The Who, What, When, Where, Why & How of Math Challenges.
I really believe in the idea of Math Challenges. The ones I am sharing here I have given just recently but I have come to realize that I have been giving math challenges in one form or another for years and years. Before I get to the challenges, here are the basics to help you decide if they fit within your math program. (Spoiler alert – they do!)
My experience has been with the middle school crowd. Depending on where you are in the world, mathematical concepts may be explored at different times, in a different sequence, or at different ages than here in Eastern Canada. Some of these challenges are appropriate for children regardless of their exposure to certain ideas while some may require knowledge of specific vocabulary or comfort with certain operations. But I am sure you can find something here that is right for your learners. Or perhaps, just reading through the challenges might spark an idea…you could tailor something you see here and create a new challenge that might work well for your group of math minds.
Complete with your class, a team, a partner, or individually. I have tested every such grouping. All have been successful. Introducing the challenge to students together as a group works well so everyone can ask questions or have that common understanding or starting point. And don’t limit yourself to students. Trying one of these challenges to kick off a staff meeting would be fun too!
What about who puts on the challenge? This is a good opportunity for teachers to work together and collaborate on ideas. If you have several teachers on your math staff, you can take turns creating, choosing, introducing, and scoring the challenges. That way students can witness a great example of teamwork, know that there is a shared view of what it means to be awesome at mathematics, and see that everyone believes math is a fun, broad, and amazing topic. Why not have your math club or kids in need of an enrichment opportunity take charge of your school wide math challenge? Having the principal give shout-outs over the announcements also makes it feel important, special, and super cool.
The actual challenges come from a wide variety of sources. Some started as games, others showcase the connections between math, art and nature. Some are familiar challenges that are already widely tried by teachers with their students and some offer a new twist on a common topic. Most are found ideas not original to me. I have often just taken ideas and created a presentation and the materials needed for use with students. I have done my very best to acknowledge my sources for the work I have included here in creating these challenges.
The beauty of these challenges is that many can be completed just about anywhere with minimal or easily sourced materials. I have used many of the same challenges just as easily remotely as was done in person.
I like to introduce a challenge to students the very first day of school. I feel that it sets the tone that math is fun and challenging, beautiful and complex. That math is more than just manipulating numbers to get the only right answer. That math often requires revision, making mistakes, learning from mistakes, and persistence. But be flexible! Challenges can be launched at any time. For the ones found here, I have begun a challenge on the first day of the week, and required submissions be in by the end of that week. Then offerings can be showcased and a new challenge given at the start of the following week. However, depending on the clientele, the challenges could go longer or get wrapped up quicker.
Challenges can be introduced that first day in place of your regular warm-up. Students can then be directed back to work on it at a designated time each day or perhaps just when their regular classwork is complete. A little trial and error will help you decide what works best for your class or school.
It is fun! Students love it! …and not just the winning or prizes…they love the math! It may also surprise you who loves it. The usual suspects you already know love playing with numbers and patterns will love this of course but other less likely participants emerge. I’ve heard comments like, “These challenges made me love math”, and “I didn’t realize I was so good at math until I did these challenges!” Don’t be surprised if you start to hear these comments too. The playing with numbers and figuring things out is satisfying. It can give students a broader view of what being good at math is, and helps showcase abilities in different groups of students depending on the content of the challenge. From a practical perspective, it acts as an anchor activity. I always have classes that include students with a wide variety of math experience. Some are quick and confident, others reluctant, nervous, or need time and individual or small group support to be successful. It is a relief to have that go-to task for students to be engaged with when their assigned work for the day is done, when they are waiting for assistance, or when a break is needed to recharge.
Find a challenge you like, make a copy and customize it. Take out links to sources so solutions can’t be easily found. What extra information or background might your students need to be successful? Will they need materials? Technology? Get organized. How will your students find out and be reminded about the challenge? How will it be submitted? I have tried a couple of things. In my own classroom, organizing was easy. I had a bulletin board specifically for my challenge that acted as a visual reminder. Materials could be located here and work from past challenges showcased. Easy peasy. My first crack at a school wide challenge had me scheduling times to go into classes and introduce the challenge myself. This was a nice way to give classroom teachers a little break and make sure that all classes had a consistent introduction. But scheduling was tricky and it meant that teachers had to give up a chunk of time. And all students were compelled to participate – like it or not. For my second attempt at school wide participation I created a google classroom just for the weekly math challenges. This included a video introduction as well as a copy of the presentation required for each student to participate. Students were invited to join if they liked. This has worked really well so far, but may be difficult to manage with a large number of participants. Try different things, be flexible. The joyful mathematics is worth it!
Have a look at the challenges I have given below. I have the presentation and/or video I used to introduce each one and some notes on the source. Test them out…help me make them better. Please let me know which ones you try and how it goes.
Weekly Math Challenges…
Factors & Multiples
This challenge was created around a game I found at https://nrich.maths.org/. NRICH is an effort by the University of Cambridge to provide rich math tasks to learners. I found this task so engaging I knew students would love it too. Looking for a low floor/high ceiling task that promotes perseverance? Then this is the task for you! (Lots of other great materials at NRICH – check it out!)
Mondrian Art Puzzles
Thanks to George Hamilton and mathpickle.com for this one.
The google slides presentation given here contains links to original sources and handouts to distribute for students to use.
This challenge was introduced as a group, a trial run done together, then hanouts given to be completed in the traditional pencil and paper style. (Also…spend some time at mathpickle.com – amazing!)
Inspired by the amazing card game, this challenge promotes flexibility and tenacity. Students can try the online version by coolmathgames.com, and/or try to make 24 with the sets of 4 numbers given in the slideshow. Options for whole numbers, decimals, and fractions. Good for warm-ups too!