I’ve made it a month into full-online teaching! I’ve got my 6th grade math class, 7th grade math class, and grades 7-9 venture class every Monday-Thursday. Friday is a day for staff development and asynchronous work. Here’s the report for these weeks and any other pro tips I can share.
I am going to jinx it, but I think I’m hitting my groove in math. I have never really taught 6th grade math before, and I’m rusty on 7th grade math, but I’m finding my way. I have found that if I take the workshop-style problems I normally would have given kids in class on paper, and convert them to Desmos activities, the lessons flow pretty well and most kids are engaged and active. I make Desmos activities for literally everything. I’m not the most advanced user of the Activity Builder, but these allow me to guide the students, fix problems and coach them in realtime, see everybody’s work, curate samples and share them out with the class… it’s getting there. Today I did an activity and I could tell some kids were flowing well with it and others were really stuck. I asked the class if they were ready for a hint, but a few students yelled loudly “No hints! I want to figure it out myself!” So then I tried a new teacher move, and I told the students if they wanted hints, to send me a private message in the chat, and I would invite them into a breakout room and I’d give them hints there. 5 students sent me messages, and I pulled them into a breakout room and gave them the hints, and we went back to the main room. It was super cool to see that students didn’t want hints and wanted to figure it out on their own, and the students that came to the breakout room were grateful.
My three teaching tools I use over and over again: I create activities in Desmos and pace them so we can discuss problems every few slides; I pause, run over to my laptop, train the camera on my whiteboard and give a few quick notes and examples; I assign homework and quizzes in Khan Academy. I assign work twice a week, always with 2 days to complete assignments. I have never gotten a good response if homework is due the next day, and some kids have busy lives and can’t rearrange everything to accommodate last-minute homework.
Here are some of the Desmos activities we did the past two weeks:
Decimal Addition and Subtraction (6th grade): The students were pretty comfortable adding and subtracting with money, so I used this activity to introduce them to adding and subtracting with more than 2 places past the decimal. After every slide we stopped, took some notes, and had a quick discussion.
Multiplying Decimals Card Sort (6th grade): Before the card sort, I gave the kids some notes showing them fraction/decimal multiplication equivalents. For example, 3/10 x 7 = 21/10 = 2 1/10. This means that 0.3 x 7 = 2.1 because 0.3 is 3/10 and 2.1 is 2 1/10. We did a few examples like that and then the students did the card sort. I paused every so often and let a student explain a match they made and why. The 2nd and 3rd slides are a warmup before we start multiplying multi-digit decimals.
Adding Integers (7th grade): I used this as the first lesson on a unit about rational numbers. The students really enjoyed it. I paced it so I opened up 2 or 3 slides at a time, and we would have a discussion and share work after each group of slides.
Adding Rational Numbers and Intro to Subtraction (7th grade): I adapted a lesson about bank statements from Illustrative Mathematics to introduce adding positive and negative decimals to the students. We introduced integer subtraction and subtracting negatives. The “bank statement” part of the lesson was very challenging, because of the many concepts and skills packed into it. Decimal arithmetic, understanding of where these numbers go on the number line, attention to precision. A gap in any of these could cause a student’s balance sheet to turn into a disaster quickly.
I’ll just quickly add that in my venture class, the students are now doing their project pitches, and although I’m nervous about running into a time crunch with the end of the quarter…. I love the project pitches they’ve given. They are all doing a project about something they already love and enjoy, and tying it into the theme of “The Impact of the Internet”. One student will be making an informational webpage about chihuahuas. Another student will be making a dog feeder from a Raspberry Pi. Another will be publishing history videos on a YouTube channel. I am cautiously hopeful that they will learn and love their projects and get a lot out of this weird quarter of school.
Each day I’ve started to add creative writing activities to Advisory and that’s been more fun than I expected. I haven’t done creative writing in a long time and I’ve even gotten sucked into it. The topics here are a little grown-up for my students, so I adapt them a little, but Jane McGonigal is a futurist I follow on Twitter and she published this “game” which is a creative thought-experiment about disaster scenarios for the information age. They’ve provoked really great discussion during a time when kids’ cameras are usually off and they’re silent, so since the kids have found this engaging, I’m sharing with you:
Try it with your advisory students – do a 5-10 minute quickwrite, then make breakout rooms and share out what you wrote and have a discussion afterward with Jane’s followup discussion points on the web link. The kids will enjoy it and so will you.
- Not really a tip so much as a life skill… you gain nothing from being grumpy with the kids right now, and they gain nothing. So just be kind. If a kid has their camera off and isn’t participating, check in on them. Say “I haven’t seen you or heard from you and just wanted to check in. Do you need any help?” And just keep asking. Wave goodbye with a smile every class. Here’s a pro tip I learned in pre-teacher service that I still use. Tell your class, every day, that they’re your favorite class and you really enjoy them. Say it for a week or two and it’ll be true, I swear.
- Get up and move. You can’t do remote teaching from your chair all day. You normally move when you teach. Shift to a standing desk or angle your camera so you can draw on a real whiteboard and stand up. It’ll help, I promise. If nothing else, you’ll be more animated and enjoy presenting more.
- I’m going to put it out there that I am very much warming up to using Khan Academy for homework and I think I’m going to use it all year. What a gift to not have to grade homework or quizzes…. I can spend more time analyzing what they know and don’t know, and less time just marking up papers. 9/10 other than a few minor complaints it is very much recommended.
- Get blue-light filtering glasses. It has made a huge difference… I used to suffer from migraines every week and I have only had one mild headache since I got the glasses. I got them for my kids too. Essential for remote learning!
- Celebrate the kids’ pets. You might as well, you can’t have them at school. Sing awkward birthday songs. Change your background. Play lobby music. Give silly attendance prompts. If doing stuff other than math content increases engagement…. then yes, do that.
- One last pro tip: If you’re teaching on a PC and not a chromebook, you can install Snap Camera and use that as your camera in Zoom. Snap Camera lets you apply filters, so you can teach with mouse ears or rainbow hair or looking like a potato. If engagement is suffering then definitely get Snap Camera.
That’s it, have fun out there everyone.
I don’t have a lot of exciting lessons to report, but I wanted to share out some tips, tricks, and general observations from online teaching now that I’m into the flow of it a little.
In math 6 and math 7, I taught the same review unit for both – fraction operations. I thought it would move faster with my math 7 crew, but I found as we got into it that they needed the review just as much as the 6th graders. The curricula diverge after this week, but it was nice to reuse the same lesson plans for a brief moment. 🙂
I continued to use Desmos as my main teaching tool. When we were working on multiplying fractions, I did try an activity with Jamboard where I put the students into breakout rooms and assigned them tasks that I adapted from the Connected Math Bits and Pieces II textbook. I thought I modeled the activity well and set it up for success, but when the students were put into breakout rooms, they got quiet, refused to talk to each other, scribbled on the jamboard and then erased each other’s scribbles and really didn’t engage with the math. Frustrating. I stopped the activity and went back to individual tasks for the moment. Flash cards still work ok in breakout rooms, but the harder problem-solving is not something I can have them do in groups yet. Here’s the jamboard in case you want to use it. Maybe you’ll have better luck or suggestions for virtual group work?
I stepped back after that activity and I changed strategies. I taught the students the algorithm for multiplying fractions (numerator x numerator, denominator x denominator, then simplify) and gave them some Desmos tasks to evaluate expressions using the algorithm and then explain why it worked using a drawing. This led to a pretty good discussion and better quality of work from the kids.
After every 2 slides, I would pause and give the students a small amount of notes – multiplying fractions, multiplying a fraction x a mixed number, then multiplying two mixed numbers.
We used this Desmos activity for division expressions involving unit fractions. It was a good activity and again, we had high engagement and a good discussion.
Now I am at a point where I want to give the students a quiz to see how their fraction operations are coming along. I have a Desmos “quiz” prepared and also have curated the Khan Academy unit quizzes covering the same topics. I think I’ll assign the Khan quiz in class, but if students need to do a redo, I’ll let them to retake using the Desmos quiz. We’ll give it a try!
One more note about teaching math: I wish I could find it now, but back in August I saw some tweets from another math teacher where she tried giving notes using the Zoom whiteboard tool, and then using a physical whiteboard with a camera trained on her, and when she asked her students what they preferred they said they liked the physical whiteboard better. I decided to try this too, and I like it a lot. If nothing else, it gets me moving – it’s amazing how much I even miss that part of teaching, the standing and the moving! So I have my desktop computer on my normal desk, and then I have a small podium where I put my laptop facing the whiteboard. I have my laptop join the Zoom call along with the students. If I want to give notes, I mute the desktop, run over to the laptop, unmute it, and write on the whiteboard. I take photos of the whiteboard with my phone so I can post notes later for students that need the notes for their accommodations.
For advisory and venture, we finally finished playing everyone’s kahoot quizzes, and I started on a lesson on identity that I adapted from tolerance.org. I think the lesson is supposed to be used for teachers to reflect on their own identity… but it was useful for students and actually generated good discussion… and good discussion is SO hard to find in online teaching! The kids asked thoughtful questions and mainly wanted to know about vocabulary terms… what is ethnicity? What is socioeconomic status? And they reflected a little on times when they took their identity for granted and when they found they had to adapt because they were not in a dominant identity group. It was good.
Here are the slides I used.
Other random tips about remote teaching:
- I have one of those Ring Lights, and I definitely prefer it to the overhead lights in my basement.
- I got a small standing desk, and at lunch I pick up my monitor and keyboard and stand for the rest of the afternoon. It helps SO MUCH.
- I have continued to start each class with broadway show tunes and a silly attendance prompt, and these routines have become really important to me and the kids.
- I ordered some blue light filtering glasses and I also turn my monitor to Night Light mode during the day. It has actually helped with headaches a lot – I can’t believe I never tried this before.
- If kids have pets on screen, of course we acknowledge them and enjoy them. I appreciate something that makes the kids turn on their cameras and interact with each other… and pets do the trick sometimes.
- I am still up late most nights and work some pretty long hours and don’t get out of the house much. Getting the content organized is a small part of the teaching challenge… organizing it so it flows online takes the most time. I feel like I have to be hyper-organized with everything. When I teach in person, sometimes I don’t even write lesson plans, I just have a rough sketch of what I’m going to do and I march in and wing it. I do not feel like I can do that right now. In this respect I feel a lot like a first-year teacher again.
- I have 5 minutes of passing period between my morning remote classes and IT IS NOT ENOUGH!! I show up late to my second class more often than I’m comfortable with! But sometimes I have a kid in that first class who needs just a couple more minutes to figure out how to attach the file, take the screen shot, find their late homework, whatever… and it’s not like I can just go find them at lunch, you know? I wish I had a little more time at the end of class for those last-minute things.
- I’m finding ways to make remote teaching work and am pretty proud of what we’ve been able to accomplish in spite of the challenging circumstances… but I ache to just be back in the classroom with actual people.
It’s now Tuesday September 1, and I’ve been teaching fully online for a week. My class is a competency-based, Project-based learning school, and this is only our third year even existing as a school, so it’s been completely novel preparing to do school this way.
I teach two classes of middle school math in the morning, and then our venture block in the afternoon. Venture projects look a little more traditional in the beginning, but as we progress through the class, it becomes more individualized and problem-based and eventually we fold in the design process and turn it into a project. My venture class has a theme of “The Internet Age”. We’re exploring the technical and social/cultural impacts of the internet, and then each kid will be responsible for coming up with a problem statement and doing a design project. I love the topic and am really enjoying teaching it so far.
I just wanted to throw out a few thoughts on things that are working and things that are challenges so far, in case it’s helpful to anybody else.
It’s HARD work. I am up late every night planning, re-configuring lessons I used to have and writing new lessons. Part of this is my prep load and part of it is that even the stuff I do know how to teach, I need to revisit all of it.
It’s exhausting. I am having a hard time telling whether first-week-teacher-tired is really that much worse than previous years. I think it *feels* more exhausting because you just never get away from it. You never get in your car and go home. I’m just at work all the time.
It’s not as soul-crushing as I thought it would be. I enjoy seeing the kids. I can still listen to their funny stories, I love seeing their pets, I love our little routines that help us get to know each other. I start each Zoom session with music, usually Broadway show tunes, and I change my background so it matches the music, and the kids guess what it is. I change up the daily attendance prompt every day so every kid gets a chance to speak and tell me more about them. I dedicate a little time twice a week for me and the kids to do a little tech troubleshooting together, and we are learning together the best practices for managing all the tools.
I have a short chunk of advisory time with my students, and for the first week, I decided to dedicate that time for us to get to know each other. So I had each student write a 10-question Kahoot quiz about themselves, and we take a couple of quizzes every day. To me it feels like a lot of Kahoot, but I think the kids love it – they ask about it as soon as they log in. “Are we doing another Kahoot? Can we do mine?” They’re freshmen in high school but soooo excited about sharing and playing their Kahoot quizzes.
For math, my favorite tool is Desmos. I feel like I have a better idea where the kids are in math than I even do when teaching live. I’ve assigned work in Deltamath and Khan Academy and I’ve also assigned Desmos activities, and with the Desmos activities I can look at the kids’ sketches and what they wrote and I know whether they understand or not. With the other tools, I see what they got wrong, but it’s really tough to tell whether or not they get a concept.
I look for problems in the old Connected Math Project textbooks, the Illustrative Math textbooks, Robert Kaplinsky’s problems, Geoff Krall’s Emergent Math curriculum, and wherever else I can find good activities. I put them onto Desmos slides, make any images into sketch-area backgrounds, add a block to enter a math formula and an explanation, and voila, it’s an awesome formative assessment, individual activity, or group activity. Here are a few of the activities I adapted. They’re for 6th grade math.
For venture, I have decided I love Mural. We do a lot of reading and discussion – and discussions are so, so hard in this virtual medium. SO HARD. Kids are so shy, they turn cameras off, they type one or two word responses in the chat, they say the bare minimum and then turn off the microphones. But if we read an article and then I give them a canvas with an unlimited supply of sticky notes, they have a lot to say. Mural has a timer so the kids have their timer in front of them at all times, and it has anonymous voting tools – so at the end of a sticky note session, the students can vote on their favorite discussion points and then they’re displayed for everyone and the conversation can actually get going.
I created a lesson on the impact of the personalized news feed on how you view the world. I really liked how Mural helped to facilitate this discussion – when we processed what we learned the next day, it was apparent the big ideas of the lesson were still percolating. In the Mural, we first read together the article in the top-left about Mark Zuckerberg’s announcement that Facebook would be changing its News Feed algorithm – and then I taught a little bit about the events in Kenosha Wisconsin – just factual information – and I had the kids split into two groups, and one group read conservative analysis about the events and one group read liberal analysis. I asked the students to imagine what they would think about the killing and the protests in Kenosha if the majority of their news feed was like the articles they read.
Here are the links to the lesson.
I do random breakout rooms. Setting up premade breakout rooms is really time consuming, but I will do it when the need comes up. So far my strategy is to just apologize for making it random and remind the kids to tell each other their names and about the basic norms of group work. Some breakout rooms work really well (I had the 6th graders do flash cards in groups of 3, and it was awesome, and the 9th graders played win/lose/or draw, and that was great) and some are completely silent and unproductive, so I am still working on how to find the magic sauce that makes breakout rooms successful more often than not.
In general, the hardest part of this teaching is student engagement. It is really easy for the kids to turn off the camera and mic and just disappear. I don’t shame them for it, but it’s awfully hard to feel like you’re teaching into a void. So occasionally I will prompt them to engage “Can you still hear me? Is this thing on? Give me a quick thumbs-up or tell me your favorite sandwich in the chat so I know you can see my screen.” Or “On a scale of 1-5, 5 being the MOST confused, how confused are you right now? Hold up fingers or type in the chat.” Desmos and Mural activities are so far the best ones to foster engagement, but I hope to add to the toolbox as the quarter goes on.
That’s pretty much what I know. Soldier on, everyone. We can do this.
I’ve been sitting back and reading a lot in the current cultural whirlwind and rejuvenation of Black Lives Matter. The movement has come a long way. The tide is turning. I feel cautious about real change happening because I’ve seen how powerful inertia can be… and if we’re going to see a true dismantling of systemic racism, it means as a society we need to open ourselves up to being uncomfortable. And unfortunately, I do not think white America is ready for that. We need to take a hard look at how white supremacy shows up in our daily lives… it’s very obvious in the context of police brutality, but we all live in it, baste in it daily without recognizing it for what it is.
To see how white supremacy manifests itself as intertia, I want to take a look at just one aspect of racism in education – school boundaries.
I’m going to show you some statistics from four schools in my city. These schools are just a few miles from each other. It’s not a huge town. The distance between School 2 and School 3 is 1.5 miles.
|% Free/ Reduced Lunch||% Hispanic / Latino||% Proficient Math||% Proficient ELA|
My town has a very small Black community but a sizable Hispanic / Latino community, and you see the racial component of this when I break out the data this way. In the north part of town, it sure looks like the school boundaries were drawn to cluster the free/reduced lunch kids and the Latino kids into School 1 and School 2. There is some white flight from school 1 and school 2 as well… some students who live in the boundaries of those schools choice into other schools in the district or go to charter schools. Even so, it is really remarkable that the boundaries are drawn this way. It’s also segregation. It’s not equitable or fair. It really wouldn’t be that hard to change, just move the boundaries literally a few blocks in one direction or another. I can tell you from talking with friends who have taught in schools 1&2 and their feeder middle schools and high schools, that those schools are really hard to teach in. You have to develop a much bigger toolkit to work there. It can be frustrating and draining and stressful. My only experience in that realm is teaching the grade-level and remedial math classes in my own middle school for a while. They were exhausting. It was so hard to cluster all of the kids who didn’t like school and already weren’t successful with math in the same classroom and try to help them grow. For a few years we de-tracked our math classes, breaking down the “honors vs. grade-level” paradigm and creating heterogeneous classes, and it was SO much better. The mixed classes were way better to teach, kids made better growth and the teachers enjoyed our jobs more. Slowly though, the old paradigm came back and we started splitting the classes into “honors vs. grade-level” again. I think you need a rich toolkit to teach heterogeneous classes, and it keeps you on your toes more, but it is overall a more rewarding experience. I did some reading on the benefits of integrating schools and I am convinced it’s something we need to do. I don’t understand why we keep drifting back into separating kids. Well, I do though. It’s comfortable. “Comfortable” is at the heart of this conversation, and to use a loaded term, “Comfortable” is at the center of white supremacy.
Around 2015, my district had some boundary-redrawing discussions as we prepared to create a few new schools. I wasn’t on the boundary-creation committee, but I attended a few meetings. I wish I had said more then. I looked up the information you see above because I wanted to have some background knowledge, and I was surprised and shocked at the level of segregation in my generally affluent, “friendly”, high performing district and town. I went to the meetings prepared to push on this – to challenge the school board and leadership team to take the opportunity to break down some of this segregation and have mixed schools. But when the meetings started, they opened with several proposals already written that made zero changes to the parts of town that, in my mind, needed them – and the comments were pretty bland, the mood was not at all contentious, and I got quiet instead of stirring things up. I regret that now. We just kept the school boundaries mostly the same and the numbers you see in the table are pretty much the same ones from 2015. A missed opportunity.
Also in 2015, a new housing development was proposed adjacent to my neighborhood. We had this oddly-shaped triangular lot next to our neighborhood ever since we moved in, right on a busy intersection, full of weeds. We knew it would get developed someday and were happy when the proposed development was a nice neighborhood – a Habitat for Humanity community. At least it wouldn’t be a KFC or something, right? I remembered my neighbors were NOT on board with this and at first they convinced me to oppose it too, but by the time the community meetings came around in 2015 I had decided to support it. Our town desperately needs more affordable housing. My dad volunteers with Habitat and speaks fondly of how rewarding it is to see a neighborhood get new life and a new sense of community when Habitat homes are built. That the kids who live there actually have their own rooms and a quiet place to study, and their grades improve. The families get financial security for maybe the first time ever. Plus, we have a Geometry and Construction program at two schools in town, and our local high schoolers actually build the homes. This was an important cause to get behind.
I went to a community meeting and was absolutely blown away by how awful my neighbors were about this “low income” housing community. It was embarrassing and shocking. Many of my neighbors made comments about the traffic and the density and how they would lose their views (over an empty lot??). The pearl-clutching over these inconveniences were out of proportion to the actual suffering we would endure because of a housing development going up. Some actually came out and said they were concerned about the “wrong kind of people” moving into the neighborhood. That it would attract crime. That it would strain the schools and “those people’s kids” would cut through our neighborhood to get to school. That our school’s quality would decrease. That our property values would go down. Now we don’t exactly live in a wealthy gated community. Our homes are really, really average homes in a really average part of town and I couldn’t believe the sense of entitlement and elitism I saw at the community meeting. Wow. I was one of two people that stood up and spoke in favor of the project. The other person was the Geometry and Construction teacher whose students would be building the homes. I think he was shocked too at how unwelcoming people would be to this project that he and his students had invested so much into.
This is a snippet I found online from the meeting. The full document with notes from all the community meetings is here. https://www.fcgov.com/developmentreview/pdf/harmony_cottages_type1_files.pdf?1558477510
The first comment is my part. The next question came from a neighbor. I don’t even know which one. So many of them said the same thing.
“Everyone loves Habitat, but not here.” Over and over. “We have no objection to Habitat for Humanity, but why in our neighborhood?” The traffic, the noise, omg the low income people living one block away and the crime and their kids interacting with our kids and going to the same school….. It was horrifying. I understood why our school board and district leadership don’t really put their whole selves into integrating our district schools over income and race. They don’t want to have meetings like this. I don’t blame them, but we shouldn’t keep avoiding this. Avoiding the backlash is why inertia sets in. Why we settle into what’s comfortable, just separating people according to our natural divisions of class and race and just not fight it. But segregated schools lead to inequities all the way down the line, we know this, we know it’s wrong and the legality is sketchy and we do this anyway – because it’s comfortable, and convenient. Comfortable and convenient are the hallmarks of white supremacy.
The Habitat community did get approved eventually. There are several houses built now and families living in them. One of my current students will be getting one of those homes with her mom. When we had online learning during spring 2020, she had to attend zoom meetings on a phone from her bathroom to get some privacy. Won’t that be amazing when she has a house? The neighborhood is super cute and we like watching it come together. My grumpy neighbors are still mad about it.
At some point in this timeframe, I was listening to the radio and a rerun of This American Life came on, and it was Nikole Hannah-Jones’ special about her experience with school integration. It was riveting. Especially the parts in the broadcast about the parent meeting regarding school integration. That meeting could have easily been in my town, my neighborhood. Here’s the broadcast.
I felt vindicated listening to the broadcast, I felt understood – my experience with my embarrassing, classist, NIMBYist neighbors was way more universal than I imagined. The wild, mind-blowing thing is that school integration, and neighborhood integration, are helpful. It’s beneficial to kids of all races and backgrounds. It makes for a richer teaching experience for the teachers. It really wouldn’t be that hard to do in my own town – really, really easy. Except for the discomfort of white people.
I realized in processing societal integration and the pushback to it, that a lot of white supremacy just looks like comfort. Anything that makes us have to put a little more effort into our lives – wait an extra minute to make that turn, or listen to the families from a different race and class over the fence, or put a little more effort into including people – and we crumble. We’ll cram into yoga studios and train for half-marathons and stay all weekend at our kids’ softball tournaments, but if we are forced to make tiny changes to our everyday lives to accommodate other people we perceive as different… we fall apart, and we do so loudly and violently.
We need to seize this moment and make positive moves toward racial equality. But to do this, we – white people – need to start letting our communities know about the changes we want to see. I really want to see my own school district develop some courage around racial integration and I want my white community to not fight it so hard. This isn’t going to happen just from my wishing it so. I need to speak up for it, and patiently advocate for it, and celebrate small steps of progress, and be prepared for backlash, because it’ll come. And YOU need to speak up for it. It’ll take white people in numbers to do this, but if we are serious about making a fairer, more just, more equitable society, school and neighborhood integration have to happen.
Along with my math preps, I also taught a venture-project class this quarter. I had planned a very hands-on project and purchased a LOT of supplies for the students to make solar lamps, solar chargers, and solar cars. When we shifted to remote learning, I decided to try and make this project run, if a little scaled down. I split the kids up into groups, and a group of 6 middle-schoolers got assigned to be on the Solar Charger team. I have never built this project with kids before and have spent the past few years trying to get the electrical design nailed down. But I really wanted to do this project. All of our ventures focus on community needs, and we’ve worked with the FoCo Cafe and Homeward Alliance over the years to bring donations to the homeless. They’ve mentioned before how awesome solar chargers would be. At the shelters, people often crowd around outlets so they can charge phones. For people experiencing homelessness, if they have a phone, it’s a crucial communication tool- a connection to the world. But if you don’t have a permanent place to live, having access to electricity can be a challenge.
Over the past year, I settled on a design for a solar charger using 18650 batteries (these can sometimes be found in laptops and vape pens, but I bought them off eBay) and a TP4056 charging circuit. It’s not a perfect solar charger. If you plug the circuit into the wall using the micro-usb port, the batteries hold enough charge to charge your phone more than once. Although the batteries say they’re 3.7v, they can be charged up to 4.2v with a wall charger. However, if you charge the batteries using the solar panels, it seems the current never quite gets high enough to charge the batteries that last little amount. I can get up to 3.95 or 4.05 volts, which is enough to charge a phone about 2/3 of the way. But after experimenting with a bunch of different charging solutions I determined that for a reasonable price, this is as good as we can do for now.
I worked out the electronics with the help of student testers over about 3 school years, but I never had a mechanical case I liked. In the past, I used upcycled food containers, and they were flimsy.
When I met with students this year in our “charger team” meetings, our first task was to design a sturdy case for the solar charger. We discovered you can collaborate in Tinkercad and it turned out to be a great solution! We all logged onto the same Zoom meeting, and then I created a Tinkercad project and clicked the Collaborate button to share it with everyone.
It’s amazing. You can all edit the same project at the same time. And with this group of kids, it turned out ok. We downloaded a couple of charging-port holders from Thingiverse and embedded them into a box, with some walls to hold the battery pack in place. The kids worked with rulers and measured battery packs and solar panels, and we updated the measurements in the file. Our first design had the voltage-in (micro USB) and voltage-out (USB-A) ports on opposite sides, with a flat lid.
This was iteration 1. The box took a really long time to print. I printed one at home, and showed them how it turned out at our next meeting. I asked the kids if we could make it a little smaller to save filament. So we moved both charging ports to the same side, and made the box exactly the same size as two solar panels side by side – and only slightly taller than the battery pack. I printed multiple copies of this version and then had a meetup with the kids to give them cases and electronics to try and build a solar charger. I parked at the school, and the kids pulled up with their parents where I handed off a bag of parts, soldering irons, and other tools.
The students worked with iteration 2, and each one in the team built a charger. I shared video instructions for creating the charger, and we had a zoom session that was a “learn-to-solder” lesson. The next time we met on zoom, they reported back that overall they liked the design, but the slots for the charging circuits needed a little re-designing. They wanted the slots overall wider, with a lip to hold the circuits in place. We made changes together in Tinkercad and then I printed iteration 3 for each student and did another round of supply-swapping. They built another round of chargers and tested them.
I started printing iteration 3 as fast as I could, and I distributed these to the kids so they could make this year’s final version of the solar chargers. I am really pleased with how they’re turning out. I’ve gotten a few back, and they’re sturdy and high quality and work pretty well!
I even had one student that designed his own case that had an angled top, better for collecting sunlight in the winter. He laser-cut it at home, and it’s awesome. I did not take a picture of it yet, but I’ll do that soon. Maybe that’ll be iteration 4 or a separate branch of solar charger cases.
This is an amazing, fulfilling project. We are going to be donating the solar chargers to Homeward Alliance right after Memorial Day, so they can be distributed to people experiencing homelessness who need them. We expect we will have over 20 chargers to donate. We will also put a link to a survey on the chargers so our “clients” can give us feedback on how well they held up. The students really loved feeling like they were making a difference and experiencing what engineering really is.
If you’re interested in making these, I have posted a YouTube video with assembly instructions, and I’ll also share the parts lists and .stl files here.
I have not blogged in a while, and it’s hard to be reflective about your own work when you’re in the moment and so unsure WHAT you’re even doing, so you can’t pause to think about why or how. But now that I’ve finished my last day of teaching online content, I think it’s time to look back on what worked and what didn’t – because chances are, we’ll be doing this again before the coronavirus pandemic is over.
I live in Colorado, and as we watched the pandemic unfold on both coasts, we knew by early March that things were going to change for us drastically. We left for spring break on March 13th right after having a big open-house exhibition at my school, and after I attended my own daughters’ spring concerts and celebrations. When we left for spring break, we knew we weren’t coming back. Although our district had only planned for a 2-week break at the time, the writing was on the wall that we’d be out all quarter. We started to plan for it.
Our administrative team did a wonderful job creating a remote-learning plan that was flexible and could accommodate as many kids as possible.
- We did some test-runs with Zoom before spring break started, so teachers and students were familiar with the platform. We created a set of school norms for using Zoom and trained all of the students on these norms. Most teachers were able to run a class or two on Zoom, just as a trial, with kids spread out around the building and teachers conducting class from our office. We continued using Zoom for the duration of remote learning although we were aware of concerns with privacy. It really is a superior platform for online learning, and for a quarter, we decided to make the tradeoff.
- We extended our spring break an additional week, to give ourselves time to check computers out to students and write lesson plans. Students came to school early the week of March 23 to pick up their technology.
- We used Google Classroom as a central point for all remote learning. We agreed to use a standard structure, where assignments were labeled by day and week, and all assignments could be done asynchronously – with short video lessons where needed.
- We posted all assignments on Sunday evenings, with due dates a week later. (I found myself breaking from this slightly, however, posting Monday/Tuesday assignments on Sunday night and Thursday/Friday assignments on Wednesday).
- We agreed to hold online, live Zoom sessions twice a week for each class. Intensive classes (the core subjects) were held Monday/Friday, Venture classes (our project-based blocks) were held Tuesday/Thursday, and Wednesday was reserved for Advisory and staff meetings. We agreed the live sessions would not be required, but would be set up to provide support or teach the content live that was already accessible in the online videos.
- We kept a checklist of all of our students, so teachers could log which students were attending class and/or turning in work. The checklist was used to follow up with kids we didn’t hear from. The checklist was just a normal Google sheet that looked like an attendance roster, and next to each name there are checkboxes to log if we had seen/heard from the student. Through the checklist, we kept track of families dealing with Covid, families that needed food assistance, and some families that other obstacles to attending school – working, taking care of siblings, or lacking any internet except a phone data plan.
This is what my Google Classroom looked like, and every teacher in our school uses the same setup.
Zoom links are always posted at the top of the page. As you scroll down, weeks are in reverse-chronological order and all assignments are grouped under the week in which they were assigned. The consistency was helpful to everyone and I am so glad our admin just set the structure up for us.
I teach Algebra/Geometry (Integrated math, sort of), and had planned to teach quadratic functions, systems of equations, and data analysis. I had gotten a week into teaching quadratic functions when the semester ended, and I know my students that wanted to move on to Algebra II next year would need to know these topics. So I had to do the best I could teaching new content in this format. For each lesson, I made a video which I posted to YouTube, created some structured notes that went with the video, and then curated some Khan Academy exercises for practice. I assigned 1-3 practice sets for each lesson, so it wasn’t an overwhelming amount of work. If we had been in the classroom, the structured notes would have been set up as group activities – I just adapted them to be individual notes instead.
I think a huge part of the value of the video is for the students to connect with me by hearing my voice and seeing my face, so the videos are probably not as meaningful for you. I know there are tons of videos out there that teach the exact same content I’m teaching – but I made these anyway, because I believe there’s value in the students hearing directly from me and knowing I care and believe in them. You can use them if you like, but I really do think your students benefit from videos you make yourself too.
Each day, I asked the students to do the Khan Academy exercises, mark the assignment as “done” in Google Classroom, and write a short reflection on how it went. For the units on Quadratics and Systems, I included a small end-of-unit assessment. For the Quadratics unit, it was a packet of problems I curated from an SAT test prep book. For the Systems unit, I assigned the students a computer programming project as an assessment.
Our grading system is a competency-based system, with marks of “Not yet”, “Basic Understanding”, and “Exemplary Understanding” for content. There really is not a good and fair way to check students’ competency levels in this kind of system. So if a student did most of the assignments and put in a solid effort on the assessment with reasoning I could understand, I gave him or her a mark of “Basic Understanding”. A few standout students received marks of Exemplary Understanding, but I reserved this for when I could tell it was really warranted. When in doubt, I used the “Basic” mark. If students did not participate at all and did not do assignments, I left the grade blank as if they didn’t take the class. They’ll get a chance to learn it in the future when learning is purposeful and planned, not emergency.
So that’s what I decided to do. Here are my reflections on how it went.
From my perspective – I felt like this was a decent first attempt at online teaching. I actually do like Khan Academy as a resource for practice problems. The students can get feedback right away, they can use the hints and videos, and I could screen-share with students during my office hours to help them with the practice. It was super useful. I probably will use Khan’s exercise sets next year when we have to go remote again. A little more than half of my students completed work regularly. About a third showed up consistently to our synchronous Zoom sessions. I enjoyed the online zoom sessions, and after I got about a month into the schedule, I really liked it. I did do some repetitive work – creating the videos and resources for the lesson, and then teaching the exact same lesson live twice, then teaching it again during office hours – but my days were so much more flexible and easy to manage. I had to carve out a couple of hours for online classes each day and then I could finish the rest of the work on my own time. At 3pm or 2am or whenever it was a good time for me. By the time May rolled around, I was very comfortable managing my time this way, taking care of my house and family and balancing the school needs. And really, I’m far less stressed right now than I usually am in May. MUCH less stressed. I’m kind of thriving on this flexible online schedule. I get outside a little every day, tinker and create, play with the pets, make a variety of food, and enjoy spending time with my husband and kids. I was really sad and stressed when the quarter started, but now that it’s mid-May I’m doing pretty well.
From the kids’ perspective, it’s more complicated. I gave an end-of-year survey to my students today and was surprised at some of the results. The first question was about student motivation levels. Less than half of my students responded to the survey, so the results may yet change if I get more.
The bars correspond to these prompts:
Students could check multiple boxes. The most popular answer was: “I didn’t try as hard as I could have”. Second most popular was a three-way tie: I was motivated because I really enjoy math, I was motivated because I’m used to trying hard in school, and I tried my best every day. It seems, though, a majority of students are disappointed in their effort.
I asked students what they thought of Khan Academy as a practice tool. This surprised me.
1 corresponds with “It’s terrible, please don’t use it anymore” and 5 corresponds with “It’s a good way to practice and you should use it next year too”. Generally students are OK with Khan as a practice tool. They don’t love it but don’t hate it. Some helpful comments included “It’s good for practice, but I don’t learn new content well from it”, “I like that I know right away if I got it right and can get help if not”, and “It was only a few questions so it wasn’t overwhelming.”
I asked the students how they felt about the feedback they got during online learning, with 1 being “Not Nearly Enough Feedback” and 5 being “I am satisfied with the feedback I got”.
I almost did a spit-take because I got REALLY behind on grading – not just summative assessments and comments, but the daily work of doing into Google Classroom and just checking off assignments and writing “Good job”. I certainly didn’t give them this feedback, unless they asked for it in office hours or zoom sessions. Strange perception. I expected them to rake me over the coals and hold me accountable for getting behind on feedback. I don’t know why they didn’t. Maybe because they practiced on Khan they knew what progress they were making? Maybe because I sent emails reminding them about stuff?
I asked students if they felt ready to move on to the next math class. This graph also surprised me.
A vast majority of the students wants some review and some new stuff next year. Huh. I would say the kids in the “I feel like I mastered it” category are also the ones I would have pegged as fully ready to move on, but some of the other kids in the 86% are ready but don’t perceive themselves as ready.
I asked students what topics they’re interested in learning more about when it comes to math. This is what they said.
Some of the labels disappeared so this is a list of the choices.
The most popular answers were: Puzzles and Logic, Computer Programming, Physics and Mechanics, Data Analysis and Statistics, Finance and Spreadsheets, and Measurement/Design/Engineering/Construction. The least popular were: Advanced Functions/Polynomials/Calculus, Probability, Solving more and more difficult equations, and careers that use math.
I brought this question up just in case standardized testing gets postponed, cancelled, or has a lower priority placed on it, maybe freeing up a little more math time for the things kids would like to learn. We do SO much with functions in high school math. It’s a bit much, in my opinion, when there’s so much math out there that kids like.
I asked one final question which was: If math is online again next year, what do you think you need to be successful? The responses were all over the map, some hopeful, some disappointed. They’re important to read. There are a lot of kids beating themselves up for not feeling more motivated and I think they’re being a little hard on themselves, considering.
So there it is, my first emergency-remote-learning quarter of Algebra in the bag. Lots to think about as we head into next fall and have to continue keeping kids safe and somehow figuring out how to help them learn.
How did it go for you? What would you do differently and what did you like about your system?
Linear functions are at the heart of 8th grade math and Algebra I, and I enjoy finding those ways we engage with functions in real-life situations… including creative coding!
As we learn about slope, it’s an interesting challenge for students to explore what kind of line would be perpendicular to a given line, and I like to use that challenge to deepen their understanding of what slope is. We start with some lines and without showing them how, I challenge them to find a line that makes a perfect 90 degree angle to the given line.
We have a discussion about when this understanding would be important. Architects or designers might use the concept, for example, if they have to design right-angles that are not perfectly aligned to their grid. Video-game designers may use the concept if a shooter is facing an enemy, and you have to strafe at 90 degrees from the angle you expect their projectile to come from.
Or, you might use the idea of perpendicular lines to just make pretty art, which is what we did with this mini-project.
I reminded the students about Tartans and how groups in Scotland use a Tartan as part of their identity – whether region, occupation, clan, or something else.
My family and I hiked in Scotland this past summer and noticed tartans of the MacDonald and Campbell clans everywhere!
We start by going over how to color the background and stroke and fill colors, and how to place points on the coordinate grid. We first discuss where (0,0) might be and then discover together it’s in the upper left (!) and I challenge students to place points in all four corners and in the center. This is what they end up with.
Then we add in the draw() loop and get the points moving.
That’s day 1. On day 2, we can introduce the project. Students have to make a personalized, unique Tartan with colors and stripe widths they choose. The tartan must have at least 8 lines on a colorful background. The lines must be perpendicular, but can’t be perfectly horizontal or vertical, or at a 45 degree angle. Lines must start at an edge.
It gives some interesting challenges as students figure out what coordinates would start a line at the edge they want, and then how to create slopes that are perpendicular. In an example video, I show how a slope of +4 in the x direction and +5 in the y direction is exactly perpendicular to a slope of -4 in the y direction and +5 in the x direction. Make one value negative, and swap x and y.
Perpendicular Lines video
My last class made some very nice tartans.
It’s a quick, 2 or 3 day mini project that gives students some context for slopes and intercepts and allows them to get a little creative.
At my PBL school, students generally start a new venture project every quarter. This quarter, I’m facilitating a venture project class called “Virtual Reality, Real Feelings” – about the crossroads of VR and empathy. The purpose of this venture is to explore how VR technology can immerse someone in a world so much that it changes their perception of the world. The students will select an inquiry question and create a VR mini-game or experience designed to change someone’s perspective.
It’s a really ambitious project and I’m more than a little terrified. We’ve essentially got 8 weeks to pull this off.
As part of our school opening, we got quite a lot of grant money for new technology. I lobbied hard for VR equipment. I have noticed how this technology inspires curiosity, engagement, and wonder. Those emotions are powerful catalysts for learning and so I see tremendous potential for using VR as an educational tool. We secured 3 powerful gaming computers with Oculus Rift S headsets, and I also purchased 12 Oculus Quest headsets and 20 decent laptops to do software development. My class has 23 students, so we have enough computers for every kid to have one and students can share headsets with a partner.
We set up the Rift systems first, and set them up in our school gallery so students could play VR games after school such as Beat Saber. I believe in using the tech for fun, because again, emotions and curiosity. 🙂 It also builds a sense of community and a shared sense of taking care of the equipment and fairness.
Before the venture started, I had to get all of the Quests set up. We have a school account on the Oculus store, so I used that along with my own phone at home to charge, update, and install apps on all 12 of the Oculus Quests. It took 2 entire evenings to do.
I brought the Quests back to school, and as luck would have it, there was an empty cabinet that exactly fit 4 Quest boxes side by side on each shelf. We drilled a hole in the back and put powerstrips in the bottom, and zip-tied the chargers to the cabinet in bundles. Each Quest box, headset, and touch controllers are labeled with their corresponding numbers, using silver Sharpie. A couple of students helped me set up our charging cabinet and get the Quests on the school wifi. We got some containers of sanitizing wipes to clean the headsets off at the end of every class. We need to work hard to keep them clean and in good condition!
It is very helpful that when you want an app on all 12 Quests, it only needs to be bought once on the school account and then all headsets can install it. The Oculus Store, unlike Steam, does not limit you to play a game on one headset at a time. All 12 can be running the same experience. It makes the software part of the setup very affordable. However, it means we can’t play multiplayer experiences unless we get more Oculus accounts and pay for the apps again.
All of this happened the day before class started. We still don’t have the development laptops, so I’m having the students empathize and design in the meantime. This is an important part of the design cycle and it’s actually convenient that we don’t have the computers, so we can focus on doing our planning well.
For the first week, this is what we did.
Before the class: several students and I attended Colorado State University’s XR Symposium over a weekend, to connect with our local university and get some ideas and inspiration.
Day 1: We introduced the class with getting-to-know-you activities, a slide presentation about the history, technical specs, and impact of Virtual Realty. We discussed the XR Symposium, and we created a class charter.
The slide presentation I used is below. You are welcome to use any of the information if you want. Here’s the link to it:
Day 2: We reviewed the learnings from yesterday, and then I gave the students a sort-of scavenger hunt I created. I called it a Questival. The goal was for students to try out 10 different VR experiences, articles, or videos, and journal about what they learned along the way. I curated some experiences that would either evoke curiosity or emotion. The VR apps I included were:
Becoming Homeless: A Human Experience by the Stanford Virtual Human Interaction Lab. This experience only works on the PC-based headsets, not on the Quest. In a disappointing twist, I could get this app to work at my house but not on our school PC’s and I don’t know why. On the school Rift S machines, the app would show up on the monitor but we never could get it to display right in the headset. I tried for a couple of days, and eventually we just demoed it for the entire class, on a big smart monitor, by holding the headset and having a student use the touch controllers. It worked, but wasn’t as immersive as actually being in it. The point of this experience, however, could still be fulfilled. In this VR Empathy app, a couple of aspects make it really powerful and interesting. One is that the programming and game design is not that complicated. You point and click at objects, and simple things happen like a sound plays, or an animation runs. It is an app in the style that a student could easily create. The other powerful aspect is that it’s not just a video, it’s interactive. I wondered if the simple choices you had made it more powerful than just an immersive video. Does the act of having to choose which items to sell create more empathy than just watching someone else do it? Does it matter that you get to choose the color of your hands?
Traveling While Black is an anti-racism experience. It is not interactive, it’s an immersive video – but it has some touches that make it more powerful than just a video. The perspective of sitting in Ben’s Chili Bowl listening to a crowd having a conversation is a powerful one, and I liked how images were embedded into the scenery to make the stories come to life. It’s a very good storytelling experience and the students thought it was powerful. Especially the white students.
6×9: A Solitary Confinement Experience is one the students have to navigate to on YouTubeVR. I did have to go in and unblock it, since the content is flagged as “restricted”, so test it at school first before you try it with students. It is intense, but not inappropriate. I liked it because it’s an immersive animation rather than just a video made with a 360 camera. The models of the cell and furniture, the paint animations, etc are all created and not photographed. And again, it’s something the students could create, not technically challenging, but powerful storytelling anyway. It’s about the experience rather than the realism. Students had no idea this was something that happened in the US, and before I watched the video, I didn’t know it was so widespread. It opened our eyes to one of the ways the criminal justice system has overstepped its bounds.
Job Simulator was an experience I curated because it evokes emotions of surprise and joy, and it’s an example of good game design that’s specific to VR. You could not create the same experience on a flat computer screen and get the same emotions. In VR, you need to design your experience with caution about movement – otherwise you’ll make your users sick! Standing or teleporting experiences are fine. Anything that involves walking or flying needs to be approached with extreme caution or you run the risk that many, many people will not use your app because they get queasy. We also discussed that although people love realistic video games, a VR experience doesn’t have to be realistic to make you feel totally immersed in it. Low-poly graphics are sometimes just what you need. They highlight the interaction rather than the object itself.
These were some of the best VR apps and experiences I had found that really get at the empathy and VR connection. I put other articles and videos in the Questival worksheet, and students worked on this on and off for the entire week. Here’s the worksheet:
I got a lot of joy from watching the kids work on this and seeing their surprise, curiosity and engagement.
Day 3: We continued working on the Questival assignment, and I gave students the prompt of considering a curiosity question (or a few candidates) for their research project. As they explored different applications and uses of VR, I wanted them to hold in their minds the questions that were coming up they wanted to dig into more. They will take one of those questions and turn it into their solo research project. Some examples of curiosity questions:
What are haptics and where will they go in the future?
How is VR used in Military / Defense situations?
How can people explore identity or body image using VR?
What are the impacts of deforestation?
What is the history of 3D animation?
Can VR be used to eliminate racism?
How can we get people to accept and care for refugees from other countries?
The students came up with some great questions on their own and I’m excited to see where their explorations take them.
Day 4: Some students, because of absences or working slowly or not knowing what was expected, were still working on the questival. For students that were finished, I wanted them to start exploring creation tools in VR. They could use Tilt Brush, Medium, SculptrVR, or Sketchup to participate in a build challenge with the theme of: Halloween. We’ll review everyone’s halloween artwork on Monday and award a prize to the best halloween designs. Artwork made in any of these media can be imported into Unity and built into an app, and I have some students who are incredible artists – unlike me!
As we continue into the coming week, I just had a couple of observations about working with class sets of VR equipment.
- Space is such a tough problem to solve. One classroom with furniture in it is a tough space for a dozen groups of students working in VR. I generally had 6-7 VR users in the classroom and then others would use the public spaces outside of the classroom. This created some conflicts when students were noisy, or were perceived as being out of class/goofing off. I had some colleagues frustrated with me because they felt their classes were disturbed. So I need to set some clear boundaries and expectations for space that help the students work while not disturbing other classes. It’s a hard problem. VR takes a bigger footprint than a school desk.
- Overall, I am very, very pleased with how easy the Oculus Quest headsets are to use. The students were able to figure them out with very little instruction. They used the sanitizing wipes and our homemade charging station very responsibly, and the ratio of 1 headset per pair of students seems just about right. It’s easy for me to manage the apps on them as well. If I purchase an app, the students can load it on a headset with no intervention from me.
- We re-norm OFTEN about expectations when using VR equipment. I boil it down to 3 basic principles:
- Be Safe.
- Be Kind and Respectful.
- Take Care of the Equipment.
Being safe involves using the wrist straps and making sure your play area is secure and nobody walks through an active play area. Being kind and respectful involves honoring time limits and making sure everyone gets a turn. Taking care of the equipment means we always play on carpeted areas, we hand off equipment carefully, and we take care to power down, wipe, and plug in everything when done.
We discuss these several times a week. You really can’t do this too much.
This coming week, we’ll take a field trip to our local science and technology museum, work on our research projects, and start choosing themes for the student-made apps. After this week, I think our computers will be in and we can start learning how to create apps in Unity and animations in Tvori.
Disclaimer: not a coding lesson! Just a reflection on teaching a notoriously tricky Algebra I concept.
In my Algebra I class, we’re learning about systems of equations. I had a career as a software engineer before teaching, and as I tell the students often, systems are actually a concept I used every so often as an engineer. Sometimes you have multiple variables or constraints that you have to meet at the same time, and modeling them as an algebraic system is helpful. I found, however, that knowing systems are useful doesn’t translate to easy teaching or learning.
I spent 5 or so lessons going through the usual order of solving-by-graphing, solving-by-substitution, solving-by-elimination. I used the Illustrative Mathematics lessons available online. They are decent lessons, but I could tell the pace was leaving some students behind. By the time I assigned practice problems, maybe a third of the class had a decent grasp of an algebraic way to solve a linear system and the other 2/3 were struggling. And, as you can imagine, the kids who didn’t understand showed me by misbehaving – fun.
What do you normally do in this situation? Over time I have learned the best approach is to back up without making it seem like you’re backing up. Increase the problem-solving load while you decrease the procedural load. Lesson planning is creative problem solving.
Sometimes my friends post math memes on Facebook – picture puzzles that are actually systems of equations. They’re fun. I did some searching for “algebra picture puzzles math” and followed the rabbit hole to pinterest boards that hosted lots of them. One site you can mine for picture puzzles is brainfans.com which is where I captured the ones I used in my lesson.
I gave the students a couple of picture puzzles to work through in small groups, along with a couple of word problems I made up about purchasing food. Here are the ones I used. I purposefully chose puzzles that always had 2 or more variables in each equation, so you needed to use the concept of elimination or substitution, you couldn’t just solve for one variable in a single equation.
Dawn went to a burger stand on Saturday and bought 5 cheeseburgers and 2 fries. She spent $21.24. On Sunday, she was still hungry and she went back to the same burger stand. This time she bought 2 cheeseburgers and 2 orders of fries for $16.14. How much are the cheeseburgers and fries?
CCCCC + FF = $21.24
CC + FF = $16.14
Dawn went to a smoothie shop on Monday and bought 6 large smoothies and 2 small smoothies for $61.64. They were so delicious, on Tuesday she went back and bought 7 large smoothies and 4 small smoothies for $82.33. How much are the large and small smoothies?
LLLLLL + SS = $61.64
LLLLLLL + SSSS = $82.33
These were VERY accessible to the kids. The students that already had a good concept of solving systems modeled the picture puzzles as equations and solved them formally. The students that were having a tough time with it used less-formal approaches that still used the idea of substitution or elimination.
For example, from the first two equations using the cars, they could tell the yellow race car was worth 2 more than the blue race car, using the concept of elimination. Then, in the third equation using the cars, they could reason out that “x + 2 + x” was equal to 32 and decide the final value of the blue race car – basically using the concept of substitution.
I could tell students got the “cheeseburger” problem correct when they shouted across the room “Why are your cheeseburgers so cheap and why do the fries cost so much?” Ha! I love gourmet fries!
In the “smoothie” word problem, most groups struggled with it at first – even those that understood symbolic equation solving so far. So I gave them a tiny hint – I asked them what would happen if they doubled the first order. How many large smoothies would that be? How many small smoothies? And the price now? And how is this new order different from the 2nd order? And every single group of students said “oh” and finished independently. Context matters!
To finish the day, we did the Noah’s Ark problem which I found a long time ago on Julie Reulbach’s blog. It uses the same concepts, substitution and elimination, and it’s just as much fun with 9th graders as it is with young kids!
The students’ assessment is to write their own picture puzzle and word problem, complete with solution, for others to solve. We’ll swap them next week!
I enjoyed this SO much more than teaching systems the old fashioned way, and the students had fun problem-solving instead of continuing to learn procedures. Math class was fun, and avoidance / bad behavior was almost completely absent today.
Hi everyone – if you’re still hanging in there with me, and I haven’t lost you due to my long absences from engaging with the blogging world, I’d love to share a little mini-project I did with my algebra class. I gotta say, I really enjoy doing coding mini-projects in math class. I like putting the projects together, the kids find them really engaging and fun, the problem-solving is interesting and surprising.
We started out the year as many algebra classes do, studying linear equation-solving and the properties of linear functions. Things have been going reasonably well, but I knew some students were irritated not knowing “when will we ever use this?” – It’s one of my ongoing pet peeves with the high school math curriculum, that the way it is expected to be learned and the way it shows up in standardized tests doesn’t really match how these concepts are used in real life. Including linear functions. These are SUPER useful in real life – in all kinds of situations where you have to make predictions involving a constant rate. But the kind of problem-solving you normally do with linear functions doesn’t always look like what we do in math class, converting functions to slope-intercept form or point-slope form, graphing on a 4-quadrant plane, etc.
I started by giving the students that basic speech. These concepts are incredibly useful, but in the real world they don’t often look like what we see in math class. So today we’ll explore one possible application of linear functions.
And I introduced them to the retro game of Missile Command.
We watched a YouTube video of someone playing the game (the screen captures were fetched from this video too):
The students were in awe. Back in the early 1980’s, we were in the end stages of the Cold War, and the threat of a nuclear apocalypse was a low-level stress always present in our lives. In the game, missiles rain down on your cities and your job is to shoot them down before they destroy your nation. You even get a little 8-bit mushroom cloud when a city is nuked. It really was a dark, terrifying video game and I remember feeling super tense while playing it. There’s no way to win. The missiles just fall down faster and faster until you lose all of your cities and the world ends.
The missiles always start at the top of the screen and rain down in a straight line. In the game, if you could predict where those missiles would land, you could prioritize which ones you needed to shoot down. As the game got faster, for example, it didn’t make sense to shoot down a missile heading for a city that was already destroyed. Focus on the ones heading for your still-standing cities.
We watched for a bit and some students insisted, “Those aren’t straight lines!” But they were, they just didn’t look straight when rendered in 8-bit. For example, these missiles below go down 2, over 1, down 2, over 1, down 2 once more, over 1, then down 1, over 1. Repeat the pattern – 2, 2, 2, 1. 2, 2, 2,1. The slope is a net -7/3. We could identify missiles with a slope of -5/2 (down 3, over 1, then down 2, over 1) and -8/3 (2, 3, 3. 2, 3, 3).
I made the students a little mini-game starter in Khan Academy. In this starter, the missile is at the top of the screen, and a house is at the bottom, but the missile doesn’t move. We did have to start with a little discussion about how the coordinate plane in many programming languages is different than the one we use in math class. Often, a computer game’s coordinate grid has (0,0) in the top left. X increases as you go right, which is what you’d expect. However, Y increases as you go DOWN the screen. It’s intuitive if you think of the way spreadsheet cells work, or the way you read text. Start in the top left, work over, then down.
The key is to change lines 31 and 32, which currently read:
x = x + 0;
y = y + 0;
If you modify the amount added to X and Y, the missile starts moving. The trick is to make the missile make a straight line and hit the house. If you hit the house, the screen turns red. Decimal amounts can be used.
Students found that if they tweaked the velocities such that the Y velocity is a *little* more than the x velocity, they can hit the house. For example, these combinations worked:
x = x + 10;
y = y + 12;
x = x + 0.5;
y = y + 0.6;
A y/x ratio of *about* 6/5 was ideal, and there was some wiggle room since the house has a hitbox about 20 pixels wide and tall. We made some predictions about other combinations before trying them.
Next, I challenged the students to move the starting location of the missile, on lines 2-3, and the starting location of the house, on line 6, and find a new y-x velocity pair that would let the missile hit the house. Some students, of course, thought of putting the house directly below the missile and using a y-velocity only, setting up a “no-slope” situation.
On line 8, there’s a line of code specifying “FrameRate”. This is the number of times the draw() function is called in one second. It’s 60 by default, so the missile will move 60 times each second. For the final challenge, students had to tweak the frameRate() and also the velocity so the missile would hit the house in *exactly* five seconds. Students got timers out and spent quite a while trying to get the missile to hit in exactly five seconds. Many figured out that if the missile moves roughly 80 pixels each second, it takes five seconds to get to the bottom of the screen… so it was a matter of finding combinations of frameRate * y-velocity that would equal about 80.
I just want to finish with a plug for Khan Academy’s computer programming interface, especially when it comes to little math mini-projects like these.
It’s my go-to resource when I want to create a quick little math activity. I don’t necessarily need my students to create a program from scratch all the time – often I’ll create a little starter program that needs fixed or modified. With this interface, I can save the program and push a link out to Google Classroom. Students click on the link, and then click “Spin-off” to get their own copy to modify. They can also see other students’ spin-offs, so if they get stuck, it’s helpful to see what someone else did. The program runs right away and needs no compiling time, so the students see the impacts of their changes instantly. The number scrubber and color picker make programming changes super easy and fun. The documentation tab is wonderful. If you’ve got students who are interested in taking the task beyond what you set up initially, just refer them to the documentation tab and there will be examples they can copy and paste.
It’s a fantastic coding environment for little activities like these, and I use it in math all the time!