Accountability – Reflection on My 2018 Spring Goals

A full week of school – the first weeks, though one was fairly productively – in and out with snow days, well – no consistency.  We were out the entire week last week – with MLKjr Day and the snow / cold temps.  So this week meant collecting and giving feedback on NTI day assignments.  Not my favorite task at all.  One class was fine- I had about 4 students having to redo assignments because they were not proficient.  The other class, I had about 4 students needing to redo, and 9! Students who did not even do the first assignment.  Phone calls and emails home…  ugh.

With all of that – we sort of got back into a routine.  So I felt it was time to reflect on my semester goals.  This post describes my goals as a result of a conversation with @misscalcul8.  Here’s the jist:

For the Spring 2018 Semester, in my 4th block Algebra I class, I will increase (currently, I do not link them in my plans) my planning of formative assessments for each learning target listed / linked in my unit lesson plans.  Twice per week, I will take time to formally reflect (written) the student work and devise a plan for next steps.   Currently, I only informally reflect / plan next steps, without formal documentation in my plans.  I hope this work will lead to better quality formative assessments that are truly at the level and integrity of the standards.

Over the course of the Spring 2018 Semester, I will develop a list of common Latin / Greek roots as related to our content in Algebra I.  Through the collaboration of my colleague, I will develop and implement a weekly system to help students learn and make connections within the content to the roots, etc.   The list, weekly quiz results and study tools will be documented in lesson plans.  At the end of each month (January – April), I will reflect on our progress, analyze the impact on student learning and adjust, continue.  This list should grow throughout the semester.  List to students, implement study tool, report student progress.

I will revisit Small & Lin’s book More Good Questions for ideas on creating Open Questions.  As part of the formative assessment tools, I will begin to include these on a weekly basis in our lessons – for feedback only and incorporate on every unit assessment (after discussing with my content team teacher).

Where Am I?

As part of our NTI PLC time, we spent time building a document to list each of our learning targets, CCSS for searching resources and link FAs documents / describe the task for each.  This was not necessarily “IN” my weekly lesson plans, but it is a living document that can easily be linked to.  I can quickly copy/paste the linking information into my lesson plans.

As part of this task – my colleague and I met, devising a system for naming our resource files as we upload them to a shared folder.  We agreed on 3 letter abbreviation for BIG idea of the unit, then use 2 digits for the learning targets.  For example, FUN 01 means intro to functions, learning target 1.  This way we can record in the IC which target that “grade” is addressing for parent and student communication.  Students receive a unit organizer at the beginning of the unit with ALL of the assessment targets listed.

Inside each folder, she suggested having sub-folders:  one for lessons, INB foldables, example for notes, practice tasks like matching or sorting;  one for FA tasks;  Summative and projects folder which will also include a unit pre-assessment and multiple versions of the unit assessment.

We have just a few more things to have everything addressed in our current unit.  We think this document can easily be added to and edited as we go through the units – adding new things, etc.  Targets highlighted in red if we need to create a better target quiz, we can quickly scan to see where we are and what we need to do.  We have a lesson plan outlined for the operations with functions target, but need to create a TQ.

Since starting our document, we have found an example from the Springboard resources that can serve as a skeleton for identifying and relating key features to the context.

From Springboard, Algebra I

 

I have done nothing with the Roots list in vocabulary.  Every unit organizer has listed vocabulary – so I am hoping to use these as I begin to develop this list.

I used one open question for a TQ this week and gave immediate verbal feedback to students with high give/thumbs up or questions/coaching.

What can I celebrate?

Getting on the same page with my colleague.  We have a plan in place.  We’ve started organizing our current resources and agree as we continue in the semester, we can easily add and adjust.  I like our system for highlighting places that need work and the ability to share found resources as we use them.

I was very purposeful in the FA used in class this week.  Even with the deltamath and desmos tasks in the lab on Friday have given me some conversation and lesson material as we move on this week.

What can I improve?

Ensuring that I have time built in for students to act on the written feedback.

Getting started with those root word lists.

Purposeful planning with the open questions – allow students to become comfortable with this style of questioning – you can tell its unfamiliar for some of them – but using strategies like “3 things” notice/wonder will help them build confidence in sharing their thinking.  I am already seeing more details in what they are writing and sharing.  I know this sounds silly, but I have noticed eyebrows raising as I put the task out there – almost as if they welcome the opportunity to think and share their thinking.

So where are you in your goals for this school year?  What are your goals?  What are you doing to be accountable to them?  Where are you?  What can you celebrate?  What can you improve?

Reflecting on Formative Assessments

Every Story has a Graph / Target Quiz

Earlier this week, I gave a short Target Quiz – just one big idea.Students were given three scenarios and asked to create a graph to model the situation.  Out of the class, there were 4 students I felt I needed to pull over to the side for some one on one time.  I found they were often drawing the “shape” of what was happening rather than comparing the distance from home to time.

The one most missed had Tom walking up a hill, quickly across the top, then ran down the other side.  Yes, most kids draw the shape of the hill.  As opposed to the distance continuing to increase as he ran down the other side.

Whiteboarding Examples / Non-examples

The second Target Quiz was on whiteboards – students had to create an example of a graph, set of ordered pairs and a table of values with a function and not a function in each example.

I laughed as one table was begging me to give “real quiz” and take a grade because they knew that they knew!!  As I walked around the room, observing, asking questions – there were 3 students with some minor mistakes and 3 who were really struggling.  Upon questioning, they were able to identify when the example was given, but unable to create examples on their own.  With some “funneling”  – they were able to get examples of each, but I have them * to keep an eye on and requiz next week.

Deltamath Practice – immediate feedback from tech;

Teacher observation & questioning

We had a very brief introduction to writing domain and range of graphs in interval notation.  We spent some time in the computer lab today practicing this on deltamath.com.   I appreciate the immediate feedback they are able to see if they miss the question.  Also, how he has programmed the many different options for defining domain and range.

Many misconceptions were cleared as we learned whether to use the endpoints or extreme values (if they were not the same).  There was discussion about the open circles and closed circles and which inequality symbols were correct to use and when.  And yes, a few realized they were mixing up the x and y for domain or range.  I look forward to practicing this skill Monday after their experiences today.

Desmos Activity – Inequalities on a Number Line – Matching Tasks

For my other class, we will be solving and graphing inequalities next week.  So while in the lab today, we worked on Desmos – Inequalities on a Number Line and Compound Inequalities.  The first task was a good review and learning opportunity for the direction of the symbols.  I still had some students exchanging those up.  Most were correct in open versus closed circles and what that meant in symbol terms.  Though I did not make it to all of the students in the second task – I was trying to catch students on the two sorting pages of the first activity as they were going through.  For some it was as simple as a brief discussion about why one was the correct choice and comparing it to their wrong match.  There are about 4 students still having troubles on the first task.  And several have not completed the last task.

I feel like looking at their responses, I can use their examples as discussion pieces while we are looking at our notes next week.

I almost feel like there were not as many issues in the second task.  However, I still have several that have not completed them yet.  But I feel like using live examples from their work and discussing maybe two stars and a wish they would have for each student – may help them steer away from making their own mistakes.

I love the real time feedback I get as a teacher and how I am able to grab kids before they move on too far and help erase some of their thinking and replaced it with correct ideas immediately.

Someday – I’ll get to have a classroom lab… I hope.  Until then, we will keep on doing what we can.

 

Heartbroken.

Heartbroken. Angry. Apalled when I see those on social media making these tragedies about something other than they are. Heartbroken. I’ve cried – as a mom. I’ve cried – as a teacher. I’ve cried – as a friend of first responders and medical caregivers. This post by a middle school Social Studies teacher touched what […]

Meal Prep for this Week

We don’t always do this, but when we do, the week runs so much more smoothly! Two hours prep and cooking and 30 minutes clean-up and dishes. Totally worth it. 3 lbs ground beef 5 lbs boneless chicken breast 1 box tangy italian kraft spaghetti 1 can tomato paste 1 can Manwich sauce, pkg buns […]

My 2018 Reading Bookshelf #MTBoSreads

At the end of every year, I look back wondering what titles I read…  I don’t do a very good job of remembering.  And when I do remember, I question if it was this year or the one before when I actually read it.  So, I plan to update this post as I finish each book – more for my self than anyone else.  Feel free to comment on other titles/authors these may remind you of for my future reading list!

Hillbilly Elegy, J.D.Vance

I finished this one December 30, 2017 – but so close to end of the year, I decided to add it on this list.  Being in rural Kentucky, I have battled for years trying to figure out why my students do some of the things they do.  What’s going on in their world?  What events have led them to these choices?  This book allowed me a brief look into their world.  I could see so many of my own students in his writing.  Often times we speak of diversity based on nationality and race – but there are many social aspects of Appalachia that are often overlooked, in my opinion, and lead to some mindsets I was not aware of.

Salt to the Sea, Ruta Sepetys

In the beginning I struggled getting the characters lined out in my head as the different viewpoints were presented in short snippets.  However, as I kept reading, there was a comfortable flow to the story.  I found myself looking forward to hearing from the other characters about a particular event they had all just faced.  Such sadness in times of war.  But the beauty of the connection that grew between unlikely friends keeps hope alive.  I couldn’t help but be heartbroken for the lives gone when the W. Gustloff ship sank.  How had I never heard of this?  I knew when I read the title what was coming…  I just had no clue what would come…  Great research by the author.  I look forward to reading more of her work.

#MTBoS in Kentucky? #MTBoSKY

This past week, #KYgodigital presented #snowdayspecial a great live session on one of our snowdays.  Here is a storify of tweets that day – and a link to the session at the top.  There were 13 presenters who were given 4 minutes each to share a tech tool from their classroom!

//storify.com/pamjwilson/kygodigital-snowdayspecial/embed?header=false[View the story “#KYgodigital **SNOWDAY** Special 1/17/18” on Storify]

 

I “met” so many new people across the state.  Grabbed some great ideas and resources to further explore.  Thanks to @mrsstevensmath for sharing out a link!  Here’s a link to her share – EdPuzzle.

This morning as I was scrolling through Twitter, I ran across #MTBoSNC so many awesome math friends in NC…  I began wondering – goodness, there were a lot of math people who shared their tech ideas on #kygodigital – people I had no clue about in my state – and I wondered – how might I connect with them?

I decided to create a google sheet for any Kentucky math teacher to share their information in efforts to connect with others who in our state, active on twitter / blogging.  I am unaware that a resource like this exists – if it does – PLEASE share!

Feel free to add your information – as much or as little as you you wish.  I look forward to “meeting” you virtually and someday, hopefully, in person!

#MTBoSKY  sheet for math – twitter – blog-o-sphere Kentucky!

January #MTBoSblog18 – Formative Assessment Strategies

From Jennifer Fairbanks…

 Jennifer Fairbanks‏ @HHSmath 8h8 hours ago

Happy #mtbosblog18 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 

• 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:

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?

Feedback with Flair #greenpens

In recent weeks, I have been re-reading Wiliam & LEahy’s Embedding Formative Assessment.  @druinok has shared that ASCD Express had many articles on Feedback in the most recent issue.  Somewhere in the reading / discussion, I recalled hearing about a green pen.  Who was it?  Almost immediately, @druinok shared a link, which led to other’s posts as well.

From Amy Gruen over at Square Root of Negative One…  a progression of her posts as her use of green pens evolved…

Green Stars, 2010

Bell Work Bliss Gone Bad 2011

Green Pen is the New High Five 2012

Giving Immediate Feedback without Breaking a Sweat  2015

And from Simplifying Radicals

Amy mentions Frank’s Orange Pens… in one of the posts.  My colleague and I have a similar system set up with our semester long spiraling Equations & INequalities Units.  You can read about it here.  I have everything updated and ready to begin next Monday for the Spring Semester!

Yes – this was the idea I was looking for – I believe it was @marybourassa who shared they use a pen on quizzes / assessments when giving students support, this way she knows who / how much she has given input.  I have tried this on several occasions and love that it feels like I have annotated our conversation right on the student’s paper.  AND  I can quickly see what the student did with our conversation as well.

Sometimes bellwork seems so, uh, I don’t know – useless.  Students wait on me to give the answers and just copy it down.  This way – I work with 4 or 5 students up front, then they become the teacher.  I can be available to those who are really struggling.

I have done this strategy before in my senior class last year.  It was pretty successful for the most part.  Yes, there are a couple of students I had to keep an eye on – but isn’t that sometimes the case?  I really have no idea why I’ve never carried it over to my Algebra I.

Well, guess what?  My green pens are ordered.

I’ll let you know how it goes!  And yes, I did order the Flair!  #feedbackwithflair

 

Reflecting on Feedback

Funny how things kind of pile on to hit you in the face!  @druinok and I are revisiting Wiliam & Leahy’s Embedding Formative Assessment;  The current issue of ASCD Express is filled with articles focused on feedback and our first day back with faculty this semester- we had a PLC about Formative Assessment & Feedback.  Though this post was more about success criteria – there are several comments concerning feedback.

Chapter 5 in EFA2 was a bit frustrating.  Initially it felt like it was saying so much of the research on feedback was not useful…for several reasons.  But as I read and later watched this presentation (while sansone walking for my cardio!) – there were some big ideas that stuck out to me…well, hit me in the face.

How when done incorrectly, feedback can have a negative influence on learners.  Some things were obvious, but others were definitely worth noting.

How we should not be expected to give thorough feedback on every single thing.  He suggested the 25% idea.  25% of the work is self-assessed, 25% of the work is peer assessed, 25% of the work is skimmed by teacher, 25% of the work received thorough feedback.  Hmmm.  This feels doable.  I have felt so overwhelmed at times in recent years.  And I also wondered if by giving too much written feedback, does it become common and expected, therefore losing some of its ability to drive student achievement forward?

The article we read during our first day back AND Wiliam in this book both said without any follow-up action, formative assessment is essentially useless.  The article said – “it is not fair to students to present them with feedback and never give them the opportunity to use it.”  In his book, he said, IF its important enough for students to use the feedback, then you must find the time to allow them to do it in class.  Ouch.  But when?  We can’t possibly get everything in!!!

This is the pie in my face.  As I was planning the FALs for my classes, I realized – that giving students feedback on their pre-assessments…being intentional with the wording, expecting them to do something with it…either answer a question, extend a pattern, redo a part of the problem, look at a specific piece of their work, sketch a new picture…

Oh my goodness.  That’s it!  When we pass back the pre-assessments… usually a few common things happen…

1.  The student is given a few minutes to revisit their work and read the feedback, then attempt to use the feedback and make their response better..  then
2.   The student is paired or in a small group and they all use their feedback to create a group response to the task.  OR
3.   After the lesson, students are given an opportunity to revisit the initial task and/or a similar but different task.  I usually copy these front/back – this allows me to flip over and see their initial work, feedback and see if they were able to clarify misconceptions and correct mistakes.

How might I use this idea to implement into my other tasks/lessons?  The time to “ACT ON the FEEDBACK” was embedded into the lesson.  Lightbulb!

Generalizing Patterns: Tiling Tables

Last fall after instructional rounds, one of the observers asked me if I would mind having some folks visit my classroom.  Sure.  They were most interested in questioning, interactions with students and use of Formative Assessment Lessons (FAL).

When they emailed to set up a date, we agreed on January 10.  Oh, wait.  This will be the beginning of a new semester with new students.  I won’t really know them.  They won’t really know me.  Great.  Now, I’m scared.  Oh well, let’s look at the positive – this will give me a chance to try out a new lesson.

I printed off 3 lessons to look at the evening before students returned to school.  I liked all three.  Building complex equations seemed perfect, so I began to prepare for it.  We were out for weather our second day back.  As I began looking over my lesson plans, it seemed the Tiling Tables was a better fit for the upcoming unit, so I switched gears.

I had done this lesson a couple of years ago, but never taught it in class.  As I began to revisit the task, I knew I liked it.  I knew it would offer some good discussion on ways to extend the patterns.  But wait.  These students barely know what a parabola is.  Would they have a clue as to how we would write an expression for a quadratic relationship?  Would I have a clue as to how to introduce it, this early in the semester?  No.

So I pondered for a while.  I would simply use the task as a way to say, we have the knowledge and tools to do parts A and B, but part C, well – that’s what we will be learning later in the semester.  It would give us a reason to learn it later, right?  Goodness.  What a canned comment.  By now, we had another snow day, so our visitors would be in our classroom on the 4th day of instruction.  I was stressing just a bit.  What was I thinking?  Starting off a new class with a FAL I had never used before?  We needed time to build some rapport.  Too late.  Let’s go with it.

I gave students the pre-assessment:

The class was divided pretty much 3 ways – Those who doubled the number of tiles, after all – a side length of 20 is doubled to get 40, right?  The second group had sketched the designed on the the grid paper which had been provided, however, they wrote answers for the 30 cm table instead of the 40 cm.  And finally, several had the correct number of tiles by extending the pattern on the grid paper.  But I ask how efficient this strategy would be for, say 300 cm table?  Hmmm.

We began the lesson the following day by giving 3 samples of work.  Last school year, I figured out, I could save paper by having them use the shop ticket holder sleeves to hold the sample work – allowing them to draw, sketch, etc with dry erase.

These instructions would help their discussions:

The first sample was Leon:

After some small group time, we shared our thinking with the whole class.  There was one student in particular who had confusion all over their face.  I encouraged them to ask the person sharing for clarification (using our starter stems).  I believe this is important to model and have them do early in the semester, so they become more comfortable with it.  Even with more explanation, they were still not seeing the pattern.  So another student shared.  Still no help.  Finally, a third students explained how they saw the pattern.  The confused student nodded and said, “Okay, I got it.”

Now, years ago, I would have said – great and moved on.  But I’ve learned…ask them to explain it to you.  They may say they’ve got it – just so you will move on, but how do you know they understand?   This student, however, could explain their thinking and were correct – they could even extend it to the next table size.

The next student sample was Gianna:

So many more of the students picked right up on Gianna’s approach.  The confused student – smiled stating they liked / could see this one better.  For me, it was listening and watching the students discussing – that brought me an a-ha!  This is the example we will use to generate the quadratic expression I was worried about!  The total whole tiles would equal (step x step) + (step – 1)x(step-1)  Yay!

Finally, we had Ava’s sample:

Many of the students could not make the connection with the side lengths on Ava’s sketches in the beginning.  Then they began going back and looking at their own sketches to verify the numbers Ava recorded in the table.  They noticed the same patterns and agreed with them.

After this final discussion – we went back to see if each student had answered the task fully.  We quickly realized though there was some good, correct thinking going on in their work – they had not addressed the questions completely.  The class agreed that Ava’s was the most complete with her table.  And it was interesting to hear their discussions of how they would explain to the other students how they could expand their responses to be better and more thorough.   One student even brought up it was challenging trying to figure out their thinking since there was no written explanations of what they were doing.  (I thought – yes, this is what I feel like sometimes too.)

As we continued discussing having thorough answers – I shared Ava’s data in a graph…  they were quick to see the quarter tiles always remained four and the half tiles being linear, a focus from 8th grade.  But what about the total tiles.  How can we write an expression to model that data?  And I took them back to the slide with Gianna’s work to look for patterns between the table size/step number and the total whole tiles.  We test our thinking with different sizes and it worked.  We tested our expression in Desmos…and what?  It hit all of the data points!

They had some experiences with the visual patterns – and good feedback to me about liking them, but still having to think.  This task reinforced some of those ideas.  IN their reflections – though many may have preferred someone else’s sample work – they “saw” how Gianna’s work led us to a more efficient expression or even Ava’s approach to orgaznizing the data in a table was pretty helpful to see the patterns so we could find describe the expressions.

Total Tiles = 4 quarter tiles+ 4(n-1) half tiles + n^2 + (n-1)^2  whole tiles.

I will definitely be using this lesson in my future.  It brought just enough confusion, but great opportunity for sharing and discussion.  And the observations were great.  Students were not shy.  At the end of the day – I was amazed we had only been together for 3 or 4 days… wow, this is going to be an outstanding semester!