Joyful Mathematical Noise

Screen Shot 2019-06-26 at 9.18.50 PMTwo decades ago, I began my teaching career as an elementary school teacher.  Pairing students up to collaboratively read these poems was always a highlight.  Diverse talents, coming together to blend their voices into a unifying theme.

Thanks to a very generous Strategic Impact Grant by the Berkeley School Fund and additional funds from Susanne Reed, BUSD Professional Development Coordinator, Berkeley Unified math teachers spanning grades 4-9 had the opportunity to spend a week together creating some incredibly joyful mathematical noise.

All three middle schools have elective classes for students who need additional support in math.  This summer work was the culmination of a year-long, teacher-led focus on creating more collaboration and coherence between the content of these courses at all 3 sites.


Monday through Wednesday was an intense focus on how we support struggling students in middle school.  Geeta Makhija, King 7th Grade Math and Intervention teacher co-led these days with me.  As we have built relationships with our struggling students we have learned that many previous teachers have not believed that they could succeed in grade level math because of lower grade skills they lacked.  Teachers continue teaching without carving out targeted instruction to support these necessary foundational skills because we often don’t know how these elementary math skills were taught in the first place.  This 3-day institute allowed us the opportunity to learn from elementary experts so that we can better support students who still need time to learn this foundational math.

Our mornings were led by Ana Delgado, former K-5 BUSD Math coach and current Math TSA at two of our elementary schools.  We wanted to more deeply understand how multiplication and fraction concepts are taught in 4th and 5th grade as they are the biggest gate-keepers to success in higher level mathematics.  


Ana used this graphic to discuss the importance of using three types of representations when teaching math.  She said the word “cat” and asked us to share what came to mind.  Teachers verbally shared the mental images which came to mind, “Grey; puffy, striped, cuddly…etc.”  No one shared the letters c-a-t.  Ana contrasted this with the teaching of mathematics where we often ONLY discuss the abstract, symbolic representation of an idea, without also discussing the concrete and visual representations.  I loved this notion and am excited to think more deeply about how to build students’ mental models of math concepts for everything that I teach.

Ana then gave us the opportunity to compare and contrast how we solve elementary math problems with how students are taught to do them.  We practiced partial quotients for division and explored both an area model and number line for fraction multiplication.

In addition to Ana, we had presentations by several teachers on classroom routines and pedagogical strategies which have been successful in their Math Support classes.

  • Wendy Lai (King) presented on how she uses math stations.
  • Robert MacCarthy (Willard) presented on what he has learned from Jo Boaler’s work on Mathematical Mindsets and how he incorporates mindset work into his classes for Mindset Mondays.
  • Geeta Makhija (King) led us in a 3-act task focused on multiplication and fractions (The Big Pad by Graham Fletchy) and discussed the power of using rich tasks in our Math Support classes
  • Joshua Paz (Longfellow) presented on how he has students doing error analysis and how he sets up his grade-book for students to understand which concepts they are strong in and which they need to continue working on.
  • Kinjal Shah (Willard) taught us how she spirals the math in her course, with explicit times each week to review material from earlier grades and other times to preview the math coming up in the grade level course.  One resources she uses for students to independently practice & keep track of their progress in foundational skills is a web site called That Quiz.
  • I presented on how Desmos’ Snapshot’s Tool can be used to bring multiple perspectives on problem strategies into class discussions and allow more students’ voices to guide class conversation.

Our end-goal was for our courses to be more aligned, so our afternoons were spent collaborating, putting shared resources into folders and co-planning our courses.   In addition to Ana, we were joined by elementary RTI teacher Vanessa Sinai.  This was truly a collaborative effort. Tons of ideas and links were shared which are all found at the bottom of our agenda here. 

We used some of our grant funds for a daily raffle where we had tons of incredible math resources as prizes including, of course, a #mathgals t-shirt.

As our team planned for this summer work, we realized that a broader outcome for this grant was to bring math teachers, together, from upper elementary through middle to 9th grade to more deeply understand students’ needs.  Thursday and Friday were led by our 6-8th grade Math Coach, Ryan Keeley.  One day was a collaboration between 7th grade math teachers and the following day was 4th-7th grade teachers.  The goals of both days were similar: develop deeper professional relationships between sites and grade levels in order to increase our common pedagogy and mathematical approaches to the teaching of big ideas.  We talked about how an idea introduced in one grade level (integer addition in 6th and 7th grade, for example) leads into ideas in later grades (vector problems involving distance and time) and the importance of using models in the lower grade which will inform those bigger ideas.  IMG_6520

For me, this week demonstrated the power of teacher-leadership and the need for sustained partnership between elementary, middle and high school teachers.  Every day we were reminded that we teach the SAME students and that improving student learning depends on us continuing to learn from one another’s expertise.  I have such gratitude to the Berkeley School Fund and Susanne Reed, Professional Development Coordinator for valuing and funding this summer work.

Evidence of this learning was evident throughout our evaluations:

“All of my learnings will go directly toward informing instruction for my students that is more relevant, engaging, thought-provoking, and personalized, and that will promote deeper conceptual understanding. I have spent the past few days excitedly building my toolbox, reflecting, and recharging to begin a deep dive into reshaping what support class can look like this year. I believe that with these new additions students will grow even more in enjoyment of the class and growth in mindset and as problem solvers, and increase retention and understanding of topics covered. I’m confident that my students will benefit because even as a participant in this work I’ve grown in these ways – I can’t wait to see where my students will go with these additions.”

“I had a blast participating and am taking away so much that I’m eager to put into play for this upcoming school year. To have this kind of energy and momentum going into summer is awesome. I can’t wait to roll up my sleeves and start weaving together all that I’ve learned, all of these best practices, to make a more effective and impactful support program for our students. Truly a wonderful professional development time.”

I am so looking forward to returning to teaching next year with these amazing colleagues and so many more not captured in this lunchtime photo.  I’m honored to be a part of this powerful group of reflective teacher-leaders.





How to Talk So Students Will Listen and Listen so Students will Talk

This week I messed up.  I got so frustrated at a student who was opting out that I didn’t stop to think about why.

Let me take a step back.

Our school’s mental health counselor often tells me that I should become a social worker.  She is always amazed at what my students tell me about their personal lives.  While flattered, in reality it makes me angry that this is seen as rare from a math teacher.  I am constantly thinking about what it means to teach for equity.  Creating a safe and trusting classroom where students are willing to risk telling me about the hardest parts of their lives is a really important part of their academic success.  If you spent only a few minutes in my classroom, you might never know that this happens because as I am teaching, I rarely pause the academics.  However, it’s the in-between moments that make the difference.  I believe these in-between moments are an important part of Culturally Responsive Teaching.

Screen Shot 2019-02-02 at 10.01.48 AMA student is doodling on his arm while the rest of the class is taking notes.  In the moment, I tell the student to stop and not get behind on their notes.  He picks up his notebook and gets back to work . But later in class, I go over, sit next to the kid, and ask if everything is ok.  I say that I noticed you’re really distracted today and want to check in.  Sometimes he says, “Nah I’m fine.” and sometimes he says, “My parents are thinking about getting a divorce and I’m scared.”  (And yes, too often he says, “I stayed up too late playing Fortnight last night.)

Screen Shot 2019-02-02 at 10.00.16 AMA girl is chasing someone down the hallway when she’s supposed to be lined up outside my door.  In the moment, I yell and tell her to get in line. But when the class comes in, and I’m giving high 5s at the door, I pull her aside, wait til everyone is in, and ask her if everything is ok.  Sometimes she says, “Nah, I’m fine” But sometimes she says that this kid just called her a bitch or that this other girl posted a picture of her on social media which she wants deleted.  And sometimes she says, I really like this boy and I don’t want my friends telling anyone.

When students misbehave, in small and large ways,  I am very strict in the moment to get them back on track, and try to later follow up to better understand why.  And often, kids tell me all sorts of personal things.  And often, I don’t have time in math class to really listen.  So when they tell me things, big or small, I then offer a time during my prep or at lunch or after school when they can come back to tell me more.

But this week, I messed up.  I have a student who has a lot going on at home including a relative who is dying.  And this student is opting out of being a student, a learner, a community member, in every way possible.  He has been opting out all year.  I have tried so many things, meeting with his mom; daily texts to his mom giving her a positive about his behavior; daily behavior goals with positive incentives chosen by the kid; checking in with his other teachers and his counselor; having a circle of support with him, led by the restorative justice counselor, to help him see what a wonderfully talented kid he is and helping him see how he has a community of adults at school who value him and are here to support him.

I messed up, because every day this week I got upset about his behavior, and the various ways he’s opting out.  I gave consequences.  But in those in between moments, I didn’t ask him how he’s doing.  I used the in between moments to tell him how disappointed I was in him instead of asking him how it’s feeling to be back at school after missing a bunch of it.  He’s a kid who has told me nothing about his life outside of school.  While I know a lot about him, it’s not from him telling me.  And that is my failure.  I need to take a deeper breath.

Taking more of these deep breaths, focusing on the ‘in-between moments’ in my math classroom as much as the teaching of mathematics, is my focus for the second half of this year.   For #TMC19 (Twitter Math Camp 2019 which is in Berkeley in July…yes!) I am thrilled to be presenting on this very topic.  Marian Dingle, an amazing elementary school teacher in Georgia who I met last summer at TMC, suggested the idea of interviewing students and families to learn about what they need from their teachers in order to be successful in school.  It feels so powerful to do this in a Berkeley school to present as an equity-strand workshop at an international teacher conference hosted in Berkeley.  I am so excited to be doing this work with my students this spring and hope that their experiences and their voice can become the beginning of a deep conversation with teachers from all over the world.

In the meantime, please watch this video, “Our Culture Our Schools-Culturally Responsive Education in New York City” made by the Coalition for Educational Justice 

This work is so important.  While I will still mess up, I will hopefully mess up less often.  And while it’s easy to talk about how to best teach that upcoming lesson on fractions, the work expressed in this video has just as big of an impact on how much students actually learn from that fraction lesson.

Unwanted Subject

Last week a man was asked by police to leave a Menchie’s Frozen Yogurt store in Kirkland, Washington.  He had been in the store for a while and hadn’t ordered anything.  He made the two employees nervous and they called the cops.  Turns out here was there for work.  He’s a court supervisor and was supervising a court-sanctioned outing between a mother and her son.  Which is why he didn’t order anything and was sitting in Menchie’s.  Would you like to guess his race?  He’s Black.  Would you like to guess the race of the 2 employees?  They’re White.Screen Shot 2018-11-20 at 2.25.13 PM

Here’s how Byron Ragland, the court-supervisor who was escorted out of Menchies by the police reacted:

“You want to stand up for yourself, as a man, or as someone who was just doing his job, and say ‘hey, this isn’t right,’ ” he said. “But in the moment I’m thinking: ‘I’m a black man, and If I start emoting, I might not walk out of here.’ And so you rationalize to yourself: ‘What’s the big deal, it’s just Menchie’s, just leave.’ But then later, you realize that you gave in — that you consented that this is the way it’s going to be, to always be.’

“Living this kind of mental life will drive a person insane,” he added.

I urge you to read the entire article from the Seattle Times, found here.

And as you are reading, ask yourself if he could have been one of your students (he could have).  And could a parallel situation have happened to one of your 4th graders, or 7th graders, or 11th graders (it could).  And then ask yourself if that student of yours would have told you about it and how you would have reacted.

Screen Shot 2018-11-20 at 2.26.38 PMFor me, this story brings up a reaction that I had to Julie Reulbach’s keynote at Twitter Math Camp last summer.  Julie eloquently brought up the countless ways that teachers are maligned by non-educators.  I absolutely agree.  She argues that student engagement shouldn’t be the sole responsibility of their teachers.  I also absolutely agree.  And yet, as math teachers (who I believe most people reading my blog are), we have to build relationships with our students so that we have ways to talk with them about what it feels like to grow up in the world in their skin.  Because that unengaged student of color sitting in my classroom may very well have had numerous experiences just like the one which Byron Ragland had as a grown man.

And as a teacher, while I can’t ultimately prevent this from happening, I can have deep relationships with my students so that they will confide in me.  Trust me with their truth.  And trust me to be a white ally as best I can.

The other day as students were walking into my class, one asked if he could speak to me privately.  Once the rest of the class was underway on their warm up, we stood in the doorway.  He confided in me that he and some friends had tried vaping and he wanted someone to know.  He was nearly in tears because it felt so good to tell an adult whom he trusted. He repeated over and over, “It just feels so good to tell you.  It just feels so good that someone knows.”

Student engagement IS my responsibility, and my work has to involve supporting students as they experience their world both inside and outside of school.  Their engagement so often is unrelated to the quality of my math lesson.  Many are facing countless challenges at home, with friends and out in the world.  I know this is part of what Julie was saying.  And that we can reach out to them so many times and there will still be issues facing teens that all of our best intentions can’t overcome.

And yet, part of my job HAS to be building and supporting my students as they grow up and become a greater part of the fabric of their world. A white student of mine may go on to become an employee in a frozen yogurt shop who calls the police because he/she feels nervous about the black man in the shop who is using his phone and hasn’t ordered anything.

And while I can’t walk in the shoes of a black student of mine, to know how it feels, I try to always assume that an unengaged student is one who I can work to make deeper connections with, to learn more, share more, and hope that I can become that teacher where, “It just feels so good to tell you.  It just feels so good that someone knows.”  And while that is part of my work with students of all races, it feels especially important with students whose race is different from mine.  THAT is part of my work as a white ally.  Screen Shot 2018-11-20 at 2.55.21 PM

Because “Living this kind of mental life will drive a person insane.”

There is some reaction happening in Seattle.  Here is a second article explaining the police department’s apology.  

What I hope is that the cops who escorted a black man out of a yogurt shop for simply doing his job will return to that shop to have an equally serious conversation with the two white women who called them in fear.  We all need to talk more about race and our implicit bias.  People’s lives (literally) depend on it.



Listening Deeply…

I have tweeted and blogged a lot lately about working to listen more deeply to my colleagues, students and their families.  It has been a tremendous help in building relationships  and becoming a part of the new school community where I am teaching this year.    As parent-guardian-teacher conference season draws to a close, the following story feels important to share.

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Last week in “Teaching with my Mom Googles on,” I blogged about how I am more thoughtful and reflective this year when calling parents about a child whose behavior I am concerned about.  My perspective changed after my son’s teacher last year called me constantly about his poor behavior.  And how I quickly I became a parent who wouldn’t call her back and who kept asking her what she was planning to do to improve his behavior.  While I have always been a teacher who knows the value of balancing positive news home with concerns (heck, I even have custom post cards for sending home good news), I never felt it as deeply as when my son’s teacher constantly called with complaints about him and expected me and his dad to fix in through a strict talking-to or by taking away something fun at home.

In response to that blog post, Marian Dingle posed a question on Twitter which gave me pause:

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Honesty, I see every family-teacher communication differently because of my experience with my son last year.  Could my thinking have been pushed without this personal experience?  Yes, if someone had shared their own personal experience with me.  It didn’t have to be my own son, but if a friend, colleague, pissed off parent of a student of mine, had the courage to be honest with me and trust I would listen, then yes. But I’m not sure that a PD where we read a case study or my principal reminding me of the value of positive calls home would have made as big of an impact.

I will forever think differently about building relationships with families and phone calls home because of my personal experience with my son and his teacher.

If you were not at Twitter Math Camp 2018 last summer in Cleveland, I urge you to carve out time to listen to Marian’s keynote address.  What so deeply moved me was her willingness to share such personal stories as both a parent and an educator.  Her speech was such a gift because like my friend trusting me to listen to the perspective of a foster child and reconsider a routine September homework assignment, Marian trusts us with some of her life experiences so that we have more perspectives to draw on as educators.  While we most certainly do not need to experience something ourselves in order to have empathy and be motivated for change, we do need to be willing to listen deeply to those who take the time to share their perspective with us.

You can read the entire keynote address by clicking here or you can watch it below.

Teaching With my Mom Goggles On

Last year, my son’s teacher called home a lot.  My son was struggling with his impulse control in the classroom and was frequently getting into trouble.  She always called me during the school day.  Sometimes she called more than once a week.  Our conversations were nearly always the same.  She’d  tell me what he had done, tell me why that made it hard for her to teach and for other students to learn, and tell me I needed to have a consequence for him at home.

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The first few times she called,  I did just that.  My husband and I talked with my son to learn more about what was going on and had some sort of warning or consequence.  We said and did all the things teachers would want parents to do.  I appreciated her letting me know what was happening and assumed things would change after we spoke with him.

The first few times.

And then it made us crazy.  Yet another call while I was at work. Why couldn’t she call after work when I could actually talk more easily? Although I never excused his behavior, I also learned from him the reasons that it was happening.  I wanted to shift the conversation to reflect together with her on WHY it was happening instead of WHAT was happening.  From there we could talk about solutions.  I was never very successful.

I stopped answering.  I stopped calling her back.  I was tired of hearing the same complaints.  Tired of the assumption that I wasn’t doing enough at home to change his behavior.  Tired of feeling that the entire onus of change was on what we could do at home: some magical wand we could wave which would get him to sit more quietly at school tomorrow.  If I had that magic wand I had several things I would wave it for.  Heck, maybe I could wave it to get him to enjoy vegetables.

I started the year eager to partner with my son’s teacher to support his social-emotional growth and watched myself become less and less engaged.  Not answering when I saw her calling on my caller ID.  Taking a few days to return her calls.  Sometimes not returning them.  Often not telling my son she had called.

Once she called and I waited a while to call her back.  When I did, I learned she was calling with something positive to say.  The relief that flowed through my body was thick.  I felt the tension evaporate.  What a difference it made to have a positive phone call home.

Screen Shot 2018-11-03 at 8.55.55 PMIt sure changed my perspective as a teacher when I reach out to families. I now filter EVERY interaction I have with families through wearing my mom goggles.

Before I email, call or text, I first consider which communication medium is best, given what I need to share and given what I know about a family’s situation.  Teachers at my school have commented recently on how I text and call so frequently, instead of emailing.  Email is nearly ALWAYS easier for the teacher.  But often it’s not a medium a family uses frequently and/or not best for the information you want to share.

Then, every time, I think about how I would hear the message if this were my son’s teacher calling me about him.  I think about what that teacher could say that would make me want to engage in a meaningful conversation.  I think about what time of day I am calling: I will text in the afternoon, but never call before 5pm.  I regularly call only with positive things to say.  And most importantly, when calling about a student who is struggling with academics, behavior or both, I reflect deeply on why I think these things are occurring and begin my conversation focusing on the why instead of the what.  And I listen, deeply to whomever I am speaking with.  I never expect a family member to fix it.  I know there is no magic wand.  I call to collaborate on how we can best support that student to shine this year.  And after every challenging conversation, I ask if it would be ok for me to text a few times in the coming week.  To let the family know their child’s progress in whatever it was that was a struggle.  Because there is always progress.  But if we don’t talk about the small victories, then the next call may be a few weeks later when something major happens again.  And I want that call to be answered, and not ignored, as I often did last year with my son.

Teaching is about building relationships with our students.  Building relationship through our communication with families is just as critical.

Birthdays and Unspoken Expectations

My dad’s birthday was last week.  He’s an avid reader of my blog, so let me start by, once again, wishing him a very happy birthday.

I thought it would be funny to have my class sing him happy birthday.  But which class?  He certainly didn’t need 4 of these phone calls, as charming as they would be.

It was an easy choice.  3rd period.  They are my ‘best’ class.  The fewest challenging students, the highest quiz average and homework completion average, and that class where I always get a bit farther in my teaching than any other class because things always flow so smoothly.  If you’re a teacher, you know that class.  You have one too.  So naturally, if I were going to stop teaching for 5-10 to do something fun, silly, and totally unrelated to math class, I’d do it in 3rd period.

And we did.  And it was so fun.  We put him on speaker phone, ran the line through the speakers of my LCD so it projected quite loudly, we sang, he gave them a spontaneous math problem, we laughed, we made a promise to meet at lunch on that same date next year to call him again, and we then went back to math.

What I hadn’t thought about in advance, was how memorable that phone call would be for that class: it brought the class closer, gave us a moment to laugh, be silly, connect us all around a family birthday, something each one of them could relate to.  As soon as I hung up the phone, feeling all warm and fuzzy, I realized I had chosen the wrong class.  3rd period already felt warm and fuzzy.  By making them the special class, the one that got to call my dad, they felt even more special.

I should have had my most challenging class call.  THAT’S the class where we need more warm, fuzzy, silly moments.  It never occurred to me to call during that class because we are always behind in that class.  Management takes more time.  Keeping kids on point takes more time.  Heck, even expecting students to put papers into binders takes more time.  I didn’t feel I had time to ‘waste.’

It reminded me of the Invisibilia Podcast, “How to Become Batman.”  It haunts me.  I believe it was Andrew Gael who mentioned it in his Shadowcon talk at NCTM last spring.  Listen to it here if you don’t know it.  

In brief, scientists discovered with rats doing mazes, if you simply expect them to do better, talk to them more kindly, they perform better.

As I hung up the phone, I realized that I was recreating this before my eyes.  By giving my ‘easy’ class more silly, fun, and bonding time; by telling them that we were going to do something fun, because I could count on them to get the same amount of math work done in a shorter period of time, by making plans for a class reunion next year at lunch to call my dad again for his birthday, they will now perform better on tests, focus more quickly when asked, and feel more trusting of one another when they need help.

So mom, since you’re also reading, when your birthday comes in October, you’ll be getting a call from my ‘hardest’ class.  Because expectations matter.

A Tale of Two Puzzles

This summer at TMC, Chase Orton (@mathgeek76) suggested that I should write a series of blog posts reflecting on returning to the classroom after a 5-year hiatus and how what I learned during that time has changed and improved my teaching.  It´s a lovely idea.  But for the moment, challenge not-accepted.

INSTEAD, I have  stories to tell from the first few weeks of school.  I have about 70 students this year which is a relatively low amount for my district.  I am teaching 80%: 3 sections of 7th grade math and 1 section of 7th and 8th grade math intervention.  I have tons of stories to tell from my year so far: highs, lows, reflections, etc; but for the moment, I want to talk about a student who is doing everything he can do opt-out of learning.  He taps on his desk, quietly at first, and increasingly louder if I try to ignore him.  He takes supplies from the student supply area and spends time hooking paper clips together or stacking Solo colored plastic cups left over from Martin Joyce´s Cup Challenge which will eventually be used for Avery Pickford´s  group-work signals of how well a group is functioning.  He argues when I ask him to sit in his assigned seat, eats in class when he knows he shouldn´t, and opt-outs of learning in nearly every way he can invent.  His behavior has clear, consistent consequences and he hears from me every day how much I believe in him and care for him.  We have had lunch together, he´s earning snacks for after class, and we are building a positive relationship together.

Students opting out of learning is something which never leaves my mind.  It happens in nearly every classroom, in subtle and not-at-all subtle ways. story, however doesn´t start or end there.  This child LOVES puzzles. I learned this during the first week of school when I had a play table with an assortment of Christopher  Danielson´s tiling turtles and pentagons.  He couldn´t put them down and made beautiful tessellations every (and yes, I do mean every) opportunity he had.


During the first week of school I hand each student a ziplock bag filled with a metal of 2 parts hooked together and they have to figure out how to get the 2 parts apart, and then back together.  The types where getting the 2 pieces apart is seemingly impossible.  I have them in 3 levels of difficulty and after solving one, I ask the student if they´d prefer their next one to be the same level or a harder one.  I am only easily able to solve the level 1 ones, so when they get stuck and ask me for hints on the harder one, I love being able to say that I have no idea how to solve them, but I believe that they will if they stick with it.  And yes, most of the diabolic ones eventually get solved.  I find it´s a wonderful way to talk about what math is to me: you don´t always know if you´ll use a day´s lesson later in life, but really good math should always feel like those puzzles…worth solving because they make you curious and fascinated.  I talk about how nearly every student I have ever had ALWAYS chooses a more challenging puzzle  after solving a previous one and how knowing that their teacher can´t solve it makes them even more determined.

We did these puzzles for a day during the first week of school and I left a few out in baskets in the back of the room as something for students to play with when they had down time.  I loved this idea, but as the days wore on, I realized how LOUD those metal puzzles can be if someone is doing one when they should be in their seat with the rest of the class.  The student who I mention above, absolutely loved these.  I offered to let him take one home each day, but what he really wanted was to do them instead of everything else we were doing that week.  And between him being off task and it being so loud, I decided I needed some quieter puzzles for him to use as brain breaks.

He is now in love with Manifold puzzles.  I bought a pack just for him (and a few others to use for other students when the need arises) The idea is to fold the paper to get a 4×4 square of black tiles on one side and 4×4 square of white tiles on the other side. They are leveled, #1-100.  The initial ones look something like this and he had really quick success:

And eventually, they become really, really tricky, like this one

And although I have not yet had a huge amount of success getting him to attempt the grade level material, he is no longer searching for a reason to opt-out of everything and is no longer disrupting us all in his search.  I have walked over numerous times, pulled a puzzle out of my pocket and said, ¨Don´t get up and don´t say a word to me until this is solved.¨ And it works.  He becomes determined to solve the puzzle and comes over gleefully once he does.  This is chapter 1 of what I am sure is a long journey we will take together this year.   And I am sure, at some point soon, I will be celebrating with him his successes on the grade level math content of my course.  He knows that´s part of this story.  I do too.

I would LOVE more ideas of low floor individual puzzle ideas which ramp up into harder challenges was shared this week through the Desmos Fellowship and it´s exactly the type of ideas I need.  But ones that involve manipulating things, like these Manifold Puzzles are even better.  I will buy whatever you recommend, so send me your best ideas! I have a list of tons and tons of ideas from Sarah Carter (, but don´t entirely have time to curate the lists and choose a few to use for now.  What I would love from you is just 1-2 of your favorite ones which can be used with minimal prep and/or minimal instructions (like the Manifolds).  THANK YOU.