As seasoned readers may know, I have always been intrigued by the beauty of math. (See here, here, or here for some examples.) Now that my job title is S.T.E.A.M. Master Teacher, I have been looking even more for ideas on how to integrate math and art.
Math Craft is a great place to start. From mathematical knitting to Sierpinski Christmas trees, there is no shortage of inspiration on this site (though it is a bit heavy on polyhedrons). Not every post gives you instructions, as some of them feature work by professional artists – but you could always pose the question to your students, “How do you think they made this?” They may end up making something completely different, but equally as beautiful, along the way.
While searching for ways to help my engineering students develop some desperately needed problem-solving stamina and spatial reasoning, I came across these wonderful puzzles that are in color – and provide solutions. (Did I mention I need to practice my spatial reasoning, too?) I gave them the TED Ed River Crossing Riddle last week, and I thought I was about to have a full-on mutiny on my hands when I wouldn’t reveal the answer right away, so I thought I would try some less complex challenges for the next few weeks 🙂
Venn Diagrams are pretty ubiquitous in school. Most students have seen and used the common form of a Venn Diagram that you see below in order to compare/contrast two things.
To be honest, after a bazillion years of teaching, I’ve gotten quite bored with using this graphic organizer. However, there are a few people who have thought up some interesting variations on this theme, and I thought I would share some with you.
First up, Venn Perplexors are a series of workbooks that have levels suitable for Kinder and up. Level A sticks with the concept of students grouping pictures and words into diagrams, but the other levels challenge students to use Venn Diagrams to solve math problems. It’s an unusual way to do algebraic thinking that is great for students who need some math enrichment.
I’ve posted about “Logic Zoo”, a PBS Cyberchase game here. It’s fun to play on the interactive board with students in Kinder and 1st.
Another interactive board possibility (for a bit older children) is this one.
Anaxi is a unique game that I included in my Gifts for the Gifted Series in 2016. Players use translucent cards to create Venn Diagram categories that require some creativity to fill. It’s challenging, so I would use it with 2nd grade and up.
Today, I had an interesting discussion with my 3rd graders with this puzzler from Math Pickle. I think this has been my favorite Venn Diagram activity so far. The free printable has 13 different blank diagrams and a list of 13 groups of 3. Problem solvers must find which diagram matches which group. For example, what would the diagram for “reptile, crocodile, and female” look like? The great thing is that the answers are NOT provided, so we were all trying to figure out the answers and debating our solutions. I loved the critical thinking that was used for this activity, though it might be better suited for 4th grade and up. I could definitely see making some of these up for other subjects, too, like geography or social studies. Also, Math Pickle has some other Venn Puzzlers which look wickedly fun here. (I want to try the polygon ones!)
Silvia Tolisano of the Langwitches Blog shared in this post how a teacher from Argentina is trying to help her first graders learn about the “tooth” traditions of other countries. Students are invited to add to this Flipgrid their own stories about what happens when they hit that favorite milestone of losing a tooth. Similar to the other lessons that I’ve shared that help students to learn about commonalities and differences throughout the world, this is a wonderful idea for crowd-sourcing knowledge from our young people about a topic that means quite a bit to them! Unfortunately, there is a disadvantage for those of us who are mono-lingual, as several of the videos that have already been shared may be in a language you do not know. (I tried using Google Translate on my phone with some interesting results…) Maybe including some hand-drawn pics like the one below might help.
I enjoyed hearing Maggie H.’s comparison of England and India (I think my students will be horrified to hear that some children plant their teeth!). Considering the wide variety in monetary value that teeth seem to bring just within my tiny class, it might also be fun to research the currency exchanges mentioned and do some math along with your geography lesson.
You can e-mail at email@example.com if you need the answers. However, I that you consider not getting the answers so you won’t help your students too much. It’s fun to do some of the challenges as a whole class so you can verbalize your own problem-solving steps with the students!
My 4th grade students are currently studying mathematical masterpieces. I love showing them examples of the intersection of math and art. When I saw a tweet yesterday morning from @TheKidShouldSeeThis with a link to the video of John Edmark’s spiral geometries, I knew right away that they would want to watch the video. It weirdly connected with the magical drawbridge from yesterday’s video, so I showed that part to them first. We have already talked about Fibonacci and the Golden Spiral, so they immediately found ways to connect both videos to their learning.
Since the students have also been using Scratch coding, I found a Scratch project for making spirals. First we looked “inside” to decipher the code. Then the students explored running the program. After that, I talked about creative constraints, and gave them the challenge of changing one and only one part of the code to see how it made the program run differently. They recorded the results of their new programs and the class tried to guess what variable each student changed based on the videos. Then I gave them time to freely remix however many parts of the program they liked.
This was one of those times that the students could happily have explored all day. It was their first time remixing a program, and they delighted in trying to take it to the extremes by putting ridiculous numbers in to see how large or small or non-existent their spirals became. Some of them created spirals so tiny that they appeared to be flowers blooming as they popped on to the Scratch stage.
And I still haven’t blown their mind with this Vi Hart video yet. With the school year almost over, we may have to take this unit into their 5th grade year. There is so much beauty in math, and we have barely scratched the surface!
I am currently offering an online Google Classroom for some students in our district that assigns them one Digital Breakout (Math) a week for 5 weeks. “Scholastic Beasts” is the 4th one in the series. For the first three, you can see:
All of these are designed for 4th grade gifted and talented students. As with the others, you can e-mail me at firstname.lastname@example.org with the title of the Digital Breakout if you need the answers – but I find that it’s better to not help your students too much!