# Open question: How do you find the hypotenuse?

In Geometry, we had a super-awesome-open-question to start the day. I just made it up on the spot, and had no idea it was going to turn out the way it did.

I was planning to put this problem up…

As I started to draw it (with a different orientation because it was from their about to be assigned assignment), I stopped here….

I changed the question from a sine question to an open question. I asked,

“What additional information do you need to find the measure of the hypotenuse?”

We had been learning about trigonometry and they knew about the Pythagorean theorem, so, I thought I’d get a range of suggestions.  And, I did. I asked everyone to take a minute to think about what they needed. Then I asked them to take share their idea with a partner. Then, I asked for ideas to write on the board. As students suggested their ideas, I replied, with, “Ah, okay. And how would you use  _____ to solve for the hypotenuse?” And, they would explain.  Then, on to the next idea.

Building their anticipation…. I didn’t tell them if they were RIGHT or wrong. It was really making them re-think as more ideas went on the board and were explained.Of course, there were many RIGHT ideas. When all of the ideas were out, I asked another question.

“Okay, there are several ideas out there. Let me ask you another question. Is there a way to solve for the hypotenuse with only ONE more piece of information?” There were many blurted responses. I really couldn’t understand what any one person was saying. So, I raised my hand as a reminder that I need a hand to go up. I called on a student and asked if they thought they could solve it with one other measure. They said YES, another angle measure.

So, I called on another student to give me a number between one and 89. They said 12, so I labeled one of the angles 12 degrees. We solved for the other angle measure, 78 degrees. We determined we still couldn’t solve it because we now had an AAA triangle, that could produce more than one possible triangle.

Okay, erase the angle measures. Ask another student for a side length. “Five.”

Okay, label the short leg 5. Can’t solve it. So, we decided we needed 2 pieces of information. But which two? Back to our list.

At this point in the hour, we had talked about many ideas, many possibilities and drew conclusions based on things we had learned. What I noticed (and knew I needed to write about) was how the level of engagement was so much higher than usual. Students who were normally a bit “checked out” were generating ideas and were “hooked” into knowing which method was going to work. Were they RIGHT?

So, I grabbed a ruler and measured the hypotenuse. It was 13 inches long. No one had suggested a ruler. So, that was just for fun. What I loved, was that no one suggested using a ruler, like they had at the beginning of the year. Back then, they would ask, can’t we just use a ruler or protractor to measure the sides and angles? Of course not, this is about relationships and we find the answers other ways. You cant’t assume things are drawn to scale, right?

We then went through each idea and tried it to see which ones worked and which ones needed more or different information. They all worked. I was pretty happy. Kids felt successful and it was a fun way to start the double block review period before the test.

I really saw how far we had come since last August. My students are amazing. God bless you, third period Geometry. I can’t wait to do this with my 7th period class nest week.

The beauty of the open question is that more kids can enter the conversation, the lesson is geared to the student’s knowledge and it’s exciting for the teacher, because you don’t know what they are going to say and you get to learn about your students. And, it keeps you very engaged, just like them. 🙂

# I didn’t teach today…

… I facilitated. It’s a review day. The kids will take a test next time I see them. My Algebra 2 kids are ready for the test. Even though I didn’t teach, I was able to check in with everyone as they worked on problems, got caught up and helped each other out. They asked good questions. I feel like they are ready.

I told them so. They seemed to like that feedback.

So, I ‘taught’ but it was on individual levels, not the group as a whole. I think I had a great day and was relaxed in part because I had spent time this morning writing about and thinking about my attitude. I brought my respect for my students to the forefront of my mind.

It was also because they are prepared, and know what they will be tested on. They felt confident, too.

Here’s a copy of last week’s quiz, a model for this week’s test…

# Attitude Matters, Everyday…

Attitude – sometimes mine’s not as good as I’d like it to be. What’s my attitude towards my students, towards teaching math, towards my colleagues, my administration, etc? My attitude may change throughout my day, week, year, and over the life of my teaching career. Or, maybe I just lose touch with why I got into teaching and why I decided to teach math, thanks to all the hurdles that seem to toss themselves in front of you.

I actually really like my students and I think my job, teaching math, is really important. But, things get in the way sometimes and my attitude can suffer.

Luckily, attitude isn’t a fixed frame of mind. It’s a changing and evolving beast and while it can get bent out of shape by other things, such as fatigue, illness, tough teaching assignments, difficult colleagues, etc. it can also be straightened back out. We really have control over our attitude. I’ve decided to focus on it for the rest of the month, and see what happens. For a better breakdown of the impact of life’s events on our attitudes, check out this article by Micheal Graham Richard, Growth vs. Fixed Mindset. It asks which one are you, but my theory is that will very likely evolve and shift.

Staying in touch with your good attitude towards your students and teaching is probably the most important thing to do everyday. In fact, I’ll argue the most important thing to prepare each day, before lessons and tests, homework, etc., is our attitude about our students. It will define our approach to problems that arise during the day. It will allow for open mindedness and acceptance when our lesson doesn’t go as planned (especially when it is way below expectations).

My plan is to think of my students as the multi-faceted creatures that they are. They have interests and math may or may not be one of them. My goal is to try to inspire students to enjoy math, feel challenged, but not overwhelmed. Sometimes, this attitude really drives the activities and sometimes I lose touch and get caught up in the ‘listen, take notes, here’s your 20-25 problem homework assignment.’ this is usually when I get concerned about how much I’m supposed to teach them in a year and how little time I feel that I have to do it. I also realize that there’s nothing wrong with notes, lecture and lots of problems. However, that can be a drag for a lot of kids, so I don’t do it everyday, and when I do I try to give lots of class time to work the problems together. Even better, I love it when I can engage them in open questions. I think that’s one of the best times I have with them.

For the rest of March, I’m challenging myself to adjust and refocus my attitude each day, before the kids arrive, and to have some good open questions ready. My hope is, by giving attention to my attitude and this one teaching tool for the next few weeks, these two things will become second nature. I’m hoping my attitude will not only be positive, but will evolve and become better as I open up to outcomes with my students. And, as I open up my questioning. I’m hoping to open my mind enough that I transform my classroom and kids experience for the better.

I think our attitudes are really important and I know I don’t give mine enough attention. I want that to change. I think attitude may be like a muscle and for it to be strong, it needs attention and proper feeding. Otherwise, it feels like I’m sometimes being swayed by the event in front of me, or the person in front of me. I want my attitude to be really strong and drive my response to that event, or that person. Teaching math isn’t easy. So, I need to tend to my thoughts, my views, my attitude towards my students, towards teaching, towards my school, my colleagues, etc.