Math is a big place, and I want my students to see lots of examples of what math can look like. One way I’ve tried to do this is through weekly challenge assignments. They meet a practical need — giving students something mathematical to do when they finish early — and they can also help broaden students’ ideas of what math looks like.
In the past when I thought of challenge assignments I would think of “problems.” The internet has lots of puzzle-like tasks that ask students to experiment, connect ideas, or have a stroke of insight on the way to a solution. Problems are one part of what I do with challenge assignments, but there’s much more out there. Students can explore different digital math tools, learn a bit about a new idea, play with interactives, create art, and more. Below is a list of some resources I’ve used to create these assignments. There are plenty of problems in there — problems are one important part of what math is — but there’s a lot of other stuff as well.
Offering broader options as challenge assignments has an extra benefit: it’s not always the students who have good grades or excel in other parts of math class who enjoy working on them. Plenty of times a student who doesn’t think of themselves as good at math finds a challenge assignment they enjoy working on. I teach 7th grade, but many of these resources can be adapted across grades.
One note before I start: I know that creating another weekly assignment can feel like an extra burden for teachers. Last year when I first designed these, I would keep a running list of potential ideas for challenge assignments. Then, about once a month, I would take 20-30 minutes to pick through my list, play with some ideas, figure out which work best, and mock up some simple assignments in Google Classroom. The assignment is usually just a screenshot of a problem or a link to a website and 1-2 quick reflection question. It is a bit of extra work, but I enjoyed that time exploring new mathematical ideas. I hope this post can act as a bank of resources for teachers to do something similar for their classes.
The Good Stuff
Ok here we go. Some ideas for challenge assignments:
Mathigon. Set students loose with a Penrose Tiles or other tiles for a tesselation challenge in Polypad, play with tangrams, work through a course (I had a good success with the graph theory one), explore the timeline of mathematics or the almanac of interesting numbers, or just grab some problems from the calendar puzzles.
Play With Your Math is my favorite resource for problems, and each problem is easy to play with and explore.
Puzzles! My students have enjoyed the Fifteen puzzle, Game About Squares, and the Blue Box Game. Naoki Inaba’s puzzles are awesome, and Sarah Carter has a great collection. This puzzle website also has a ton of different online puzzles with different difficulty options (scroll down to see the different puzzles).
The EDC’s SolveMe puzzles are fun, and have an option for students to create their own.
Ben Orlin’s Math Games With Bad Drawings is a great source of mathematically-oriented games. If you search around on the internet you can find some of his games without having to order the book. Ben’s probability fables are also thought-provoking, and while they’re better for older students I enjoyed using “The Wise Monkey.”
Explorables. There are lots of places on the internet where you can explore an interactive simulation and see what happens. Complexity Explorables are really interesting — while many of them are over my students’ heads, it can still be fun to explore and try to make something pretty, and the epidemic and traffic ones are more accessible. Vi Hart and Nicky Case’s Parable of the Polygons is really thought-provoking and well-designed, as is this gerrymandering game.
Euclidea! I find these puzzles so much fun, and they’re a great introduction to constructions for students of different ages.
Finally, some miscellaneous fun: broken calculator puzzles, the nerd search, Vi Hart’s hexaflexagons, the locker problem, the Josephus problem, and just randomly searching the internet for “riddles” or “logic puzzles.”
This isn’t anything close to exhaustive. But I hope this is enough to get a teacher started, and get a glimpse of how much is out there.