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 student.desmos.com 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.

#DebateMath: Day 1

If you ever have an opportunity to see Chris Luzniak speak on Debate Math at a Conference, I highly recommend it. I didn’t see him at CMC South because my friends Patricia Vandenberg and Matt Vaudrey were speaking at the same time on Bring Peace to your Pacing Guide. And I didn’t see him speak at the CPM Conference because there were already two colleagues from my district in his session, so I thought I’d get the information later from them, and went somewhere else.

Then, on Tuesday after the CPM Conference, I brought a former student who is getting a math credential to observe Patricia teach an Integrated Math 1 lesson, and we walked into her second day of Debate Math. The Chapter they were in was all the Congruent Triangle Shortcuts. I was blown away by the arguments Patricia’s students were making. The students seemed to use the sentence frames “My claim is….” and “My warrant is…” to stand confidently and share with the class.

One of the things I noticed immediately was that Patricia’s students used academic language and correct mathematical reasoning in their warrants which gave clout to their claims. And I think the students felt this because their body language standing up and stating their argument reminded me of a lawyer in court.

Another thing my former student thought of was that the debate math sentence frames could be used to have the students justify a statement while solving a problem. There was a point that the students were finding the missing leg of a right triangle and they had set up 3^2 + x^2=5^2 and he leaned over to me and whispered “Oh my gosh, you could have them do a Debate Math statement to explain how they set that up!” 😳 Immediately, I could see the possibilities for everyday lessons. (Thank you Patrick.)

After I witnessed that 1 lesson in Patricia’s class, I knew I had to have my students debate math. Patricia shared with me how her day 1 went so that I could try it too. (She used some different questions than mine below. )

The debate information to get them started:

So on day 1, give your students some generic, non math topics to debate. This will allow them to practice the sentence frames “My claim is” and “My warrant is” in a low stakes, easily accessible way. Also, it’s fun.

I gave my students 30 seconds to think, and write before sharing with their team. (They sit in teams of 4.). Then I did a whip-around. (A cooperative strategy where each team shares 1 thing.) I told my students that I needed one volunteer from each team and that on the next topic, I would ask for a different volunteer and they wouldn’t know what that topic was.

I went first.

“My claim is that Daniel Tiger’s Neighborhood is the best show on television. My warrant is that it teaches me how to talk to my 2 year old when she has a meltdown at the grocery store. ”

The class burst into laughter.

Students shared their favorite shows. I heard Friends, Family Guy, Seinfeld, Jeopardy, Spongebob, the Office, and a bunch of shows I’d never heard of.

Second question. Same routine. Think time. Write. Share in teams. Whip around.

Groans. “I don’t drive. ”

I glance at that student. “My 7 year old daughter has an opinion about this. If you ride in a car, you have an opinion too.”

The younger students needed help knowing which freeway was which number, but soon there was a buzz.

My claim is the 10 freeway is the worst freeway in Southern California. My warrant is that there’s always traffic no matter what time of day. ”

“My claim is the 57 is the worst freeway in SoCal. My warrant is that where it merges with the 60 it always creates a backup. ”

“My claim is that all the freeways are the worst. My warrant is they all have traffic. ”

These were clearly Southern California kids.

On to question 3.

I explained to them that I wanted to know about middle school because I really didn’t want to hear how I was their favorite teacher 30 times.

This question really got the students talking. When it was time to share, they were jumping out of their seats.

The warrants I heard were all heartwarming.

“He believed in me. ”

“She always let me make up tests.”

“He was always cracking jokes. ”

“I learned so much in her class. ”

Topic 4. I saved the toughest for last.

The class oooooooohed at this one.

“What if we are in the middle?”

I told them they had to choose sides. At this moment in time, where do they stand on this debate?

For this one, since the debate was binary, I had the “yays” go to one side of the room and the “nays” on the other. I had them share their warrants with each other and choose three they thought best represented their side.

Believe it or not, there were students who chose the side to get rid of social media. The warrants?

– cyber bullying is on the rise.

– teen suicide is rising too.

– its a distraction.

– quality of life was better without it.

– it’s addicting

– it’s not really social interaction

– one student argued he’d never had social media and he was proof it’s possible to live without it.

Arguments for keeping it?

– all the people who work for the social media companies will lose their jobs. (?!?!?)

– it gives students a platform and an opportunity to voice their thoughts and opinions. (Think Parkland teens)

– a way to stay in touch with friends and family

– use it to learn and for school

I was impressed with their arguments on both sides. Most students admitted after that question that they were in the middle of the issue and could see both sides of the issue.

After these 4 topics, my students were ready to debate math. But I will leave that for another post.

A little over a month has passed since this initial debate lesson. I finally got to see Chris Luzniak speak on Debate Math at NCTM. And he’s writing a book on Debate Math that will be coming out next year!

I’m finding as a teacher, it’s easy to find moments in a lesson where a debatemath moment emerges. I think like Notice and Wonder, it’s going to be a simple addition to any lesson I already do but with maximum impact.

Notice and Wonder tapped into my students curiosity and observation skills. Debate Math harnesses their desire to share their thoughts but in a constructive way. Once you use these with your students it’s simple to add into any lesson.

Baby’s first… Desmos!?!?

Baby’s firsts are so important to new parents. And with first born children, we document them and share them, too.

I’m sure everyone celebrates Baby’s first Pi Day, am I right?

But this mama is a math teacher. And when my mama circle and teacher circle overlap, it’s like the best Venn Diagram ever.

I love Desmos. I love the graphing calculator. I love the activities. I love Polygraph. I love Marbleslides. I love it so much I bought the socks and the shirt and put the sticker on my chrome book. My students have asked me if I’m sponsored by Desmos. (I’m not, but I wouldn’t turn it down! I tell them we are all sponsored by Desmos. )

In my district, I am fortunate to be a teacher and a coach. And I’m also a parent. My daughter is in 2nd grade at Roynon Elementary, the elementary school a block from where I work. I try to tread lightly as a parent-teacher. But math is my thing, and it’s really important to me. I don’t want to step on toes or make a teacher feel like I’m interfering in their classroom. So each year, I introduce myself. I let them know I’m one of the secondary math TOSAs and then wait.

This year, I’ve had lots of math conversations with my daughter’s teacher. She even invited me in to do a Clothesline Math lesson with her. So recently, at the parent teacher conference, I brought up Desmos because I was going to be co-presenting about it with Matt Vaudrey at the CUE Conference in Palm Springs. We had been looking for elementary math Desmos activities and I wanted to share them with her.

So today, my daughter’s teacher sent me a message that she was going to try the Kitten Desmos thing. (Desmos Polygraph with 16 kittens.)

I couldn’t wait to pick my daughter at after school care.

Me: “your teacher told me that you did Desmos in class today. ”

Daughter. “Yes! We did.”

Me: “I love Desmos and have my students use it all the time. I’ve met the guy who invented Desmos. ”

Daughter. “You did? Is he a kid?”

Me. “No. “. 😂

Daughter. “What’s his name? Where did you meet him?”

Me. “At all the math conferences I’ve been going to this year. His name is Eli. Can you tell me about what you did on Desmos today?”

Daughter. “Well, there were all these pictures of kittens. And another team across the room picked a kitten and we had to ask questions to find out their kitten?”

Me. “Oh? What kinds of questions did you ask?”

Daughter. “Is your kitten Orange? Is your kitten have gray on it? Is the background have gray on it?”

Me. “That sounds like fun. Were you able to figure out their kittens?”

Daughter. “Sometimes.”

Me. “I do that game with my students. Did you ask if any of the kittens were cute?”

Daughter. Looks at me like I’m not right in the head. “No mom! They’re all cute!” Like it’s so obvious. 😂. She’s 7 and I’m getting used to this look. 😂

So then we talked about questions that wouldn’t work and would work.

Does your cat say “woof woof”? Is your cat asleep? Can you see the tail?

Me. “Is your cat a tiger?”

Daughter. “You could ask, does your cat look like a tiger?”

Daughter. “It was so fun! But mom… why did she have to PAUSE us so much?”

Me inside:

Me. “Oh? She paused it!? What did she do when she paused it?”

Daughter. “Oh, you know. Teacher talks! I didn’t want her to pause it! I wanted to play longer!”


That’s exactly my High School students response when I pause the activity.

So now, this math teacher mama is entering in a date in the baby book.

4-10-19. Baby’s first Desmos Activity. 💚💚💚💚💚

Classroom Culture

I changed my seating chart in August 2015 from this…

Search results - Google Drive.clipular

to this…


If you are curious about that journey, you can read about it at My Journey from Rows to Groups.

One of the biggest changes I’ve noticed is how changing the furniture arrangement and then incorporating more cooperative structures has changed my classroom culture.

I’ve been teaching since fall of 2003.  I would frequently ask students to pass back papers and they would always bring me back a stack of 5-6 papers of different students that they did not know.  And this frequently happened even at the end of the year.

What kind of culture did I have in my classroom those first 10-11 years, if there were students who did not even know the names of all the other students?

That means, there were students sitting in my classroom, who WERE NOT KNOWN BY EVERYONE IN THE ROOM.

That is NOT acceptable to me.  It’s not what I want for any of my students, to feel invisible at school.  School is a place where they spend 1/3 of their day.  As a parent, it’s the last thing I want for my daughters.

We live in a culture where our students are “connected” (supposedly) now more than ever.  But are the connections they make on social media and via texts, enough?

When my students come into my classroom, I want them to feel like they are seen and heard by both myself and the other students in the room.  So that when they leave my room and walk across campus, there are 36 students that know them.

Check out this video below.  I took this on Monday: the Monday returning from Spring Break.  This is my FIRST PERIOD class of Integrated Math 3 students.  They have math first period.  (Do you get my point?)  The volume was soooo loud, I had to get out my phone to record this reunion.  The tardy bell had not even rung yet, and they were greeting each other and talking and sharing.  (Our tardy bell rings at 7:40 AM.)

This is the  Class Culture I want.  And I want them to do some math.  But first, I want them to be in a community that sees them and values them. Thanks for coming to my TED Talk.

(PS.  Yes my desk is a mess.  I need Marie Kondo to come and bring joy and peace to my classroom. LOL)


What’s your favorite thing to teach? (Besides students of course)

I have a confession to make. I love math, but I don’t love teaching all the math topics. Polynomial long division, factor trees for simplifying radicals, hyperbolas, and the formulas for chords and secants and tangent lengths of circles.

Last weekend, I was fortunate to attend the CPM Conference in San Francisco, and meet some new people and have lots of conversations about math. Julie, a #MTBoS friend who I finally got to meet in person, asked me what is my favorite thing to teach? The answer was easy: trig. Specifically, the unit circle and everything about the unit circle.

But this got me thinking, what would be in my list of top 10 things I love to teach or do with my students ? (Oh, and I’m an introvert and this is a great conversation starter at any teacher conference.)

10. I taught Geometry for so many years. My second year of teaching, I bought this workbook (it was 2004 and the internet wasn’t a great resource yet).

There was an activity in which you fold a dollar bill into an equilateral triangle, and then unfold it. The diagram you end up with has so much in it. I loved to do this activity on a minimum day because it didn’t feel like they were doing math, but by the end of the period, they could easily tell me 100 true things about the figure.

9. In Geometry, using graph paper to help students conceptualize area and the area formulas.

When they piece together the area formulas for parallelograms and triangles… the look on their faces. When they finally make sense of something they already knew, it’s my favorite thing.

8. http://www.visualpatterns.org/

Specifically, pattern #106. I was stumped the first time I saw this pattern. I don’t want to give anything away, but the number of ways you can describe how this pattern grows is breathtaking.

I love visual patterns because there is always a low-floor and high-ceiling. If is teaching with these where I saw the power in multiple representations to describe the same thing, gives you a more complete picture. My Algebra 1 students at the time, could confidently discuss if a pattern was linear and discuss from the table, graph, equation, and scenario. And they were better at it than my pre calculus students.

7. Using tables for everything in Algebra 1 after we switched to Common Core. The first year my students look at a table of a linear, quadratic, and exponential function and discussed rate of change, I was floored. I had some students do rate of change twice on a quadratic and discover that the “second slope” as they called it, was constant. They didn’t believe me when I told them that they’d just figured something out I didn’t learn until Calculus.

6. Transformations of parent functions with graph dancing. Because dancing is awesome and anytime you can get them up and moving is better than sitting and writing. I stole this from my Alg 2/ Pre Calc teacher.

5. Doing a table to explain zero power and negative exponents. Especially when it’s with a student who was just taught the rule, not why. So 2^1=2, and 2^2=4, and 2^3=8. Then 2^4=16. 2,4,8,16, what’s the pattern? As the exponent increases 1, you multiply 2 to the last on. So 2^5=32. 16•2=32. If you look at the sequence backwards…. 32,16,8,4,2… the pattern is division of 2. Or multiply by (1/2). So the next number is 2^0=1. 2/2=1. And then 2^(-1)=1/2 and 2^(-2)=1/4.

4. For years, I played Deal or No Deal as a culminating activity with my pre Cal students at the end of permutations, combinations, and probability unit. I started by making my own “briefcases” with notecards and progressed to a free version of the game on the Internet. It was the most fun day of the year. And no one ever went home with a million dollars.

3. Reading “the Dot and the Line: a romance in lower mathematics” to my students on Valentines Day. I haven’t done this in a while. I missed Valentines Day, maybe prom?

2. Desmos anything. Marble slides. Polygraph. Desmos graph. All of it. The amount of self checking and exploration and learning and connections my students are able to do with Desmos each year is phenomenal.

1. The Unit Circle. I taught Pre Calculus for 10 consecutive years. There are so many patterns and discoveries in that thing. I was still finding more the last time I taught Pre Cal a few years ago.

So now I’m curious. What are your favorites?