Free Math Distance-Learning Problems & Project Templates

Last week, I shared a project that I gave my students to help them both understand the realities of the coronavirus world, and to get them in the habit of being regularly informed and engaged in societal conversations. I think it’s a project that everyone who has some time on their hands right now would do well to complete themselves, so I encourage you to check it out and possibly even do the project. 

However, this week I want to share some thoughts for educators who are now learning how to continue teaching courses in an online manner. I will end by sharing a examples of mathematics projects that are NOT related to the virus (I’ve given quite a few assignments on the virus at this point, so this one is a return to ‘normal’ mathematics). Let’s jump into it! 

To begin – some considerations for educators now teaching through online learning. 

1. As a teacher, release yourself from the expectation that you have to make kids learn content. Embrace the fact that you get to provide them with the opportunity to learn, and begin convincing them that it’s worth it. 

If you’ve read this blog before, you know that I believe the job of the educator is not to make kids learn… it is to provide opportunity and access to learn, and to facilitate learning through the creation of worthy and locally-relevant tasks. I know this is a tricky nuance to comment on, but the reason I believe in this so fervently is … well, it’s got a whole host of reasons. 

On the teacher side of things, I think there is no better way to make a young, inspired, and passionate teacher absolutely HATE the profession and rapidly get out of it than to put them in a classroom with kids who don’t care and aren’t allowed to fail, and to say ‘by the end of the year, these kids must know this list of hundreds of standards’. That sort of a system makes inspired, passionate teachers (which we desperately need) feel disheartened, and it leaves behind teachers who have disconnected and emotionally-hardened themselves (aka lost the passion) in order to keep teaching. 

Secondly, it does a disservice to students. When I, as a teacher, accept the fact that the great ‘low-floor, high-ceiling’ question that I asked (see below) is simply not going to capture the attention of 40% of my class, it allows me to choose to let that 40% ‘just get the question done,’ and I can focus more of my attention on the 60% who say ‘this might not have been what I chose to do on my own today, but you are excited about it and I know you always support me when I get stuck and stick with it all the way to the AHA! Moment… so yeah, let’s get into this thing!” Eventually, members of that 40% begin to see that it’s just easier to just get into a topic, especially when you have to be in the class for the next hour anyways, and when a lot of people around you are into it, the energy often brings the entire community along. Kids need communities like that around them, and a teacher can’t create that community when they are worried about forcing that 40% (or whatever you percentage is) to come along rather than coaxing them into coming along by keeping your own teacher-stoke levels high and then creating the community that actually has some fun learning. 

2. Cool it. 

Now that you’ve released the expectation that kids HAVE TO LEARN EVERYTHING THIS YEAR(!!!), cool it down. The online environment simply will not look like the classroom environment, and although we’ll comment on some of the specifics of what that looks like later on, for now understand that the amount of work that you assign can and should decrease, and the nature of the work should change correspondingly. We’ll talk about this more below, but for now understand that if your normal math class has a lesson, 20 in-class practice problems, and 30 homework problems, your current situation may now need to be 5 practice problems a day, or one problem a week depending on how you structure it. This is because while we think students have plenty of time right now, we don’t actually recognize what their family structures look like or how well parents can support them in getting work done. Sure, there may be some students who are just playing video games all day, and we want them to be using their brains instead – we have to accept that we can’t make those students learn, and there are plenty of others that are not in that situation who we can’t stress out because of wanting to force a few students change their habits. 

3. Create tasks that are ‘low-floor, high-ceiling’. 

For all the students who are currently spending their days playing video games 24/7, there are also a TON of students still pushing themselves educationally – especially if you’ve cultivated a classroom community of curiosity by giving students the opportunity to learn (with authentic failure as an option) rather than forcing students to learn. In order to have your assignments be more meaningful, shift away from questions that have one, correct response, and use questions instead that are ‘low-floor, high-ceiling’. These sorts of questions allow anyone to access the content, but provide ample space to take the solution much further by developing theories or algebraic equations to support the basic findings. The project that I have attached is intended to be an example of this sort of question, because anyone can dive into the question by physically modeling the situation and beginning to find some patterns; however, students who really want to take it further can develop a theory of mathematical structure to help them support their findings. 

4. Now is the time for writing, even in mathematics. 

This year, one of my personal projects has been integrating literacy into mathematics. I know, I haven’t written about this enough yet! However, one of the major challenges that I have faced (and that has given me a TON of respect for my colleagues in humanities that edit papers all the time) has been that I don’t have enough time to formally edit the writing that my students produce. Given the fact that (even as a mathematics teacher) I believe the one skill that everyone must gain mastery over in the modern world is editing our own writing, this lack of time was concerning to me. Now, I think I have the time to edit student writing with greater depth, and this is important because even in mathematics we learn important things about our students’ thought processes through their writing. 

For example, as a math teacher, you might try asking the question: What is multiplication? Ask for a written response, though it can include a diagram if the student desires. The responses – how your students conceive of a basic mathematical technique – may surprise you. Some students will brilliantly explain that multiplication is a way of expressing sets of items – for example, three sets of coconut milk packages which each contain four coconut milks make twelve coconut milks. Eight sets (groups) of seven people make 56 individuals, which is far too many together at once in today’s world. 

I know it feels like asking students to write an explanation about how they would solve one problem isn’t developing the same skills as asking them to factor thirty quadratics. However, you may be surprised by how much depth of understanding and appreciation for the field of mathematics kids gain through actually understanding Why the techniques exist. Here are some supporting articles on that point: Introduction to Mathematical Literacy, Mathematics and Why?, and Teaching Trigonometry for Understanding

Obviously all of the projects that I share below have a writing-heavy focus as well. I grade students as much (actually, kind of more) on the extent to which they are able to explain their process than whether or not they did the math ‘correctly.’ For examples of viable, written-response/low-floor, high-ceiling humanities questions, I refer you to the COVID-19 Analysis Project I gave my students last week. 

5. If you do assign problems with one answer, post a review of those problems with it. 

Yes, that could allow students to ‘cheat’ by simply checking out the review before ever starting on the problems. That’s OK… see tip #1 and get over it! However, as a second tip on this suggestion, I handle it by including in the instructions that I post a statement that says something to the effect of: Answer the question below! DON’T WATCH the video until AFTER you have tried the problem on your own, because as you know, if you are just handed the answers, your brain is like “oh man, cool, that didn’t require much effort, no need to keep any of that stuff around in here!” If you try it yourself first, then watch the video, your brain says the opposite “Hmm, that was a lot of effort! Well, let me see what my teacher said in his review video that he made… OHHHHH! That is a clever way to approach it! Man, I should hang on to all of these methods of thinking because it seems like the time I’m putting in makes it worth it.” I know, that was a great impression of the brain 🙂 

6. Keep connecting. 

There’s a reason (that honestly requires a longer explanation than I can give here) as to why free, online courses that provide some of the same content as is provided through very expensive, university-level courses are not being completed by a majority of the population. At least one of the reasons is because it’s hard to stay inspired when we’re at home all alone. Don’t underestimate the value of leveraging technology to inspire students – as social beings, we need to connect with and derive excitement from others. While doing this via sound-recordings or video conferences may not be perfect, when students just hear the excitement in your voice or think about a comment that someone else in the class made on an (optional!) conference call, some of them will re-engage where they weren’t before. Of course, right now, it’s not all about curriculum, so make sure to also include some updates where you are just checking in and saying ‘hey, remember that there’s someone here who cares about you and your continued growth into an awesome human!’ 


The Projects: 

Below are links to some projects that you are welcome to adapt in your own classrooms. To invoke Prince Max and Kurt Hahn here, I am proud of the fact that there is nothing original in here – this is all adapted from other geniuses like Jo Boaler, the Interactive Mathematics Program, or other ‘lore’ problems because “It is in education as in medicine, you should harvest the wisdom of a thousand years,” as Hahn said of Salem. Feel free to contact me for support if you’d like – I can make a Khan-style video for any of these projects that will get students started if they are stuck and need a little boost. 

The Light Switch Project. Number Theory. Found in Francis Su’s Mathematics for Human Flourishing. You will notice the formatting on this project – I experimented with kind of ‘forcing’ kids to get started on the project early by doing the math part of it as ‘a test,’ which they would then go back and use to finish the rest of the project. Make it your own – this one is AWESOME in terms of “why these numbers though?”

Broncos Score Dilemma. Linear Systems. I kept this from back a few years when the Broncos were good! (but you could always update for last season’s real stats). 

Jazz-Pop and Hip-Hop. Linear Systems of Inequalities. Adapt the characters in this project to be characters at your own school to make it more fun!

Squares Upon Squares. Introduction to quadratics and non-linear functions. Adapted from Jo Boaler at 

Picture Story. Number Theory / Introduction to Non-Linear Functions. Adapted from Jo Boaler at 

Longboard Design. Quadratics / Geometry / Substitution. 

Broncos Field Design. Quadratics. 

Somebody’s Birdhouses. Finding the coefficients of a standard-form quadratic by solving a system of three equations for three variables. Adapted from IMP. Adapt the names to your own students for fun. 

Maetatron’s Cube. Intro to Conics / Graphing Tools. 

Have fun, get inspired to create a new cool project, and share it with us! 


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