Translations, rotations, and reflections, used to appear as maybe one question on the California Star Test back when we taught under NCLB. Most years, I didn’t teach it. I really didn’t understand it’s value in the curriculum.

After we switched to Common Core and our school adopted the Integrated Pathway, Transformations were the area I had the most to learn about. See

It’s so funny how the more you teach a topic, the more connections you make to different topics. I taught Pre Calculus for 10 years and absolutely loved teaching students the Unit Circle. Each year, I’d find a new pattern I’d never noticed before.

My last year teaching Pre Calculus, 4 years ago, I showed my classes a bunch of sine curves and had them make a list of everything they noticed about eacH graph. I also had them predict the equation of the curve.

What do you notice? What is the equation?

Y=sin(x) they figured out but when I revealed y=sin(x/2) they gasped. They had predicted y=sin(2X). So when they started talking about what happened to the period they described the period change as 2pi/b. All by themselves.

Can you figure out why they predicted y=sin(2X)?

I had to give up Pre calculus to be a part time math coach for the past 4 years, so this past week is my first time introducing students to the unit circle since then. This is my first group of students to learn the Unit Circle who learned about transformations in Integrated 1.

Can I say that I now see the importance of learning about Translations, Rotations, and Reflections?

My students found the coordinates of points on the unit circle given an acute angle. Then, without any direction from me, just by reading a question in their CPM textbook, reflected the triangle over the x and y axis to find the points in the other three quadrants AND their angles from 0 degrees.

The textbook has them plot the points of the height of those triangles based on specific angles to initially discover the sine function and make observations about the points on the graph. Some students observed to find the other points on the sine curve with the same and opposite values, you reflect over the y-axis and translate it. And others observed the points on the sine curve were a 180 degree rotation about the point (180,0).

I’m 17 years in this profession and I’m still learning how everything is connected. My reflection is that we might not fully understand the impact of the mathematics we teach, but the significance is there and it may not appear for a few more years.

(Also, my reflection is that reflections are important. )

Rethinking Assessment for Mastery over Time

What is mastery?  When does it happen?  What does a grade measure?  What ‘should’ it measure?  What should go into a gradebook?  Once it’s in the gradebook, does it have to be in ‘permanent marker’?  Or is it ok if the grade is in pencil?

These are all questions I plan on exploring at my #CMCSouth Session in Palm Springs, CA, on Saturday, November 16, 2019.

I don’t promise to have all the answers.  I don’t think I have even most of the answers.  But I think the conversation surrounding these questions is important enough to have, because our students are suffering under our grading practices.

What are we trying to teach our students?  What do our grades communicate to our students about our beliefs in their ability to be resilient, to persevere, to learn deeply over time, to make mistakes, to learn from their mistakes, in their potential as human beings, or hope that they can achieve?

I want my students to learn the tools for success for their own learning of mathematics so that no matter who is their teacher next year, they can be successful.  Education isn’t being done to them, they are active participants.  They need to become experts in their own learning.  Rethinking assessment puts them in the driver seat.

Learning takes time.  And mathematics is sequential.  So, if students need a strong foundation to be successful at the next level, then we need to give them time to show mastery.  Why would we penalize those that take longer to master a topic, if they eventually master the content?

My best friend in high school took her driving test twice.  The first time, she failed because she did one of those automatic fail things.  Does that mean her driver’s license is a lower level than mine because I passed it the first time?  She also got a very high score on the SAT the first time she took it.  I took the SAT three times before our scores were similar.  Did the colleges penalize me for taking the SAT three times?  Did I get a “minus” on my SAT score to show that it took me longer to get that score? NO!!!!!!!

Over that past 7-8 years, I’ve changed my teacher practice to reflect the new standards and mathematical practices.  I asked more open-ended questions, included tasks with a low-floor and high ceiling, put students into groups, got them up on whiteboards to do interesting math, etc.  But here is the tough question, we all need to consider.  Does my assessment practice match my teaching practice?


10 things I wish you knew as my students

Earlier this month, I saw a thread on Twitter titled “What I Wish My Teacher Knew” from the inspirational Mrs. Hall @MrsHallScholars and then read her blog post Dear Scholars I wish You Knew….  I believe 100% that in order to teach my students math, they need to trust me and that trust is founded on a relationship first.  So I need to let them in first.

I wrote this letter to them on the day of their first test.

Dear math scholars,                                                                                           September 10, 2019

I am writing you this letter to share with you 10 things I wish you knew about me as your teacher.


  1.  I wish you knew that you are the reason I love my job.  You are my reason why I come to work every day and think about math and how to teach math constantly.
  2. I wish you knew that my daughters are 8 and 3 and they are also the reason why I work so hard every day.  I want to be their example of a strong woman who is passionate about her work and is a lifelong learner.  
  3. I wish you knew how difficult it is to parent a 3 year old!  She is adorable and funny and also loud and frustrating and throws lots of tantrums right now.  So if I come to work tired, it is because she is in a difficult stage right now. (If you don’t know about 3 -year-olds, go home and ask your parents what you were like at that age.)  
  4. I wish you knew how fun and amazing math is.  It’s puzzle solving and making mistakes and thinking and arguing and being creative.  I hope you get a glimpse of this side of mathematics in this class.
  5. I wish you knew how fast high school goes.  Don’t be in too much of a hurry to grow up. You are only this age once.  Enjoy this time at school with your friends, learning about things but also figuring out who you are and what you want to do when you grow up.  
  6. I wish you knew that it’s also ok if you don’t have your life figured out right now.  There will be lots of opportunities to change your mind about your path, to change your major, to switch schools, to fall in love with a hobby, etc.  I’ve known I wanted to be a teacher since the 3rd grade, but that is rare. And it’s ok if you don’t know yet.
  7. I wish you knew that my only regret in college was that I didn’t study abroad in a Spanish speaking country.  I let our family’s lack of resources stop me. I could have researched financial options, etc. I’ve never had the opportunity to do that again, and it’s the only thing I regret.  But, I learned from that experience that I don’t want to live with regret.
  8. I wish you knew that if you focus on learning the content in this class, your grade will follow.  It doesn’t always work the other way around.  
  9. I wish you knew that for my New Year’s Resolution this year, I set a goal of reading 52 books (1 for each week of the year).  I enjoy reading for pleasure and just finished my 32nd book this past weekend.
  10. I wish you knew that this room is a safe place for you to make mistakes and learn.  And I hope you know that if you need an adult to talk to, you can speak to me about anything.  Also, every adult on this campus is a mandated reporter, so if we suspect that you are in an unsafe position, we are obligated to report it.  This isn’t to get anyone into trouble, but it is to guarantee that the children in our care are safe. I want you to be healthy and safe.


I am fortunate to be your teacher this year.  I look forward to working with you and seeing everything you accomplish.


Mrs. Verti  

{On the notecard I will give you, please write a few statements you wish your teacher knew about you.  Start each statement with “I wish my teacher knew….”. If you want to make it anonymous, that is ok. }

Even though many of my students responded anonymously, I will not share what they wrote here.  Many were funny, heartbreaking, sad, hopeful, and a lot of other descriptors.  Some described past experiences with math that were good and/or bad.  Some described outside responsibilities that are mind-boggling for any high school student. Some describe hopes for their future and fears about leaving home in the next few years.  All seemed open and honest.

I am now officially 1 month into my 17th year as a classroom teacher.  It’s getting more difficult to learn another group of names and more difficult to muster up the motivation to grade those quizzes, and I’m feeling older and less sure in my ability to relate to some of their interests in music and shows (lol)… but as I think about the next 13ish years of my career, I still love my job and wouldn’t want to miss 1 day with my students.

Whose Classroom Is This?

This picture appeared on my FB memory feed earlier this week of my teacher desk from 6 years ago. It was back to school and I was ready for my students.

As I look at it now, it makes me wonder what is communicated to a student who walks in on the first day. I’m the teacher. This is my work space. I need all this space to do my important work.

Fast forward to what my room looks like now… (ignore the clutter, my Marie Kondo post before and after will be coming soon😉).

But this classroom isn’t really for the important work I’m going to do here. And this space isn’t about me.

This space is for my students and the important work they are going to do in this room.

Who’s classroom is it? My name is on the door, but this is their classroom.

Writing Letters of Recommendation: Some Advice for Seniors

As a math teacher and a non-senior teacher, I only get a few requests for letters of recommendation per year.  When I taught Honors Pre Calculus, the volume was a little higher, but still nothing like the senior English teachers I know.  Either way, the experience usually goes something like this…

Student walks into my classroom.  “Mrs. Verti, do you mind writing me a letter of recommendation?”

Me.  “Of course not.”   There’s usually a long pause in which the student waits, so I start to ask a series of questions.

  • Where are you applying?
  • When do you need it by?
  • How do I get the letter to you? (Usually, they are not my student anymore so I don’t see them daily.)
  • Is it through commonapp?
  • I need you to fill out this form first, and hand them a form.  This helps me write a better letter with information about you that I don’t know.  Sometimes a student mentions that they have a resume for me and I will tell them to attach it to the form.

I created the form because it is really difficult to write a letter of recommendation without knowing anything about the student other than they completed homework assignments, participated in class, got an A- in my class, and played a sport.  When I write a letter with that information, it is going to look like every other letter that is sent out.

Over the years, the questions on my form have evolved.  I realized that as much as it helps to know what my students did in high school, what I really want to know what they want to get out of college and what they plan to do in the future.  So here are my questions now…  I have them submit these on a google form.

  1. What’s your email address? (Too often students ask me that are no longer my students and I don’t have an easy way to get a hold of them.)
  2. Last name, First name (I ask this because I want to spell their name the way they prefer.)
  3. Will you require an electronic submission of this letter? If so, where? (So many times they ask and don’t give me this information.)
  4. What schools are you applying to? (I’d like to know this!!!)
  5. What year’s were you in my class? (Please help a teacher out.  I’ve been teaching for 16 years and they are all blending together now.)
  6. What activities were you involved in at Bonita? (I like to know what they were involved in at Bonita because I know there are things they did that I was not aware of.)
  7. What activities have you been involved with outside of Bonita? (This one always surprises me.  Our students are involved in so many community activities, church groups, volunteer, educational, jobs, sports, etc.)
  8. Do you work? where? how long? (I think this is an important question because it shows that students can juggle responsibilities.)
  9. What do you want to study in college? Why? (I want to be able to talk about your major!!!)
  10. What is something that is going on in the world that you are passionate about? Explain.  (This question sets students apart.  The passionate ones have a fire and a drive and will finish the degree and change the world.  And if they aren’t passionate about something, then I try to have a conversation with them to find their passion.   Because if they can identify that, then it will give them a direction.  Also, I can write one heck of a letter if I can include this.)
  11. What problem in the world would you solve in your chosen field of study? Explain. (This goes with the question above. )
  12. What do you want to be “when you grow up”? Why?  (If they have an answer, I like to include this in the letter.)
  13. What accomplishment are you most proud of? Why? (Many times this is non-academic.)
  14. Have you ever had a difficult situation you’ve had to overcome? What did you do to get over it? (Listen, life is going to be difficult.  College is going to be difficult.  Many students know already how to get through the difficult things and thrive and so they show that they will do the same at university.)
  15. What do you want to get out of college?  (Do you like the size of the school? Big? Small? Small classes? Diversity? Big city? Small city? Study abroad? Sports program? etc.)
  16. What did you learn from your experiences in extracurricular activities or high school?  (What are the life lessons these taught you?)


To all the seniors in high school about to approach a teacher with a letter of recommendation request:

We want to help you.  Please come prepared.  Feel free to bring your resume as well as answer the questions above.  Know when you need the letter by and how you need to submit it.

If the teacher is not currently your teacher, provide the teacher with a way to contact you when they are finished.

Also, when you get accepted and decide on where to go, go back and let the teachers know.  Not just those who wrote you letters, but also your freshman math teacher.  She really wants to give you a “high five”.


Your freshman math teacher

I haven’t been listening to the flight attendant

(Taken Saturday of Memorial Day Weekend at urgent care. Ear infection diagnosis & week 1 of cough.)


I looked at the doctor last night and sighed, and said, “you know what? I’m the parent that puts my kids oxygen masks on before my own. I’m last.”

And it’s really showing. I won’t be able to put my own oxygen mask because I keep putting everyone else’s on first.

Yesterday was the first Monday of summer. So I went to the doctor last night for a lingering cough that’s lasted a month. And then while I was there, I also asked about my left wrist cause it’s been bothering me for a month, and my high blood pressure. (Because working teacher mom, I push all my stuff until summer or fall or winter or spring break. Except NCTM was my spring break this year. 😂)

So as I’m explaining all the things to the doctor and he checks my records and listens to my breathing and coughing, he asks me some questions.

“Your wrist has been hurting for how many months?”

“Well, since January, possibly longer. I distinctly remember not being able to do downward dog at the Sunrise Yoga session at NCTM in early April. But it had been bothering me way before that.”

He looks at me over his glasses.

He refers me for an Occupational Therapist and we move onto the topic of my blood pressure.

Now I’ve seen Dr. Talithia Williams TED Talk on being an expert on our own data and know I need to be taking my blood pressure at home, but I can’t seem to figure out where to fit it into my daily routine. So the doctor says, come back in two weeks for a BP read. I say I will and will also take my blood pressure with the monitor they sent me home with after my blood pressure was high after having my 2nd daughter.

So then I had to say out loud to him that since I’ve been on the Amoxicillin when I was diagnosed with an ear infection two weeks ago, I’ve been inconsistent with my BP meds and Lexapro. 😬. Saying that out loud was like full on admitting I really don’t plan on putting the oxygen mask the plane will have because I have two perfectly formed lungs. 🙄. Out loud.

So not only is my BP elevated but I’m not taking my meds consistently and, although the nurse was nice and weighed me in kilograms, Kaiser gives you a printout with the number in lbs.😳 no I won’t tell you that number.

I’m sharing this because I have a feeling I’m not the only person that is putting themselves last on their list of priorities. Because now my body is sending me some pretty big signals that I need to be my big priority for a while. It’s great that it’s summer, but I will need to figure out how to transition prioritizing myself in the school year.

Survival mode isn’t cutting it.

This is me putting on my hypothetical oxygen mask first. And reminding you to do the same. Please.

(I live in Southern California, about 40 minutes give or take without traffic from the beach. This is my happy place. Who can be upset with the sound of the waves? I need to bring this more into my school year. 2019-2020 goals)

Teaching Math has a Learning Process

In the fall of 2004, I was a newly married, second year teacher, at a new high school with a new prep: Geometry. I hadn’t taken Geometry since freshman year of high school and so I was relearning most of the theorems and terms and processes.

At a meeting early in the year, the Geometry teachers in my department were discussing an upcoming test and one veteran teacher scoffed and said in a scornful tone, “I can’t believe anyone would teach these angle relationships without forcing their students to write the Geometric Equation before substituting the values. They’ll NEVER be able to do proofs if they don’t write the GE’s!” Everyone around the table nodded and agreed and added that they couldn’t believe someone would not teach the GEs.

So here I am, a first year Geometry teacher who hasn’t taught anything higher than Algebra A (the first year of a two year Algebra 1 sequence), who doesn’t know anything yet about teaching Geometry. I’m not gonna lie, but the conversation made me feel stupid. Like I should have known such an obvious thing. I also learned that this particular group of teachers were not people I could safely turn to with my pedagogical questions.

What I understand now is that encouraging the students to write a geometric equation helps them understand the various relationships between different figures. It also helps students make a connection between Algebra and Geometry. And yes, it helps them write proofs.

But, for all you new Math teachers, you aren’t stupid for not knowing that. How could you know that when you’ve never taught the entire course? And then taught it again? And again? And then taught the next course in the sequence?

Knowing math is one thing, but teaching math is an entirely different thing. So, don’t feel like you aren’t a good teacher because you don’t know all the “obvious” things you see the experienced teachers talking about in the department meetings or on Twitter.

Join in the conversations and ask the questions. And find the people who will help push you forward.

Mother’s Day. A Personal Story

One of the few redeeming features on Facebook lately, for me, is the memories. It’s like opening a time capsule every day and getting to relive moments, both big and small.

Today, I found this.

Back in early May 2010, I was 8 weeks pregnant. After 5 years of infertility, I was pregnant and hadn’t shared the news with anyone. You know, everyone says to wait until you’re out of the dangerous first trimester, just in case something happens.

We scheduled the DR appointment to hear the heartbeat for the day after Mother’s Day. Mother’s Day was exciting and excruciating because no one knew but my husband and my mom. I wanted to share our good news with everyone.

The plan was to go to the DR, hear the heartbeat, get an ultrasound picture, take some flowers to the gravesite of my husbands mom who had passed in January of 2009, and then go to his dad’s house to share the news.

When the DR took the ultrasound and said “there’s no heartbeat and no baby”, it was devastating. It was a blighted ovum. So there was implantation, but somehow the body sensed an abnormality and didn’t develop the baby. It counted as a successful pregnancy, but that was small consolation.

We left the appointment, went to my MIL’s gravesite to leave flowers and still went to my FIL’s house to tell him our news. I think I posted this Bible Verse then.

A few weeks later, I had to take a few days off work to have a D & C and then that was it. I wasn’t pregnant anymore.

It’s a lot easier to speak of this event on this side of it. With two beautiful girls who call me mama.

But… when I was going through it, when I didn’t know if my prayers to be a mom would be answered, there was so much pain and fear and confusion. Infertility is a lonely journey and no one likes to take about it much. Which is why I share my journey to mama hood. You never know who needs to hear it.

I especially share on Mother’s Day because this is a difficult day for those who struggle with fertility. The questions and comments from well meaning friends and family and acquaintances are hard to bear today.

Here’s a Mother’s Day greeting to all the mamas. To the women who dream of motherhood. To those waiting for news of a foster placement. To those who want to adopt. Those that are in the middle of the infertility roller coaster. To those who conceived on the first try. To those who don’t want their own children but love all the kiddos in their lives fiercely. To those whose babies are leaving the nest. To those whose babies are in heaven. To those with grand babies.

Happy Mother’s Day from one Mama to another.

‘‘Twas the last class before state testing…”

”Twas the last class before state testing and all through the school…” that’s all I got. I’d like to be the teacher that composes the funny poem based on the Christmas Eve poem I only like a few lines from. But I’m not.

Listen. Tomorrow, my juniors are taking the math CAASPP. And my freshmen, sophomores, and seniors are being shuffled elsewhere for a few days. And the juniors have been English testing for what seems like months and we’ve been talking strategy and had pep talks and celebrated and we are all tired.

On this, my last day with them before testing, I really don’t think there’s much I can do more to get them ready. They’re as ready as they’re ever going to be.

I had this on the projector as they walked in.

Today, I wanted them to have fun, in a mathy way. I also wanted them on the chrome books so if one of them was acting funny, I would know today and not tomorrow. I wanted them relaxed and doing math.

So we started with Desmos Polygraph: 3 dimensional shapes. My students are in Integrated Math 3, and it was an opportunity to discuss vocabulary in the third dimension. And also plant a few seeds with “who’s Katherine Johnson?” Or “I’m Isaac Newton!”

I paused them exactly three times in the first game.

Pause 1: To discuss vocabulary. Because there was some tension around the question “is it a rectangle?” And “you have to ask me a yes or no question !”

Pause 2: me. “Hey guys! You know my 7 year old daughter who goes to Roynon? Her teacher did Desmos Polygraph with her second graders and she thought the kids were so concerned with who they were playing with that they weren’t paying attention to good questions. And we thought it would be fun if her class and you guys logged into the same game at the same time and played with each other! What do you think?”

So when they heard that they all thought that was a great idea and forgave me for pausing them. I think.

Pause 3: this last pause was to tell them we were done playing.., groans… and to go back to and login to the next code. “Yay!!!”

The second polygraph we played was on scatter plots. I didn’t tell them that is what they were and they immediately said “this one’s going to be difficult!” So after some time, it gave us an opportunity to review some scatter plot information.

The third Desmos activity was an activity I built about Parent Graphs and Transformations. They needed some extra practice on this and I prefer to use a Desmos activity on this than a worksheet. They didn’t have enough time to finish and I made it due Next Friday, May 3. (Whenever I assign anything online, I give some time in case students don’t have Internet access at home.)

So that’s how I spent my last day before testing. I wanted them to know Math is fun and we had fun. 💚

Big 30’s

When my eldest was 3, she came up with a with a phrase to describe the space between two numbers.

From the age of 3 until 3.4999999, you are called “little 3”. And once you turn 3.5 and older, you can call yourself “big 3”. She intuitively understood that she was 3 for a long time and wanted to have a more precise way to describe how old she was. Because she also understood that there was a BIG difference between just turned 3 (practically a 2 year old) and almost 4 (a grown up woman).

And some ages are so magical, they change you. This happened the second V turned 4. Gone was the threenager that pouted and whined and fought us on everything. Overnight, she became a lovely, polite, curious and helpful person.

So when V was “big 4”, she became a big sister. And then, much to my delight, she described her new baby sister as “little zero”.

Where am I going with this?

All my life, up until this point… up until I was “big 38”, I’ve not had a backbone. When I pictured my career in the future I never pictured myself as an administrator because I’m not good at the difficult conversations. I never counted myself out, I just knew maybe as I grew in wisdom and age, that might come.

I am now little 39. During spring break I had the pleasure of attending NCTM in San Diego.

And I came back on fire. I was ready to spread the word that mathematics is for all and that our job is an important one. I came back with ideas I wanted to immediately use in my classroom. But I also came back with ideas to help affect real change in my district.

As I was telling someone one of my ideas, they commented that I was being feisty and they liked this side of me.

It dawned on me that inside, I felt different than the Claire of before. I felt confident and convicted. And I laughed and told my friend, “I just turned 39. It must be because I’m almost 40!”

So, as I look forward to this last year in my 30’s… big 30’s as my daughter would say… I hope there are continued changes within me. I hope I grow in confidence and purpose. I want to see where these internal changes take me. I’m an advocate for the students in my district and the teachers I work with. I’m a math evangelist. Will I go into administration? At this point I don’t think so. But I’m a leader in my small pond. And, I’m going to continue help grow the math culture we have in our district.

And I’m in my big 30’s. Not quite 40… but definitely NOT 29.