Two Weeks Through The Looking Glass: A Journey of Student Creativity, Curiosity, and Collectivism
Numbers. Your basic operations. Some advanced operations — “power ups” as wonderfully coined by the wise and whimsical Berkeley Everett, who is K to 5 Math Facilitator at UCLA Math Projects. His background also includes being a classical and jazz pianist.
Two weeks ago, I showed a particular set of four Albert’s Insomnia cards that I dealt out a few years back. They looked innocuous, but some magic lay far up ahead to those particular cards.
The rules were straightforward. Use to one to four cards(no duplication) and the operations of adding, subtracting, multiplying, dividing, factorial, roots, and exponents to create PEDMAS questions from 1 to…
Our 6th grade Math Recess class went to 200. There is actually a 4th and 5th grader in my class.
While we obtained over 90% of the numbers from 1 to 200, the story of our class lies in the interstitial space between these discrete objectives. We literally went through the Looking Glass, and seeing numbers through a different lens. Here are some of the highlights I would like to share.
As we progressed through the numbers, certain numbers became “anchors” and were used repeatedly to generate numbers in close proximity to them. Numbers were considered anchors if we could only use 1 or 2 cards to get them. In the beginning, 24 — derived by 4! — was used quite often. Later on the number 84(7 x 12) became a fixture for many answers. And, once we got passed 110, the magic of 5!(120) allowed us to generate all the answers from 111 to 130 in a symmetrical fashion. The 3 and the 4 could be used to generate all the numbers for one to nine. As such, on one side of 120, we subtracted them. On the other side, we added them. We blew threw these twenty numbers, as a class, in about 2 minutes.
As well, on every board I circled the primes. So, not only were kids learning about primes, but they were beginning to realize that they might always be the tougher ones to get — because we would never be able to multiply two numbers to get them. We would have to land close and get lucky with the remaining numbers and required operations.
This is inherent. Almost primal. Students needed to play with numbers, mix them with all the operations available, and get creative to obtain some answers. 12^(root 4) to generate 144 became mundane to all very soon. It just became a portal to having students stretch their creativity and imagination. As we got past 150, students started searching for anchors in this space. One must realize that most had gone outside their comfort zone of the cliched 12 x 12 times table. Sure enough, 24 x 7 equals 168 was manifested. The 24 coming from 4!.
Something very cool happened in the 160’s. Seraphina, a 5th grader, went way out into orbit to see 720 to build the anchor 180 — she used double factorials. Two weeks ago, she didn’t even know that operation. Now she was wielding that operation like a Jedi Knight with a light sabre. But really, so many of them do now. Such great contributions from students like Givi, Bowser, wilmatuker, JMassey, and others.
Another inherent, built-in trait of this game. The more stubborn an answer appeared, the higher the resolve from the class to find it. Some of these numbers may turn out to be impossible, but that didn’t deter the class. This critical mathematical trait was developed organically and intrinsically. Worse part of each class was when it had to end…
This was probably the most satisfying thing to come out of the last two weeks. The encouragement from the students to each other for finding certain answers or getting close/making a mistake with one of the rules. There was no competition whatsoever. Students cheered each other on.
To witness this collectivism/energy, I invited Berkeley Everett and Nikki Rohlfing(United Kingdom) to join a stream. They both witnessed the buoyant energy of the class — which had only gotten higher in the second week. Some students contributed more than others, but all students were appreciative of the surprises, which often resulted in obtaining some of the higher numbers.
Quite often that student was me!
Today is a wrap up day of our two weeks. We will take one last look at the numbers that eluded us. We will share our whys as to why we became enthralled with numbers and our messy playing with them.
Before we close the book on this one, I will open up a rabbit hole for them. I will mention the number 27. That it could have been an anchor number with just a 3 and 2. I will wait for perplexity to come to a rolling boil.
Then I will drop the hyper-operation, tetration on them:)
Curiosity is never quenched in mathematics — for anyone. Thankfully.