Systems of Equations: Take 2

We started systems of linear equations on Monday in AFDA and things could not be going better! Now don’t get me wrong, students are still struggling. But they are making sense of word problems, using different methods to solve problems, getting better at using technology, and learning how to ask for assistance. It’s great.

Monday was our first day but we didn’t actually do anything involving systems. We spent the beginning of class doing our warm-up and going over the quiz and midterm that had been taken last week. The rest of the block we worked on numberless word problems. I got this idea from Julia Finneyfrock and it was exactly what my group of students needed because they did exactly what was expected – when they didn’t think about the problem, they just added the numbers up! So we worked on reading comprehension, drew pictures, acted things out, made estimates, wrote different equations on the board… we thought. And they thought they were easy, but I know this time was well spent.

Tuesday the students started off with guess and check word problems. All I did was give each student a copy of these problems, read the problems aloud one at a time, and encouraged them while they worked. We talked strategy, used technology, students collaborated, and the pride they displayed when they finally worked out the answer was palpable.

We worked through examples using each method by writing and solving more systems using word problems on Tuesday and Wednesday as well. The class did the majority of these problems together and some students remembered some of these methods from Algebra 1 but most did (do) not. The students were then grouped into 2-4 each and each group was assigned 1-2 word problems from the matching portion of the packet linked. Each group had to identify their match, get it peer checked, and then show their work for solving and explain what the answers meant in the context of the problem.

Today, the students again worked in groups but today was more rote practice. Groups of 3 worked together to find the solution to different systems, with each member using a different method and making sure they all got the same (correct) answer. I found my worksheet on TeachersPayTeachers but you could really use any worksheet and just assign students different methods for each problem I suppose. I  don’t know whether or not the purpose of this got through to all of my students but I know it did for some; I worked through a substitution problem involving fractions with a girl and she said “All of that just for (7, 0)? Isn’t there an easier way?”

You might have noticed that missing within all of this are the different types of solutions to systems of equations. Not to worry! We’ll be addressing that on Monday with one of my favorite MAP activities: Classifying Solutions to Systems of Equations. The students will take their first quiz of the unit after that, so I guess that will be the real test. But the conversations that we and they have been having are giving me really good vibes about this unit!

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Time to Check In

There have been a fair share of issues so far this year, and those were made very aware to us over the past week with parent teacher conferences and other communication from parents and students. So today during lunch I decided that we were going to start class by having a bit of a reality check and refocusing on our goals and the goals for this program.

We posted 8 sheets of paper with various prompts around the room and instructed students to spend 5-10 minutes writing a response on each one. I’ve shared the responses for three of the prompts below.

When I have an issue with Canvas (learning management system) or course material, I can…

  • try and solve the problem myself
  • talk to a teacher/ask the teacher for help/email my teacher
  • talk to my parents
  • communicate with others
  • google

Not so helpful but still semi-serious responses included:

  • wait and procrastinate, then complain to my teacher
  • blame it on technology
  • have a panic attack

When I have an issue with my group or someone in Pathways, I can…

  • talk with the teachers
  • talk with my group to resolve the problem
  • ignore them
  • get over it
  • talk to the group member in question

Not so helpful but still semi-serious responses included:

  • yell at the person
  • call them out

Jobs that require working on teams in some capacity include…

  • actors and actresses
  • people in doctor’s offices
  • business partners
  • law firms
  • teaching
  • engineering
  • pilots
  • designers
  • surgeons
  • coding
  • making movies
  • military
  • sports
  • scientists
  • construction
  • mechanics
  • assembly line workers

This gave us the space to hold the conversation about becoming self-advocates (“I’m sure your parents are great but we don’t teach them, we teach you! So you should be emailing or asking questions when you come in!) as well as a reminder that jobs across all career pathways are going to involve group work, so it’s important for us now, in high school, to gain the skills to be good group members (“Who wants to be 45 and working in an office and still picking up the slack on a project? Do you think you’ll enjoy working unpaid overtime because you procrastinated?”)

The rest of the day went well. Most of the time these kids are great. It’s important though, as freshmen and students in a pilot program, for us to have these conversations periodically so nothing blows up.

Carnival Rides

The Pathways Project is off to a fabulous start. Both the Physics by Design and Humanities by Design courses are hard at work on their projects, and (most of) the projects are great.

Yesterday the students presented their second projects in Physics by Design – a small carnival ride. Small carnival rides are rides like the Tilt-A-Whirl, Ferris Wheel, and Merry-Go-Round.

Each presentation is supposed to sell their ride to our fictional amusement park. So the groups started off by introducing their rides and talking about their designs. You can see one group’s design process  for their hover bumper cars below.

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Some groups included a story for their rides or the history of their rides.

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All groups created scale drawings of their rides within the first two weeks of this unit. Some groups created scale drawings using paper and pencil while others branched out on their own to create digital models using free online design software. The awesome thing was that as soon as one group began creating theirs online, six other groups of varied abilities created 3D models online as well. We did have a lot of groups switch between Imperial and Metric systems which was a little frustrating at times but I think they worked it out in the end.

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Each group also created free body diagrams, labeling each of the forces being enacted on different parts of their ride.

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Since the presentations were basically a sales pitch, their conclusions needed to include why they wanted their rides in the park. Many of the groups also included safety considerations without being explicitly instructed to do so.

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My favorite thing about teaching this course so far is watching the students of different math levels interact with each other and grow at different paces. We have students who failed 8th grade math last year, students who are going to finish Algebra 2 in a semester, and everyone in between. During this unit we introduced the basic trig functions and some of the Algebra 1 students picked up on it immediately while some of the Geometry students are still struggling with understanding them. We had Algebra 1, Geometry, and Algebra 2 students being remediated on solving distance/velocity/time word problems while the other half of students (still Algebra 1, Geometry, and Algebra 2) went into solving systems of equations word problems using a variety of methods.

This is such a change of pace from the collaborative courses I have taught the past two years, even though this is still technically a collaborative class. There are still loads of classroom management issues, interpersonal issues among the students, and students who are struggling to keep up with the work, but overall this has so far been a success.

I am really excited to start roller coasters. The students are excited to start roller coasters. These next five and a half weeks will probably be long but I can’t wait for our next set of presentations!

Project 1 – Carnival Game

This past week our students finished up the first part of their first project in our physics/math project-based learning course. Our first unit has been mostly about measurements and data analysis, so students created carnival games and then we hosted a carnival at a football game last week. They collected data at the carnival and are going to analyze it, write a report, and give a presentation this week.

I didn’t get any pictures of the actual carnival due to being the adult-in-charge for the first part of it, but the day before the carnival we were able to have one of our self-contained classroom come visit and play the games with us. Some pictures of that are below!

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What I loved most about this was the interactions. The games weren’t the best and we were loud and everyone else near us probably hated us during this time but everyone was having so much fun. The self-contained students obviously don’t get to be out with the rest of the students very often, and the regular students got a great opportunity to learn patience, encouragement, and how to better explain the rules of their games.

This has been the highlight of the year so far. We’ll see what, if anything, will top it.

#teach180: This year’s first classroom

It’s been too long and I didn’t do much worthy of a #teach180 tweet today so I’m doing a #teach180 blog post instead. Going to try to blog at least once a week during this school year, we’ll see how it goes. Be forewarned that there are a lot of pictures in this post!

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I’m traveling between three classrooms and two offices this year. It’s a pain. Thankfully the classrooms, my students, and my co-teachers are generally awesome and so far it’s been worth it. The first classroom is really long! When you walk in, you’re in a small entryway. On one side of this entryway is a supply table which has calculators and anything students leave behind. Don’t freak out too much, the keys are mine.

 

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Right past the supply table is the weekly schedule board and the teacher space. I didn’t take a picture of the board, but it’s broken down by day and each day has two parts to it:

  • broad topic (this week’s is probability)
  • daily question we’re working toward being able to answer (“what happens when events depend on each other?”, “what happens when probability changes based on given information?”, “how many different outcomes are possible for this experiment?”, etc.)

 

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On the far left of the board I also have the weekly homework assignment posted. On the far right of the board I have my weekly paper holder. Our copiers are unreliable, so I try to only make copies once or twice a week for all of my classes. I also don’t take work home during the week and rarely on the weekends, so this helps me keep organized.

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Currently students are in sets of two or three facing the front of the room. The teacher I’m sharing the room with and I have developed four seating patterns that we think we’ll be using regularly throughout the year:

  • black, which is individual seats (for standard assessment days)
  • green, which is the sets of two or three that they’re currently in (for notes or partner work)
  • green, which is two teams facing each other with students in pairs (for debates and games)
  • red, which is groups of four to five (for small group work)

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In the front of the classroom there’s a cabinet in the corner, which is where we have supplies that students can always use. Right now it’s pretty empty and only contains scrap paper, scissors, pencils, colored pencils, and highlighters. There’s also my “student of the week” trophy and two dinosaurs that I occasionally give to students who need them.

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Immediately to the right of that cabinet is our school rules bulletin board, which currently has the schedules, tardy policy, and electronic device policy. My classroom-sharing teacher is planning on changing the tree scene with each season.

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On the far end of the classroom are two boards for student use. One has the 2016 Challenge thanks to Sarah Carter at mathequalslove, and the other has Sudoku thanks to Christie Bradshaw at Radical4Math. Students can use these during our study hall time or if they finish something early in class.

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Finally, in one set of cabinets in the corner my students have personal boxes. This is where students can keep personal supplies, papers they don’t want to lose, etc. from day to day and it’s also where I put work when students are absent and where I pass back 98% of papers to. All of the cabinets are built into the wall and a lot of my stuff is in electronic form so this was a good way for me to utilize that space!

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So that’s my current AFDA classroom. I’m in there for first block every day from now until the end of January, when my schedule changes and I’ll be moving again for the spring… sigh. Bonus pictures below of decorations on our math department office windows. A handful of quotes I’ve collected over the past few years that are school-appropriate and potentially teenage-worthy as well as a collection of photos from Sara Van Der Werf’s Math Wall of Shame.

 

Tracking Student Achievement #MTBoSBlaugust

I blogged previously about how next year our math department has decided to move toward a department-wide grade replacement policy (see #MTBoS30 Day 9: Grade Replacement vs. Standards Based Grading) and I’ve been working on figuring out how I can still include students in the process. I enjoyed using Dan Meyer’s concept checklist over the last two years. Sometimes it was a hassle, but for the students that actually kept track of theirs they enjoyed knowing what their strengths and weaknesses were (and getting those stickers!)

Last spring semester I taught a new class called Algebra, Functions, and Data Analysis – this is a class that is not tested by the state but still has standards. I mostly used stuff from the other teacher who was teaching AFDA at the same time as me and only glanced through the standards before teaching the course… good job, past me. But, we live and learn. There were some days that seemed too easy and repetitive and others that seemed totally over my students’ heads, and the same was true about the quizzes and projects they completed as assessment. I didn’t really enjoy that, but I felt a little overwhelmed without a planning period so I kept pushing through. Well I’ve finally sat down and looked at the standards and boy did we do some interesting things. We taught multiple things that definitely are not required! Some of which I’ll be keeping, and some of which will probably get tossed.

ANYWHO, I digress… After reviewing our curriculum map and the state standards, and a little inspiration from someone on Twitter (I forget who) I made up slightly new Achievement Trackers. My plan is to have students keep these at the front of their assessment section of their binders so they’re easy to find.

Things I Like:

  • students being cognizant of what grades they’re earning (and hopefully why!)
  • helps me better plan lessons and assessments
  • the students have less to keep track of compared to the old concept checklist

Things I’m Not Sure I Like:

  • some of the wording isn’t necessarily the most student friendly/some boxes have a lot of text
  • it will take up two pieces of paper front/back
  • the homework section at the beginning of each unit

Let me know what you think and if you have any suggestions!

Experiential Learning #MTBoSBlaugust

hated history class growing up. HATED. I’m pretty sure this probably broke my dad’s heart on more than one occasion; a long-time English teacher who had struggles in math and science, I know that my dad had (has!) a passion for history. By the time I got to high school it was pretty much the only subject he could help me out with, and I needed it a lot. But all I remember is learning about the explorers, the American Revolution, the Civil War, and more over and over and over again. Why, by the time I got to my junior year of high school, did I still need to be spending time in class learning about The Boston Tea Party??? To me it was so incredibly pointless. I spent a lot of time agonizing over readings from my textbook and complaining about all of the people and events in there.

Fast forward to now, and I still don’t like history class. But I do enjoy learning about history. I love living in “America’s Historic Triangle” and getting to touch and see and do things like the Native Americans, early settlers, and soldiers in the American Revolution did. Two years ago I spent part of spring break at Independence Hall in Philly and walking the Freedom Trail in Boston, and last year I did historic walking tours and visited plantations in both Charleston and Savannah. Sunday morning I did an audio tour of Alcatraz. All of those experiences were awesome.

Being able to interact with history through artifacts and storytellers is what makes me enjoy learning about it still to this day. Is it possible to bring some of these things in the school environment? Yes. Is it possible to do the same in a math classroom? I’m not sure.

There have been a lot of amazing #MTBoS teachers doing awesome things involving the history of math; I’ve seen mathematicians of the day, research papers, poster projects, and more. And there are even more teachers doing amazing work within the classroom to help make math accessible to students. But again, how much are those practices helping students connect with and experience the math? I’m not sure. I’m not sure what the best way is for students to experience math. I’m not even really sure what that means. It probably means something different for everyone and there are almost assuredly different ways to do it.

But this is one of my goals for the year: to have my students experience math in a way they haven’t before. I know that this will happen in the Physics by Design class I’m co-teaching (which I’m super excited about and will blog about later this month) so really the focus will be on Algebra, Functions, and Data Analysis. Last year we did exclusively alternative assessments for each unit’s summative assessment but I was unhappy with them as a whole. So here we go. Year 3. Time to pull out those old assessments and get to work.

P.S. I also learned a lot about water this summer through my awesome time in Sarasota with DukeTIP, way more than I ever thought I’d be interested in learning. I can boil it down to: nature is pretty awesomely resilient, but we’re working pretty hard to ruin that.