Category Archives: problem solving

Remote learning starts tomorrow

I never signed up to be a remote learning teacher.

Learning is a social activity and a big part of that is being together to share, discuss, argue, and show our support. It’s difficult to practice social distancing in a school setting. If your picture of a classroom is desks in rows 3 feet apart, with the teacher lecturing and students taking notes and working in quiet isolation, then you need to update your perspective. I’m not saying that isn’t still the case someplace. It’s just not the case for me and many of my colleagues (not just talking about my colleagues at Baxter Academy, either).

This morning, school districts all across Maine have announced that they are closing for the next two weeks, or longer. How do you take an active, noisy, dynamic classroom and transform it into something that can work remotely, with everyone working individually? We’ll muddle through and learn together.

On Friday night I sent this message to my advisory students and their parents:

Hello advisory students (and parents),
** This is a long email because I didn’t see you all on Wednesday. Sorry about the length, but I have lots to tell you. Thanks for reading it all the way through. **
Well, here we are in uncharted territory. I never signed up to be an online instructor, but that’s what I am now. I promise you that I will try my best to continue to support all of you through this most difficult time.
That said, I encourage you to become more engaged with your email. And turn on those Classroom notifications that you’ve turned off. This is the best way to stay informed and stay connected to what’s happening over the next few weeks.
I’m not saying that it’s going to be easy. And we have to remember that it’s hard for all of us, teachers and students included. We will all try our best. The thing to remember is that you need to check into Google Classroom to find out what the expectations are for the day, including Flex Friday. As we get better at this new reality, we might be able to post longer term plans for you. In the meantime, understand that we are learning along with you. And be kind. Be kind to each other and be kind to us.
Amos’s message implies that all of your classes will be held through Google Meet, a video conferencing app that allows you to log in with everyone else in your class, along with your teacher. I doubt that will happen every day, all day. I suspect that will happen a couple of times during the week, with the other days using Google Classroom posts similar to snow day learning. Your responsibility is really to get your work done. There are “office hours” every afternoon when you can ask your teacher questions – via email or classroom comments or whatever mode your teacher uses. Ms Lucy will be communicating with Mei about the best ways to keep BLC hours, options, and sprint courses going. Take advantage of those opportunities. Do your work. Ask for help. Help others.
Several of you are also taking college classes at USM, which will be moving to strictly online following spring break and will stay that way for the rest of their college semester.
I’m attaching a graphic that does a good job at explaining online learning etiquette.
The good news is that Slate seems to be working, complete with 2nd semester rosters. Give your teachers a chance to upload grades. But at least you will be able to monitor your progress now. Remember, this is about learning. Your teachers will continue to provide you the opportunities to learn – even if it’s in a different mode than what you’re used to or what you prefer. Only you can take advantage of the opportunities we provide.  (Speaking for my colleagues, based on conversations from today, we would prefer to be with you live and in person.)
I anticipate that you will be asked to give some feedback on the processes that we are testing out and trying to use through this difficult time. Give your feedback and use your voice.
The digital learning schedule is also attached. Remember, the main thing is doing the work. It’s nice for you to “show up” if your teacher invites you to a Google Meet session. It makes us feel like you care and value us. But, if that’s not possible for you to do, then be sure to do the work and turn it in on Classroom. That’s going to be our main mode of communication. So show up, check in, and be present.
Unless you are feeling sick, nothing about what we’re doing mandates that you stay home while we are learning this way. That said, we are all trying really hard to slow the transmission of this thing, so use your best judgement – stay out of crowded areas, but go outside and soak up some sunshine; practice good hygiene, but don’t shake hands; if you work in retail, wash your hands a lot, seriously.
Like I posted on our Advisory classroom, let me know if you have any questions or need my support in any way. This is going to be new for us all and we need to support each other. I am grateful that you are my advisory and I am grateful for your parents’ support.
Be well and I hope to see you all soon.
If you are a teacher in the same situation that I am in, feel free to share strategies. I will try to log my successes and failures, too.

Leave a comment

Filed under Baxter, problem solving, teaching

Mobile Algebra

Following the introductory use of structure and emoji math to introduce systems, my teaching partner and I continued with mobiles as suggested by the authors of “An Emoji is Worth a Thousand Variables.” EDC has this great website, SolveMe Mobiles, that has 200 mobile puzzles like this:

mobile1

Each shape in this mobile has a value (or weight) and the total value (or weight) in this mobile is 60 (units). Go ahead and solve the mobile.

This mobile represents a system of four unknowns. Using traditional algebra symbols it might look like this:

mobile2

A couple of those equations have just one variable, so it may not be quite as intimidating to look at the traditional symbols. On the other hand, the mobile shapes are just so accessible to everyone!

We needed to move our students away from systems that had one variable defined for them, though, and the SolveMe site, as great as it is, always includes some kind of hint. So we started to make up our own mobiles.

 

As first, students used a lot of educated guessing to solve the mobiles. Then there was a breakthrough.

Take a closer look at the left-hand mobile.

mobile3

Students realized that they could “cross off” the same shapes on equal branches and the mobile would stay balanced. In the example above, you can “cross off” two triangles and one square. Whatever remains is equivalent, though it no longer totals 36. Therefore, two triangles equals one square. Using that relationship, some students then substituted two triangles for the one square in the left branch. Then they had a branch of 6 triangles with a total of 18. So, each triangle is worth 3. Other students used the same relationship to substitute one square for the two triangles in the right branch, resulting in a branch of 3 squares with a total of 18. So, each square is worth 3.

We were floored. We had never discussed the idea of substitution, but here it was, naturally arising from students reasoning about the structure in the mobile.

mobile4Looking closer at the center mobile, students used the same “cross out” method to find the relationship that 2 triangles equals 3 squares. If we’d been teaching the substitution method in a more traditional way, kids would have been pushed to figure out how much 1 triangle (or 1 square) was worth before making the substitution step. We knew substitution was happening here, but we didn’t invent this approach so we just followed closely to see where our students took us. Since 2 triangles equals 3 squares, some kids substituted 3 squares for the two triangles on the right branch of the mobile. Others made two substitutions of 6 squares for the 4 triangles on the left branch. Either way the result was a branch of 7 squares that totaled 14. It seemed quite natural to them.

What would you do with this one?

mobile5

Next up: Moving to traditional symbols. The final (?) post of this saga.

Leave a comment

Filed under #CCSS, BMTN, problem solving, teaching

Impressive

I spent today at Baxter Academy. Actually, I’m still here. See, I have a group of students working on Moody’s Mega Math Challenge. They have 14 hours to complete their solution to the problem. The clock starts ticking at the moment they download the problem. That was at 9:00 this morning.

I am impressed that this group, who in class is lucky to remain focused for 35 minutes (in a 55 minute class), has pushed through today with so much focus – I am assuming. You see, I’m not actually in the room with them. I make this assumption based on observations when I go and take some pictures or get a food order. I had to remind them about food, not the other way around.

Prior to today, they had done a bunch of work in class, on practice problems, getting organized, reviewing the modeling & problem solving process. One thing I learned from all of that is that we are definitely teaching these skills here at Baxter Academy. These students never once thought they wouldn’t be able to tackle any problem thrown at them. They would come up with a plan for what to do before the M3Challenge folks sent out their tips or hints.

Here they are, 8 hours into their day.

img_-nkfa5p

That was four and a half hours ago. Now, with less than an hour and a half to go, it’s truly crunch time.

Leave a comment

Filed under Baxter, problem solving

Tidbits from the Week

I tried my #LessonClose a couple of times this week in my 3D geometry class. The first time I used the Collaboration poll and the second time I used a new Learning from Mistakes poll. Both polls were given while working on the question: “Which Platonic solids can tessellate space?” It was clear that cubes would work, but there was some disagreement about the tetrahedron.

Student comments about how they collaborated included:

  • I was part of the conversation when we were brainstorming answers
  • I participated but did not lead
  • I argued about shapes that would or wouldn’t work
  • Everyone’s voice was heard

Student comments about Learning from Mistakes included:

  • I assumed an angle stayed that same when rotated on the plane. This turned out to be false, and I had to later revise my answer.
  • I forgot Trig, and I may have messed up a little bit with the answer of #1
  • A few times, we started to follow a faulty train of logic, based on angle assumptions, that messed us up until we figured it out.
  • I wasn’t exactly wrong just wasn’t very sure. My group had made a prediction that was actually true.

I’m finding it difficult to decide on the specific poll to give. I might create a new poll that let’s the student select which aspect they would like to give me some information about. This is the heart of the PDSA cycle – learning quickly and making changes to improve.


Earlier this week, Dan Meyer wrote this post about explanations and mathematical zombies using z-scores as an example. In the comments I shared an activity that I’ve used, one that I posted about last year. It so happened, that it was time for that activity again this week. In both classes, students were able to develop the reasoning behind the formula through discussion. One student even described what we were doing as a transformation to the standard normal distribution. Never once did we write a formula.


Once again my Flex Friday work connects me with students who are new to Baxter Academy. This year we are teaching them skills through workshops. This Friday’s morning workshop employed design thinking: asking and answering “How Might We … ” (HMW) questions. (For more about this approach check out The Teachers Guild or the d.school at Stanford.) Once you have a bunch of HMW questions, you attempt to answer each one in as many ways as you can think of. My colleague called this “thinking around the question” and illustrated it with the question, “What’s half of thirteen (or 13)?” And here’s what we came up with.

img_20160916_120055631

 

Leave a comment

Filed under Flex Friday, problem solving, teaching

“That’s a Big Twinkie”

You know the quote. You can watch the clip.
twinkie

Yesterday I brought a box of Twinkies to class so my students could check Egon’s math. They measured twinkie dimensions and borrowed scales from the science lab. They made the classic error of not paying attention to units. And they argued – consulted – with one another. They didn’t quite finish during class yesterday. I predict that they will be somewhat surprised by the results.

Leave a comment

Filed under MTBoS Challenge, problem solving

Dan Meyer, Girl Scout Cookies, and a Nissan in the driveway

A couple of days ago, Dan Meyer posted this new 3-Act problem about boxes of Girl Scout cookies being packed into the back of a Nissan Rogue. It came at exactly the right time for my 3D Geometry class. We’re entering the last couple of weeks, so I’ve been posing review problems each day to help them remember all of the topics we’ve tackled. As I was considering the plan for Wednesday, one dropped right into my inbox.

We watched the Act 1 video. I asked for questions:

  • How many boxes are there?
  • How many different shapes?
  • How many cookies?
  • How much do all those boxes weigh?
  • How much would that cost?
  • Could they have fit more?
  • Could they have packed them more efficiently?

I asked for estimates, including guesses that they thought were too low and too high: The too low & too high estimates ranged from 1 to 1,000,000 and the guesses ranged from 206-3000.

I asked for the information they would need:

  • How big are the boxes?
  • What is the cargo space?
  • How much do the boxes weigh?
  • What’s the maximum payload?

I knew that Dan would provide some of this information in Act 2, measuring the roguebut my students are very inquisitive and quite resourceful. They wanted to figure these things out for themselves. And as luck would have it, our principal drives a Nissan Rogue. We also had Girl Scout cookie experts who were quick to point out that not all cookie boxes are created equally. We sent a group out to measure the cargo space while two other groups worked on the problems of cookie box sizes, cookie box weights, and Rogue payload capacity.

In researching the payload, the group found that Nissan noted that the Rogue had a cargo capacity of 32 cubic feet, not the 39.3 cubic feet noted in the video. Guess we need to work on those research skills – clearly. The payload capacity was about 1,000 lbs.

Measured cargo space came out to be about 25.8 cubic feet (or approximately 44,600 cubic inches).

The group researching the cookie boxes decided to take a sample and find some average measurements. As a result, our boxes measured 2″ x 7.2″ x 3.5″ and weighed an average of 9.3 oz (or 0.58 lbs).

Final calculations showed that the Nissan we measured could fit about 885 boxes, which would weigh a little more than 500 lbs. But that was a pure volume calculation and the students knew from previous packing problems that we had done, that the reality would be less than that, and that there would be empty space.

Finally, we watched Act 3 (this is the Nissan version). We noted that the Rogue in the video was a different model year than the one that we measured. The measuring team also noted that the Rogue in the driveway had a floor at the level of the lift gate – it didn’t have the same depth as the model in the video.

So thanks, Dan, for the great set-up and giving my students the opportunity to revisit some of the work they’d done earlier in the term.

1 Comment

Filed under Baxter, problem solving

“How Do We Know That?”

questions

I’m teaching this 12 week geometry class focusing on 3-dimensional figures. It’s a brand new class, like many at Baxter Academy, so I get to make it up as I go. Since our focus is on 3-dimensional figures, I thought I would begin with some Platonic solids. So I found some nets of the solids that my students could cut and fold. Once they had them constructed, there was a lot of recognition of the different shapes and, even though I was calling them tetrahedron, octahedron, and so on, many of my students began referring to them as if they were dice: D4, D8, D12, D20. Anyway, I must have made some statement about there only being 5 Platonic solids, and they now had the complete set. One student asked, “How do we know that? How do we know that there are only 5?” Great question, right?

I really felt that before we could go down the road of answering that question, my students needed a bit more knowledge and exploration around these shapes, and maybe some thinking around tiling the plane would help, too. So we spent some time trying to draw them, counting faces, edges, and vertices, visualizing what they might look like with vertices cut off, unfolding them into nets, and wondering why regular hexagons tiled a plane, but regular pentagons did not. We played around with the sides – a lot – and even talked about this thing called vertex angle defect. Then we returned to the question of why only five. Students were able to connect the need for some defect (angles totaling less than 360 degrees) and the ability to create a 3-dimensional figure. Through the investigation, they were able to see that the only combinations of regular polygons that worked (by sharing a vertex) would be 3, 4, and 5 equilateral triangles, 3 squares, and 3 regular pentagons. They could give solid reasons why 6 triangles, 4 squares, 4 pentagons, and any number of other regular polygons could not be used to create a new Platonic solid.

I had not anticipated this question, and had not included it in my plans. But, because it was asked, thankfully, by a student, it pushed us into thinking more deeply about these shapes (and their definition). And, ultimately, my students were able to answer the “why only five” question for themselves.

7 Comments

Filed under MTBoS Challenge, problem solving, teaching