Gordon Hamilton is the amazing mind behind one of my favorite math sites, Math Pickle. (For a list of interesting math sites, check out this post.) Numberphile is an awesome YouTube channel for anyone passionate about math. So, when the two collaborate, you know that it is going to be good. “Frog Jumping” is one of Hamilton’s recent math challenges featured on Numberphile. I would definitely invite your students (probably 3rd grade and up) to try each problem he poses throughout the video – pausing for them to make their attempts. As for his final frog-jumping challenge, I may have to take him up on it, although it’s hard to imagine that I could solve something that eludes Gordon Hamilton!
My students, especially my 4th and 5th graders, love math challenges. If I can, I find ones that don’t show the answer so we can all try to figure them out. I think it’s good for the students to see me struggling (and I really do!), and how I handle frustration over particularly devilish problems. Last week, my 5th graders and I spent a good 30 minutes on this “easy” problem on Steve Miller’s Math Riddles page. (Technically, they had an excuse since they hadn’t exactly learned the math skill needed to solve the problem – yet.)
If you are looking for some unique math problems that will feel more like brainteasers than standardized test practice, here are some sites that I haven’t mentioned before:
- Steve Miller’s Math Riddles
- Plus Maths Puzzles Page
- Wild Maths (Click on Pathways at the top to get different puzzle categories.)
And here are some that bear repeating (*sites include activities for primary grades, K-2):
- Greg Tang Math Games
- Math Pickle*
- Would You Rather Math
- Math Monday
- SolveMe Mobiles
- Open Middle*
- Video Story Problems
- Erich’s Puzzle Palace
- Fido Puzzle
- Which One Doesn’t Belong?*
With more and more articles coming out every day about the importance of modeling a good attitude toward math (like this one and this one), it seems kind of as simple as 1+1=2 to come to the conclusion that the people who have fun doing math will be more inclined to do it more often.
In my 4th grade gifted and talented class, the students study masterpieces. In addition to masterpieces of visual art, we talk about literary, musical, and even mathematical masterpieces. When I saw the title for Roger Antonsen’s TED Talk, “Math is the Hidden Secret to Understanding the World,” I thought it might fit in well to the mathematical masterpiece section. Little did I expect that it would tie everything together that we had discussed all year.
I should mention that this year’s 4th grade class has some very passionate mathematicians in it. They worship Pi, see Fibonacci in everything, and sit on the edge of their seats whenever I mention that a math activity is imminent. But I wasn’t sure they would find Antonsen’s talk as revolutionary as I do. I was willing to overlook the mathematical examples that were over my head in exchange for appreciating the bigger picture, but would they?
Fortunately, Antonsen’s visualizations managed to maintain their focus, and even their awe at some point, as he gradually brought his audience around to the idea that mathematical equations and representations are actually different perspectives (a few heads raised a bit whenever he said this word, as we regularly talk about multiple perspectives). The “a-ha” moment, however, was when Antonsen said this, “So let’s now take a step back — and that’s actually a metaphor, stepping back — and have a look at what we’re doing. I’m playing around with metaphors. I’m playing around with perspectives and analogies. I’m telling one story in different ways. I’m telling stories. I’m making a narrative; I’m making several narratives. And I think all of these things make understanding possible. I think this actually is the essence of understanding something. I truly believe this.”
There were audible exclamations in my class when the word, “metaphor,” was used. We started the year by learning about figurative language. And the concentration in 4th grade in Texas is on Writing as it is tested at this level for the first time. So, looking at math as a way to tell stories and show different perspectives really captured the attention of my students.
I often tell my students about my childhood struggles with math, how I was often congratulated on my writing skills but made holes in my math assignments due to all of the erasures. It wasn’t until high school that I had a few great teachers who taught me to love math and helped me to see that my only obstacle had been my own fear of the subject.
If I had seen Antonsen’s TED Talk when I was in 4th grade, things could have been different for me far sooner. Instead of feeling like math divides people into those who can and those who can’t, I might have realized that math is actually the language that brings us all together.
I am such a geek. Last night, I was researching mandalas for an upcoming lesson with my 4th graders. I remembered that Richard Byrne had just published a post about a new online magazine creator, so I thought it might be fun to try it out and let my students collaborate on the magazine. Then, I started looking for images to put on the magazine cover, and came across a mandala that used words instead of symbols. There was no information on how it was created, so I did a search for word mandalas – and that is how I landed on Mandific. (I still haven’t discovered how the original word mandala picture I found was made, but that’s okay.)
Type a word into Mandific, and it will create a mandala for you using the letters of the word. You can adjust the color, the spacing of the letters, and the design. See if you can figure out my word in the mandala below.
H/T to GeekMom for sharing this tool on a blog post.
Then, I continued my search (I won’t tell you how long I spent on Mandific before remembering my actual mission.) I found MyOats.com. Still not exactly what I was looking for, but it gave me another alternative for including words in a mandala.
As you can see, I didn’t spend a lot of time on that one because I had suddenly become obsessed with finding the perfect word mandala generators.
My next attempt was with using the word cloud generator, Tagul.
I also tried Tagxedo, which will allow you to upload your own image to make into a word cloud. However, I had so many problems with it not loading correctly on three different browsers, that I finally moved on to some iPad apps.
WordFoto has always been a favorite of mine. I uploaded a photograph of a mandala from the web, and then added some text. If you are not familiar with WordFoto, here is a post I wrote about the app.
My last word mandala attempt was created with the TypeDrawing app. I uploaded a mandala photo, and then traced the main lines with words and some of the symbols offered in the app. After completing my drawing, I changed the photo opacity setting so that only my drawing shows. I have to say that this was my favorite creation.
I will keep you posted on what we use! If you have any other ideas for word mandalas (that don’t require expensive software like Photoshop), please let me know in the comments below.
Perhaps my interest in the infographics on “Common Mythconceptions” led me to Visualistan, which I bookmarked in my Pocket account awhile ago. The specific infographic I thought might be useful for my students was, “How Long Did Famous Structures Take to Build?”
Having time during this Spring Break, though, I found some others that might be of interest in educational settings. For example, if your students are doing animal research, you might want them to take a look at, “Travelling Speeds of Animals,” or “Sleep Habits of the Animal Kingdom.”
You can also find more infographics at Visualistan
You can also find more infographics at Visualistan
Another one that I find intriguing is, “Cultural Differences in Teaching Around the World.”
Like “Common Mythconceptions,” I would not recommend the entire site of Visualistan for elementary students, but single infographics from the site could certainly be used at all levels. There are many real-life math applications and engaging topics, from “Lego Bedrooms,” to the “Evolution of Video Games.” You could create your own questions, have students create questions, and eventually allow students to create their own infographics!
This year I seem to have a group of students in each of my grade levels who are passionate about math. Every time I pull out a math activity, they devour it with glee. It has been a challenge for me to give these students assignments which maintain their excitement for “hard” math without discouraging them with work that is too difficult. Their classroom teachers are facing the same dilemma.
A couple of weeks ago, I decided to see what my 4th and 5th grade gifted students thought about Prodigy. Prodigy is an online math game that is free. (It is also available as an app.) Teachers can add classrooms of students, and can manage the math topics students practice, as well as the levels at which each student plays. I immediately assigned all of my students to topics above their current grade levels. After introducing it in class, I gave them their individual passcodes, letters for their parents, and the caution that playing Prodigy was completely optional. I also notified their homeroom teachers, and made it clear to the students and the teachers that it was completely up to the teachers to decide if the students could play the game in class.
My students say that the graphics are apparently reminiscent of that popular game, Pokemon. The students create avatars and can battle each other by doing math problems. They can also earn different abilities as they progress through the game.
There is a paid option for Prodigy, where parents can buy memberships. This allows the students to access a few more features than the free version. I have one student who asked his parent for permission to get the membership so far; everyone else seems satisfied with the free game.
I like that I can see individual student reports with Prodigy and that I can differentiate for each child in my class. I am also pleasantly surprised to see how excited the students are about playing the game. In addition, the privacy aspect seems fairly good, as the avatars do not give away any student information.
Prodigy does not teach. It is not a substitute for engaging classroom lessons that include higher order thinking skills. I enjoy using it as a formative assessment as it gives me reports on the strengths and weaknesses of each of my students in the skills they are assigned, but I would be appalled by any teacher who used Prodigy as their only method of assessment or differentiation.
As long as my students continue to be excited about math, I will view Prodigy as one of the many tools at our disposal that supports their learning. But I will also continue to provide them with real-life opportunities to use math in relevant ways.
Don’t tell anyone, but Greg Tang Math penetrated my incredible resistance to e-mail spam and persuaded me to visit the site out of curiosity. I’m not really sure why the persistent e-mails that I kept trashing finally grabbed my attention, but I obviously wouldn’t be writing this post if they hadn’t eventually been successful. (If you happen to be a spammer, please don’t think I am encouraging you to try the same strategy; I can promise you that it was a one-time-thing…)
The good news is that I actually found some unique math materials on the site. There are plenty of free resources that you can download, and even some interesting online math games. For gifted students, the Kakooma and Expresso pages are great challenges. (There is also an online version of Kakooma on this page.) In addition, there are some printable math games on the resources page.
Of course, there are plenty of things you can purchase on the site. Otherwise, what would be the purpose of the e-mail barrage? But I think that you will agree that there is a generous dose of free materials, which makes some advertising bearable 🙂