Measuring Angles (Plus a Little Dancing)

Geometry A is working through a unit on definitions and introduction to proof, with a good dose of reviewing key ideas that may or may not have been learned in middle school math. Our topic today was recognizing: vertical angles, linear pairs, corresponding, alternate interior, alternate exterior, and same-side interior and how to use that information to start building proof.

I put up a set of lines and a transversaIMG_0065l and had student call out angles that fit the above terms. Then I had them all choose a set of taped lines that were spread around the room. We went through each location again, trying to find as may pairs that fit said relationship. After students were comfortable with each, I hooked up “Dance, Dance, Transversal.” I have no idea who I first saw the idea for “Dance Dance Transversal” from or I’d give credit, but there are lots out in the inter-webs of math land, so if you want more, Google returns many hits. We played a few rounds to warm up. Basically, I had a PowerPoint set up to cycle through the terms (I limited it to vertical, AIA, AEA, and corresponding) and students had to jump to the correct location. We had music going and in later rounds, judges. We crowned the class champion and I let them know they’d have to dance on the unit exam.

Then, each student was tasked with getting a protractor and measuring the eight angles formed by the transversal. I had purposefully used both parallel and non-parallel set ups (About 2 parallel for every non-parallel). After measuring, they walked around and had to write down at least two notices IMG_0058and two wonders. (Examples “I noticed all the vertical angles were the same.” “I won
der why some gro
ups have only two different angle measurements and others 4.”   “I noticed an error, or what I think must be an error in set B.”   “I’m wondering if my tape was messed up, because it doesn’t look the same as most of them.”)

We were running short on time, so we shared out a few of the Noticings and Wonderings as a class and we’ll pick back up there tomorrow. The plan is to agree upon, prove, and then practice with the key ideas.

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Time Distance Graphs

Algebra 1A is reviewing parts of a graph, writing stories from graphs, and graphing based on situations. I ran across a really fun idea from Mr. Orr where he had students create motion videos, create an answer key (i.e. a nice graph of the scenario) and then gallery walk and try to create graphs based on each pairs video. I knew I wanted to do it with my class. I am not one to one, or even close to that, though, so I adjusted the activity to fit. Instead, we all had to share the one iPad I did have.

Each student got a set of steps and a place to sketch what they thought the steps would look like on a graph. I didn’t give them much direction here. As they finished, I pulled students out into the hall to film there series of steps. I asked them to think about the distance they traveled over the course of doing the activity and re-sketch the graph if doing it changed their minds. (So in the worksheet below, most students had two sketches for #1).

Time Distancedirections

After the videos and sketches, we talked about what a time distance graph shows. I projected a completed graph and students try to come up with a story. Each student then graphed there own graph on a full sheet of graph paper. I checked over them for accuracy, asking students to explain areas I wasn’t sure about and re-draw until we both agreed. They stapled a blank piece of paper on top and wrote the letter of their story on the outside.

Overnight, I collected all the different clips and arranged them by letter. I also taped up the graphs around the room, with only the letter showing. We opened the next day by watching all the clips as a class. Each student sketched what they thought each graph would look like and labeled it with the correct letter. After the clips, students walked around the room to check their answers. I also asked them to write down any “Notices or Wonders,” especially if the graphs didn’t match they had drawn.

Here is a sample video and solution:

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We got back together as a class and took a poll on which graphs had matched or not. We re-watched the most troubling clips and discussed what made them harder to draw. We also talked about how the graphs might not mach exactly, but still be considered correct. Without having actual measurements on the ground, “fast walking” might always be steeper than “slow walking,” but by how much would vary.

Then, students were given a reflection/exit ticket. Instead of creating graphs, they were given a graph and had to create the story.

exit

The whole thing took about 1 class period, but split into two days. (The end of one class and the first half of another. I have 50 minute classes, but they are small. With a larger class it might have taken longer, or with more iPads it could have been shorter as we wouldn’t have had to watch all the videos together before the walk. Mr. Orr had the iPad videos sitting around the room, one video at each poster.)

It was a fun and active way to introduce motion graphs. I will definitely be using it again. Hopefully next time with more video devices.

Day 3: Woo Hoo

We made it to Day 3. That might not seem too exciting to anyone else, but it is September 21st and only the 3rd day of school due to a contract issue and teacher strike. As of 7 pm last night, I didn’t know whether or not we’d be having Day 3 today or weeks from now.  Now, I feel more grounded. School is off and running.

Monday started off and running too. We drove right into challenging material and students doing the hard work. I love walking around the room taking notes, peering in to conversations, and not talking back. For most of the students, this was a shock to them. They seem on board, but I’m hoping soon that they, too, prefer working this way.  Attendance was better than I was expecting which was exciting as well.

The Bridge to College class did Dan Meyer’s Bucky the Badger and followed up with  a quick reasoning with numbers activity to close out. They had to take a multiplication fact and justify other multiplication and division problems without using a calculator or an algorithm. (Example: If 17 x 22 = 374, what is: 17 x 2.2;   2200 x 170;   374/0.17  ?)

Geometry is working on creating and using definitions. I provided each group with cards that had vocabulary terms and pictures that were example and other non-examples of said term. They had to create definitions and then switch with another team to try draw examples from the definitions only (no term). Tomorrow we’ll revisit the definitions with feedback included and they’ll be tasked with rewriting them.

   
 

Algebra is working on inequalities, using some guided exploration to review/discover the effect of operations on inequalities. My other 3rd year class was picking out linear, quadratic, and exponential patterns from tables and creating equations. Lots of good energy today!

Spaghetti Challenge

I wanted to start the year with a project. I value discussion, team work, and creating and I wanted students to know this from day one. I threw around some grand ambitions, but settled on the spaghetti/marshmallow challenge mostly because the supplies were cheap and easy to jump right into. I was worried that students would have done it already or be bored, but I was definitely wrong. Students were thrilled. My favorite comment of the day “You aren’t tricking us right? I hope math class will be good all year and not just today.”

I had students fill out reflection forms and I got all fives, with the exception was of two fours. (1-5 scale). All groups begged to stay longer after class. Two groups worked through lunch hour, and one group tried to stay into their next class.  I’d call that a good opening. I also got pages of notes of individual students learning styles, ability to work together, communication skills, etc.

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One interesting note was the responses to the question: What worked well? Students  tended to choose their own contribution to the tower. For example for one group, one said “adding something to pull back the wobbly parts” (her idea) and the other: “making a triangle at the bottom to make sure its even/balanced.” (again, said students idea). Their tower was successful at 26.5″ and there was no way to tell tell which one made the difference, if both were needed, or something else entirely. On the flip side, the “What would you change” was usually more supply or group oriented. “Be neater” “Use material smarter” “Be less wobbly”. This may be normal, but we started doing community circles this year and the students had been really critical about themselves earlier in the day, so I was excited to see them proud of their contributions.

IMG_0459-0     IMG_0474

In most of the groups they started out two people working on totally different ideas for same tower and it slowly turned into better team dynamics. A few groups hit it off right from the start and only would do work if both agreed. A few assigned tasks and then came together at the end.

We had some good discussions. What assumptions can we make? How long does it have to stand to count? (The absolute highest was 30 inches. it stood alone for about 1 or 2 seconds and fell. Another at 26.5 inches stood until the group karate chopped it down at the end of class). Is height really the most important part? What are we learning?  “We can go higher!”

Also, I forgot string was a material, so they only got tape, spaghetti and a marshmallow. Three separate groups came back later to tell me a brilliant new idea that “Would for sure be the highest.”  One of the the more inventive ideas was to make a long thin strand and tape the marshmallow to the top of the spaghetti and the ceiling so the long, thin strand didn’t have to actually hold weight.

We Are Finally Back

After a crazy non-start to the school year, we are finally officially have students in school. It has been a slow day, but I’m hoping it will pick up quickly as I am ready to start this year.

A few changes. I’m at a new site. Same school, but totally different part of the city, all new work colleges and students. As a wanderer, its been fun to start anew without actually having to totally start over. I’m also teaching a brand new class called Bridge to College Math which seems like a great opportunity for the students. What’s one more prep to add to the other 6? 😀 I truly appreciate I will never be bored at work.

I have nothing too exciting to report yet, but I am going to strive to post more regularly this school year so I had to start with the right foot forward. I did, however, find a scary bat when cleaning out the classroom so she is now hanging from my wall.

TMC15…Thank You

I’m not sure why I originally thought it was a good idea to go to TMC15. In fact, I didn’t have a blog or Twitter at the time…I left those spots blank on the form. It was a few months later I figured that if I was going to fly to California I could probably sign up for Twitter. I do know that MTBoS has been a valuable resource for far longer than I’ve claimed to be part of it. It’s actually why I loved it in the beginning. I could read all these amazing things, try them with my class, realize I was not alone in thinking math teaching needed some making over, and I didn’t have to do anything. Until I did have to do something. I had to jump in. I did it very tentatively. I still don’t tweet much and my blog is sadly dark more often than I’d like it to be. I’m working on that.  But I had to jump. If this is the future of math education, the future is bright and I want to play my part in it.

It will probably take me awhile to process TMC15. I’ll post a more thorough write up about it later. But I wanted to take a moment to say thank you. Even three days into the conference I was wondering why I was there.  I didn’t know anyone, I didn’t *really* belong and I didn’t want to intrude. This was all in my head. The signs to the contrary were there all along. I had amazing conversations will people from day one. Starting with Lynne, who although it was also her first time, made sure to let me know she’d look out for me all the way to Mr. Stadel who didn’t know me and still drove me to an airport 45 minutes away even though he had a full day preparing for another conference ahead of him. There were so many instances like this in between I couldn’t possibly list them all but please know that I am grateful.

To anyone reading, you are already part of this community, even if you don’t think you are. This is a math blog and you are reading it. You don’t have to take the leap (I didn’t for a long time and still got a lot out of it), but please consider it. I have never met so many people willing to help with anything and everything.

Week One

One week of summer school down and no posts to show for it. I thought blogging would be easier with half days, but apparently not. I can’t take any pictures since I’m in the detention center, but hopefully I can still share some mathy insights. 

We are running short mini units as the population fluctuates and most students aren’t in for very long. We started out simple with solving equations. This coming week we are going to cover sleep, staring with Fawn’s great into stair activity and moving on from there. It’s been interesting to think about teaching with very little supplies. We have to use golf pencils and that’s about all we have. I borrowed a bunch of paper rulers from a large furniture store to use for the stair steepness activity since I can’t bring in actual rulers. 

I’ve been opening with a WODB each day and they seem to really get into it. Trying to build a community of learners where it is not all that natural for them to do so and its been one part of class where the majority of kids will add something to the conversation. I feel I will do the most learning this summer, but I’m hoping to leave them with something as well. 

End of the Year Reflection — A Few Days Early

We are almost done with the school year…. 3 days! Last night was graduation (amazing) and next week is a field trip and a day of wrapping up, making summer school plans, and finalizing everything.

It has been a crazy (mostly in a good way) 1st year out here in Seattle. I only have one day off before I start my summer teaching assignment, so I suppose its not really the end quite yet. This is the first time ever I’ll be teaching the same classes at the same school next year (There are two new ones to add in as well.) so I’m pumped about that. It is making the end of the year clean out harder. Moving around, if it wasn’t digital or extremely amazing, it was gone. I still feel like that, but I have a box of maybes to go through here soon.

Plans for Summer:

Teaching Summer School (in a Youth Detention Facility. I’m really excited to see how it works out)

Rework/Develop class and unit plans for next year. I love the content/ideas behind a lot of what I did this year, especially with the emphasis on the practice standards and novel problem solving we did. But paper work wise/tracking wise it was not as successful. I am at an alternative high school that brings a lot of unique issues with it. I am excited to  rework things into a format that will make both my life and the students’ learning better.

Go to TMC15! (Woohoo!)

Do some PD/training for the new math classes we are introducing

Hopefully do something fun. I assume the 2 year old will demand it and I certainly need it.

***Big hope for*** Find a way to get some tablets for next year. I’m loving Teacher Desmos and want to encourage that sort of sharing/collaborating, but we don’t have that ability right now. Especially now that I know two of my go to math people are joining the team!

Figure out a plan/goal for the blog next year as well at twitter, and other online mathy things. I barely scratched the surface this year with MTBoS and I want to jump in!

Crazy Taxis and Trig Ratios

Short class Wednesday had me on two different sides of the teaching spectrum today. Algebra 1A and 1B did Mr. Orr’s 3 Act Taxi problem complete with great discussions and hard working students. Geometry A and B had a makeup work day because no one was caught up and it’s crunch time. I had avoiding letting the Wednesday be a make up day all semester, but I cracked today. 

Note: My kids think taxis are really expensive or Mr. Orr thinks they are really cheap. I can’t tell because the only time I’ve ridden in one in recent memory was in Korea and the exchange rate doesn’t lend itself to great comparisons. 

  

Math Art

We are doing state testing today, so my room will be a quiet place. Thought I’d share some math-y art instead:   

Posting regularly is harder than I’d imagined it would be. Maybe it wasn’t the best idea to start at the end of the year in the midst of all the craziness that happens. I’m teaching over the summer, but a reduced load… and ‘m planning on setting some goals for more regular posting next year. I’d love to do a 180, but I’m scared to commit 🙂 Hopefully TMC will be a good push into really jumping into the MTBoS.