Category Archives: strategies

Personal Reflection 3-2-1 #MTBoSchallenge


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? 


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.


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


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.


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. 

My Experience with Counting Circles #julychallenge Post 14


Still addressing 14 ways of thinking about good teaching from this post

2.  Plan goals for both the long term and the short term.

My number 1 goal is to help students grow – personally and academically.  My wish is that they leave my classroom believing in themselves, more self-confident than when they entered. 

Ideally, I do want every student to reach proficiency, but I am also a realist.  When students come to me with *ACT-PLAN scores in the 10-14 range, proficiency is not an immediate goal…growth is, pure and simple.  My class becomes the stepping stone to reach proficiency.  Students in this range generally have major gaps in number reasoning.  They are just now beginning to develop understanding and knowledge of assessed skills.

Last year, I wanted to use accessible tasks to begin each day…Counting Circles, Number Talks (pg 4 of link) and my post, Estimation180, and Visual Patterns were staples in my Algebra 2 classes.  Students in these classes ranging from ACTPLAN scores from 10 to 23-wide range of abilities and varied confidence levels.  These tasks were approachable for all students and I feel helped in developing number sense which allowed several students to make significant gains on thier ACT.

Counting Circles (Thanks to Sadie!) was very popular in both classes.  We literally got out of our desks to create a “circle” around the room. Yes, it seemed trivial at first, but I was able to see student confidence grow as they strengthened numeracy skills.


My Routine
We have a starting number and a number to count by.  In the beginning, I choose nice numbers, then some that required a little more thought.  Eventually, I allow students choose our counting number and starting point.  I would have expected them to take the easy route.  Not at all.  They like to challenge themselves.  We also countdown.  I like to write their responses on the board for them to visually see the patterns.  When a student makes a mistake, I try to not point it out, but rather, allow students to have opportunity to voice their concerns with a response, respectfully, of course.

After going so far around the circle, I stop and ask, What will _______ (a little further around the circle) say next? 

We usually get a couple of responses, so I allow them to explain their process then, as a class, they determine which one makes more sense.

Also, I like to ask…who will say ______ ?

Side note: Later in a functions unit, while looking at finite differences, a student explained, this is similar to what we were doing with Counting Circle the other day!

Our First Counting Circle – Count by 10
I began with couting by 10 on decade numbers, by -10 on decade numbers, then on numbers like 11 or 14, counting by 10 in both directions.  It was a great way to model the routine.  Students are comfortable with it.

Next week, we counted by 2s, up and down, starting on positive and then a negative.

Several students are all in – they’ve got this!

Then by 5s.  On 15, 70, -85 then numbers not ending in 0 or 5…. 37, 128, -89. Both up and down.

I began using single digit integers then a few double digits.

Next week we worked with decimals +3.7,  starting with an integer, then moving to devimals 11.2.  One student this particular day was quickly running through their numbers.  When I asked their strategy, they responded….its easy, add 4 then count .1 back 3 times.

We also use fraction expressions as well.

I already know my stronger numeracy students-those with “high status” in class (Ilana Horn).  So do their classmates.  What I love about counting circles is choosing different students to explain.  Struggling students pick up on numeracy techniques as explained by their peers.  They are able to see those high-status students’ thinking and realize, “I can do that too.”  Its a win-win.

Yes, at high school age, I have students who don’t want to participate, but with a bit of coaxing, they come around. It becomes a game.  Classmates encourage those who struggle.  We don’t laugh or make fun.  They celebrate when ‘that’ student experiences success.  Most of all, they smile.

Generally, it takes anywhere from 5-15 minutes depending on number choices, discussions, size of class, experience with the routine.

Suggestions:  pre-cal count around unit circle, elementary use money as a context, what others can you share?

Long term goals and planning changes with each group of students.  Having access to learning routines like these allow me to tailor toward each groups’ needs.

*In Kentucky, every student takes the PLAN during sophomore year and ACT during their junior year as part of our state accountability model.  To measure student growth from state data, students are grouped by their PLAN scores, then compared to others in this scoring band.  Once the ACT scores are available, they are given a percentile rank from within that initial grouping.  I, the teacher, can view this and whether they had high growth, expected growth or below expected growth.  The state assigns me an overall rating and this will eventually become 20% of our Certified Evaluation plan.  The other 80% is determined locally and by student growth and proficiency goals I personally set for my students early in the school year.

#5things to Do with Sticky Notes #julychallenge


2-Minute Assessment Grid ideally is for the end of a learning task, but is a great reflection tool used toward the end of an entire unit.  Each student gets 4 sticky notes to respond on for each prompt as seen in the picture.  I like it 3 or 4 days before a unit assessment.  I am able to create a chalk talk with the questions they still have-which allows students an opportunity to respond/learn from one another before I intervene.  Read post here.


12×12 Sticky Notes These were a treasure from our local Mighty Dollar store.  25 large sheets for $1.  Yes, I bought all 10 packs!  I basically cut apart a pre-assessment and tape one question to each giant sticky then distributed them to pairs of students.  They responded to the question, then hung the sticky on the wall.  Students carouseled around…responding they agreed or disagreed with suggestions.  I believe this particular one had 9 stations and I asked that they visit at least 5 or 6 in the alloted time.  We then discussed their responses and arguments as needed. Full post here.


Post-It Note or Stop Light Quiz has been around for several years, post here.  The basic idea is for students to place their name on the back side of the quiz.  They respond on the front side, self-assess to determine their level of understanding/confidence and place it in the corresponding space.  Its a nice visual for me yo scan as they leave the room in determining what’s next the following day.  I have RYG folders for them to drop their papers into when we aren’t using stickies.  Red – needs some help, most of the time these are the students who have been absent.  Yellow – still lacks confidence, maybe a little more practice.  Green -Got it! Ready to move on.


Flip for Answers -I like having sttudents create their own problems.  When they enter class the following day, they can exchange, work each other’s problems, then check.  The sticky can serve as a cover-up for the solution. 


Notice & Wonder The last suggestion came during our ppschat last winter Powerful Problem Solving by Max Ray, his post here.  If you aren’t familar with it, you need to look it up!  His Ignite talk is great too!   With student work displayed, either patterns, data collection, graphs, various models or solution approaches…give each students 2 stickies, preferably 2 colors.  One is for something they notice, the second is something they wonder while viewing other student approaches, etc.  They attach it to the samples.  Continue to visit each station, reading others notice and wonder postings.  This should be a nice springboard for class discussion. 

Gallery Walk #ppschat Challenge


A common theme in many chapters of Powerful Problem Solving is Gallery Walks. Several techniques are offered throughout the book, but the common goal is to allow students to view their classmates’ approaches to problems.

One of my faults with online book chats is lack of follow-through. I can sometimes use an extra nudge of accountability. There are often so many great ideas and strategies in the books we are chatting that I get overwhelmed and not sure where to begin. Advice: pick 1 thing. Try it. Reflect. Revise. Try it again.

So here is my attempt at a gallery walk. I simply cut apart a pre-assessment for a Formative Assessment Lesson and each pair of students taped it to a large sticky note, discussed and responded. I was confident in many of the questions, but my goal was to identify the few some students were still struggling to understand completely, mostly questions involving transformations.


1. The large majority are fine with creating a possible equation, given the x-intercepts.


2. Initially these students tried -6, -4 and 2 as their intercepts. I asked them to graph their equation then reread the instructions. Oh. They had read write an equation, looked at the graph for possible intercepts and failed to read the y-intercept of (0, -6). One quickly stated the connection between y-intercept and factored terms and was able to adjust their response with ease. I believe it happens often to see a graph skim question and think we know what we’re supposed to do, only to realize skimming sometimes results in miseed information.


3. Within the lesson, many students quickly realized when a factor was squared it resulted in a “double root” and the graph would not actually pass through the x-axis at that point.

The 4 transformations seemed to causes the most disagreements. These were the ones we discussed folowing our gallery walk. However, it was during the gallery walk most students were able to adjust their thinking.


4.i. Listening to students as they were at the poster helped me realize there was not a solid understanding of the reflection across x-axis and maybe we needed to revisit. Possibly, they are confusing with across y-axis?


ii. A few students disagreed initially, but the convo I overheard was addressing that changing the x-intercepts was not sufficient, they looked at the graphs, then said, the functions needs to be decreasing at the begiining, that’s why you have negative coefficient.


iii. Horizontal translations always seem to trick students up. One disagreement actually stated ‘they subtracted and did not add.” Of course, we definitely followed up with this one.


iv. This pair of students argued over which one was right. The expaned version or factored form. Simple, graph the new equations and compare to see which one translates the original up 3 units.


A1 & A2 I believe they’ve got this one.


B1 & B2 some confusion here due to the extra vertical line in the graphic. This student was also interchanging graph & equation in their statement.

I thought the gallery walk was a good task to overview some common misconceotions. It was not intimidating, students were able to communicate their ideas, compare their own thinking to others. I truly tried to stand back and listen. They were on task, checking each other’s work. Each station allowed them to focus on one idea at a time. They were talking math. Most misconceptions were addressed through their discussions or written comments.

Having a moment to debrief the following day highlighted the big ideas students had addressed the previously and reinforced the corrections they had made. This was so much more valuable than me standing in front of the room telling them which mistakes to watch for. Their quick reflection writes revealed majority have a better ability to transform the functions, which was my initial goal for the gallery walk. A few still have minor misgivings that can be handled on an individual basis.

No jumping in, silent/listening, no repeating & my win for the day #ppschat


Our #ppschats the past few weeks have brought some a-has and good reminders for me.  Here are a few adjustments I am trying to mindful of:

1. When students are working in small groups, I have often jumped in to their conversation when I heard them going in the wrong direction.  Of course, my intentions may have been to redirect them. 
Needed adjustment:  Be silent and listen.  Giving them space to muddle through their own thinking without jumping in and telling them what I think they should think.  A key for me may be to keep my tablet, clipboard, post-its to jot down notes of their conversation.  Key points to reference back to later.  Jot down questions I might like to ask.  Not sure when to ask /share, maybe as a quick revisit before the end of class?

2. In my efforts to “value” what a student shares, I often find myself repeating. Afterall, those softspoken students need to be heard, so I repeat it so classmates across the room “hear” them.  Oh, no.

Needed adjustment: Ask student to speak up so others can hear.  If they are intimidated, offer an encouraging word, let them know you like it, find it interesting or you want others to hear it.  When I repeat, I am causing others to not listen because they know I’m going to repeat.  Oh, my.  Guilty.  Who knew?  What are ways you create a listening community of students? 

3.  I may ask for volunteers and the same 8 people are sharing.  Spread the love.

Needed adjustment:  I tried to be very purposeful in sharing this week.  In geometry, I picked a problem several seemed to have trouble with.  I structured the task with Know: what information is given, Notice: what do I notice about the diagram? Other information I can use to move me further?  Wonder: What other measures can I determine? How can I justify my reasoning? 

Students took couple of minutes individually, to jot down a couple of things in each bullet, then in their groups of 3 to discuss.  I asked each group to pick 1 thing they felt was important to share.  Yep.  Good ol’ Think-Pair-Share.  As I went around to groups, I arrived at one who said…they already shared ours, so I used the suggestion from PPS to +1 on the board.  It seemed that others were really listening to what was being said.

A win in class today as I gave students a diagram with no questions.  They noticed/wondered and it was a statement from a student that 2 chords were congruent.  When I asked them to convinece me…their statement was quite fuzzy ending with “it just seems like they would be.” I challenged the others to prove or dispute the statement… 

“Oh yea” high fives, “we got it!” & “you’re genius!”  Students celebrating something they hadn’t seen before. 

What was even better, the way they justified their reasoning…all different, not one that I had seen myself.  And that is why I don’t care for the answer key as the answer key. Students sharing their strategy and each confirming the others.  Hearing them say ‘that’s cool’ to another student’s strategy.  Engaged while looking at a different approach.  I truly feel the take aways from a single problem approached this way is valuable.  It was a productive day.

Student Reflection on HW


When I get back from a conference, I have the best intentions of sharing, but its nearly 3 weeks later and I am just starting to get caught up…only to realize there are less than 3 weeks of instructional time before Christmas break. 

Starting to stress in my Geometry blocks classes…similarity (although I tied in some with our congruence unit and they used dilations in our transformations unit…) right triangles and circles…then a super dooper quick approach to modeling via 3-d problems.  Anyone have an amazing project that ties circles and right triangles together?  Anyway, a bit off topic, because the stress causes me not to focus.

  I attended a session led by @ottensam sharing different approaches to ensure we are integrating the SMPs in our instruction.  He was very engaging and shared some simple, research-based strategies.

A great idea he shared was to change up the way we approach homework.  One simple suggestion was to ask students to eflect on the problems…which were most alike? Most different?  Why? Which one did you think was easiest? Most difficult, why?  I had students to do a quick write using this idea this past week.  Once they were finished, they had to meet with someone they did not sit next to and share their responses.  Finally, I called on students, asking them to share -not what they had written- but something they had heard. 

I am always amazed at student responses when I use startegies similar to this and could kick myself for not being more intentional, more often.  Several shared exact similar/different pairings but for totally different reasons.  I love it, being able to see and hear their ideas and thinking. 

#WTPW Simplifying Radical Expressions-Rationalizing Denominators #tlapmath


I am not sure how exciting this lesson is, but I believe the idea beats the run of the mill take notes-practice on a worksheet.  It gives students opportunities to notice patterns on their own, a chance to share and discuss those ideas as well as consider ideas from their classmates.

I appreicate Math Equals Love Walk the Plank Wednesday post and will definitely use some of her ideas with the “why” we do this.

My goal is for my students to be able to determine if expressions are equivalent, so I am beginning with a simple card matching task.  As students enter the room, they will receive a card with a radical expression either simplified or not (similar to set A).  As we begin class, they will be asked to find their match…without verbal communication…while I post attendance, etc.  They will come to me with their match and I will confirm if they are correct.  Yes, I will allow calculators.  I know, not too high level on the thinking scale.


I will have several sets of cards similar to those they matched.  Each group will then be asked to complete an open-card sort.  This simply means, I do not give them any direction on how to sort their cards.  The only stipulation is they are ready to explain why they chose to sort them as they did.  When the timer goes off, we will share sorts (both volunteers and any I find that are interesting to me).

Part C, I will have concept attainment cards placed around the room.  Each card will contain examples of radical expressions labeled simplified and expressions labeled not simplified.  Students will carousel to different cards, noticing patterns, trying to develop their own rules.  After a set time, they will do a quick pair-share to summarize their findings before we have a whole class discussion. 

Hopefully their ‘rules’ will encompass all we need to know, but if not, I can always use their ideas to lead us to our goal.

We will create a set of notes for our INBs.  Part of their HW will be a LHP assignment to give examples of expressions that are simplfied and not simplified from their earlier carousel work.  Ideally, they would create their own expressions.

If students need practice with skills, an idea from a workshop several years ago…on a page of say 30 problems, I pick 5 I want them to do, then they pick another 5 or 10, whatever I/they feel is necessary.  By giving them this option, I have more success getting them complete the practice.  I would much rather have 10 complete than 30 incomplete or not even attempted.

An idea for formative assessment…return to card sort from Part B.  They should sort into groups of simplified/not, even match up equivalent expressions.  One person stays with the sorts, while others go to different groups to peer assess.


Possible written assessment questions, a) give a bank of expressions to match equivalents, noting simplified terms; b) given a simplified expression, create an unsimplified, equivalence.

This is a very generic layout, but I can use the sequence with whatever level of Algebra I am working with.

I will post again when I have sets of cards completed. 

Feedback to move forward, ideas  for improvements are welcomed.

Pam Wilson, NBCT
Currently Reading
5 Practices for Orchestrating Productive Mathematical Discussions, Smith & Stein
Teach Like  a Pirate, Dave Burgess
From Ashes to Honor, Loree Lough

Chalk Talk part 2 #makthinkvis


Another task I presented students in the form of a Chalk Talk

We had previously used a patty paper lesson to construct our kites. image

Simply enough, we constructed the kite by first creating an obtuse angle, with different side lengths. Folding along AC, tracing original obtuse angle using a straightedge to form the kite. Immediately students made comments about the line of symmetry. They were given time to investigate side lengths, angles, diagonals, etc. forming ideas and testing them to prove properties.

Their Chalk Talk task was to devise a plan to calculate the area of a kite.







Most every group approached the problem by dissecting the kite into right triangles, then combining areas. Several approached dissection as top triangle/bottom triangle, but would have to adjust their thinking when I asked them test their idea with specific total diagonal lengths. Some even extended the kite to create a rectangle. In the end, our discussion centered around 3 statements/procedures for finding area of a kite.

1/2(d1*d2) (d1*d2)/2 d1*d2

Allow them to determine which will /will not work and share evidence as to their conclusions. (Hello! MP3 critique reasoning of others.)

Sure, it would have been quicker to say here’s the formula, here’s a worksheet, practice, learn it. But its so much more fun “listening” to their Chalk Talk. Again, the end discussion is key-allowing them to think / work through each group’s findings, address any misconceptions and finally coming to a concensus as a class.