created, and how the Fibonacci sequence relates to real l ife and the perfect spiral. Students will practice drawing perfect spirals and l earn how patterns are a mathematical concept that surrounds us i n real l ife.

This l esson i s designed to take 3 to 4 class periods of 45 minutes each, depending on the students’ focus and depth of detail i n the assignments.


CCSS.MATH.CONTENT.HSF.IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain i s a subset of the i ntegers. For example, the Fibonacci sequence i s defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n1) for n ≥ 1.

CCSS.MATH.CONTENT.7.EE.B.4 Use variables to represent quantities i n a realworld 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, i ncluding computing actual l engths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Middle School

Objectives:

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 twodimensional figure i s congruent to another i f 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 twodimensional figures using coordinates.

Students will review the Fibonacci sequence learn how to draw a perfect spiral use art to l earn about math and how i t relates to

real l ife have fun l earning math

Materials:


Samples pictures of perfect spirals i n nature Sample of a perfect spiral on paper (included i n l esson) Grid Paper (about 0.75” squares) Color pencils (blue, orange, red, green and yellow)

Knowledge of Fibonacci, good but not required

How to solve one face of a Rubik’s Cube (edges and corners)

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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 lifein the form of what is known as the “perfect spiral.”

3) Show examples of real life perfect spirals, pointingout the sequence in each.

4) Explain the steps for drawing a perfect spiral bydemonstrating on the dry erase board

1. In the center of the graph paper outline a singlesquare. See purple square on perfect spiralexample sheet (included)

2. Go to the square to the right of the 1. Outline thatlittle square to represent the next number in thepattern, another 1! (outlined in light blue)

3. Use the line above the two 1 squares to outline asquare that is 2 little squares long and 2 littlesquares high. This represents the next number inthe sequence – 2. (Outlined in brown)

4. Now move to the right of the 1 and 2 squares. Usethe right side of the 2 square and the right side ofthe second 1 square to draw a square that is 3little squares high and 3 little squares long. 3 is thenext number in Fibonacci’s pattern. (Outlined inlight purple)

5. Use the bottom of both 1 squares and the bottom

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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, andthe 5 square. Use their left edges to make the 8square. (Outlined in green)

7. Continue this way until you run out of room orhave enough spirals to work with.

5) The next step is to draw Fibonacci's spiral. All youhave to do is connect one corner of each square withthe opposite corner of that square with a sweepingcurve. You may need to practice a few times to get itright. 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 beerased or used to create an abstract piece of art.

7) Show examples of what can be drawn out of theperfect spiral and have students create a picture withtheir spiral that can be pixelated using the colors of theRubik’s Cube.

8) Once the picture is complete have the studentscreate their masterpiece using Rubik’s Cubes.


Notes to Teacher:

Information about perfect spirals and spirals in nature can be found at https://www.goldennumber.net/spirals/

The more examples you have, the better idea it gives the students.

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For students that need a challenge, have them draw a double spiral or create a pattern using multiple spirals (have examples available).

Drawing a l arge example on the board i s 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. www.youcandothecube.com/lendinglibrary

This l esson was written by Kim Hyde.

Use this as an example to follow.

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Example of a double spiral abstract

20

Perfect Spiral Example page:

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Examples of Rubik’s Cube mosaics of perfect spirals:

22

In this lesson, students will experience the engineering process when creating modifications to a familiar game.

Next Generation Science Standards

Materials:


Procedure:

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.

Copies of Ultimate Tic Tac Toe game boards, or blank white paper Pens/ Pencils Computer w/ Internet connection & projector 3x3 Rubik’s Cubes

Students should know how to play the traditional tic tac toe. If not, they can certainly be taught very quickly.

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.

Game Variations: Ultimate Tic Tac Toe

Middle School

Part 1 Learn a New Game 1. Teach Ultimate Tic Tac Toe to students.

a. Project game board for Ultimate Tic Tac Toefrom website onto white board(ultimatetictactoe.creativitygames.net) ordraw a few tic tac toe grids on chart paper

b. Challenge a few students (one at a time) totraditional tic tac toe.

c. Explain that i f both players are payingattention and reasonably i ntelligent mostgames will end i n a draw/ tie.

d. Challenge the computer player to UltimateTic Tac Toe and have students observe.Talk through some of your moves,discussing the strategy of why you would orwould not choose certain squares.

2. Pair students up and have them challenge eachother. If you have an odd number of students, theteacher can play against them, or l et them playagainst the computer. They can draw the grids onblank paper or you can make copies of thesupplied game board.

Part 2 Analyze Traditional / New Game 1. Discuss:

a. How does the new version “ultimate tic tactoe” 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 tictac 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.

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3. Discuss as a class some of the problemsencountered when using Rubik’s Cubes to play tictac toe. (Example: How to make a move without“undoing” your opponent’s move, or maybe this isa strategy and part of the game.)

4. Discuss how could these problems could besolved, and how some students may have takenthese issues into account in their own gameversions.

5. Allow students to share their various modificationsfor the game.

6. Send students ‘back to the drawing board’ tomake adjustments to their game and try out theirrevised versions with a partner or small group.


Notes to Teacher:

Ultimate Tic Tac Toe can be played online here: http://ultimatetictactoe.creativitygames.net/ This site could be used when demonstrating how to play the game, or the students can challenge the computer or play 2 players online.


Ultimate Tic Tac Toe rules/ description can be found online here: https://mathwithbaddrawings.com/2013/06/16/ultimatetictactoe/ or search “ultimate tic tac toe” online for many variations.

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Ultimate Tic Tac Toe

Image is screenshot from http://ultimatetictactoe.creativitygames.net/

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http://ultimatetictactoe.creativitygames.net/

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.

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Mixed Up Math

This l esson can be adapted for younger students to practice other computational math concepts. In addition to the content math standards, students will strengthen l ogical thinking skills and time management.


Objectives:

Materials:


Procedure:

CCSS.MATH.CONTENT.6.NS.B.3 Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm f or each operation.

CCSS.Math Practice 6 Attend t o precision.

Students will practice adding, subtracting, and multiplying multidigit numbers with decimals.

3x3 Rubik’s Cubes Pencils & paper f or math calculations

Students should already know t he procedures and rules for adding, subtracting, or multiplying multidigit numbers with decimals.

With students: 1. Assign a numerical value to each color on the Rubik’s

Cube. For the first activity, these will be single digitnumerals. (Example: Yellow = 1, Red = 3, Blue = 5,Green = 7, Orange = 9, and White =0) Record these assignments on the board where studentscan reference them, and where they can be changed i fdesired.

2. Explain that the center tile on each face will be used to identify the face (“green face” means the face with the greentile i n the center) and will also be the decimal point i n thenumber.

3. Show students how to ‘ read’ the face of the cube, by startingat the top row, reading from l eft to right (see example).

Middle School

4. Create problems for the students and challengethem to be the student with the l argest (orsmallest) answer.

5. Students can also be challenged to create thel argest (or smallest) answer by being allowed a few seconds to manipulate (twist) the cube after the problem i s announced.


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: https://www.grubiks.com/puzzles/rubiks/cube3x3x3/ Or https://www.google.com/logos/2014/rubiks/iframe/index.html

Variations Depending on the ability l evels of your students,you can choose the operations to be used, thevalue of the colors, and the number of tiles to beincluded.

You can use single digit numbers and practiceproblem solving across j ust one row of the cube.Start with + + and j ust one row of the cube,increase to + x, and then beyond. You could alsofocus on the four corners and use all fouroperations. Recommended order i s + x

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Require that all students make at least three twiststo their cube before announcing the nextsequence. Allow students to make twists to createthe best scenario (largest sum/product), or just tosearch the six sides to find their best outcome.

Notes to Teacher:


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Pixel Art: Design a Rubik's Cube Mosaic

Designing a Rubik’s Cube mosaic involves creativity, collaboration, pattern recognition, and computer skills.


Next Generation Science Standards

CCSS.Math Practice 1 Make sense of problems and persevere in solving them.

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).

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.

All grades

Objectives:

Materials:


Procedure:

Students will design their own pixelated picture or pattern and then replicate i t using Rubik’s Cubes.

3x3 Rubik’s Cubes Colored Pencils Graph paper or use i ncluded student page(s)

Mosaics can also be made with the help of online programs, i n which case you will also need: Computers with Internet access Color printer

It i s helpful i f students know how to solve one face of the Rubik’s Cube (manipulate edges and corners), but students can also l earn that skill while working on this lesson.

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 athttp://tinyurl.com/ycy5unnh for yourself. If studentshave their own Google drives, share a ‘ view only’copy with them before they do part 2 of thislesson.

Watch the video at https://youtu.be/ENLdthKtsJc forinstructions on part 2 of this l esson (using GoogleSheets 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 ontothe template sheet, or grid paper, using one colorper box.

2. After templates are designed, students can use 9,16, or 25 Rubik’s Cubes to create their mosaic.

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Part 2: Design a template using Google Sheets . Instructions for this part of the lesson can also be found in this video: https://youtu.be/ENLdthKtsJc

1. Make a copy of the Google Sheets file found athttp://tinyurl.com/ycy5unnh (The file has “ViewOnly” restrictions, so you need to make a copybefore you will be able to edit it.)

2. After sharing a “View Only” version of the file withyour students, have them save a personal copy ofthe file. (Or send them to the original file to maketheir own copies.)

3. Students will use the “Fill Color” tool to color thepixels in the template grids to make their ownimages and designs.

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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:

Notes to Teacher:

Students can also examine how adding more cubes / more pixels to their design affects the area of the mosaic.

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. www.youcandothecube.com/lendinglibrary

Teachers and youth leaders can borrow Mosaic Builder Sets sets of 50600 Rubik’s Cubes from You CAN Do the Rubik’s Cube at no cost other than return shipping. https://www.youcandothecube.com/mosaics/borrowaset/

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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.

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36



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In this lesson, students will compare the 2x2 and 3x3 Rubik’s Cube and examine the ratio between the cubes.


Objectives:

Materials:


CCSS.MATH.CONTENT.6.RPA.3 Use ratio and rate reasoning to solve real-world and mathematical 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.

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.

Ratio & Reasoning: Examining the 2x2 & 3x3 Rubik's Cubes

Middle School

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 foreach student.

Part 1- Comparing Cubes 1. Using the student page as guide, have students

use rulers to measure different aspects of the 2x2and 3x3 Rubik’s Cubes.

2. Students will also list the ratio between the cubesfor each aspect. Discuss with your class how youwould like the ratio written. What format wouldbest represent the data?

3. Have students analyze the ratios of the differentcube 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 classto view, and also hand out copies of the mosaicfor each student.)

2. Examine how the mosaic is set-up. 36 cubes, 6rows of 6 cubes.

3. ASK: If you wanted to create this mosaic, but had2x2 cubes instead of 3x3 cubes, how many cubeswould you need? (Allow students to wrestle withthis question. You may also want them to explaintheir 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 theiranswer. Is there a formula that can be used?(Students may count the cubes by sectioning the

39

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 https://www.youcandothecube.com/mosaics/mosaic-templates/ .Examine how the number of cubes needed for each mosaic compares as a ratio.

a. The 100 cube mosaics are made with 10 rows of10 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 of15 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 of20 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 the3x3 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

3. Have students resize the pattern and color in thetemplate for 36 2x2 cubes.


Optional Follow Up / Extend the Lesson

Notes to Teacher:

Students can modify and use the Google Sheets program used for the previous lesson for redrawing the 2x2 mosaics.

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)

2x2 and 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. www.youcandothecube.com/lending-library

41

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 (cm2)

Surface area of cube (cm2)

Volume of cube (cm3)

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

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

_______________________________________________________

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?

_______________________________________________________

5. Using your data from Part 1, what size frame would you need for a

mosaic with 36 3x3 Rubik’s Cubes?

44

Mosaic Template for 3x3 Rubik’s Cubes

45

Mosaic Template for 3x3 Rubik’s Cubes

46

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

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.


Next Generation Science Standards:

RST.6-8.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

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.

Codon CrittersMiddle/High School

Materials:


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.

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

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 asingle gene can influence more than one trait.

The characteristics of an organism can bedescribed in terms of a combination of traits.

Although different species might look dissimilar,the unity among organisms becomes apparentfrom an analysis of internal structures and thesimilarity of their chemical processes.

Vocabulary: adenine DNA

guanine

transcription

translation

thymine

amino acid

codon

cytosine traits

49

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 sideshows 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. Whenreferring to the “yellow face.” this means theface of the cube with a yellow center tile.

b. The diagram at the bottom of the handoutshows a way to look at the cube soeveryone is using the same row for thesame trait. It’s not absolutely necessary thateveryone does this, but it helps illustratethat even when reading everything thesame way, odds are you’re going to havedifferent traits.

3. Distribute Cube Critters handouts to students.Read through instructions together.

4. Give each student (if working individually) orgroup a Rubik’s Cube. The cubes can be alreadyscrambled, or if the start with solved cubes,instruct the students to mix up the cube byperforming at least 10 random turns.

5. Be available to help students as they workthrough the activity.

Technology Connection

Students can practice transcription and translation with this online activity: http://learn.genetics.utah.edu/content/basics/transcribe/

50

Optional follow-up/ Extend the lesson

Notes to Teacher:

A teacher’s answer key is available for download at https://www.youcandothecube.com/downloads/ The file is called Codon Cube Critters Checker.xls and a how to use video is online: https://youtu.be/TL6WYIOsOM8

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.

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. www.youcandothecube.com/lending-library

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

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

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

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 thecube and the base in the area provided.)

4) For each set of three bases, find the corresponding amino acid on the CodonTable.

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 andmatching the amino acid to the trait description.

9) Once all trait descriptions are written, draw a quick sketch of what each trait willlook like in your finished critter.

10) Carefully Draw and color a detailed image of your newly created critter on aseparate sheet of paper, making sure to include all 18 of the traits in yourdrawing.

Codon Table

*In a real codon table, the codons UAA, UAG, and UGA are considered “stop” codons where translationwould end. For this activity, they are replaced with two imaginary amino acids fakeinine and pretendisine,and translation should continue.

54

Colo

r =

Base

Colo

r =

Base

Colo

r =

Base

G=

GY

=A

W=

UA

sp

artic

Acid

Tra

it 1=

==

Tra

it 2=

==

Tra

it 3=

==

Tra

it 1=

==

Tra

it 2=

==

Tra

it 3=

==

Tra

it 1=

==

Tra

it 2=

==

Tra

it 3=

==

Tra

it 1=

==

Tra

it 2=

==

Tra

it 3=

==

Tra

it 1=

==

Tra

it 2=

==

Tra

it 3=

==

Tra

it 1=

==

Tra

it 2=

==

Tra

it 3=

==

Data

Tab

le 1

Gre

en (G

) = G

uanin

e (G

) Yello

w (Y

) = A

denin

e (A

) W

hite

(W) =

Ura

cil (U

) Blu

e (B

) = C

yto

sin

e (C

)

Red (R

) (on fa

ce w

ith Y

ello

w, O

range o

r Blu

e c

ente

r) = G

uanin

e (G

) Red (R

) (on fa

ce w

ith W

hite

, Gre

en, o

r Red c

ente

r) = A

denin

e (A

)

Ora

nge (O

) (on fa

ce w

ith Y

ello

w, O

range o

r Blu

e c

ente

r) = U

racil (U

) Ora

nge (O

) (on fa

ce w

ith W

hite

, Gre

en, o

r Red c

ente

r) = C

yto

sin

e (C

)

Base 1

Base 2

Base 3

Row

EX

AM

PLE

Am

ino A

cid

YellowOrangeBlueWhiteGreenRed

Face

55

55

Data Table 2.

Face Row Amino Acid Description

Y E L L O W

Trait 1- General Appearance

Trait 2- Body Size

Trait 3- Body Type

O R A N G E

Trait 1- Base Color

Trait 2- Pattern Color

Trait 3- Pattern

B L U E

Trait 1- Leg Length

Trait 2- Tail Type

Trait 3- Foot Type

W H I T E

Trait 1- Muzzle

Trait 2- Ears

Trait 3- Eye Color

G R E E N

Trait 1- Wings

Trait 2- Fire Color

Trait 3- Horns

R E D

Trait 1- Biome

Trait 2- Time of Activity

Trait 3- Egg Type

56

YELLOW Face = Appearance

Trait 1: Coverings

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

ORANGE Face = Colorations

Trait 1: Base 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 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

WHITE Face = Head Structure

Trait 1: Muzzle

Short Long Short Beak

Long Beak

Curved Beak

Arginine Fakeinine Glutamic Acid Phenylalanine





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

BLUE Face = Extremities

Trait 1: Leg Length 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

GREEN Face = Fantastic Add-Ons

Trait 1: Wings 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





61

RED Face = Environment

Trait 1: Biome 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

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