Math Fun with The 12 Days of Christmas 2021 Style

Interesting math patterns make me happy, so I really enjoyed doing a unit on math masterpieces with my 4th graders several years ago that included Fibonacci, Sierpinski, Pascal, and the 12 Days of Christmas. Unfortunately, several of the links that I included in that post back in 2016 no longer exist. But the good news is that some newer ones have surfaced. Time, then, to go back to the drawing board…

If I was doing this lesson today, I would begin by posing the question of how we could figure out exactly how many presents the extremely generous “true love” would have purchased by the end of the famous “12 Days of Christmas” song. After some discussion, suggestions, and student collaboration (and maybe listening to this funny version from Straight No Chaser), I would then introduce this great spreadsheet Eric Curts just posted. It will help students think about their math and learn a few spreadsheet skills. After students complete this and you debrief, you could then ask them what they think the price of all of those gifts would add up to today. PNC has a nice summary of the cost of each gift and the total, but don’t show it to them until you’ve gotten some estimates! Students who need a challenge could be tasked with designing a new spreadsheet for those calculations.

Next class, I would introduce them to Pascal’s triangle. I wouldn’t tell them what it is at first. I would give them this worksheet, this one, or the first page of this one to complete. You can see on the latter link that there are some additional pages that give suggestions for patterns students can look for in the triangle once they have successfully added the correct numbers. Even more patterns can be found here. Note the Fibonnacci numbers, and how you can get Sierpinski’s triangle by coloring in certain numbers! And then, you can point out the pattern, shown here, that reveals how many total presents are received each day. (The printable triangles I linked to don’t have that many rows, so it’s up to you if you want them to make that connection on their own.)

For more advanced students, you can show them this video, which demonstrates how Pascal’s Triangle can be used to find coefficients or probability. Here is an interactive from Mathigon for those students who want to go deeper, too. Shodor also has an online triangle you can manipulate and color as well as recommended lessons. This Geogebra one is fun to play with, too.

If you’re loving these math resources, don’t forget that you can go to my Wakelet page, where I have links to two different math collections full of engaging activities, “Math, Art, and Nature” and “Math Sites that Won’t Make You Fall Asleep.” You’ll also find my December collection and Fun Stuff!

Coding with Poetry

As I mentioned last week, the International Hour of Code Week is coming December 6-12, and I think it is an amazing experience for students and teachers. I understand that it can be daunting for anyone who has little or no experience with coding, but the people at Code.org really make it easy for anyone to participate — even if you have no digital devices in the classroom. One of the things that may seem like an obstacle to many teachers during this year of “catching up” is trying to fit coding into the curriculum. Code.org provides many tutorials that can be used in different subjects and this week, I noticed they have released a new tutorial that would be awesome for ELA teachers in grades 4-8. Through the “Coding with Poetry” tutorial, students will learn how to animate some classic poems, and write and share their own poetry to animate. With short videos, examples, and the option to have instructions read out loud, this lesson is a wonderful step-by-step walk through that will help students to feel like accomplished authors and coders by the end. I particularly like the introductory video, where a student named Caia explains how her passions for both poetry and computer science intersect.

Learn about how Caia combines poetry with computer science in this video from Code.org.

For an example of one way my students have mingled coding and poetry, visit this post from when we used Scratch and Makey Makey to make interactive onomatopoeia poems. And, for many more coding resources once you and your students get hooked, here is my Wakelet collection.

five bulb lights

Gifts for the Gifted Teacher — Creative Acts for Curious People

I’ve been doing my “Gifts for the Gifted” series for almost 9 years. Though I freely admit that the title is a bit of a misnomer because my recommendations are not just for students who have been identified as gifted, I am about to launch another series that may also be misunderstood. At least no one can accuse me of inconsistency. With that in mind, here is the inaugural post of “Gifts for the Gifted Teacher.” While I got a lot of joy out of the books, games, and toys I’ve bought for my students over the years, there are some things that I just think are great for teachers, themselves (which will indirectly benefit their students, so win/win). And during these times when teachers are, quite frankly, getting the shaft, I would like to make some explicit recommendations for anyone who wants to show their appreciation to an educator with a thoughtful gift.

Definition of Gifted Teacher: An educator who loves to learn and to challenge, engage, and empower her/his/their students with relevant and meaningful curriculum. p. 1 of the Engage Their Minds Dictionary, 2021

My first entry for “Gifts for the Gifted Teacher” (oops, that almost became “Gifs for the Gifted Teacher” which I am now officially copyrighting for my next series…) is a book called, Creative Acts for Curious People by Sarah Stein Greenberg. The foreword is written by David M. Kelley, (not to be confused with David E. Kelley, famous writer/producer of a billion television dramas) the founder of IDEO and a professor at Stanford. David M. Kelley is someone I’ve admired ever since I’ve done my deep dive into design thinking, and Stanford’s d.school is the dream school that I would have totally applied to if it existed thirty something years ago.

The book is thick, which is always a huge plus for me. It is full of activities curated by Sarah Stein Greenberg from great design thinkers at the d.school and beyond, and includes some challenges to try out. Though I see teachers finding it to be an awesome resource, I feel like anyone who has had a problem to solve or may have one to solve in the future could use Creative Acts for Curious People. It’s not just about brainstorming new ideas, but looking at things through different lenses, team building, and working to develop empathy. Altogether, there are 81 Creative Acts in this book, and many could be used with any age group.

I took this book on a trip, and devoured it quickly. My one regret was that I forgot to bring a highlighter, so I’m now re-reading the book and highlighting suggestions that give me ideas. In other words, I am basically coloring every page. I was going to wait until I finished this task to write this review but I got so pumped while I was doing it that I stopped to type this post instead.

I am going to restrain myself from gushing about each and every activity, and just give you a couple of samples. A simple one that you could easily use with students in elementary and up is “Expert Eyes”, where you assign them a place to walk around and make observations on their own by drawing them. Then you have them walk with someone else (for school this could be a buddy from another grade level, parent, teacher, volunteer, etc…) and do the same walk and draw what the companion describes out loud. Depending on the age, do this one or two more times with different people. Then compare the drawings from each time and discuss the new insights you might have gained from looking at the same area through someone else’s eyes. Simple but powerful.

Another example I got really excited about is “The Monsoon Challenge” which would probably be better for older students. The assignment was given in a course called, Design for Extreme Affordability, and the students had to design something to collect as much “rain” as possible. The rain was a sprinkler on a ladder. With less than a week and $20 for each team, the students needed to ideate, build and (hopefully) test prototypes that could be adjusted and ready for the class day of the demonstration. I won’t give away one of the truly genius solutions one group designed, but it’s worth reading the book to find out!

If you know a teacher or leader of problem-solvers who is innovative and loves to guide others through the design process, this book would be the perfect gift for them. I know I will be incorporating a lot of the ideas in my workshops and would have enjoyed using them with my students when I was in the classroom. You can get Creative Acts for Curious People where I purchased it, Nowhere Bookshop, or your favorite independent bookstore. I’ll also be adding this recommendation to my collection of “Books for Maker Ed/Design Thinking.”

Gifts for the Gifted – Genius Square

Several years ago, I thought I would help out the parents of my gifted and talented students by writing about some games, toys, or books that I thought might make good purchases during the holiday season.  I called the series of posts, “Gifts for the Gifted,” and I have continued to do it annually (except for 2019) on every November and December.  These gifts are suggestions for any child – not just those who qualify for a GT program. Sometimes I receive a free product for review, but I am not paid for these posts, and I never recommend a product that I wouldn’t buy for my own child.  For past “Gifts for the Gifted” posts, you can visit this page. I also have a Pinterest Board of Games and Toys for Gifted Students. 

I am linking this product to Toyology, an independent toy store in Michigan, which has a few locations and an online store. Thanks to Kimberly M. for this tip!

This is the earliest I’ve ever begun this annual series of posts, but you know pandemic, supply shortage, blah blah blah… Plus, I’m switching to Mondays because I usually do my Anti-Racism posts on Fridays. Another new change (yes, I know I’m full of them today) is that I devised a bit of a rubric to use with the games/toys. I was always using a sort of mental rubric, and just decided this year to make it visible to everyone else!

I’m starting this year’s recommendations with a game called Genius Square. When I began looking for ideas a couple of months ago, I reached out on various social media channels, and several teachers mentioned that their students love this game. The game can be played by one or two people, and includes two grid boards, two sets of Tetris-like pieces, a set of wooden peg blockers, and a set of dice. You roll the dice to determine where the blockers should be placed, and then try to fit all of your colored pieces on the board around the blockers. With two people, you are racing against each other, but a one-person game is basically just a great way to practice your spatial skills.

If you recall, I wrote an article for NEO on spatial reasoning back in February, and I feel that this is an area that is often ignored in formal education though extremely useful in real life. (Try packing a carry-on suitcase with everything you need so you don’t have to pay for a checked bag on an airline, and you will see what I mean.) Genius Square is a fun way to work on developing this skill, and I love that it has the option of competition or solitary enjoyment. It’s also great because there are often (maybe always?) multiple solutions. And, with all of those dice and grid placement options, chances are you will rarely get the same challenge twice.

I did score the game a little bit lower in the durability area due to the multiple pieces. Parents and teachers know the frustration of lost parts on a daily basis. But it wouldn’t be that difficult to make your own replacements (especially if you have a 3d printer!). In fact, I saw some pics on Twitter of people who were using some pictures they had drawn and cut out due to that issue. I also want to thank Christine Dale (@DaleDaze) for her Tweet about the Mathigon virtual version of Genius Square that you can play.

The lower Extendability score is based on how directly this game could apply to curriculum or real-life. I mean, yes, we use spatial reasoning a lot, but no we don’t often have to pack an exact number of Tetris shapes into a grid. And, I don’t feel like there’s a whole lot of strategy involved in the game as there is nothing you can do to keep your opponent from winning except to think faster.

Although the box says 6+ for the age, I think kids slightly younger could play, and I would even encourage it. I also think it’s great for people of different ages to play against each other, as it does not require reading, trivial knowledge, or counting. (You may need to place the blockers for younger children, though.)

I’ll be adding this to my Spatial Reasoning Wakelet. Also, if you are new here, you may want to check out some of my math Wakelets.

Got a toy/game/book suggestions for me to review? It’s not too late! Comment below or email me engagetheirminds@gmail.com

photo of young girls looking through microscope

Microbe Art

I have long been fascinated with the intersection of math, nature, and art. From Fibonacci to fractals, I find it intriguing to recognize patterns and similarities in natural objects and animals that also appear in those created by humans, and that we can imagine wildly creative innovations from very logical, patterned, or symmetrical visions. When I came across this video of the “Art of the Microcosmos” by Emily Graslie, I had a feeling that it would lead me down a rabbit hole of Fibonaccian proportions, and I was correct. Her interview with James Weiss made me wish I had him as a Biology teacher in high school, or that I had even once gotten the chance to observe the incredible microscopic animals shown in the video. Of course, I’ve known about the tardigrade (also known affectionately as “water bear”) for a few years, so I definitely have no problem imagining it or any other of the strangely beautiful creatures in this video as artistic inspiration.

Following Emily’s film, I had to look up Klaus Kemp, who creates diatomic art, and then I made the mistake of Googling “art made with microbes” and found an entirely different branch of scientific art grown in petri dishes.

After a couple of hours of being transfixed by so many things I had never seen or even known about before watching Graslie’s video, I finally had the wherewithal to drag myself away and try to do something somewhat productive (though not even minutely creative). I started a new Wakelet of “Math, Art, and Nature,” and I even used Wakelet’s new layout option of columns to attempt to organize it a bit. (You may need to scroll horizontally to see all of the columns, and scroll vertically within a column to see all of the links.) This is, of course, separate from my “Math Sites That Won’t Make You Fall Asleep,” collection, but I went ahead and added a link to it in that one, too.

Just a reminder that, even though fancy microscopes might be nice, you can always get your students started with observations of that microscopic world with an inexpensive Foldscope. You might be surprised at the incredible images you can view with this simple tool.

microscopic shot of a virus
Photo by CDC on Pexels.com

3d printed boat

Rob’s Tinkercad Classroom

Rob Morrill is a Innovation Lab teacher who was invited by Tinkercad this summer to write regular blog posts about projects he has done with students. You can read more about Rob’s experience and expertise in his introductory post. One way to keep track of the projects he adds is to visit this page, which is a “roundup” of all of the posts he has published so far. You can also visit Rob’s website. I’ve been wanting to try a lithophane project, and now I’m even more inspired after seeing his instructions and examples.

In case you’ve missed it, Tinkercad is one of my absolute favorite entry-level design programs (and it’s free!) that I discovered when our school got its first 3d printer. It keeps improving, and you can move from simple designs to really complex ones to accommodate all abilities. Here is a post I did at the end of last year about Tinkercad Design Slams. It’s also one of my recommended online tools to help students develop their spatial reasoning. You can integrate so many parts of your curriculum (especially math) into Tinkercad projects, as well as develop creativity and that Design Thinking mindset. Even if you don’t have a 3d printer (see my post on questions to consider if you are thinking of acquiring one), students love to show off their Tinkercad designs virtually, and they can be exported into other programs. For more ideas on using Tinkercad with Design Thinking, see this post on the City X book.

By the way, Tinkercad has a teacher dashboard that you can use, where you can add classes, students, and assignments. And, did I mention it’s free?!!! Don’t worry if you haven’t used it before. They’ve got you covered with their tutorials, and your students will help each other out. (Mine invariably discovered something I didn’t know about the program every time they used it.)

Thanks to Rob for sharing his innovative ideas!