I taught my son how to do the 3x3 when he was 8 (he's 9 now). He's sub30 now and has done several sub 20 solves..Hello! I am looking to find an easy cube/puzzle for my 10 year old sister. Eventually I’ll teach her 3x3, but right now she doesn’t have the patience to learn a ton of algorithms. I was considering 2x2, but I think it is better to learn 3x3 before that. Anyway any suggestions?
I did it by teaching him the 2x2 cube, layer by layer method. I started by teaching him the basics of cubik notation. Then I showed him how to get the first layer which is really easy to learn even for the most alg averse people. I showed him how to get the first bottom corners using simple URU'R' or U'L'UL depending on where the face is and if the face is on top, I taught him how to do it twice. Then I showed him one repeatable algorithm for one of the 7 possible top positions ( this position was headlights with the headlights on the left) F(RUR'U')F' and taught him to repeat that until he actually gets headlights and then do it again to orient the layer.
Then I showed him the PLL headlights algorithm (headlights in back) (L'UR')D2(RU'R')D2RL, (Sometimes you have to do this alg twice if you don't have headlights). I wrote these algorithms down on a piece of paper. Then I slowly fed him some of the the other LL algs that are similar to the first one, like Pi (putting the side bar on the left) F(RUR'U')(RUR'U')F' and H (setting the bars up and down) F(RUR'U')(RUR'U')(RUR'U')F' And then I wrote down the remaining four algs on paper (making sure that I only gave him algs that translate to 3x3 without moving center pieces that aren't on the top layer).
Once he saw how impressed the other kids were that he could do the 2x2, it gave him incentive to learn 3x3. I taught him how to get the cross (actually he figured that out on his own), he already knew how to get the bottom corners because of 2x2. I showed him how to get second layer using cube rotations and setup and (URU'R')(U'F'UF) or (U'L'UL)(UFU'F').
For the last layer, I showed him Corners first because he already knew how to do that with 2x2, then I showed him how to orient the top middles with basically two short algs that are repeatable. I called them step and eyes. If you have two adjacent faces facing up (steps), you put them on the lower right (looking down at the cube from above) and do F(RUR'U)F' U2 F(RUR'U')F'. This is easy to learn because he already knew this alg. And if he gets two opposite facing up, (eyes), you put them horizontal to you and do F(RUR'U)(RUR'U)F' U2 F(RUR'U')(RUR'U')F' he also already knew these algs. If he has all the middles facing up, he only has to do one of these two algs and it will give him eyes or steps and then he performs the other of these two algs to orient.
Then I taught him my variation of the 3-cycle top middles. It moves the two horizontal middles and the middle closest to you, counter clockwise. x('U'RU)M'(U'R'U)(UL'U')M(ULU')x'. At first he would just cycle through that to solve the cube, but then I gave him in writing the clockwise version of this. He only has to repeat this alg if he has all four corners out of place (eventually on his own, he learned H-Perm and Z-perm from the internet). Then I gave him the algs that cycle clockwise and counterclockwise that orients and permutates the last middles in one shot.
He learned fairly quickly because there isn't much to memorize with this beginner method which allows for sub30 times. He has gotten several sub 20 times, but he has already gone on to learn some algs from the internet. But it was fairly painless for him. Now he does Pyramix, mirror, skewb, and several other puzzles. He learned them on his own.