INB Resources

Just want to share the love!  I’ve created/revised/massaged/borrowed resources for my geometry students’ interactive notebooks and wanted to share some of them.  If you would like a Word file to tweak for your own use, just send me a message.

Flash Cards I created on Slopes of Lines for our Coordinate Geometry Unit.  The original idea came from Sarah Rubin and her wonderful blog, Everybody is a Genius.

More flashcards inspired by Sarah Rubin on Congruence Shortcuts:

This graphic organizer on slopes of lines accompanied our lesson on the fabulous Slope Dude.  My co-teacher, Mr. Peterson and I created it together.

Finally, a foldable I created for our Special Quadrilateral unit.

I hope some of these resources are as useful to others as all of the shared resources out there were to me.


Auspicious Beginnings

On a break just 8  days into the Spring term (ironic as that denotation may be), I’m feeling more energized than my 7 a.m. start time would suggest. It’s a great relief after an angst-ridden fall term, and while I am not looking this gift horse too closely in the mouth, I am reflecting on how I managed to scale the wall that felt insurmountable just a few weeks ago.

IMG_4654In Algebra 2, the term begins with an introduction to Trigonometry, which makes me unspeakably happy. We started out by discovering radians with paper plates, exploring arc length and special right triangles (I am not sure why they are so special, Dan Meyer, but the universality of those ratios resonating throughout math and design is, in some literal way, awesome. Call me crazy, or nerdy, or both.)

Screen Shot 2015-02-17 at 11.03.06 AM

IMG_4670Proving the Pythagorean Identities was also a wondrous exercise, even eliciting applause from a student who clearly has a future as a math teacher.  I’ve got a better understanding of how to sequence the content this year while keeping pace with my department’s calendar, and I’m finding time to infuse class with discovery.  Thanks to the generous assistance of Audrey McLaren and the thoroughly spot on webinar by Crystal Kirch, I’ve begun some forays into the flipped classroom.  I started with a VoiceThread on reviewing the basic trigonometric functions, which met with a lot of student approval and enthusiasm.  I wish there were a few more hours in the day to incorporate all the ideas I’ve got, but I’m committed to starting to build my own library of flipping resources.  More to come.IMG_4671

1238962_10100612775140764_910897993_nWe’ve also gotten off to a great start in Geometry, due to several factors.  The programming office shuffled the students between the sections of the course, and the resulting rosters are more balanced, with some of the more toxic behavioral combinations disassembled. There has been a 4th section of the class created – I was teaching three of them in the fall –  and as a result, my BFF at work and I are planning together; he has been given one of the sections to teach solo, and we are co-teaching the ICT class (never mind that neither of us is a special educator – that’s a long story, and another blog post).   This is the first time in a long while that I have had the opportunity to engage in true common planning with a like-minded colleague, and it has made a huge difference in alleviating the stress and isolation involved in creating a new course single-handedly.  Mr. P and I have always shared ideas and experiences, but as c0-teachers, there is a true collaboration happening, which fosters more thoughtful planning.  In trying to be always on the same page in a busy classroom (aka the 3-ringed circus of math), we have debated classroom decisions, pushing back on each other’s thinking, and in the process, crafting more authentically reflective policies and procedures.

IMG_4674It was gratifying to see that the students who had been in the class last term, fell quickly back into the established routines of the Daily Quiz*, the Interactive Notebooks, and collaborative work at the tables.   Bringing the new students up to speed on the Interactive Notebooks has been more of a challenge; we spent a lot of time setting them up and working on the intent of the notebooks in the fall.  Again, the group at each table provides a support for the newbies.
We spent the first two weeks reviewing special quadrilaterals, completing a graphic organizer (link below), a chart in which the properties of the polygons were compared and sorted in a Venn diagram, and Lisa Bejarano’s Always, Sometimes, Never activity.  When we return from break, we will begin working on equations of lines as a lead-in to Coordinate Geometry.

When I go so long between posts, there’s always too much to say – some very, very dear friends of mine are relocating – one to California for graduate school, another to Shanghai for an amazing career opportunity.  This has, inevitably, got me reflecting and rethinking choices I’ve made, and continue to make.  But my own children continue to pursue their own unique interests and education with passion and talent, reminding me that every child deserves that chance – and brings me back, once again, to why I teach.

Speaking of my amazing children, which I can’t help myself from doing, my younger one is involved in a project to produce animated films in collaboration with NASA scientists working on the Fermi telescope – how completely cool is that?  Read about it here, on the Tumblr run by Geo.


*The Daily Quiz is a low stakes formative assessment used as a warm-up for class which sparked an interesting twitter conversation last night, and which I may write a separate post about later this week.

What’s Working/What’s Not

I need to know her secret!

I need to know her secret!

I started this post last Sunday, and haven’t finished it yet.  Last night I asked Justin Aion how he manages to write so prolifically and so frequently – he told me he keeps his post open all day long and writes a bit at a time.  So it’s 7 am, it’s the last day of the fall term, and I am re-opening this post, determining to post it by the day’s end.

From Sunday: It’s 4 days from the end of the term.  I’ve been informally reflecting in my mind since we returned to school on January 5.  I am trying to be constructive with myself, and to silence those demons that Mattie B wrote about earlier in the week at Pythagoras Was a Nerd (although Vi Hart says Pythagoras was actually a crazy cult leader in this epic video) – the demons that continually point out everything that is going wrong in my classes or lacking in my practice.   Mattie says his kids are lazy, selfish and possibly stupid – well, mine are ungrateful, inattentive and rude.  And, for the most part, eminently lovable. (Last aside: recommended reading on this topic – Matt Vaudrey’s post on Stupidity and Adolescence – one of my all time faves.)

So I started a page in my planner called “What’s Not Working/How to Fix It”, with a positive section entitled “What’s Going Well/Modifications” – because nothing is ever going well ENOUGH.  I want to write some of this publicly; it will help me process, and hopefully garner a few suggestions from the Math InterBlag.

Here’s a picture of my list so far:IMG_4583 It’s not much, yet.  But it’s a start at hitting the reset button for the Spring term.

My students, particularly in my Geometry classes, lack independence.  I provide as many cues for them as I can to help them execute their jobs as students each day.  We do have a routine (Daily Quiz, notes, practice or Daily Quiz, exploration/group work/tiered practice), but for a reason which mystifies me, beyond that Daily Quiz opener, my students do not avail themselves of the tools at their disposal, i.e. agendas on the tables, directions on the board, spoken word by teacher.  I know they are checked out [until they are ready to check in], and I want to engage them more quickly, having motivated them to participate in the learning that is going on in the classroom.  (As I typed the word ‘engage’, an image of Dan Meyer popped into my head, exhorting me to PERPLEX THEM, BE LESS HELPFUL – stop boring them! [last bit was mine, not Dan’s]).  Concomitant with the mental absence from class, naturally, is the lack of deep understanding of the content.  So while I am closing out the term today, I am trying to glean some insight into my students’ perception of what’s going on, and hopefully get some constructive feedback from them.

Yesterday was a fairly terrible day – I discovered a plethora of methods students were using to copy work on a final packet – from plain old copying from the original to sharing photos of a completed packet by text, and actually transferring the information during in class in front of me.  This incensed me on so many levels, particularly in light of my school administration’s utter lack of an electronics policy.



But mostly it made me sad – very sad – because I haven’t managed to create the culture I want in my classroom, a culture in which students take pride in what they have learned, and are willing to exert some effort to practice with this newly acquired knowledge and demonstrate their geometric understanding. (Sorry – it’s been a long week – maybe geometric prowess is going a bit far.)  I can – and will – reflect on whether the assignment was appropriate for this purpose, and what its place in the course is, but the dishonesty is on the part of the children, and I saw enough of it in more than one class to know that it’s not just a couple of kids.



I’m finishing out the day and term by grading some notebooks.  I’ve got a monstrous stack of papers to go through this weekend, and I am having an internal debate on how to grade the work that I know was completed dishonestly by some percentage of the students.  At the same time, I am working on (a) ways to prevent this while still maintaining a workload that I can handle (110 individual assignments is just not feasible) and (b) assigning meaningful work (online homework is useful for some purposes, but not all).  Meanwhile, I am looking forward to reading some of their comments on the end of term course evaluation as further fuel for reflection.

Who says triangle shortcuts can't be pretty?

Who says triangle shortcuts can’t be pretty?

{I would like to note here that my participation in the#ElemMathChat and #LGBTeach chats last night, two chats in which the power of the online education community to share and support its members was fully demonstrated, restored me and my faith in why I teach.}


Ruby and her Sun Lamp

Ruby and her Sun Lamp

Congruence Check-In

IMG_4434After the investigation I discussed in my last post, we spent the rest of this week learning about triangle congruence in my 3 geometry classes.   The students took notes, identified congruent parts, wrote congruence statements, and made flashcards.  [All files linked below.] An assignment in which they had to identify the appropriate shortcut from a marked-up sketch was fairly successful.  On Thursday, I introduced the idea of drawing secondary conclusions from given information, and actually writing down those conclusions and why they were justified (a.k.a. proof) using this great exercise from the Oswego City School District Regents Exam Prep Center:   IMG_4435

IMG_4437And then we began to talk about proving triangles congruent.  Many of these students have already taken (and failed) a term of geometry, and if they haven’t, they have heard from friends the perceived horrors of two-column proof.  I have thus deliberately avoided introducing that type of rigid structure, and I believe that it has kept many of the students who might have checked out in despair in the geometry game, willing to go further with this new subject.  But I could see from the one exercise we did that making this leap is a huge stretch for so many of them, and I am wondering this evening how to proceed.  Do I ‘super-structure’ it – create fill-in-the-blanks examples?  Do I switch to a more accessible activity?  Can I handle differentiating this topic?  The students are at such mixed levels to begin with, and with the added disparities in their Van Hiele levels of geometric reasoning, I am not sure how to create a meaningful activity which will bring them a little closer to understanding the nature of proof.  My dining room table is currently piled with the resources I have culled in my hours of researching.  The ideas are buzzing around my head  – both outside and in – and with 2 days to go before the holiday break, and less than three weeks when we return on January 5, I want to get the biggest bang for my lessons possible.

Too-Many-IDeasI’d love to do the MARS Analyzing Triangle Proofs formative assessment lesson, but I’m afraid I really, really don’t have time if I am going to cover the content that I need to by January 26 (and for those of you who say better to cover this topic in depth and leave out another topic, well, the Geometry Regents waits for no teacher, so to speak, and I need to hedge my bets).   But I’m also laughing at myself, because I am spending a weekend evening wringing my hands over Monday’s lesson, which will be taking place on December 22.

IMG_4437Writing this post has helped me realize one great thing – that my students, who do not generally like or succeed in math, don’t dislike geometry, don’t think it’s some Rosetta Stone of which only their math teacher can make sense.  They are willing to try the work presented to them every day, and believe they can learn it.  And that’s not nothing, believe me.

On an unrelated, but critically important topic, I want to share images of 2 quilts which the president of my quilting guild, Sylvia Hernandez made in response to recent events.  She is an inspiring woman, and her quilts about the deaths of Trayvon Martin, Michael Brown and Eric Garner and the disappearance of students in Mexico moved a room of 150 quilters to tears.  I envy her ability to put her feelings into fabric art so eloquently and efficiently.


Quilt by Sylvia Hernandez

Quilt by Sylvia Hernandez

I’m not convinced

When I was planning the unit on congruence for my Geometry classes, I wanted some new activities to introduce the triangle congruence shortcuts to go along with the hands-on discovery approach I am using in this course.  We are not doing formal (2-column) proofs, so I am working on eliciting verbal justification from the students.  I combed through the notes I had saved in Evernote (thank you, Anna!) and came across this post by the ever-inspiring (and challenging) Fawn. Her discovery activity for the congruence shortcuts was exactly the approach I wanted to use, especially the part about avoiding lecturing.

IMG_4422The straws which were originally earmarked for stellated icosahedra seemed perfect for our triangle sides ( Fawn used barbecue skewers but they had pirate sword fights as the least objectionable activity in my classroom written all over them), and since my students are not adept at copying angles, I created some angle templates for them to use.  I attempted to debug and envision the activity as thoroughly as I could, using in-house counsel – my 23 year old daughter, who, although in graduate school, remembers her high school days very well.  In truth, I was not confident that the activity would succeed this IMG_4423morning, but I was determined to go ahead and see what my students would make of it; I wanted them to engage in this very open-ended process.

IMG_4429The first class is always a little sleepy; many students have a punctuality disorder.  That said, they are good-natured about trying new things.  They did agree on the SSS shortcut, but didn’t come up with enough evidence to support their claim.  My third period class, after a slow start, dug into constructing triangles with the straws, and we had a lively discussion about the minimum congruence requirements put forward by the different groups:  2 sides, 3 sides, 2 sides and 1 included angle, 2 sides and 2 angles.  However, I was still not able to push the students towards providing solid evidence.

IMG_4430The big disappointment came in my fifth period class.  This class – my hugely mixed bag of emotional, language and learning issues – is capable of great enthusiasm and conversation; my challenge is channeling it towards the content rather than everything else they would rather talk about.  But the week before the holiday break is a tough one – emotions are high and distraction is everywhere.  My co-teacher and I could have 2 clones each and the room would still need more adult presence (basically, each of the 8 tables could use a teacher).  Of late, I am detecting undercurrents of tension, bromance, and harassment, and phone use is rampant.  I confront unacceptable behavior and language decisively and publicly whenever it appears, but there’s too much going on simultaneously in that room.  I know the students are learning geometry, and I know many of them want to learn more.   But teaching them, many days, is an uphill and exhausting exercise.  Today was one of those, although to their credit, the straws were mostly used appropriately.  After a chaotic attempt at discussing the results of their exploration, I put the notes for the S.S.S. and S.A.S. congruence shortcuts up on the SmartBoard and stopped talking.   At least they were writing while socializing.IMG_4428


Looking at these pictures, it appears that discovery is happening.  But I was disappointed in the results that my efforts produced.  I want to try this activity again next year – I am convinced it is worthwhile – but I’m unsure of how to modify it for greater success without giving too heavily-handed direction.  And I’m unhappy about the scene in the 5th period class, although a week ago, I remember being pleased at how well many of the students were working together.  It seems that the specific attendance on any given day greatly affects the classroom dynamic.   And, honestly, I think by the time I figure it out, the term will be over.

Good thing that every day at school is a do-over.

What I wanted to say/What I have to say

IMG_4305I wanted to write a post about what was going on my classes.  I wanted to share some of the work of my students, talk about progress I’ve made in creating a classroom culture of cooperation and inquiry, self-sufficiency and collaboration. IMG_4389 There have been a lot of tough days, but also moments every day of accomplishment, humor (“Don’t sniff the glue stick, Louis”), and connection.  There are students for whom following directions is a major hurdle, and others who produce beautiful work which reflects our learning objectives.  And then there are the true rewards of teaching – being able to write glowing recommendations of students who have grown up in front of you, or receiving some excellent work from a student who just 2 years ago spoke no English, and had spent little time being formally educated in her native country.



I wanted to write a post to document some of the things that have been going on during this tumultuous year – the progress of the Geometry course I am writing, the challenges of teaching in a completely group-oriented environment, the hopefully productive struggle I am engaged in while taking Calculus III on line.  Last night my daughter, who knows me so well and is sometimes so wise for her 23 years, told me to write a blog post, because they always make me feel better.  Knowing she was right, I began to mentally plan it today.

And then the news that there would be no indictment in the Eric Garner chokehold case was released, and in my disbelief and outrage, I knew that I couldn’t spend the evening celebrating my accomplishments in the classroom.  I don’t even have words to describe my horror at being part of a racist system in which this is not an uncommon occurrence.   And while I was wondering how I can address this sensitively, honestly, somewhat productively in my classroom, my principal sent a message to the entire staff suggesting that we AVOID discussing this in class, that the issue is too emotionally charged, and that this is perhaps not the best teachable moment.

Not the best teachable moment?  I think this is the ULTIMATE teachable moment, albeit one that I have no idea how to teach.  My classroom is richly diverse – ethnically, linguistically, culturally – and students have been known to use inappropriate and offensive vocabulary (in a variety of languages) as part of casual conversation.  I am afraid that a conversation about this decision could become explosive, and that I lack the skills to keep things productive and safe for everyone.  While I don’t walk in the same shoes as all of my students, it is important (I think) that they know I am an ally rather than a censor, or perhaps worse, that I am indifferent, because I am neither.

I welcome your thoughts.

ADDENDUM: I hope this post does not convey the impression that I will be silent, for that is completely not the case.  I know what the right thing to do is; I’m just a little anxious about it.  Seems like the right feeling.


Planning cities


City Designs


Triangle Sort


Triangle Quilts a la Tina Cardone

We’ve been busy in Algebra 2 as well…

Just a few highlights from the last 2 weeks in Algebra 2:

My first foray into VNPS (Vertical Non Permanent Surfaces, I think?) – I had the students go up to the board with their entire table to answer a series of questions as we began our unit on Quadratic Equations.  I can honestly say I was filled with delight – truly – to see all thirty kids at the board talking to each other about math.  The novelty of it excited them, and this normally passive class has been enlivened ever since.  Not all of the work was accurate, but when they sat down and looked at everything they had all shared, they were visibly impressed, as was I.  And most amazingly, I had NOTHING to do while they were working except observe.  And that’s a very unusual feeling.
VNPSicosa mathnot so good

Then, doing a 180, so to speak, I taught one lesson as a screencast.  The students were 2:1 on the iPads, and they worked through a lesson on Dividing Complex Numbers that I created using Explain Everything.  It was a bit time consuming to create, due mostly to my home technology situation, but the kids loved it.  I saw a lot of pausing and ‘rewinding’, stopping to work examples and then resuming the lesson, and also a lot of cooperation between the 2 students sharing the iPad.  (I even brought along alcohol swabs for the shared earbuds.)  The response was very positive – although I don’t think it would remain that way if I did this more than once every couple of weeks.  One student who struggles told me she felt like I was tutoring her.  There were, interestingly, several students who were adamant that direct LIVE instruction was better, but the overwhelming majority liked this approach.  For me, lots of work up front, but the class itself was a breeze.  And, of course, now that I have the screencast created, it can be reused.  I made an error (found by the first class) in a worked example, which I turned into a challenge for the second class – find the error, get a free homework pass!  I wish I didn’t have to block out the faces of these happy students – most kids duck when I am snapping my photos, but they posed!


And speaking of amazing students, the latest from my animated progeny studying animation/illustration:

Isn’t this a book you want to read?