Lesson Focus & Standards p Review Prior Stages... p. 3. Lesson Content p Review.. p. 9. Math Connection. p. 9. Vocabulary... p.

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2 Contents: Lesson Focus & Standards p. 1-2 Review Prior Stages... p. 3 Lesson Content p. 4-8 Review.. p. 9 Math Connection. p. 9 Vocabulary... p. 10 Trivia. p. 10 Another Look at the White Cross. p. 11 Scrambling Practice.. p. 12 How well do you know the Cube?... p. 13 Turn Reference Card.... p. 14 0

3 Learning & Innovation Skills: Creativity and Innovation Critical Thinking and Problem Solving Communication and Collaboration 21st Century Learning Skills Life & Career Skills: Flexibility and Adaptability Initiative and Self Direction Social and Cross-Cultural Skills Productivity and Accountability Leadership and Responsibility Media Literacy: Information Literacy 1

4 CONTENT STANDARDS & SKILLS: LESSON 2 Grade Common Core NCTM K-2 K.G.1 Names of shapes 1.G.1 Defining attributes of shapes 1.OA.B.3 Apply properties of operations as strategies OA.B.5 Apply properties of operations as strategies 4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. 4.G.1 Identify angles, perpendicular and parallel lines in two-dimensional figures EE.A.3 Apply the properties of operations to generate equivalent expressions. 6.EE.A.4 Identify when two expressions are equivalent 7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. 8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations. Geometry describe attributes and parts of twoand three- dimensional shapes create mental images of geometric shapes recognize shapes from different perspectives relate ideas in geometry recognize geometric shapes in the environment Number and Operations Geometry identify attributes of two- and three- dimensional objects; develop vocabulary to describe the attributes describe objects and patterns recognize geometric ideas and apply them in the classroom and everyday life Geometry precisely describe two- and threedimensional objects using their attributes 2

5 The questions on these slides are meant to focus students on the characteristics of the Rubik s Cube. Depending on the grade level of your students, these questions may or may not be appropriate. Many of the slides are animated so what you see in this guide may not appear all at once in the presentation. Each lesson in this series begins with a review of the previous lesson and ends with a review of the current lesson. The review of the current lesson is always followed by a math extension which may or may not apply to your grade level. The last slide in each lesson is a trivia question. Please modify your presentation to best meet the needs of your students. Review: Slides 3-7 As you review the parts of the cube, emphasize the orientation (i.e. the FRONT face faces you) and how this differs from the color of the faces which is determined by the CENTER tile. The EDGE pieces will be the focus of the WHITE Cross so make sure students can readily identify those pieces. HINT: Have students place their flat palms on the face you want them to turn. This is a good strategy to use at any stage of solving the cube. HINT: Keeping the cube on the table or desk may help students attend to the orientation of the cube which is an important concept as they solve. 3

6 Lesson Content: Slides 8-24 In order to solve a Rubik s Cube, it must first be scrambled. A scramble is 25 random ¼ turns. Have the students look at the sequence. Notice that there are no adjacent moves that are opposites of one another. (Ri never follows R.) Have students explain why this is true. The difference between layers and faces can be confusing. The cake analogy may help. Layers of the cube are like layers of a cake. Faces on the cube are the frosting on the cake. In this lesson, talking about the layers is an intermediary step to getting the WHITE tiles on the UP face. This will probably make more sense in the next series of slides. 4

7 Slides In Part 1, you put all the EDGE pieces that have a WHITE tile on the TOP layer. Because we are talking about the layer, the WHITE tile of the on those EDGE pieces may not be on the UP face (as seen in the top left cube in the slide). At this point, that s OK. While there are many ways to accomplish the task of getting the EDGES with WHITE tiles on the TOP layer, there are fewer adjustments that need to be made if you go in order around the lateral faces. We begin with the BLUE face, then the ORANGE, then GREEN, and finally, RED. If your cube already matches the goal, you do not have to follow these steps. HINT: Have students pinch the WHITE/BLUE EDGE piece with 2 fingers (thumb and index finger) so they know they have an EDGE and not a CORNER. HINT: Have students put their flat palm on the face that has the WHITE/BLUE edge. Now turn that face until the WHITE/BLUE EDGE is on the BOTTOM layer. The last item of this slide is VERY important. If the WHITE tile of the EDGE piece is on the RIGHT face, the next slide will show how to flip the EDGE piece around so that the WHITE tile will be on the UP face. 5

8 Slides Part 2 will flip the EDGE piece if needed. If the WHITE tile fo the EDGE piece is next to the WHITE CENTER, you have accomplished the goal. You only need to flip the EDGE piece if the the WHITE tile of the EDGE piece is not on the UP face but on the RIGHT face. 6

9 Slides repeat the steps used to place the WHITE/BLUE EDGE piece. This time, the 0 entire cube is rotated 90 clockwise so that the FRONT face is BLUE. The RIGHT face is ORANGE. ** Read the NOTE below before you start the ORANGE face. ** ** NOTE: As you position an EDGE piece to the BOTTOM layer, make sure that the WHITE/BLUE EDGE piece remains in its correct position. Since the EDGE piece has 2 tiles, you ll have 2 choices for how to turn to place it on the BOTTOM layer. For example, Suppose your cube looks like this: Remember, the BLUE face is on the RIGHT. To place the WHITE/ORANGE Edge piece to the BOTTOM layer, you could turn the FRONT face clockwise. Now your cube looks like this: The WHITE/ORANGE EDGE is on the BOTTOM layer on the FRONT. Mission accomplished without moving the WHITE/BLUE EDGE! YES! But, you could have turned the RIGHT side counterclockwise and you would have had this: The WHITE/BLUE EDGE has been moved! Stay calm and cube on Make a DOWN turn in either direction to move the WHITE/ORANGE EDGE out of the way. Now, reverse the first move you made, RIGHT clockwise now, to return the WHITE/BLUE EDGE to its proper location. You ll need to think about this NOTE each time you place an EDGE piece on the BOTTOM layer. 7

10 Slides repeat these steps again but does not specify the color of the side. Modify as your students require. These slides may need to be repeated for the 4th side. 8

11 Review: Slides These slides could be printed as a reference for students, perhaps in a learning center. Math Connection: Slide 28 Any computational algorithm could be used here. 9

12 The slides on this page could be part of a class book, student journal, research project, or bulletin board. Vocabulary: Slides Trivia: Slide 31 Reading large numbers and rounding to a specific place are great math connections here, too. 10

13 Another look at the WHITE Cross As mentioned earlier in this guide, there are many ways to accomplish the task of getting the EDGES with WHITE tiles on the TOP layer. Here s another method, sometimes referred to as the daisy method. 1. Hold the cube with the YELLOW on the UP face. (That means the CENTER tile will be YELLOW.) 2. Look for EDGES that have a WHITE tile and place them on the UP face. The WHITE tiles on the EDGE pieces should go around the YELLOW CENTER to make a daisy. It doesn t matter whether or not the other color tile of the EDGE matches anything. When you are done, the UP face will look like this: 3. Now look at the RIGHT face of the cube. If the TOP EDGE piece color does not match the CENTER tile color, turn the UP face until it does. Then make 2 RIGHT face turns. (Does it matter if the turns are R or Ri?) a. Repeat these 2 steps for the other 3 faces. b. Match the TOP EDGE color with the CENTER using UP turns. c. Turn the face you matched twice so that the WHITE EDGE tile is on the BOTTOM layer. d. There will only be the CENTER of the daisy left. All the petals will be on the BOTTOM layer. 4. Turn the cube over so that WHITE is the UP face. You should have the WHITE Cross! NOTE: #3 and #4 are very similar to the algorithms described earlier in the guide. All of the algorithms presented earlier are an excellent introduction to analyzing how the smaller cubies move within the larger cube. Flipping an EDGE is an especially helpful skill to have and should be revisited. 11

14 SCRAMBLING PRACTICE Use the following sequences to practice scrambling your Rubik s Cube. Sequence A - Will everyone s Cube look the same after this scramble? Why or why not? Sequence B Sequence C - Record your own 25 turns to scramble a cube. Any 25 turns of a Rubik s Cube is called a scramble. The goal is to mix the cube up as much as possible. Some scrambles might be better than others. What would be a bad scramble? Why? 12

15 How well do you know the cube? Here s a Rubik s Cube with a completed WHITE CROSS. The gray tiles could be any of the Rubik s Cube colors. It doesn t matter for this activity. Color the cube below so that it shows what the hidden sides of the cube above look like. 13

16 QUARTER TURN REFERENCE SHEET 14

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