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 Post subject: Methods for teaching kids cubes
PostPosted: Sat Mar 26, 2011 5:46 am 
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Hello Friends,

I have decided to start this thread after a discussion with Rline. We both teach high school age students to do the cube. My intention is to make public some methods that I have been using to achieve this, for others to access, and to get feedback (because I always consider my methods a work in progress).

Better ideas on wording or clarity would be appreciated (for this reason I will include the whole methods, even the terminology page). I believe that the instructions will be better if they work without illustrations (even though I use diagrams). That way the illustrations `enhance` the instructions. So I will include only an example illustration. I can include more if people want, but later.

I will only include `non layer` methods so far, although I have taught a 5 year old and I used a layers method (because it does not involve as much analytical thinking). I would love to hear about the methods others use to teach young people, particularly early teens, and what is successful.
Acknowledgements= `Adam’s Rubiks Cube Solution` and `The Ultimate Solution to the Rubiks Cube`.

Thanks for your input,
Burgo.

General Cubing Terminology

F= Front face U= Upper face
R= Right face D= Down face
L= Left face B= Back face
y= turn the whole cube around without changing the U or D faces.
Reorientate the cube= turn the whole cube around without turning any faces.
E row= the horizontal layer in between the U face and the D face.
M row= the vertical layer in between the R face and the L face (M= turn it downwards M'= turn it upwards).
F= turn the front face 1 turn (90 degrees) clockwise.
F’= turn the front face 1 turn (90 degrees) anticlockwise.
F2= turn the front face 2 turns (180 degrees).
The colour scheme I will be referring to is standard on most cubes, where the `yellow face` is opposite the `white face`.

Corners First Method

The good thing about this method is that you can begin it with a 2x2 cube for quick success, and then add directly to what you have learned to complete the 3x3 later. It only requires a small amount of patterned, sensible sequences to learn. They are actually quite fast too because they are mostly located on the U and R layers. If you are a lefty, be sure to change all the Rs to Ls and anything clockwise to anticlockwise.

2x2 Cube

Lesson 1 Make a `white face` on the underneath side of the cube (a white face with matching colours on the sides of the pieces).

Place a `target piece` above a `target position`. Turning it into position depends on the orientation of the `white sticker` in relation to the `white face` you are making.

a. If the white sticker on the target piece is on the side of the cube, turn the face that the white sticker is on UP so that the white sticker stays in the top row but goes backwards. Then, turn the U face towards you so that the `target piece` takes its original position. Last, Turn the face you `first turned` back DOWN. Sequence: L’ U’ L or R U R’
b. If the white sticker on the `target piece` is on the top of the cube perform the sequence: R2 U R2 U’ R2 This exchanges the `top, right, front` piece with the `bottom, right, front` piece.
If you have built the first layer correctly, the colours on the sides of the cube will also match each other. The cube will look ½ solved.

Lesson 2 Orientate the yellow face (place all the yellow stickers on `the top face` but don’t worry about matching the colours on the sides of the pieces).

Turn the white face to the TOP of the cube. Notice the orientation of the yellow stickers, they all need to face downwards. Choose a `face` to be the front and (remember the colours of the `top, left, front piece`). `This particular piece` must continue to be in the top, left, front position for the start of every sequence in this step. The `target piece` is the bottom, right, front piece (the piece you will orientate). The sequence you use depends on the orientation of the `yellow sticker`, whether it is on the `front face` or the `right face`. You will orientate one piece at a time, then turn the D layer around, orientate the next, and so on until all pieces are orientated.

a. If the yellow sticker on the target piece is on the side of the cube, perform the sequence: (RUR’U’)X2 and then turn the D layer until the next target piece is in the target position.
b. If the yellow sticker on the target piece is on the front of the cube, perform the sequence: (URU’R’)X2 and then turn the D layer until the next target piece is in the target position.
The white face temporarily messes up as you go but it will return when you finish.

Lesson 3 Place the top layer pieces (switch 2 top layer pieces at a time until all are placed).

Move the yellow face back to the top of the cube and perform this sequence: (R2 U R2 U’ R2) y’ (R2 U’ R2 U R2) to exchange the 2 RHS top pieces (without changing their orientation). Look for a pair of adjacent, matching stickers and place them on the L face. If there are no pairs, apply the sequence randomly and there will be.

You can now apply this to the corner pieces on the 3X3 cube (ignoring the edge pieces) and then continue with lesson 4 to solve the rest of the cube.

3X3 Cube

Lesson 4
Place 3 U and 3 D face `edge pieces` on the 3X3 cube.

We will now use the E (equatorial- horizontal) row as a distributor to place the correct edge pieces in the white and yellow faces. And we will use `gaps` (incorrectly placed edge pieces in the U and D faces) as crossroads. We will need to keep 1 yellow edge and 1 white edge as unsolved `gaps` until Lesson 5.

Turn the white face to the top. Locate an edge with a white sticker in the E row. Turn the cube until the piece is on the F face with the white sticker on either the R or the L face. Turn the U face until the corresponding target position is on the opposite face (eg if the white sticker on the target edge piece is on the L face, the target position will be on the R face). Turn the D face until a `gap` is situated underneath the target position. Turn the target position onto the F face with either R’ or L. Use an E turn to place the target edge piece. Reverse the R or L turn to return the pieces to the U face. Continue placing the white and yellow edges in this manner until 3 of each are placed.

Lesson 5 Place the last U and D face edge pieces (fill in the gaps).

Place the yellow `target edge piece`, inverted, into the `white gap` (or vice versa). Now place the correct edge piece as normal, and the first edge piece that you placed will be placed correctly at the same time. Occasionally you may find that both pieces go into the gaps and you get a stalemate. You need to place one piece in a gap, move the E row (with the other piece in it) to separate them, and then try again.
Lesson 6 Position, but not orientate, the edge pieces in the centre row.

Reposition the cube so that the solved faces are on R and L, therefore E becomes M (middle- vertical) row. Search for a correctly placed edge on M (not necessarily orientated, but `placed`). Position it in the lower, back position. To cycle the other edges around in a 3 cycle perform the sequence: M’ U2 M U2 (top rear > top front > bottom front). You may need to do this twice. And if no edge pieces are placed, applying it once randomly will place one.

Lesson 7 Orientate the remaining M layer edge pieces.

Reposition the cube so that 2 edge pieces that need orientating are in the M row and on the U face. You may need to do a move like F2 or B2 to put them both there (and undo it after). Perform the sequence: (M’U)X3 U (MU)X3 U

Advanced Lesson

As you get better at this technique, you might want to quickly place the first 4 white corner pieces without colour matching the sides, and then incorporate these extra sequences into Lesson 3:

0 If there are no adjacent pairs: R2 F2 R2
1 One pair on the lower left: (R2 U R2 U’ R2) U R2 U’ R2
2 Both pairs on the front: (R2 U R2) U2 y’ (R2 U R2)
4 Either the U or D layer solved: Use `2 pairs` twice, start anywhere.




Edges First Method

In its `pure` form, this method uses only ONE simple `4 turn` sequence to solve the entire cube. It does not make a very good 2X2 technique, but it will give you a strategy that you can use on all sorts of other twisty puzzles. For the beginner method, I will use 2 additional short sequences to replace a confusing step along the way (I will include the `pure` method in the `advanced lesson` at the end). I will use `non standard` terminology that may confuse some veterans, but beginners will find it sensible (for veterans L=F).

Terminology

Hold the cube with the `yellow centre sticker facing up` and the `white centre sticker facing down`. Turn the cube diagonally so that one of the side faces is on the left (we will call it L) and another side face is on the right (we will call it R). Notice the absence of an F face. The B (back) face will be opposite the L face (we will not use the face opposite the R face).

The sequence is: R’L RL’ and its mirror is LR’ L’R (down, down, up, up)
Upside down it looks like this: RL’ R’L and L’R LR’ (up, up, down, down)

Lesson 1 Complete the white cross.

a. Turn the 4 white stickers on the `edge pieces` to the `white centre` to form a cross on the D face.
b. To be in the correct place, the other sticker on these 4 `edge pieces` must also match the colour of the `centre piece` on the same side of the cube. Hold the cube so that a colour-mismatch occurs on the R face.
c. Perform R2 to put the white sticker on the yellow face.
d. Turn the U face around until that `edge piece` colour-matches with the correctly coloured `centre piece`.
e. Hold that face as R and perform R2 to correctly place that edge. Another incorrectly placed edge will now have the white sticker on the U face. Continue until all edges on the white cross are placed correctly.

Lesson 2 Place the 4 edge pieces in the E (equatorial) layer.

Look for an edge piece on the U face that does not have a yellow sticker on it (it will belong on the E- equatorial row).

a. Turn the U face until the sticker on the side of that `edge piece` colour-matches with a `centre piece`.
b. Hold the cube so that the colours of the `centre pieces` of the R and L faces are the colours on your chosen `edge piece`.
c. Turn the `side face` that the `edge piece is on` down. This is the first turn of one of the sequences: R’L RL’ or LR’ L’R (down, down, up, up). Continue until all `edge pieces` in the E row are placed.

Lesson 3 Make a yellow cross on the U face (orientate the edge pieces).

Perform the sequence: L UR U’R’ L’ to the following patterns of orientated yellow pieces (it may take more than 1 application to form the cross):

a. No yellow stickers facing up: perform the sequence randomly.
b. Yellow stickers form a straight line: perform the sequence with one orientated yellow sticker on R.
c. V shape: perform the sequence with both orientated yellow stickers in the back positions.

Lesson 4 Rotate the top edge pieces into their correct place.

The sequence: R2 U LB’ R2 L’B U R2 rotates 3 edge pieces on the U layer (back > right > left), without changing their orientation. Turn the U face until 1 of the edge pieces is colour matched with a `side centre piece` (and no others are). Hold the cube so that the mismatched edge pieces line up with the positions that will rotate and apply the sequence. If 2 pieces colour match, just apply the sequence randomly (it may take more than 1 application to finish).

An easy way to remember this sequence is to follow the white rabbit (white sticker): Out of his burrow (R2), U turn, down a side entrance, around underground (R2), up the other side, U turn, and down the original path (R2).

Lesson 5 Place all corner pieces (not orientate).

Place D face corners (using down, down, up, up).
Use white as the D face, and place all but 1 white corner (from the yellow face to the white face).

a. Select a corner piece on the U face that has a white sticker.
b. Turn the U face until the target piece is directly above its target position. Hold the cube so that this occurs on the intersection of the R and L faces.
c. Perform the sequence: (R’L RL’)X3 to exchange the `top corner piece` with the `bottom corner piece`, without displacing the edge pieces. Do this for 3 of the 4 white corners.
Place U face corners (using up, up, down, down).
Keep yellow as the U face and place the 4 yellow corners (from the white face to the yellow face).
a. Select the remaining corner piece in the D layer that has a yellow sticker.
b. Turn the U face until the target position is above the target piece. Hold the cube so that this occurs on the intersection of the R and L faces.
c. Perform the sequence: (RL’ R’L)X3 to exchange the `bottom corner piece` with the `top corner piece`, without displacing the edge pieces.
d. Another incorrectly placed edge piece with a yellow sticker should be in the lower front position. Turn ONLY the U layer until the new `target position is above it, and continue until all corner pieces are placed (not orientated).

If you choose to notice, 2 other lower corner pieces will exchange also, but if you don’t turn the D face they will just continue to exchange with `each other` and be correct at the end.

Lesson 6 Orientate all corner pieces:

Look for 2 adjacent corners that need orientating (if there are none adjacent, you can simply turn a face until they are, and then return that face afterwards). Reposition the cube so that the `unorientated corner pieces` are the 2 corner pieces at the intersection of the U and L faces. Perform the sequence: (RL’ R’L)X2 U’ (L’R LR’)X2 U this will reorientate both corner pieces one twist. If neither become orientated correctly, try it again and both will orientate. If only one orientates correctly, just move to the next 2. Continue until all corner pieces are orientated correctly.

Advanced Lesson

a. For faster turning, change all L & R turns to U & R turns (or U & L turns if you are left handed) and you will be able to finger flick the faces around quickly. 12 turns can be done in a few seconds.
b. For more efficient orientations, look for patterns where the colour of the U face is the same as both of the stickers on the L face. Also if there are 3 corner pieces that need orientating on the same face and all of the matching stickers are on different faces: Make that face the U face, and place the `uninvolved` corner piece on the intersection of R & B (on the top right). If the `front corner piece` has the matching coloured sticker on the L face perform the sequence: [(RL’ R’L)X2 U`]X3 U2 and if the matching coloured sticker is on the R face perform the sequence: [(L’R LR’)X2 U`]X3 U2 Given these hints, you should also be able to determine which way to orientate any nonadjacent corner pieces that you are left with as well (because they must orientate in the same patterns).
c. You might want to try this method in its `pure` form, using only ONE simple `4 turn` sequence to solve the entire cube. I will include alternative lessons to replace lessons 3&4:

Lesson 2 Place only 3 of the 4 edge pieces in the E (equatorial) row.

Lesson 3 Orientate 3 yellow edge pieces and leave one yellow edge in the `gap` in the E row.
With the `gap` at the front, use either sequence: R’L RL’ or LR’ L’R (down, down, up, up) and then turns of the U face, and repeat until you achieve this objective. This step can take some getting used to, but persevere, it’s worth it. There are optimal paths but they are not necessary to know.

Lesson 4 Place and orientate the last 4 edge pieces.

Reposition the cube so that the R and L faces contain both the `yellow face` and the `edge piece in the gap (with its yellow sticker on the U face)`.

Now turn the yellow face until `2 of the orientated edge pieces` are in the `closest positions to the edge piece in the gap`. This creates a pattern that allows the cycling of ONLY these 3 edge pieces, with either sequence: R’L RL’ or LR’ L’R (down, down, up, up) without changing their orientation.

a. Cycle the 3 yellow edge pieces (that you have prepared) until the correct one is placed next to `the other yellow edge piece` (so that if you turned the yellow face they would both land on the correctly coloured centre pieces). There is a trick to this: 2 of the 3 orientated edge pieces on the yellow face must be aligned correctly (if rotated), but the other edge piece must have a colour mismatch with its centre piece (if rotated). If all 3 are matched, turn the yellow face to place `the other 2` orientated edge pieces in the `3 edge piece cycle (ULR intersection)`, and redo this part until only 2 edge pieces are aligned correctly.
b. Turn the yellow face until the 2 adjacent edge pieces (that you colour matched with centre pieces) are in the furthest positions from the `gap` (the edge pieces in the `ULR intersection` should now be: the final non-yellow piece, the yellow piece in the `gap` and the incorrectly colour matched orientated piece).
c. Perform the sequence: R’L RL’ again until the whole yellow cross aligns on the yellow face and then turn the yellow face until the edge pieces match the centre pieces (you may need to apply the sequence twice).


Attachments:
File comment: RUR' Example illustration
'-2x2-cube.gif
'-2x2-cube.gif [ 9.43 KiB | Viewed 1607 times ]

_________________
1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)
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 Post subject: Re: Methods for teaching kids cubes
PostPosted: Sun Mar 27, 2011 12:04 am 
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Joined: Fri Jan 07, 2011 2:37 pm
Overall, I think that you explained the methods well. Good job! Here are some of my thoughts and comments.

I think that the term "orientation" should be explained in the terminology section.

In Lesson 3 for the 2x2, when there aren't any pairs, is that the situation where the sequence needs to be done twice? If it is, you could explain why that is.

In Lesson 4 for the 3x3, it might be good to explain that it is possible to not have an edge with a white sticker on it in the E layer (they could all be in the U or D layers). There is also a something like this in Step 2 of the Edges First Method.

In Lesson 4 of the Corners First Method, the solver is instructed to "place" six edge pieces. Are these edges supposed to be solved? I am not sure because in Lesson 6, the person is told to "position, but not orientate, the edge pieces in the centre row." To me, position and place basically mean the same thing. You could consider using the word "solve" instead of "place" when you mean that.


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 Post subject: Re: Methods for teaching kids cubes
PostPosted: Sun Mar 27, 2011 3:33 am 
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Location: Australia
Thankyou Zeotor, for taking the time to make some comments, I think I will edit the method over time in case people want to copy it out and use it (it might take a few days to get the time ATM). It is quite a hard thing to do, writing a method out, you have to balance covering enough information without making it too long and boring (especially for my target market). I have tried to keep it to 2 A4 pages ea. I've found a few inconsistencies myself too that I will fix also.

I would also like to hear from people who are not familiar with the methods who want to give something new a go, if you could post `where you got stuck` or found it harder to understand, that would really help out.

Other poeple must have some good methods for beginners too, I'm always looking for new ones.

Cheers,
Burgo.

_________________
1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)


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 Post subject: Re: Methods for teaching kids cubes
PostPosted: Thu Apr 21, 2011 8:59 pm 
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Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
I put up a You Tube video for the `single algorithm` edges first method in this thread if anyone is interested.

Burgo's Rubiks Cube `Edges First` Beginner Tutorial (Part 1 of 2 )
http://www.youtube.com/watch?v=U0zK7gXxQ60
Burgo's Rubiks Cube `Edges First` Beginner Tutorial (Part 2 of 2)
http://www.youtube.com/watch?v=jB6Qe6zaghI

Burgo's Rubiks Cube `Edges First` Pure Method
http://www.youtube.com/watch?v=iNrpyHJUFR0

EDIT*I have also added the following (Corner's First tutorials):

2X2 Cube `beginner method`
http://www.youtube.com/watch?v=EXBGM22BuNI
2X2 beginner > competent `extension` lesson
http://www.youtube.com/watch?v=MxzZbAkq9tg

3X3 `solve the 2X2 on the 3X3`
http://www.youtube.com/watch?v=kc7vLIGIU6E
3X3 `Corner’s First` method
http://www.youtube.com/watch?v=P3vhPXkiAtU


I am going to use it in conjunction with the written method. I think video is the ultimate teaching aid (it will save my voice :wink: ).

Cheers,
Burgo.

_________________
1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)


Last edited by Burgo on Tue Apr 26, 2011 7:25 pm, edited 3 times in total.

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 Post subject: Re: Methods for teaching kids cubes
PostPosted: Sat Apr 23, 2011 1:43 pm 
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Those are good videos. I was wondering about something. In the beginner's tutorial video, R U R' U R U2 R' is used in place of R2 U LB’ R2 L’B U R2, which was in Lesson 4 in your earlier post, right? If so, you might want to change the algorithm in your post to the one used in the video. It might be easier for someone to remember a sequence that only involves turning two faces than one that involves four.


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 Post subject: Re: Methods for teaching kids cubes
PostPosted: Mon Apr 25, 2011 10:58 pm 
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Location: Australia
I have been meaning to get back to this for a while, thanks for the reminder. Konrad helped me with replacing that alg (and full credit). It really opened my eyes to the versatility of Sune.

I am going to use both resources together (at school), currently I am putting the `2x2 / Corners First` method on video. I have also recieved some help with the text by PM which I intend to incorporate. I am just working on the video at the moment. It's a big job. I thought I was under the radar..

Once I started making the vids for school (they will be DVDs because the school has no access to You Tube) I thought that I might as well make it public too, hey. That's why there is such a disparity in the content on my channel. I actually really hope that I'm not patronising anyone (putting up beginner methods here for experts to look at), you get self conscious when you start doing this sort of thing.

Cheers,
Burgo.

_________________
1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)


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