# How 2 questions took 1 hour to solve

I was responding to a post by Dan Meyer about his awesome recent talk at NCTM. Here’s what I wrote in my comment:

I am working hard to keep engagement high. This week, we actually started with two blank triangles, one right and one obtuse. I asked kids to solve the triangle, and ask me questions. There were no measurements on the triangles. The triangles were to scale. They could ask me for one value.

From there, they had to measure another part of the triangle and let the solving begin. They could only measure one other part, no more. So, depending on what they chose, they would use different tools to solve the rest of the triangles. They used rulers or protractors, ratios, triangle sum rule, right triangle trigonometry and Laws of Sines/Cosines. They worked in groups to try to figure out what information they needed, they worked together to try different strategies. In the end, the only way they knew the answers were correct was by rationalizing whether or not they made sense.

We spent 1 hour on two problems. Engagement was high, completion rates were nearly 100%, participation was 100%. It was a really great day for me and I was able to coach them. They did the lifting. It was great. Great conversations.

So much of Dan’s work inspires mine. I love his 3-act-math ideas, though I don’t use them much. More so, I respond to the idea of opening up questions. I love the idea of putting out a skeleton and asking kids what they need. They actually answer, they actually engage in the problem and start to think and ask questions. Once they are invested like that, they don’t like to give up. Giving up has been like an epidemic in mid level high school math classes like geometry and Algebra 2.

Today’s geometry warm up looked like this:

We didn’t even get to the third problem. Yes, it was hand drawn. Like, free hand. That actually made the problem kind of interesting because I don’t really have a right triangle, do I? Just almost one. So, depending on what side or angle students measured (by the way I told them the base side of the triangles in both problems one and two was 15 units) the answers they got might be a bit different.

It was also a great talking point about how real life problems are rarely perfect and we rarely get to check the back of the book to see if we did it right. We have to trust our methods and our team.

Great conversations. Such a great day. It was hard for some of them to keep going to finish the second problem. They were a bit tapped out. We have block schedules, which means 90 minute periods. This took way longer than I expected. But, totally worth it. We’ll do the third problem next week. They actually asked for a book assignment when we were done. I guess their brains were tired. But, they did it! And, they did really well! Go team!

More about problem three in another post. Maybe.

# The origin of a project…

It wasn’t until they actually took a bite of the hot dog that they had an authentic experience. That bite transformed what was kind of a silly project meant to be fun into a life skill for cooking food when they are hungry and have no other resources. Like camping. Or, maybe lunch.

Two of my enthusiastic students were so happy with their results, they asked to have a couple more hot dogs, skewers and buns so they could cook more during lunch.

Yes, we made solar hot dog cookers.

This year, I said, let’s make them. I didn’t really have a rubric and didn’t want to give them instructions. After all, this stuff is all over the internet (just Google it). I also didn’t want to make this so complicated that I would feel overwhelmed. And, I didn’t want to take away from the much more involved project one of my collegagues does with his Engineering student (we have a couple students overlapping our classes).

So, to me this is a great evolution of a project. Think about it, try it, formalize some things for next year. The kids said I should always do this, so I have to take that feedback at point value.

This year, I made it optional. Next year, everyone must do it. This year, I planned it for this week, which is right before spring break. I thought this was a fun thing to do during this week where lots of students are absent due to trips or have big tests or papers due in other classes. Next year, I’ll do the same. This was a good week for this, luckily.

This year, vague rubric written on board:

For a C, it must be parabolic and made from inexpensive materials, with the hot dog at about the right place.

For a B, document your process: how did you decide your shape, take some pictures while building, record problems and your solutions to the problems. Present in a power point, a paper, a movie or a poster board (or whatever other great idea you have).

For an A, all of the above and a calculation showing how you determined where your hot dog should go. And, maybe present it to the class. Actually, I have one student who wants to present, so he is.

Next year, I’ll type that up. I actually think it’s pretty good and the kids didn’t balk, complain or ask for clarification. Well, maybe some clarification. But, next year, I’ll have photos and example to show!! Yay!

# Flipped Circles Unit in Geometry

I made a run at a flipped unit for my Geometry classes. I’ve done flipped lessons and some flipped units before, with pretty good results, so I felt good about putting this unit together. To see the plan, click HERE and click on the link for the unit plan at the top of my page. It will download a word doc which is editable and has links to the tutorial videos.

Why I did it:

1. I knew I’d be taking a bunch of sub days, for various reasons. And, I wasn’t totally sure when they would all be. Some were known, others were a bit up in the air.
2. There have been and would continue to be many student absences. We have a bunch of field trips scheduled during March and April, then special testing in May. Plus, it seems it’s just been a bad flu year, too.
3. I want to expose students to lesson resources beyond just their teacher (me) because I think it will good for them to have more places to find information. Especially in light of our limited time together, thanks to reasons 1 and 2.
4. When students have seen some of the concepts before class, they are more prepared when they are first discussed in class. They’ve had time to digest some of the information.
5. When they have more class time to work problems and do activities, there is more of a chance that they will be able to ask questions with peers and with me. And, there is more chance that more students will complete most assignments.
6. With more time for activities and interesting problems, our classroom climate is stronger. We all become learners and can ease some pressure and stress.

FYI, reasons 1-3 were my immediate concerns, but 4-6 are the reasons I’ve used flipped teaching in the past.

What happens:

Ideally, students watch a video lesson before coming to class. Then, the key points are summarized in class and students have more time in class to complete problem sets or other activities. It can be as traditional or project or problem based as the instructor determines.

I purposefully excluded Mondays as due dates. These are built in buffer days. They can be used for getting caught up after absences, explorations, team activities, short assessments, etc….

How I did it:

Well, I pretty much followed the topics in the order of the text, except for the first couple of sections. I merged and re-ordered those a bit. Some might be critical of following the text, but I think for the circumstances and reasons for the unit, it was a good approach. This way the students and substitute teachers have something to go by.

I would seek out videos on Khanacademy or YouTube, with YouTube really being my go to resource for video lessons. I would review them and go with the ones that I felt were most similar to the content and terminology of the text and my own vocabulary. I would try to find different instructors, so that kids could see the assortment out there.

When kids come to class I know they haven’t all watched the video. I’m not worried about that, because it’s meant to be an introduction and I equate with the fact that not all kids will get all their homework done, no matter what it is.

So, I ask the students what they remember from the video. We talk about vocabulary, and keep track of formulas. Then I supplement with more information and we do a couple of examples together.

Students spend the rest of the class working on an assignment. They have more time to work on it, because there’s been less time spent on whole class instruction. And, I have more time to get to students, group or partner them and have a better knowledge of what they understand well, and where they still need guidance.

Having Mondays left with no due dates was an unexpected gem. I think it’s a great take away in terms of leaving some breathing room in the plan. On a regular week at our school, every class meets on Mondays. Then, you see the students two more times for a 90 minute period. Absences are a real killer. Mine and theirs. For our school, flipped teaching (especially for math) makes a lot of sense.

What the plan doesn’t show:

Engaging openers and open questions. It’s so important to include these during class. There’s a book called 501 Geometry Questions. There are some great questions in there. We focus on HOW to solve problems. They are great to use for creating open questions. You can omit some information, or they may spark creativity to generate open question.

Assessment schedule: yeah, no planned quizzes in there. I really wasn’t sure when I’d be there. So, I left that a bit open. The kids don’t seem to mind. Because of the break next week, I may just do a project type assessment after the break. I plan to figure that out during the break. Sometimes, I have them take partner quizzes. They like those, because I tell them if something isn’t quite right. They go back and try again. Usually with some serious debate and excitement.

How I’ll make it better:

Before class: Someday, I’d like to have my own videos. But, that would defeat the value of reason 3 above (expose them to other resources).

During class: I’d also like them to have a more organized place for a running list of formulas, etc. And/or, hand out a practice test or something, so they can “document” their learning at certain points.

Also, I’d like to modify the assignment instructions so they have a choice over which problems they are working. I’d like to assign 20 and tell them to complete 15, of their choice, and let them know which ones are more straight forward, and which ones are more challenging.

After class: Move closer to a 2-4-2 homework model with the flipped lesson.

I’d also like to find a better way to regularly assess than the the big unit test on a certain date. I do that with quizzes, of course (not for this unit, granted), but I still would like an assessment that’s more interesting than that. At least sometimes. So, for this unit, I’ll be doing that over the break, and can add it to the plan for next year.