the radical rational…

in search of innovative ideas with a well-balanced approach for the math classroom

Dollar Spot Finds

I live about 90 miles from the nearest Target.  Last Friday I made a point to run by when in town.  It amazes me how chalkboards are everywhere! 

My first years of teaching, I had chalkboards…then overhead projectors with transparencies.  Does anyone remember how stinky green overhead markers were?  Like, soured stinky.  I remember once standing at the overhead, writing out an example and thinking, “Shew. Someone’s got stinky feet.”  Only to realize it was the GREEN marker!

So back to my find…


5 x 7 chalkboard clipboards from Target Dollar Spot.  I added ribbon for my color-coded classes.  I haven’t decided quite yet exactly how these will be used.

Maybe a student of the week display?  Or monthly birthdays in each class?

Hmm. What ideas would you suggest?

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Do You Let Yourself Fail?

Pam Wilson:

I am currently reading Make It Stick, Peter Brown, et al. Chapter 6 states that we can sometimes experience the Curse of Knowledge (Eric Mazur)… The better you know something, the most difficult it becomes to teach it.

It reminded me of Megan’s post – how we need to practice struggle as a reminder of how our students feel.

Originally posted on Number Loving Beagle:

I sat down this weekend to do some recreational mathematics with a friend.  Maybe you know him; his name is Justin Aion.  He writes a pretty cool blog over at Re-Learning to Teach.

I made it a goal of mine this year to work on some geometry for a few reasons.  First, I’m not that great at it.  Second, the students at our school historically struggle with it as well.  Two of the problems we chose were from the Five Triangles blog.  And to be completely honest, I sucked.  I sucked a lot.  I sat there for much of the Google Hangout drawing and drawing the figures and then writing down what Justin had eloquently discovered.  And then nodding in agreement. Here are pictures of Justin’s and my respective work:


Then we decided to work on something I thought was more my cup-o-mathematics tea.  Turning to the Math Forum, we tried

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My Take on National Board Certification

The initial process of National Board Certification can seem overwhelming.  I think about my “box” that arrived in the fall of 2001 and how it evolved into a smaller package that arrived for 2012 renewal.  But the big ideas remained the same.

I had a lot of sticky tags and highlighting on my first book of standards.  But a jump-start session at Western Kentucky University helped me process the renewal a bit differently.

Looking back, here’s what I would do, knowing now, what I did not know then.

1.  Internalize the 5 Core Propositions – what I mean, is to read them, pause and think about what these mean to me, what they look like in my classroom, within my professional learning community.  Each and every decision I make as a teacher and how that decision will impact student learning eventually ties back to these 5 Core Propositions.

2.  Initially, read the standards for my area of certification.  No notes, no jotting ideas.  Just reading.

3. After a day or two, I would skim the standards again – highlight cue words, but in the margins, add post-its that include the standard in my own words or create questions to ponder for that particular standard.  Even jotting things I may currently do to support this standard.

4.  Step away from the standards, get post-its or index cards and list individually – accomplishments in the classroom, professional arena, within my school and community – that link to student growth.  By accomplishments, this could be: strategies used in classroom, structures/routines to improve student engagement, ways I’ve strengthened my content knowledge, events/training/collaborations I’ve participated in, initiated/organized – and how they impact student learning within my classroom, school, community.  Events could be anything from an RTI structure, tutoring, parent nights, community support, etc.

  • In the classroom – suggest an area of need and specific strategies / structures I learned about to improve as a teacher in order to meet this need.  How did these strategies impact student learning? What evidence do I have to support this claim?
  • In the school – suggest an area of need within your local learning community – what role(s) did I take to help improve this?  How did this impact student learning?  What evidence do I have to support this claim?
  • In the professional community – how do I lead/learn with other colleagues – either within my local community or in state/national/online networks?  How does my participation impact student learning?  What evidence to I have to support this claim?

The above questions are important because I could write about some cool technology or app I used that was fun or even a colorful foldable.  But if I could not show evidence of how it impacted student learning, it was useless.

5.  Sort my accomplishments – creating a web in a sense connecting these to the specific standards.

6.  Look for gaps, where are standards I have nothing or very little?  Ponder – is there anything I already do to impact student learning in this sense?  If not, then that would be an area of growth.

7.  Create a file for evidence of me as a teacher, learner, leader.  These may be certificates, agendas, anything that supports my work in these 3 roles.  I would tag each artifact with a post-it briefly explaining how it impacted student learning and what standard it supports.

8.  In choosing student work samples, I looked at different types of learners – one identified with a specific learning disability and another who was GT.  This allowed me to show how assessment and learning tasks were modified to support each learner.  The whole idea was to show growth, so its not necessarily about the best student work, but how you can use their work, identify misconceptions and help them move forward.

9.  As I begin to plan for first entries – in each entry, I literally typed and highlighted each question that needed to be addressed.  When writing my response, I had to remember to be concise- say what you’ve got to say, tying back to student learning and support with evidence.  In my writing, I answered each question connecting my response to appropriate standards using common terminology.  After having a couple of colleagues – one math, one non-math, read my responses, I would delete the initial questions.

10.  The entire process is about looking at where I was as a teacher/learner/leader, using reflection and analysis to determine what’s next.

Always, always, always asking myself:  What impact will this have on student learning?   How can I improve this learning experience next time?

My take-a-way from the entire process…which still stands today…

I became a reflective, more purposeful teacher with students truly at the center of every decision I made.

Advice:  set apart a time each week to commit working on the process.  Treat it just like you would any other teacher-education course.   I highly recommend you are away from home/distractions during this work time.  By beginning early,  you will allow yourself time to step away from the process as well. Closer to submission, you may wish to increase the time.


Crab Rangoon Flatbread #nonmath

I’m a fan of crab rangoons.

This spring while at KCM Conference, we had lunch at Saul Goods.  I ordered Crab Rangoon Flatbread. Yummo.   It hit the spot.  I craved it for weeks until I could make it back to Lexington and get another.

And then I thought…I could make this!  I searched Pinterest and found this link.  I made it a couple of times and this is my version:

1 8 oz block cream cheese
1 can crab meet, drained
3 green onions minced
1/2 tsp garlic powder
Sprinkle of ginger
2-4 flatbreads, I used store bought.
Italian blend shredded cheese
Sweet Chili Sauce
Several sprigs fresh cilantro, chopped
Won ton wrappers

Preheat oven 400°.  Mix first 5 ingredients. Generously spread onto flatbread. Sprinkle with cheese.  Bake 20 minutes or until cheese is bubbly and golden. 
Remove from oven.
Place won tons in oven along side flatbread – careful not to burn. When golden remove from oven.  Cool and crumble.

Sprinkle flatbread with chili sauce, cilantro, crumbled won tons.
Cut into slices. Serve warm.


This pic was my second attempt. My wontons got a little brown but still a great little dish!

If you’re out of wontons, my daughter was crumbling white cheddar Gold Fish crackers on hers this evening!


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Flip Chart Review

This review tool from Math Teacher Mambo


and this formative assessment/student engagement reminder tool form Stat Teacher


inspired a chat with @druinok & @gwaddellnvhs during spring semester and led to this flip chart review for AP Statistics.


Ours started at bottom right corner and worked up, then over to bottom of left hand side.  That seems weird to me now, but I think my initial idea was to build the flipchart as we go along, adding cards after each completed unit.

We ended up creating ours late in spring, just weeks prior to AP Exam.  We will create them in one setting, then go back and add information as we complete units.

This was a tool several of my students stated was beneficial to them.  A couple even went on to say, they closed their eyes to visual the flip chart on the exam – which helped ensure all steps on a test or specific details on a response.  They only wished we had created them earlier.

Start with cardstock folded in half.  Wow. That’s exciting.


We attached 26-28 index cards.  Tape first card at bottom.


Next card is placed up just enough to leave space for Chapter & Title.  If using lined cards, you can turn upside down and used top line to add Chapter & Title.


If using pens, make sure ink  won’t bleed through.

The idea is not to include every single detail – but quick reminders, mnemonics, anything they struggled with on the assessment.  I encouraged them to spend 10 minutes each day leading up to the exam.

I also like how Math Teacher Mambo created a flipped video for students to know important things to include.

If I get them started earlier, I will encourage them to spend 10 minutes reading through 3 or 4 times per week.

This envelope attached to inside of INB back cover is perfect for storing the Review Flip Chart.



Scrap Paper Pocket INB

I am one of “those” who prefer to keep students on same page of INB.  If you’re not, that’s great, too.

Anyway, the question arose how do you keep everyone on the same page?  Some students take up more space to answer questions or write larger than others.

I teach them how to do extension pages (thanks Megan!) -you can read more here.

You could also begin each unit with a 2 page pocket-directions and post here.


But last spring, we created quick pockets out of scrap paper.  

1.  Start with scrap paper, slightly smaller than width of page and twice as tall as you want your pocket.


2.  Fold it in half, tape down top/back.


3. Tape each side to INB.


4.  Fold work in half and insert into pocket.


5.  Thanks to @druinok, I used her outline & layout with Chapter Essential Questions, vocabulary, Learning Targets and suggested practice all on a half sheet.  I then taped it to top of page so I can quickly flip up to access work stored in pocket.


As always, this may or a not be of help to you, but just another tool available.

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Reflecting on the Year #junechallenge 3

wordle 2

As I begin to read through responses to class/teacher evaluation for Algebra 2, most are encouraging.

So much of distress I felt this year was due to outside circumstances – as much as it was within my reach, I tried to keep my classroom going.  But it was difficult and draining at times.

How can I continue to offer a classroom that’s inviting, open-to ideas and encourages students to work through challenging tasks?

1.  There must be a relationship established – I feel it takes several weeks, even months to establish this.  Students must trust that you are there for them.  You must reassure them they matter.  Your actions must confirm your words.

I think of a couple of students in particular this year who pushed back – often in the beginning of the year.  I continually had to remind them they were valued and help them see they were learning.  One in particular lashed out during class and refused to participate in a task they felt was not helpful.  The other refused to work in a group of students because that wasn’t “how she learned math.”

In the end, they both experienced success.  Maybe not at the level the state deems readiness, but such big strides moving their thinking forward and growing their confidence.  Each will experience success in life because they are hard workers and they have seen that failing at a difficult task does not define them as a person, but their response to that failure is what builds them.  It was rewarding to watch them pick up, look for ways to improve and after some more effort, smile at the final result, realizing how far they had traveled as a learner.

Taking time to listen to my learners and their ideas – allow them to know I value their thinking.  I need to consider this while building learning tasks and make sure to allow for time to do this.

2.  There must be variety – routines are important but continuing the exact routines all year long becomes mundane and boring.  For example, I like students having a task to begin class – but I also know that changing some of these up every few weeks keeps their interest peaked a bit.  I’m not sure I will have every single thing listed here, but some of my favorites:

Estimation 180, Counting Circles, Visual Patterns, Would You Rather?, Krypto, Math Dice, Flashbacks, Time-Distance Graphs, StatRat from USAtoday.

We were supposed to implement Leader in Me this past year.  Again, one of those things that could have a huge impact, yet, if no follow through, it sizzles out.  Which makes me sad.  One quarter, I used Make a Difference Monday.  I copied articles from What Do You Stand for? (Barbara Lewis) – students read, then on a post-it would respond briefly to a prompt I had on the board pertaining to the article, but relating back to their life / choices.

Test-Prep Tuesday was essentially flashbacks to pre-algebra and geometric concepts – intended to help students study for upcoming ACT.

Fast-Five Friday was a flashback of big ideas from the previous week.

Some ideas I want to add for next year:

Graphical Data is presented, but students create the questions.  Understanding data displays is so important – so I hope to build a file of examples to use here.  Now I need a cool, catchy name for this structure.

Function Junction – using the NAGS format, I will give students one of the models, they must fill-in / create the other 3.  Possibly even use a railroad/train format in graphics that connect each model: Numerical/table of values, Algebraic / Equation, Graphical, Sentence / Context description.

Literacy and Vocabulary strategies are important to me.  I feel several of my students struggle with reading and comprehension, so I am hoping to build a structure to help them link new terms to prior knowledge.

3.  Communication with home is vital, yet I continue to fail at doing a good job.  I start with good intentions.  Do parents even know who I am?  Do they know my views on education?  Do they feel I am approachable?  Again, it will be a goal to make positive strides to utilize home as a resource and support.

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Summer Reads #Summerlist #junechallenge 2

I totally believe if we wish to instill a love for reading and learning in our students, we must be a model for it.  In class, I often share connections “I read…” – and students pay attention.  Once a group asked how much I actually read – that I was constantly referring to a book, an article or research in our discussions.

I want to sequence / plan lessons effectively – help students develop soft skills that lead to learning and individual growth.  Some of this can be modeled, but some will need to be incorporated into daily routines.

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I wish I could be an effective leader in my department.  Hoping to gather some ideas for our PLC from Tim Kanold’s book.

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Previously read Jo & Steve’s work but revisiting – to reinforce foundational ideas.  I was intrigued by things Pam Weber Harris shared at KCM this spring and look forward to incorporating some ideas into classes as opportunities to let students develop their numeracy.

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A colleague shared how much she enjoyed What if?

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And one of these 2 books just to have some references / ideas to share in AP Statistics next year:

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My colleague made fun of me one morning – talking about my reading choices for summer – how I bring my “math books” to the pool.  If I wait until the school year begins, I may not have time to focus on professional reading.  Don’t worry, professional reading is not my exhaustive list…I begin each day with a devotional-driven book and end each day with simply non-thinking fiction.  I feel its imperative to keep my brain moving with different styles of literature.


Frustration with Class Attendance #junechallenge 1

I have had so many thoughts running through my mind the past 2 weeks – wanting to put them down, yet trying to get through the final days of school.

I struggle with Algebra 2.  It is frustrating to me – SOOOOO much stuff jammed into one course.  I feel there is simply not enough time to really develop true understanding of many concepts.  I try to pick big ideas – focus on enduring skills –  from our curriculum that best suits our students in Room 123 and search for strategies that will best meet their needs, helping to move them forward.

As I look at these students at the beginning of the school year, three are meeting college readiness.  Several fall within the 10-15 ACT score range and majority in the 15-20 range.  Majority are down on math, do not enjoy it and feel there is “only one way to get THE right answer.”

I recall one particular day in class – a student stating, if you don’t get what the teacher said, they move on without you and you’re stuck, set up to fail.

Our goal: to make it accessible, less painful, allow students room to think on their own, discuss their claims / strategies, test one another’s suggestions and move their thinking forward.




A look at 3 years of EOC results shows improving results.  Is it enough?  Not sure, I’ll need to look at our district projections.

The 4th year is hypothetical – 20% of  students missed the next achievement level by 1 question.  1 question.  This is frustrating to have several that close to moving up another step, yet barely miss the mark.  Yet, we’ll celebrate their growth anyway!

I am concerned about this though because I experienced a high level of frustration the last quarter of school.  Added to weeks of snow days, no spring break to make up some time, it seemed our class attendance was the worst in recent years.  In the last 9 weeks prior to EOC testing, there were 33 days instructional time was interrupted – either by scheduling presentations, other state testing, benchmark testing, college visits, competitions, field trips, field trips.  The day prior to EOC testing, there were eight students on a reward trip.

Don’t get me wrong – student life and involvement is imperative – some of these activities are the only reason a few students even make an effort to be at school.  I would never want to take away these opportunities – they deserve the best.  However, I feel that our instructional time is valid, important and needs to be protected in a sense.

I am not a worksheet kind of person.  So much of what we do in Room 123 is hands-on, small groups and class discussions.  Its impossible to capture those same learning experiences when you’re not there. Trying to continue in-depth discussions and learning tasks was merely impossible.   There was no continuity with 7 students out one day and 6 out the next with a different 8 students out on a third day.    I failed because I gave up.

What if I had kept pushing through?  Maybe those  students would have reached their next level.

I’m not trying to whine – I’m looking for strategies – how others handle these same frustrations.  This summer, I intend to find or outline a resource, update an old class blog – something to provide for those students who are absent for whatever reason.  I’ve tried Edmodo (its okay), Class blog (very few students utilized it).  What about evernote?  One Drive notebooks?

So, how do you handle it when a students asks “What did we do?  What did I miss yesterday?”  How do you fill-in  for in class learning tasks for your absent students?



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What if I Never Taught Factoring

While working in our polynomials unit, a page had some review problems.

Students where given equations similar to:


And asked to solve. 
I changed the directions… to graph the expression in Y= and record the x-intercepts.
Then look for connections between the intercepts and given equations. 

Some nice conversations took place. 

After a discussion/sharing, there was some confusion about signs being different from the expressions.  We talked about the location of the intercepts, sharing how we could create factors…which connected back to translations.

Some students shared how to tell if intercepts were on same side of origin or one positive, one negative.

Others shared – if they substituted the x-intercepts back into the equation, the result was zero.

And finally, someone shared how when they looked at the coordinates of x-intercepts (x,0) the y-value was =0. Bingo. Connecting to the functions zeroes.

So, I asked…what happens when we’re given this x(x^2+5x+6)=0?

Their thinking and reasoning can show through… I  just need to get out of the way.

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