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!

Gifts for the Gifted — Charty Party All Ages Edition

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, including my 2021 list, you can visit this page. I also have a Pinterest Board of Games and Toys for Gifted Students. 

Way back in June of 2020, I wrote a post about Charty Party, a game similar to Apples to Apples but with graphs. At the time, the company was in the middle of a campaign to raise money for an “All Ages Edition” as the original version was for ages 17+. Eager to see if the new game would be appropriate to play in classrooms, I contacted the company to see if they would send me a set to review and they graciously agreed.

Now, even though it is labeled “Charty Party: All Ages Edition,” the recommended ages are 10+ on the box. You will want to play with participants who can read well and can interpret basic graphs. I haven’t read all of the playing cards, but we used a great number of them and I didn’t see anything involving alcohol or sex. There are some gross ones (like a chart of the loudness of farts), but most kids would find those extremely appropriate 😉

To play the game you technically need at least three players, but my daughter (18) and I have a great time playing our own modified version. As in Apples to Apples, there is a rotating judge, but we just agreed to choose the card that got the most laughs as the winner for each round. Standard play involves a judge revealing one of the white chart cards and the players (who each have 7 orange cards) each choose one from their hands that they think would be a good label for the y-axis to give to the judge. The judge (who doesn’t read the cards yet) shuffles the cards, then reads them out loud, and the person whose card get the most laughs as it pertains to the graph wins the white chart card. Everyone draws a new orange card, the judge rotates to the next person, and the rounds continue until someone wins 5 cards.

Below are some examples, and I’ll let you decide the winner of each round:

We turned over the “Instrument You Play” chart that showed that the y-axis dramatically increased for drum-players. My daughter (a Music Ed major) played the card, “Belief You’ll Have a Successful Career in Music” and I turned over “Creepiness of Mustache.” No offense to drum players out there, just trying to put down the funniest card…

The next example shows an increase during middle school, and my daughter played the left card while I played the one on the right.

Above you can see that something increases equally with the type of mood you might have at a funeral and the type of mood you might have at a surprise party.

And, lastly, a fart one…

You will note in the rubric below that I gave the game high marks for “Replayability” as my daughter and I stopped counting who was winning and just kept playing until we finished the charts. We also played some charts again with different card hands for added fun. The possibilities for probably not infinite if you do some mathematical calculations, but they are a lot.

I also gave this game high marks for “Extendability” because there are so many ways to integrate this into your classroom. In fact, there is a flyer with “Classroom Activity Ideas” included in the box as well as a page on their website.

The cards are durable, and losing one or two will not impact playing the game. Though there are some constraints, the game rates highly in the Strategic, Creative, and Spatial reasoning areas as well.

You can currently buy Charty Party: All Ages Edition directly from their website with free shipping. I can’t wait to play it with larger groups, especially family during the holidays!

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!

The Almanac of Interesting Numbers

I am living proof of the myth that only some people are “math people.” For years, I suffered under that delusion — and that I was definitely not one of those people. But things changed in high school. I won’t go into the long, boring story, but I realized that I enjoy math. And while I am not a lightning fast mental problem solver, the logic and patterns fascinate me. That is why I started collecting fun math sites for my students, and made this public list of Math Sites That Won’t Make You Fall Asleep. I also started following fascinating people who tweet about math (#MTBOS is a wonderful way to start), which includes Sunil Singh (@MathGarden). Singh is a Content Writer for Mathigon.org, one of the Math Sites That Won’t Make You Fall Asleep. While I’ve included Mathigon on the list, I didn’t notice the “Almanac of Interesting Numbers” until Singh tweeted about it.

Although I don’t believe that only some people have a “math gene,” I do know that there are some of us who find math far more intriguing than others. I’ve had students like that, and if you have them in your class you should show them this interactive number line that will give them amazing facts about numbers. I found the easiest way to navigate the number line is to put a number in the search box and click on the zoom in/zoom out magnifying glasses at the bottom of the page. That’s how I discovered that 40,585 is the sum of the factorials of its digits (4! +0! + 5! +8! +5!) and that 25 is the smallest square that can be written as the sum of two squares.

If I don’t publish any more posts this week, I think you can guess what I’m doing instead…

yellow sunflower in close up photography
Photo by Flash Dantz on Pexels.com