Intro to Systems of Equations with Gallery Walk

This year I ran across a document in my Google Drive that Sonya New and I made in order to introduce solving systems of equations. I decided to do this on the first day back after Christmas break in order to get us "back on track." We have solved systems algebraically and had begun discussing the substitution and elimination methods the week before school let out.

I loved doing the assignment. I only had 6 groups but I still wanted to have them graph all 8 systems so a few groups had 2 systems to graph. I did not call them systems. I just told them to graph both lines on the same coordinate grid. I first allowed them to graph the lines on graph paper and then I had them put them on chart paper. Afterwards I assigned each group a different color marker to write with and had them do a gallery walk and put feedback on the graphs. If they agreed with the graph they put a check mark. If they thought there was an error they had to place an x and then tell what they thought was wrong. The last direction I gave them was to write down the solution to the system of equations. (We have been talking about solutions for systems of equations ALOT in class. I have even OPENED and CLOSED class MULTIPLE TIMES by randomly calling on a student and asking them, "What is the solution to a system of equations?" AND offered candy when they get it correct!! Many of them still don't know. I accept various answers: an x and a y that make both equations true, the point of intersection, an order pair that works for both.... It hurts my feelings but I still haven't gotten it to "sink in.") I had one student in the room that asked me if I meant for them to write the ordered pair down so eventually everyone caught on. Almost every group asked me what I meant by the solution but I would not tell them. I told them to discuss it within their groups because we had talked about it in depth before Christmas. Anyway...after they completed their gallery walk we "debriefed" as a class and settled any differences of opinion. It was a wonderful way to review graphing and reintroduce them to solving systems of equations - we had one no solution and one infinitely many solutions so we also discussed what those would look like algebraically. I did have them solve a couple of the solutions algebraically (using substitution) at the end of class.

Here is the document if you would like it.

OBSERVATIONS:
1. Even my best students needed the graphing review. I had one of the top students in my class put his y-intercepts on the x axis!! I want to do a better job of spiraling my algebra class. I love that our Meaningful Math Algebra books include graphing in every single unit! I hope to incorporate more spiraling review as my warmups this semester.

2. It scares me how much my students forget AND it bothers me that I have to move on when I have so many who have clearly not retained what we have learned.

3. Many of them wrote that the solution was 5 and 2 when they really meant (5,2). They think I am being picky when I make them write the answer as an ordered pair.

4. Students like the opportunity to get out of their seats! I did have some really good student dialogue and I feel that it was a productive first day back after Christmas:)

2016 MTBoS Blogging Initiative - Why?

I am excited to be joining the MTBoS Blogging Initiative this year. I started blogging about a year and a half ago. I was teaching a problem-based curriculum for the first time and wanted to record my "teaching transformation." I really started blogging for myself - so that I could look back at how the lessons went and use my reflections for future years when lesson planning. I feel like viewing blogging as a tool for me instead of being concerned about how my writings are being taken by others was THE BEST PART. However, Shelley Montgomery, the instructional partner at our school, encouraged me to go ahead and share my blog posts on Twitter. Through conversations I had with her I began to realize that even if one other person could benefit or be encouraged by my writings that it was worth it. Tracy Saltz...whether you realized it or not...you were that one person. We met on Twitter because you were also teaching the IMP Meaningful Math curriculum for the first time. Since then I have met a few others at workshops or via comments on my blog or Twitter that have enjoyed reading my posts. It is an encouragement to think that I have contributed in a way that was helpful to other teachers. I have learned so much by reading the tweets and blogs of other teachers and I did want to contribute instead of just being a "user."

So...why should you consider joining this blogging initiative? I think that blogging helps me to reflect on my teaching practices and organize my thoughts for lesson planning. An added bonus is for you to share your thoughts with other teachers so that they can learn from you and/or be blessed to learn that they are not the only ones that have similar struggles. I think that everyone benefits whether from the collaboration/encouragement of other teachers OR the benefits of reflective writing.

Problem of the Week success:)

This week I graded what I think was the third POW writeup that I have assigned. Once again (even though I dread grading them) they provided "teacher encouragement." My 2 favorite comments in the "what I learned" portion were:

If you listen to the teacher she will give you hints that really help you. 

My parents said they didn't get to do fun assignments or sit in groups in their math class. (She thinks math can be fun??? = total success!!) 

I think the one about listening to the teacher is funny; the truth is many of my students tune me out while I am addressing the class as a whole. Then when the realize I've stopped talking they look around and say, "What are we supposed to be doing?" Ugh! I am trying some tricks to try to improve my students listening skills. One is to randomly call on a student at the end of class and ask them a question that they should know the answer to if they listened in class. I don't always ask them a math question either. I reward them with candy or letting them leave the room first.

One other thing that encouraged me this past week was noticing that I had one student use tables to graph lines. As a math teacher I think that is strange because I used to always put my equations in slope-intercept form to graph. Teaching from the IMP Meaningful Math Algebra book has helped me to allow students to discover the way that works best for them (believe me I always tell them the way I think is easier!! Haha!). I taught slope-intercept form (conceptually first in Overland Trail), graphing by intercepts, and graphing using tables almost simultaneously. I would stress the easiest way depending on the way the equation was written but told them over and over to use the way that makes the most sense to them. Out of 21 students I had 1 girl get 8 out of 9 graphing questions correct using tables. Even though it was only one student who chose that method it really encouraged me to see that some students really do benefit from the "alternate" approach. I have spent many years teaching them with the methods that I think are the most efficient. I feel like what I am doing now benifits my students more.

Questioning and group work

My newest focus is to improve at using quality questioning to improve discussions and student engagement in my classroom AND to learn how to better manage group work. I have just recently decided to really narrow my focus to these 2 things for the rest of the year. There are so many teachers that I have talked to about these things and I have come to realize (again) that just because something works great in someone else's classroom it may or may not work in mine.

Here's an example...I had someone (Tanya Barnes) to tell me that I should rarely be the one at the board going over problems. She said the students should do it because then they take more ownership. My argument was that I do sometimes have my students go to the board to share their thoughts or answers on a task. However, more often I stand at the board and lead the discussion and write down the answers the students say so that the class can decide if it is correct. It is so much faster!!! And I have alot of material to cover!!! So...I listened to her and made a concentrated effort to have students go to the board today to share out. I even let them do the examples  (when I had a student that understood). You see....I teach freshman. And I have several competitive boys in my classes AND a few girls who love to prove people wrong. It takes twice as long (or longer) when they go to the board because they have to turn around every time someone makes a noise or comment....then they have to be a comedian....then they have to pop someone on the back of the head on the way back to his seat. Ugh!!! I caught another teacher walking by my room (good ole Amy Walker) and said, "There are some strategies that just DON'T WORK with all classes!" I told her what I was attempting and she reminded me that no one else knows my students like I do. Even if another teacher has freshmen they aren't exactly like our freshmen. I AM THE EXPERIENCED PROFESSIONAL....I AM THE EXPERIENCED PROFESSIONAL.... (excuse me while I try to convince myself....haha!). I know how to make adjustments based on the students in my classes....right?

Ok....so then I thought about it and remembered how I have judged people for trying something one time and then giving up on it. So, my commitment is to keep on trying this "strategy" until Christmas. I am hoping my students will get more accustomed to listening to their peers and using the question stems I have hung in my room without being so immature and silly. But....I teach freshmen. I am just hoping the percentage of silliness lessens. I know it will still happen. My goal is to not be writing on the board if I have a student who can be doing the work instead. It's like a balancing act at the circus. If I lean too much in the wrong direction it's not good. (Did I really just compare my classes to the circus?) Here is hoping for a great balance of mathematical discussions, productive groupwork, and teacher-led discussions.

I appreciate the input and opinions of everyone and hope to use them all to find what works best for me and my students.

Celebrate Life!! Yes...especially the teacher's life!

My pastor talked to us today about how we should be celebrating life. He spoke of how we should be different from the rest of the world. We should not be shrinking in fear of the events that are happening in the world but we should be a light and an inspiration for those around us. Encouragers. Inspirations. (I may be using my own words a little...but this was my take away today.) I sat there and thought about how I can apply that to teacher life.

What would it mean to celebrate teacher life?

• Staying focused on the incredible calling and responsibility we have to teach, motivate, and love the students that we have the opportunity to work with
• Avoid feeling frustrated every time the decision makers that be change/create policies that don't seem to make sense...(by remembering the reason you became teachers to begin with) - if you let it get to you then you will be unhappy all the time!!
• Celebrate the successes of your students and fellow teachers
• Try not to speak negatively about colleagues and administrators even when you don't understand or agree - everyone is human which means they will not make be perfect (and neither am I!!)
• Remember how much I love being around teenagers. I hate being serious all the time (and so do they). I like to be silly and have fun. Teenagers (and children) seem to appreciate that a lot more than adults do! HAHA!
• Remember that we knew when we entered this profession that we could make more money if we chose different career paths. We have a job that is often thankless. Are we here to hear thank yous or to make an impact on the future of our communities? (Of course thank yous are always nice...do you thank the teachers and coaches who invest time in your children?)

I read a book one time entitled Pushing Up People by Art Williams. It has been a long time since I read it but I remember the basic premise. We should be encouraging and promoting those around us...especially our bosses and school leaders. When we operate with this philosophy we model some valuable lessons for our students, fellow teachers, and families. That is a great way to celebrate the teacher life!

Positive phone calls made my day!!

This afternoon I was feeling frustrated. I am drowning under a stack of papers to grade (I should be grading now instead of writing this!). Also, I have been trying to figure out a strategy to improve the investment that my students are making into one of my classes and I have not reached a solution. Every time I try to have a conversation with them it seems to turn negative. UGH!

So, I was sitting there looking at my stack of papers to grade and then I saw a reminder to make my positive phone call. Thanks to the leadership of our new principal, Ryan Barkley, I have been asked to try to make one positive phone call per week. I am behind on this project so I decided to call 2 parents this afternoon. It was the BEST thing I have done all week. The excitement and pride in the voices of the parent and grandparent that I spoke with was so rewarding. It truly brightened my day and reminded me of all the GOOD things that are going on in my classroom. I have some incredible students.

Are you feeling frustrated? Think about the students who are making progress and call their parents to let them know about it. It will be the highlight of your week.

Hey...I still love math:)

I know this is a strange comment for a math teacher to make. For years I have just taught math. I chose to become a math teacher because I love math but to be honest all the years of teaching math to people who do not really want to learn it had just "sucked the life" right out of my math enjoyment! I was covering the standards but rarely ever used any activities that peaked the curiosity of my students.

Thanks to our "Meaningful Math adventure" (see this blog post for an explanation) I am having fun teaching math again. I see my students having more fun learning math. Last week I had a student to tell me that she had fun in class that day. I also had some students tell me that we do the most work of any of their classes but my class is also the most fun. I read Teach Like a Pirate this Summer and I have come to realize that it is okay to have a goal of having fun with your students...as a matter of fact we need to throw in some activities that the students will consider a "fun break" from "regular math."

Today I also found myself sitting at my desk working on the High-Low Differences activity in Overland Trail's supplemental activities. I was "noticing and wondering" myself! I was thinking that I really need to find some extra time to investigate why this works like it does. Then I was so ambitious that I answered one of the questions (in a survey I had to take) to indicate that I considered myself to be a mathematician! (HAHA!) I have found value in addressing problems from a student's perspective. Our new textbooks from It's About Time give me many opportunities to have fun working on math and then turn it around to my students as an opportunity to problem solve and enjoy themselves while they do it. I asked them a few times last week if they wanted me to "introduce" them to the activities or let them just try to figure it out on their own. I was amazed at the number of students who wanted to try it without any assistance.

Now, don't get me wrong. I still have students who sit there like "knots on logs" and wait for the problems to be presented to the class so that they can write down the answers - they just hope that when I roll the dice to call on someone that their number is not called. And when I do call on them they tell me they didn't do that problem...and then I talk them through it until I pull the answers out of them...in some cases it would be easier to pull their teeth without anesthesia. I also still have students who gripe and whine and ask for help before I even get the page number out of my mouth. However, it is so cool to catch that student who says he hates our textbooks truly engaged and enjoying himself during an activity (because he figured it out by himself!). This certain student that I have in mind was "called on the carpet" when I told him that I noticed he had fun working on the activity for the day - which just so happened to be "Getting the Gold" that I blogged about here.

I would like to end this blog with a funny picture of what some of my students did last year after I had gotten onto them for sitting there like "knots on logs" instead of doing their work.

Comedians!!