Five Great Things This Week: Puzzles, Google Slides, Rubik's Cube, Spirit Week, and Math Community Service

Fifty! Phew! I made it! It was a fabulous birthday with a ton of surprises and so much to be grateful for! I'm also SO grateful for my job. Every day, I come home nourished (and tired!) and here are a few reasons why.

1. PUZZLE OF THE WEEK

This is a fun weekly international competition that you can sign up for here. It's created by @asharpeducator. My Problem-Solving class and math club really enjoyed it. It's tough enough yet doable and got a lot of kids talking...particularly the calculus-loving student who doesn't get to see problems like this much. But really all kids can do it with a little help. I'm going to see if we can send this problem out to all students via email so that any student can access if they want.  Even if only five students in the school open it, that's still more students talking about math! I'm hoping it will be a good problem for teachers to throw on the board if they have some time at the end of class. Sign up and give it a try!

2. WRITING LESSONS IN GOOGLE SLIDES RATHER THAN WORD

I Started rewriting all of my lesson plans in Google Slides instead of word this year afer initially seeing @mathycathy's short ibook: Using Keynote to Explore Math Relationships Visually Now I know I'm using Google Slides and note Keynote...our school uses everything Google, so it made it easier for me. But she really opened up my eyes about how much better it is than word. And then @howie_hua tweeted this:

Adding comments after the lesson is a GAMECHANGER!! Every year, I forget to change the one mistake on a lesson and don't remember until I'm in the middle of the class...no more!!

Here is a lesson I made on Inverse Functions that I taught to my Pre-Calculus AB class using Google Slides. Give it a try!

3. RUBIK'S CUBE

All 13 of my Problem-Solving students solved the Rubik's Cube within 3 minutes after only a week and a half of learning how to solve it! I purchased Art Benjamin's version on Amazon, and we watch the first four of eight algorithms together as a class. I find that Art Benjamin's method is the easiest for students (and me!) to learn. Then, I give students either the link to my blog post on solving the cube with extra videos of me explaining how to solve, or I give them my Youtube playlist. Some students really need me to go through every algorithm with them, which I do either on the side or during extra help, but others wanted to learn it on their own and were able to watch the videos at home. Anyone really can solve the Rubik's Cube...my favorite year was when I learned it along with the students, which I highly recommend! My class is probably the only one where the teacher allows  the clicking of Rubik's Cubes all period as students solve problems...they are learning kinesthetically!

4. DRESSING UP FOR SPIRIT WEEK

Kids love it when teachers dress up for spirit week! Even though it can be out of your comfort zone, you must do it! We had "Dress as a Movie Star" day, so my colleague and I dressed as Tina Fey and Amy Poehler from Baby Mama., but of course, we were "PreCalc Mama." So fun!

5. MATH COMMUNITY SERVICE

For my math club, I reached out to Florence Fuller Childcare Development Center to see if they needed math tutors. They do! After a few weeks of emails, back and forth, we had two people from the center come out and talk to our club about how we can tutor their students during their aftercare program. They talked to our students about how meaningful it is both for their students and for ours. The club members seemed really interested. We are hoping to send a few students each week to meet with kids and help them with their math homework and hopefully to form a meaningful bond and mentorship program. Is there an economically challenged development center in your neighborhood? Reach out and see how your kids can help! Our math club is a lot about competitions, but it's equally about community service and peer tutoring. I hope this will be a meaningful experience for all involved!

It's been quite some time since I blogged, but it feels good to be back. Let me know if anything worked for you!

How to Solve the Rubik's Cube 2.0

When Art Benjamin visited our school, I bought his DVD called "The Mathematics of Puzzles: From Cards to Sudoku." "Mastering the Rubik's Cube" was one of the 12 lectures on the DVD. I watched it this summer and was surprised how easy his method is. I broke it down for my students in my Problem-Solving class, and here are the 8 steps. I do think it's easier (and clearer instruction-wise) than my former blog post on solving the Rubik's Cube. Also, here is my post on why I teach it in my class and a link to the mosaic contest in which we won 3rd place.

8 Steps

First Layer

1. The Daisy

·      https://youtu.be/QzP1cI-1Oks

·      The yellow face is on top

·      White petals will surround the daisy.

2. The Easy (bottom edges) 

·      https://youtu.be/Cp8G1W6LNmw

·      The yellow face is on top

·      Twist cube so the white petal finds its center

·      Rotate face 180˚

·      Repeat for the other three white petals

·      Flip Rubik’s cube upside down and look at white cross 

3. The 123 (bottom layer) 

·      https://youtu.be/icnjPpdIdZA

·      With white daisy on the bottom, find a white corner on the top rim

·      Twist it until its other color finds it’s center (it matches in color with the center color)

·      Hold the cube so that this white cube is on a side.

·      ONE: Point with your index finger to the white. If you’re pointing with your right hand, you will twist the right face away from you. If you’re pointing with your left hand, you will twist the left face away from you. (UP)

·      TWO: Right hand, twist the top CLOCKWISE. Left hand, twist the top COUNTERCLOCKWISE. Either way, whites will match up.

·      THREE: Right hand, bring right face back down toward you. Left hand, bring left face back down toward you. Either way, now white corner is in proper place on the “daisy.”

Note: a 1-2-3 always starts with an “up”

Complications:

What if there are no white corners on the top rim, but there is one in top face?

            1. Rotate white so it’s directly above a non-white (unsolved) on bottom face.

            2. Perform 1-2-2-3 move

            3. Now the white is on the rim, so you can repair with the 1-2-3 move.

What if you don’t have any whites on a tip rim or face? Do a 1-2-3 move, and it will move a white piece into the top rim or face, and then you can repeat. 

Second Layer

4. The Middle Layer 

 https://youtu.be/xP8ywEBpxB0

·      With white daisy on the bottom (or yellow face on top—same thing), practice this move:

UP	TWIST	DOWN	TWIST	UP	TWIST	TWIST	DOWN
1	2	3	2	1	2	2	3
R	U	R’	U	R	U	U	R’

(NOTE: the above does not have anything to do with the middle layer. It is just for practice for later)

·      Only have to change 4 edge pieces.

·      Start by looking at the top layer and see if there are any edge pieces on the rim that do not use the color yellow.

·      Find one that does not use the color yellow and twist it so that it matches its center color.

·      The color of the top edge will either match the left or right face. Whichever side it matches, give that side a mental “slap.”

·      Twist the top in the direction of the slap.

·      With same slapping hand, perform the 1-2-3 move.

·      Lost a white, fix it by moving the color on the white cubie to match its center.

·      Perform the 1-2-3 with the side that contained that white face (white should be on the side, NOT facing you.)

If all four-edge pieces have yellow, we need to move a piece out of its wrong place. 

·      Find the piece that needs to be moved and perform a 1-2-3 move (no slapping required.)

·      Fix the white piece by moving it to match its center and follow with a 1-2-3 (note: the white will be on the side)

Third Layer

5. FUR U’R’F’ move (top cross) 

·      https://youtu.be/zyP4sP9U7Uk

·      F = front, B = back, R = right, L = left, U = up, and D = down

·      When you see these letters, always move the face clockwise

·      If you see these letters with a ‘ by it, always move the face counterclockwise, for example R’ is moving the right face counterclockwise.

·      Up face is always yellow, down face is always white

·      L moves toward you, R moves away from you

·      Perform at “9:00”

·      If you don’t have “9:00,” do FUR U’R’F’. You may have to do this twice, but then you want “9:00

·     

·      Do FUR U’R’F’ one more time to get the yellow cross.

Just a reminder: R is up, R’ is down, L is down, L’ is up

6. The Fun move (top face yellow) 

·      https://youtu.be/xEsrHF9YJF0

·      Count the number of yellow corners on the top. Best case is one. You can only have zero, one, or two.

·      With 0 or 2 yellow corners, rotate the cube so that a yellow is in the upper left corner of the front face.

UP	TWIST	DOWN	TWIST	UP	TWIST	TWIST	DOWN
1	2	3	2	1	2	2	3
R	U	R’	U	R	U	U	R’

·      Repeat until you have only one yellow corner

·      Orient the cube so that the one yellow cube is in the bottom left corner

·      Repeat the “fun” move and the one yellow cube in the bottom right corner until you have the top face yellow.

   

7. The R’F move (top corners) 

·      https://youtu.be/5j-3uDsoTZs

·      Look around the top rim and see if any of the top sides have matching corner colors

·      If not, then do: R’ F R’ B²      R F’ R’ B²       R²

·      When you have matching corner pieces, move them to the back face

·      Repeat R’ F R’ B²      R F’ R’ B²       R²

·      Orient so that all corners should now be matched

(remember, R’ is “down”)

 (or, know that Up or Down refers only to the right side, and the mantra is:

D F D B²      U F’ D B²       U²

8. The “FFURL” move (top edges) 

·      https://youtu.be/edToGuRKlqY

·      All should be in proper orientation except for three or four edges.

·      If you only have three edges out of position, then you have one perfect side, which you want to move to the back

·      FFU   R’L   FF   RL’  UFF (or, FFU, both sides down, FF, both sides up, UFF)

  

All on one page:

1. The daisy

2. Bottom edges

3. The 123 move (bottom layer) (123 always starts with an up)

4. Middle layer (slap 123, adjust white 123)

5. FURU’R’F’ (look for 9:00)

6. The fun move (start with right up)

7. R’ F R’ B²  R F’ R’ B²       R² (where R’ is down) or D F D B²      U F’ D B²       U²

8. FFU, both sides down, FF, both sides up, UFF

I heard from a former student who is a freshman in college and who told me today, "It's so much fun to know...I always use it as a fun fact during ice breakers!" Love. I hope you'll have as much fun, too! My fastest time is 2:45, but normally it's around 3 minutes. There are definitely faster ways, but this method is, to me, easy to teach...as long as you have willing students. 

My plan is to have my class teach some of the 5th graders at our school how to solve the first and possibly the second layers, so that maybe they will want to learn the rest on their own. I've joined a national Rubik's Cube club, and we may host a competition...we will see! Just like the Rubik's Cube, one step at a time :)