Category Archives: Make Thinking Visible

January #MTBoSblog18 – Formative Assessment Strategies

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From Jennifer Fairbanks…

Happy Day – Our 1st one of 2018! Join us and blog today! Share anything you want! When you blog, tweet out the link.

Join us as we all blog on the same day – the 18th of each month!  Blog about anything.  Write at any time.  #Pushsend on the 18th.  Then, we will all have a plethora of good things to read.  We can use Twitter and the hashtag #MTBoSBlog18 to encourage and remind people to blog.  If you are interested, record your name and Twitter Handle, areas of interest/teaching/coaching, and a link to your blog’s website.  Don’t have a blog? 2018 is as good a time as any to start.  Take a risk and dive in! Or, read and add comments!

Hmmmm.  WElllll.  Okkkkkkk.  What do I blog about?  Here goes…

Our schoolwide focus this spring is on revisiting what we know about good formative assessment and putting it into practice.  Eventually, we will be encouraged to ensure we are utilizing the practice of PA on a daily basis – for those not already doing it.  After speaking with our SLC, we thought it would be a good use of time for our department virtual PLC – on our NTI (aka Snow Day) – to work on ensuring that each learning target in an upcoming unit has a quality FA in place.  And if not or if it really doesn’t measure what the target is intending, then plan a better one!

As we began building the document for Algebra I unit on Functions, I was reminded of so many great strategies  learned through the years and new strategies shared by others.  Most of these have been learned through trial and error, they didn’t “just happen.”  When trying new things, sometimes you need take NIKE’s advice and Just Do It!  See what happens, reflect and try it again!  So here is a list of a few things we ran across while working this morning:

  • Every Graph Has a Story

    When given a graph with no labels, numbers, etc. – can students devise a story that will related key features of the graph to the context of the story?

Here is @heather_kohn’s Ambiguous Sports Graph sports graph

  • Thumbs Up, Thumbs Down

Was reminded of this one by my colleague.  Basically, you can pose a question to the entire class, then ask for a Thumbs Up or Thumbs Down as to if it is true/false, example/noonexample, linear/nonlinear, function/not a function

  • Green Pens –

    I am super excited that my green pens arrived today!  I plan to use Amy’s idea for Bell Work, but integrate into independent practice time.  Students will have a brief practice page – when one finishes, I will check – if all good, they will receive a green pen and help me mark other papers.  After I have 3 or 4 Green Pen Helpers, I will have time to visit each table group for one-on-one help.

 

  • Give One, Get One –

    I believe the first time I ever used this was out of a Kagan book in Geometry.  In this unit, I plan to give students graphs of functions.  Before we begin, I will ask them to list 3 things they notice about the graph.  They will then have 4 or 5 True/False statements to respond to.  Here’s the GO-GO:  They will write one more True statement about the graph, then go visit someone else across the room, sharing / discussing their true statement, and receiving/discussing/recording their friend’s new statement.

 

  • White Boards & Summary Notes

    Individual to practice writing inverse function equations.  Nothing new here, I give them the function, they practice rewriting the inverse on the whiteboard, I walk around the room observing and noting…  Then I will address any common errors I see.  After reading this tweet:

debrief notes

and a discussion a few weeks ago with @druinok about student notes from the teacher – I was reminded…  we will discuss big ideas we noticed in our white boarding, then turn to our INBs and generate our own Summary Notes.  Since these are 9th graders, I will likely give them a few unworked Functions / Inverse examples to help them get started.  Once they have completed their Summary Notes, there will be some time later for independent practice.  Maybe even pull out those green pens again!

  •  Open Sort & Card Matching –

Years ago, I was taught about open sorts from a colleague who had attended John Antonetti training.  I plan to use this structure by giving students cards with several types of graphs, in the discussion with their noticing and sorting and support of reasoning – I am anticipating something coming up about dotted / point graphs and connected graphs.  In the debriefing of the sorting task, this will allow me to introduce / review the idea of discrete vs. continuous graphs.

The second part of this sort will be to place those cards inside the ziploc bag and get the other color cards out.  These cards will have various domains and ranges listed.  Again, in the discussion of their reasoning for their sorts and debriefing of the task,  I am anticipating someone sorting based on listed numbers vs. intervals, which will allow me to make the connection between the different notations for domain and range.

Finally, the matching task will be for students to match the correct domain and range to the correct function graph.  The best way for FA assessment to happen here – is to walk around, listen/observe and ask questions, never telling them, but helping them think on their own.

After some practice and discussion, I feel like this might be another great spot to have students create their own Summary Notes of the ideas shared / discussed.

  • 2-Minute Assessment Grid

Goodness, this may be one of my favorite student reflections.  You can read about it here.  You can copy the grid and have students fill it in.  However, I like creating a large grid on my board and giving students 4 sticky notes on which to respond.  Basically Students are asked to tell ! Something they want to remember.  ? A question they still have.  @ An A-ah – lightbulb moment and + One improvement they can still make / need ot study.

  • Class Closer Reflection

An easy, quick one sentence reflection – have students choose one of these sentence starters and complete it…  Something I’ve learned,…, Something I realized….  OR Something was reminded was of…

Follow-Up Action is what matters most.

As with any FA – its not about the strategies – they only provide a vehicle for the information you get from student learning.  What happens next is very dependent on what information you receive.  In class strategies, you must be present, listening, allow yourself a few seconds to think through their responses / questions before responding to them with a question.  With reflections, exit tickets, target quizzes, we have the opportunity to filter through all of their responses, looking for commonalities and misconceptions – that will help us plan our next actions.  Do we need to address with the entire class?  Are there a handful we need to pull to the side while others are completing bellwork the next day?  Is everyone on the right track and ready to move forward?

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I Still Have a Question About…

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We did not get through all I intended today to allow some students who wanted to watch the inauguration that opportunity.  But we did address a couple of more questions from the 2-minute reflection students had completed.  You can look back to the previous post to see the original task.

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We addressed the two blue questions in the after lunch class.  Why can’t you multiply the numbers by each other?  Well, lets see.  Again, as I did with another class, I asked them to add two numbers that would give us 18.  We graphed our responses, then graphed the equations x+y=18.  And likewise, give me two numbers that would multiply to give us 18.  We graphed our responses along with xy=18.

When we added the equation to the product set, students were caught off guard with what they saw.  WHY is there a graph in the third quadrant?  Will that red curve ever cross the y-axis?  Doesn’t it eventually get to the axis?  Again, just attempting to address their question, by looking at a couple of horizontal translations and introducing them to that boundary line called an asymptote, led to even more wonderings.  Which is what math class should be about.  As long as they were on task, I continued to go with their questions.  Only 3 students were not interested, who would likely have been off task no matter what I chose to do, so I made the decision to keep going with the majority’s curiosities.

Another student asked about our statement “x cannot be in the denominator” but yet when we find rate of change with a table of values, we compare y over x. Hmmmm.  Good question.  So I gave a table of values, asked the student to talk me through finding rate of change.  When we wrote our ratios, what values did we use?  Not the actual y and x values, but the change in y over the change in x.

The entire class really reminded me that we can say something with an intent, but what our students hear is something else…how important communication is, how important is it that we allow some time to process and clarify their misunderstandings.

Finally, we addressed the question, we’ve been told x’s exponent must be 1 in the linear function.  We’ve seen greater than 1, but if it is less than 1, can it still be linear?  Let’s see.  Go to y=, type in x and choose an exponent less than 1.  What do you see.  Share with your neighbors.  So, how would you respond to this question, students?

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To me, this was one of the most productive two days I’ve had in this class.  Students were engaged because we were addressing their questions.  I’m not sure I actually answered their questions, but I provided them with some examples that allowed them to answer their own questions.

Identifying Linear Functions

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Linear Functions Organizer this does not include arithmetic sequences, which was earlier in the year, but I can refer back to our work with them to activate prior knowledge for this unit.  The next unit will be linear regression which will include correlation, describing scatterplots, finding regression equation with technology, using the equation to predict and finally introduction to residuals.

Students started with a pre-quiz similar to the one below.

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Identify Linear Functions This is a booklet with a Frayer Model for our notes, a variety of math relations to identify as linear or not and a 2-minute reflection grid on the back.  Prior to beginning our notes, I gave them 1 minute to jot down anything they thought they knew about linear functions.  Then we pair-shared before sharing with the entire class.  Then we took our notes. (as a follow up the next day, I gave them 2 minutes to jot down all they could remember about linear functions as a small retrieval practice).

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Our next task was created by cutting apart these relations and posting them around the room with a chart that asked if they agreed or disagreed with the example being a linear function.  Students received stickers to place on the chart as they visited each station.

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I was fairly accurate in which ones I thought we’d have to use for discussion, but a couple really surprised me.  These are the 4 we discussed following the carousel activity.

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I. y = 2x was the one I was not expecting.  When I asked if someone would share their thinking, one student said they thought x was an exponent.  Another shared they did see “the b” for y-intercept.  We looked at a table of values and graph to agree, and show the y-intercept was at the origin and indeed y = 2x was linear.

The other I failed to snap a picture of was graph K, a vertical line.  Yes, it’s linear, but not a function…two students got that one correct in this particular class.

Using the 2-minute reflection grid as our exit slip to see students thinking about the lesson, I was excited about some of their “I still have a question about…”

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On the reflection grid, if they have no questions, nothing is confusing, I ask them to give me a caution…something to be careful or / watch for.  Several of these questions encompass multiple students.  Some of them I only needed to clarify what was said.  Its pretty clear I was not communicating very well on a few of the.  I hear my “expert blind spot” showing up…”Of course squared is not linear, we learned it was quadratic in our functions unit!”  But so many students on the pre-quiz used vertical line test as their reasoning for linear…we had some side conversations about this misconception…that it shows functions, but does not prove if its linear.

Some of the questions, I allowed other students explain their reasoning to help clarify their understanding.

I know I shouldn’t have favorites, but in this list…

Why can’t you multiply the numbers by each other?  We tried it.  Add 2 numbers that will make 18.  Create table of values, find rate of change, graph it.  Yep, that’s linear!  Multiply 2 numbers that will result in 18.  We created a table of values of their answers, found the rate of change and graphed them.  No, that’s not linear!

If an exponent is less than 1, can it be linear?  We will try it tomorrow as our bell ringer.  But I look forward to exploring their questions more!

I told them how excited I was about their questions and posted them on our “THINKING is not driven by answers, but by QUESTIONS” board.  One student had the biggest smile and as she said, Look!  I’m so proud, my question is on the board!  Something so simple, yet, my hopes are that it will encourage her to ask more questions.

One student asked me, but isn’t it disrespectful to ask questions and interrupt the lesson?  Nooooooo.  I love when you ask purposeful, curious questions you wonder about!  Finally, a break-through to get them to start asking and wondering more…

My Hopes for #MTBoSBlaugust 2016 Post1

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mtbosblaugust2016

Thanks to @druinok I have a new challenge for August.  This has been a great summer filled with new adventures learning.  My hope is that the Blaugust challenge will allow me to focus my summer learning at I gear up for students August 10, but also, that I can utilize the challenge to develop a habit of daily reflection once school begins.

My goal is to blog more this month.  My ultimate goal would be a post a day, however I may just settle for multiple posts on days when I have the time.  Like most of you, my first days of school are Ca-RRAAAA-ZZZ YYYYY.   WE are using Springboard for our Pre-AP courses this year, so that means I’ve got to dig in with that since we just got access end of last week.  Not to mention my daughter is in marching band this year, a small part in The Little Mermaid (The Star Theater) at our local theater the last two weekends of August.

I will be outlining my first days plans this week, preparing for open house Thursday night- hopefully will post pics of room, initial training for Google Classroom pilot in our district tomorrow.  Yep, I think that qualifies the end of summer for me.  Though the pool is on our radar today and maybe some water fun on Friday.

 

May Day, May Day #MTBoS30 #5pracs

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Thursday night, I printed off a packet of handouts from a session I’d led at KCM conference in 2012, simply because there was a data collection activity “Look Out Below!” I wanted to use in class on Friday.  As I flipped through the pages, I was taken back by what I used to do.  And it made me sad.  I walked in Friday morning, straight over to a colleague’s room and asked for accountability these last few weeks of school.

Multiple times the past several months  I have been directed back to 5 Practices for Orchestrating Productive Mathematics Discussions, Smith and Stein 2011. I read the in book even participated in a chat.  The following school year, I implemented a few lessons purposefully using this structure.  I found that the FALs from Mathshell often followed the same format.  It led to great discussions, thinking and sharing in my classroom.  So, what happened?  A rut.  I still used the structure, but not intentionally planning NEW lessons, just recycling the ones I’d become comfortable with.

Last November, I attended an ACT Boot Camp sponsored by@UKPIMSER, one of the strategies shared was the 5 practices!  This winter, we had 8 Non-Traditional Instructional Days in our district- where students / teachers participated in learning tasks during Snow Days.  Our department used NCTMs Principles to Actions book, focusing on the 8 Mathematics Teaching Practices, one of which was promoting whole class discourse, and using Smith & Stein’s outline.  This spring, I have come across several chats mentioning the 5Practices for discourse.

Just today, I read @marybourassa’s post Day 80 Ropes and Systems, that described how she used a chart to track observations and conversations inspired by this book.  I also read @bridgetdunbar’s Teach Math as a Story post as well as watched @gfletchy’s Ignite Talk on becoming an 83%er – one who is asking questions to effectively engage students… We must focus on task planning – better questions (Frank’s hot sauce!) in order to listen to our students rather than for their responses.  (S/O @maxmathforum 2>4 Ignite!).

As soon as I arrived home, I grabbed a box from the shelf to get out my #5pracs for a revisit.  And all these treasures were there with it!20160501_145551.jpg

As I flipped through my book, I found these notes…penned on the last day of summer break, on a final trip to the water park, I’m assuming 2012…reading while my daughter and her friend splashed in the wave pool.

I was preparing for the first few days / unit of Algebra 2…

So, here’s my goal for the #MTBoS30 challenge: to revisit #5pracs and plan a couple of intentional lessons, ask better questions, monitor observations and conversations – maybe even record with my phone in pocket and see if  can accomplish some of the “Try This” Smith & Stein have outlined in their book.

I’m asking for accountability, MTBoS.  Mayday! Mayday!

The title, I thought was fitting, rather than sink these last few weeks – which normally kick my butt, I am determined to finish strong in an effort to leave a great impression with my budding, almost 10th graders – allowing them to see that math is more than just math.

from etymonline:

mayday (interj.) Look up mayday at Dictionary.comdistress call, 1923, apparently an Englished spelling of French m’aider, shortening of venez m’aider “come help me!” But possibly a random coinage with coincidental resemblance:

“May Day” Is Airplane SOS
ENGLISH aviators who use radio telephone transmitting sets on their planes, instead of telegraph sets, have been puzzling over the problem of choosing a distress call for transmission by voice. The letters SOS wouldn’t do, and just plain “help!” was not liked, and so “May Day” was chosen. This was thought particularly fitting since it sounds very much like the French m’aidez, which means “help me.” [“The Wireless Age,” June 1923]

 

Personal Reflection 3-2-1 #MTBoSchallenge

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Our school district will begin using a new Certified Evaluation Plan this year.  The CEP has 2 major components: Professional Practice and Student Growth.  As part of the Professional Practices, each teacher is asked to consider various pieces of evidence and complete a self reflection which eventually leads to their individual Professional Growth Plan.

I will be completing my self reflection this upcoming week, which has had me wondering this weekend, what are my goals for this school year? 

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3 things I want to learn, incorporate, practice:
I have read about Flipped Classrooms since before I began blogging.  Watched a couple webinars, read several blog posts, articles.  Its always been of interest, but I just didn’t have take the time.  I have recently begun my first Flipped Unit in my Algebra 2s.  It nothing major, I have linked to videos readily available on You Tube, but have quickly learned if students are accessing on their school accounts, YouTube is blocked.  So I am now looking for possible places to host my own videos (eventually, I want to use my own).   

My interpretation is either introduction or skills needed for problem solving which in turn allows students time in class for real application of math.  Following each video, I include 3-5 questions of the big ideas/takeaways for student self-assessment of the video.  When I begin creating my own, I intend to keep them around the 4 minute range, continue including self-assess questions.  For student who dont have access, they can come to my classroom prior to school/class and complete, but they are not allowed to participate in the days activities until they’ve completed the video or shown understanding to me.

Lesson Study – I have read some posts, been involved in a few informal twitter chats, even discussed the process with colleagues at TMC14.  I have located some resources through our PD360 I intend to utilize, but now, I have to find a friend and convince them its worthwhile to journey with me.

Talking Points -I want to ensure that every student feels like they can share their ideas and be heard.  Talking Points is the key for me developing this culture of learning.  I look forward to learning more, sharing with my students and implementing this as a classroom norm.  Here is a place to start.  Severval MtBoS have implemented them as the school year began.  I will share my experiences soon!

2 things I want to continue improving:
Literacy in Math Class- Whether reading, interpretting/deciphering informational text, writing, reflecting on their learning, verbally communicating or strategies to help studentsconnect vocabulary to prior knowledge…communication is a key skill they can use elsewhere.  Last spring, I participated in a webinar based on the book Vocabulary Their Way.  I sincerely feel providing students with similar tools will enhance their learning across all discilpines.  I plan to use some of the structures I’ve learned from Kagan resources and develop some of my own activities for student interaction with peers.

Standards Based Grading – about 5 years ago, I became very interested in aspects of Standards Based Grading.  It just made sense.  I had read, researched, even implemented some successful approaches.  I have heard through the grapevine, theres a possile push for our district to move this direction.  Even though it has not come from an official administrator, I’ve heard teacher conversations outside of vertical meetings that sounds like it may be on it’s way.  I am uber excited.  I have been looking for some good quality resources to share, should the time arise.  @mpershan shared a link this morning for a couple of good resources.  Scroll down to Garry Chu SBG.  Although, I think the Jeff Harding’s video following it gives a fun analogy to show how ridiculous some of our grading practices are-supporting Why we should consider SBG, then Mr. Chu shares some great ideas on How to implement.  I look forward to getting to move on this journey again (finally).

1 thing that’s Imperative in My Planning…
Standards of Mathematical Practices Yes, I am very familiar with them, yet I have not been so intentional in my planning and inclusion of them.  I had a major a-ha last year that I had missed the boat when first becoming familiar with CCSS.  The SMP should have been the anchoring foundation prior to transitioning to CCSS.  As I plan this year, I will be intentional and very explicit in providing students opportunities to use them.  But also in asking students to reflect on their uses of them.  I look forward to reading NCTM’s Principles to Actions, hoping it will guide me in this goal.  Another resource I plan to revisit is Making Thinking Visible.  I read it a couple of years ago, but feel it provides quality routines to enhance student learning that support the SMP.

Week 1 3-2-1 Sunday Summary #MTBoSchallenge

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My first week kicked my patootie.  I slept from 6 Friday night until 6 Saturday morning.

I was nervous, anxious about starting school with all of our continued renovation but all in all it was a very smooth start to the year.

3 good things…
Day 1 began with Notice & Wonder of Pascal’s or Sierpinski’s Triangles or some type of data collection activity in every class.  I feel it sets the tone for the year.  I addressed syllabus big ideas throughout the week.

All classes have their INBs set up and ready to go.  Several comments such as you really have thought this through, or do you really research your teaching that much?  Yes.  I have a plan and purpose for just about everything we will do.

Ending the week focused on 1 positive thing from their week was the best way I’ve ever ended week 1…

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2 goals for growing…
I downloaded a reflection packet for NCTM Practices to Standards and use it as I read throughout the semester.

Revisit previously read books…Making Thinking Visible and Embedded Formative Assessment.

1 goal for the week-
Get my bulletin boards completed…

Math and Kentucky Program Reviews (Art, Writing, PLCS)

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In Kentucky, we have Program Reviews for Arts/Humanities,  Writing a nd Practical Living / Career Studies (PLCS).  My interpretation… the idea is to ensure all teachers across disciplines are integrating concepts, strategies into their classrooms on a regular basis in efforts to make connections with student interests and enhance their learning experiences. 

I have used many routines from Making Thinking Visible over the past two years to improve writing-to-learn and writing-to-demonstrate learning opportunities for students.  I feel they will tell you our reflection and analysis of work through writing and discussion makes their learning stick more.

As I plan to revisit these routines with @druinok and some other stats peeps, I was exploring this and ran across Artful Thinking.

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Definitely check out the Thinking Routines and Curriculum Connections links for some insightful resources that can help other content areas find purposeful, quality connections to art for their courses. 

Finally, a tweet from @approx_normal the other morning provided these awesome classroom tasks focusing on Career Technical Education.

Hope this provides some helpful information for teachers looking to make connections in the areas of Arts, PLCS and useful thinking routines to help with Writing implementation. 

#tmc14 My Favorites

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Chalk Talk, Making Thinking Visible
Intro to Thinking Routines

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Black Lights and Highlighters

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Ghosts in the Graveyard, Kim Hughey, Math Tales from the Spring
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Grudge, Nathan Kraft’s I Shall Never Play a Review Game Again
Used most Fridays, either first or last 10-15 minutes of class to highlight our big ideas/skills from the week.

Plickers all you need is paper and a smart phone. New app for me, so I am still learning. What little we’ve played around, it has some great potential!

Setting Personal Social-emotional Goals pt. 2 #julychallenge Post #17

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This morning as I responded to a commented from @bpagirls on my post about an Essential Questions Board, a thought hit me, so I typed it in my reply so I wouldn’t forget…

… I have just realized as I type, why not add a spot for personal-social goal-setting on my organizer for each student to set, write and reflect.

It stems back to this post and one of the 14 ways to think about good teaching post, 3. Include social-emotional learning goals as well as academic goals.

I got that I needed to do this, but I was not quite sure how to set and record these goals.  My plans are to include a place on the back of our unit organizer students receive at the beginning of each unit.  These are formatted in a booklet style to fit our INBs.  Students can set a personal/social goal to focus on for the duration of the unit. Ideally, following the SMART goal format.  Commit to it by writing it on their organizer.  I will ask to see it, but they may choose whether to share with a peer.  Wouldn’t it be great to have accountability partners for the unit? 

Throughout the unit or even at beginning of class, ask them to read it to themselves.  Maybe even allow someone to share their progress.  Revisit them as we end the unit and write a brief reflection:  How did I do?  Did I meet my goal?  If not, did I at least move toward it? What do I need to modify?  Follow the format: 2 stars and a wish for their quick-write reflection.  Celebrate their progress, maybe through our Shout-Out Board (more on that later).

I realize this type of goal setting may be tough for students… I am hoping after completing this task, it will allow for students to generate ideas.

Initially, I think goals can range from:
Improved / good attendance
Be to class on time
Being prepared for class
Completion of assignments
Asking for help
Asking questions or participating in class discussions.
Attend tutoring if needed
Work in a group with people I don’t know.
Share my ideas in class
Share my assessments and progress with parents/guardian
Choose better practice/study options
Listen to others ideas
Evaluate how my choices are impacting my learning.

Here is a sample of the back of my unit organizer.  I plan to insert personal goals below the unit reflection.  Here is an updated version of a complete unit organizer and student assessment tracker. Feel free to modify for use in your personal classroom. Thanks to Crazy Math Teacher Lady and Math = Love for inspiring through their posts?

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My next task is to locate a fill-in the blank for a SMART to include on the first unit.  Kind of a madlibs style to get us started.

If you have a system in place or use LIM or AVID in your school, I welcome input and suggestions.