2x2x2 lesson plan with a surprisingly easy solution

Background

  • I’m running a math club for my daughter’s class (Grade 1).
  • Next spring I’m going to introduce Rubik’s cubes (2x2x2)
  • I’m not an expert cuber.

My objective

  • Create a very simple introduction to cubing with 2x2x2 cubes.
  • Without algorithms.
  • Without notation.
  • Emphasis
    • common sense and observation
    • patterns
      • Surface
        • 1/2 SURFACE SOLVED
        • SURFACE SOLVED
      • Layer
        • 1/2 SOLVED LAYER
        • 3/4 SOLVED LAYER
        • LAYER SOLVED
        • 2 CROSSING LAYERS SOLVED
      • Cube
        • 1/2 CUBE SOLVED = LAYER SOLVED
        • CUBE SOLVED
      • Patterns that you need to detect
        • READY TO MOVE UP
        • MUST MOVE DOWN
        • SQUARE HIDING ON THE BOTTOM
        • 3/4 SOLVED LAYER + READY TO MOVE UP
        • READY FOR SIMPLE SOLUTION
          • LAYER SOLVED
          • HALF SOLVED LAYER
          • HALF SOLVED SURFACE
          • unsolved layer looks like this
            • Solved cube > B’R’BR and BLB’L
            • 3 of half-surfaces are pairs of same color
            • opposite side of the solved surface
              • correct color: 1/2 SOLVED LAYER
              • wrong color: 1/2 SOLVED SURFACE
    • only three simple twists
      • MOVE UP: you can move square up to top surface
      • MOVE DOWN: you have to move square down from top surface
      • GET THE HIDING SQUARE FROM THE BOTTOM
      • SIMPLE SOLUTION
        • MOVE UP (left)
        • MOVE UP (right)

Supporting printout for learners

  • color
  • black and white (let the kids color the squares)
  • colored squares
    • opposite colors
      • white | yellow
    • can be used as a reminder
      • when you choose the color you want to work on then put an eraser on the square of that color
  • maybe questions

Lesson plan

1. Get familiar with 2x2x2 cubes

  • How many colors?
    • one color = one surface
  • How many surfaces?
  • How many small squares each color / surface has?
  • How many corners there are in the cube?
  • How many smaller cubes make the cube?
  • How many colors each smaller cube has?
  • When you twist : you twist one layer
    • top/bottom
    • left/right
  • What’s the difference between a surface and layer?
  • When the cube is solved?
    • every surface has squares of one color only
      • note: can happen: one surface can be solved, but neighbour surfaces are not solved
    • all small cubes are in correct places
      • note: can happen: in a-not-solved-cube the small cubes can be in wrong places
    • all small cubes are in correct positions
      • note: can happen: note: in a-not-solved-cube the small cubes can be in correct place but the small cube can be in wrong position
  • In how many different ways the cube can be twisted?

2. Holding the cube

  • Put the cube on the table.
  • Take the cube
    • both hands
    • thumbs in front
    • index and middle fingers in the back

3. Twisting the cube

  • Twist only the layer you want to twist.
  • Cube stays in one place.
    • Other hand keeps the cube
    • Other hand makes the move
  • Cubing is not like wrestling or yoga
    • just stand/sit straight
    • let your fingers do the work

3. Let’s make one surface

  • one surface all squares are of same one color
  • select your color (YELLOW)
  • find one square of your color
  • turn the cube so that the square of your color you just found is on the top
  • keep the cube in this position (your chosen color will be built on top surface)
  • in the bottom layer: find another square of your color on the outside
    • keep the cube straight, just turn the bottom layer (no wrestling!)
  • FOUND IT?
    • get ready for lifting your color from bottom layer to the top surface
      • on top surface: some other color near you (to be replaced)
      • right below it: bottom layer outside surface = square of your color that you want to move up
    • twist the bottom layer to the other side
      • if your square on the right side then take it to safe place by twisting the bottom layer to the left
    • twist down the side of the wrong color
    • twist the bottom back to it’s original place (your square replaces the wrong square)
    • twist up the the side (your square goes to correct place on top surface)
  • DIDN’T FIND IT?:
    • just find another square of your chosen color and turn the cube so that it is on top
    • look again
  • if there is no your color on the outside of the bottom layer
    • if there is a square in top layer that  has your color in wrong place or in wrong position, then you can ’take it down’ using the same twists as above
      • why? because when you lift a suare up then the replaced square will go down (obvious: you cant’t have 2 small cubes in the same place.

4. Let’s make one layer = half cube

  • one layer of a 2x2x2 square is half of the square
  • one surface solved so that the squares below on each of the surfaces are of the same color

5.  Let’s keep on practicing

  • so you have one layer solved
  • observe
    • check the opposite side of the solved surface
    • can you see any squares of correct color?
      • if yes, then move it to correct place and position
      • can you see 3/4 SOLVED LAYERS?
      • can you immediately solve one 3/4 SOLVED LAYER it with MOVE UP?
        • if yes, just do it
        • if no, use other moves
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