How I Use “Between Two Numbers”

I’m overwhelmed by the number of teachers who have asked how I use Between 2 Numbers (B2N) in my class. So this post is for all three of them and for anyone else who might be interested.

It has become one of our regular warm-up routines. (We do visual patterns and math talks, too. Duh.) Before I launched the site, I was just referring to this routine with my kiddos as a “tidbit.”

Take tidbit #5, for example. I ask three questions on Google Form, the first two are identical.

Question 1 is asking for a guess, an estimate, a gut check, a what-do-you-think.

Question 2 is the exact same question, except now, students are allowed to search the internet and use their calculator to figure out the answer. However, on a few of these entries — like #2 and #6 — I let kids know ahead of time that they may NOT search the internet but may still use their calculator. The reason is the internet readily provides the answer with a simple search.

Question 3 is always the same.

When about two-thirds of the responses have come in, I then make an announcement that I’m setting a timer for two (or so) more minutes. When the timer goes off, I ask for all students to please submit their form.

I show the class their guesses for Question 1.

In their math journals, we go over the calculations to get to the answer. Then, I reveal their responses to Question 2. (Thank goodness this class had done well on this question. On others, not so great and some downright dismal results, yup, my kids need more practice working with ratios and using the calculator.)

The site has allowed us to:

  1. Learn some fun facts
  2. Explore large numbers, imagine the magnitude of these numbers relative to other large numbers
  3. Work with scientific notation and use the [EE] key on the calculator
  4. Work with equivalent ratios

We have a friendly competition among the four classes (two 7th-grade classes and two 8th-grade classes). One of the students suggested this scoring scheme, and it’s what we use: 3 points for the class with the highest percentage, 2 points for second place, 1 point for third, and the 0 for the lowest.

Of course, Jules Bonin-Ducharme (@jboninducharme) is responsible for translating all the entries into French! (You just need to hover your mouse over the section links near the top to see the entries in French.)

I hope you can find some time to try this with your kiddos, and I’d love to hear how it goes.

Posted in General | Tagged , , , , , | 3 Responses

Send Doughnuts

I had a wonderful time working with a roomful of teachers over two days at my Grassroots Workshops last week. During a morning break, I talked with a teacher who was concerned about not being able to reach all her kids, that there was a handful of students who were failing the course, and that she’d tried everything. I said, “But you are reaching the other 25 or 30 kids in your class.” She said, “Please tell my principal that.”


Dear Principal,

Your teachers are working really really hard at this thing called teaching. The role of a teacher is not unlike that of a parent. And if you’re not a parent, then think of being a neurosurgeon or an astrophysicist, being a parent is way harder than that.

It’s practically guaranteed that your teachers have not reached all their students today. But, there is tomorrow and the day after that. Please remember that Teacher A in room 23 may not have reached all her students in the academic sense, but she smiled and said hello to Melissa, gave Joey a granola bar and Jake a sharpened pencil, laughed at Amanda’s joke.

Your teachers need your implicit trust and continued support to thrive. Show them you have their back and give them feedback frequently, but wrap each feedback in kindness, empathy, and humor. This makes all the difference in whether or not they want to show up for work tomorrow.

Some years ago, I had a principal who asked me the same question more than once, like he forgot or didn’t hear my answer the first time. He asked, “Fawn, how do you motivate kids?” I replied, “I don’t know. If I knew the answer, I’d write a book and make millions and quit teaching.” Now that I think about this, clearly he thought I’d given him the wrong answer, therefore he had to ask me again in hoping that I’d learned something over the course of two weeks.

Before I became a parent, I judged all parents. You’re a horrible parent because your child is a brat and disrespectful. It’s your fault that your spoiled kid is ungrateful and entitled. What a loser of a parent you are that your kid fails half of her classes and makes all sorts of excuses while doing so. You must be a bigger asshole than the little asshole you’re raising.

Then, I gave birth to three kids. At one time or another, honestly, more like an extended period of where’s-the-goddamn-light-at-the-end-of-this-tunnel, my own flesh and blood were disrespectful, ungrateful, entitled, jerks, assholes, whiny, rude, arrogant, mean, neurotic.

But, if you had said any of these things about my kids to my face, I’d probably stab you with a fork. I’m equally defensive as I’m protective. Until you walk in my shoes, you have no right to judge me. I’ve been a teacher longer than I’ve been a parent. One role blended into the other.

When an administrator makes a statement or asks a question to imply that his teachers are not working hard enough, it unravels the trust like pulling on a loose thread of yarn. Sure, there’s ineffective hard work, but it’s hard work nonetheless. Teachers want pretty much anything and everything to help us do a better job, but this advice or suggestion cannot come at a cost of making us feel any smaller and more unappreciated.


Dear Principal,

Please stop being evaluative, start being helpful and send doughnuts.

Posted in Teaching | Tagged , , , | 4 Responses

Green Olives

My 7th graders are working on “percentages of” problems currently, and late last night, I saw this problem on one of Don Steward’s handouts.

There are 75 olives, 40% of which are green. I eat some of the green olives until 10% of the olives that remain are green. How many green olives did I eat?

How would you solve this?

I solved it using algebra. Then, immediately, I thought, Fawnzie, since when do you use algebra to solve stuff like this. C’mon, do your rectangles.

I think of 40% as 2 of 5 boxes.

So, 75 olives must split into 5 groups of 15, so there are 30 green olives.

Then, I ate some olives to end up with only 10% of the remaining olives are green.

Well, since I didn’t eat any of the 45 black olives, so these 45 must make up 90% of the olives remaining [in the 9 boxes], so 45 must split into 9 groups of 5.

Oh, look! I began with 30 green olives, I now only have 5 green ones left, so I must have eaten 25 of them.

Okay, your turn.

There are 80 olives, 75% of which are green. I eat some of the green olives until 20% of the remaining olives are green. How many green olives did I eat?

Because if I tried to show my kids the work below, or versions thereof, a few might just shit in their pants.


Posted in Algebra, Course 2 (7th Grade Math) | Tagged , , , | 11 Responses

Global Math Week Starts on October 10, 2017

It was the summer of 2012 when I talked my colleagues, Erin and Melissa, into signing up for a week-long training in Palo Alto, California, to start a new Math Teachers’ Circle (MTC) program in our area.

It was there that I first learned about Exploding Dots from Diana White, an associate professor from the University of Colorado Denver. Diana said that Exploding Dots was developed by James Tanton — and I recognized his name instantly because I have his book Solve It and have seen many of his great videos online.

Exploding Dots is way fun! It was like playing a game [with an exploding dot machine] that became more and more challenging, and this machine invited us to make connections and explore different algorithms. And when we got to explore a fractional base, my mind was blown. Of course, we wanted to share Exploding Dots immediately at our first MTC, so here’s Nate Carlson, one of the leaders at our site, facilitating the session back in September 2012.


If you’re not familiar with Exploding Dots, you want to get in on this!

And this brings me to the Global Math Project (GMP)! Founded by James Tanton, Raj Shah, Brianna Donaldson, and others, the GMP is launching its first Global Math Week, starting this October 10, 2017. Its goal is to do what the Hour of Code did for coding, but for mathematics. The goal is to reach 1,000,000 students across the globe to do Exploding Dots! (Over half a million students in over 100 countries have already registered!)

Please register and join me and my 130 students in grades 7 and 8 to experience this wonderful and joyous content of Exploding Dots!

Posted in General, Problem Solving | Tagged , , , , , | 2 Responses

Upcoming Grassroots Workshop in December

I’m super excited to announce my upcoming Grassroots Workshops event being held on Friday, December 8 and Saturday, December 9. It’s the first time that I get to spend TWO FULL DAYS sharing math teaching, math learning, and math awesomeness with teachers.

So, if you teach mathematics (grades 6-12), please-please consider signing up! Registration does not open until October 16, but I know requests for funds can take time, and you’d want to ask before your school’s budget goes to curriculum X and supplies Y that may end up collecting dust in storage land!

Even if you live in Brussels or Shanghai, you should still try to make it because Disneyland is less than 3 miles away from the hotel. Yup! So, bring your whole family and make a vacation out of it. :)

I’m still in the classroom full-time, and this year I’m teaching Math 7, Math 8, and Coding. I feel your pain. Yes, we work too hard for too many long hours. Yes, we grade papers while we scoop dinner onto our face. We have the most neglected bladders of all humankind. We lie sleepless at night because we want to find a better way to explain concept A to Johnny and build math confidence in Mary. And I share your joy. If teaching mathematics is not a joyful profession for you, then maybe we can talk about that. We need to talk about that. Our failure is not here to shame us, it’s there to remind us to seek smarter and kinder ways to operate.

I’m truly hoping that you’ll come away from the two days inspired and motivated to make your classroom the best that it can be for all the math learners in your care.

If you sign up using this link — — then we’ll email you a pre-sale link to register before the general public and a discount code.

This is an incredible opportunity for me, and I’d be honored to share the learning with you.

Posted in General, Teaching | Tagged , , | 3 Responses

Between 2 Numbers

I created a new site, it’s called Between 2 Numbers.

From the About/Contact page:

The inspiration for this site came from John Allen Paulos’ book Innumeracy. I read the book back in 2008, but reading it again this past summer reignited the inspiration and turned it into fruition. In my lesson plan spreadsheet, I started a column of “tidbits” to share with my students; it’s filled with mathematical fun facts, latest news, and stuff you see on here. I teach middle school mathematics, and ratios and proportional reasoning make up large portions of the curriculum, so I’m always comparing stuff, like tossing my flipflop onto this big Danish clog while visiting Solvang, CA, and wondering how big or tall the person wearing such clogs would have to be.

My goal is to have at least 40 entries to match the number of school weeks.

I would love to hear how you would use the site with your students and any other feedback.

And I hope your school year is off to a great start. I get to teach 7th and 8th-grade math this year. We’re on a block schedule for the second year now, and I’m getting used to it. Be well and teach well, my friends!

Posted in General | Tagged , , , , , , , , | 5 Responses

All I Got on Classroom Management

Not enough people write about classroom management in a practical and realistic way. But this does! Helpful tips.

— Michael Pershan (@mpershan) August 9, 2017

Classroom management is hard, and what’s “practical and realistic” for one person could be entirely impractical and unrealistic for someone else to follow. Take a math lesson taught successfully at a parochial school in a class of 12 students wearing uniforms and bring it into an inner-city public school in a class of 37 students wearing skins in shades of brown, black, and yellow, and you might find that you need to tweak the lesson a bit.

You and I are two different people. You and I are two different teachers. What irks me may not even faze you. You and I can tolerate different ranges of decibels emitting from classroom activities. You like foldables, and I like baguettes.

Your students are different than mine. The humans in our classrooms are fussy and demanding and moody and social and shy and are constantly muttering under their breath I-hate-this-shit. Good luck with that lesson on factoring trinomials.

Therefore, any advice on classroom management is making huge assumptions about who you are, what your students are like, and what your admins had for breakfast. I don’t blame you if after reading a how-to book on classroom management, and you feel stuck at step 4 below.

Unfortunately, the final step of “add small details” is what you must do — like practice, fail, practice, fail, shit, practice, shit, fail again — in the classroom!

No book is gonna help you master this thing. I’m sorry. You don’t become a chef by reading cookbooks. You just gotta go into the kitchen, roll up your sleeves, make a big mess, and voila boeuf bourguignon! Or not.

But before you accuse me of writing a post that is completely useless and unhelpful, please allow me to offer just these three tidbits.

Observe your colleague.

Intentionally schedule a time when you may come in to observe a colleague whom you hold in high regard and whom you may ask a thousand follow-up questions. It’s equally important that this colleague reciprocates the observation and gives you constructive feedback. Most likely you know this colleague better than you know any author of some book, and of course, you two share pretty much the same clientele. For optimal efficiency, and if possible, choose a time when your colleague has the same students who seem to be giving you trouble. Kids act differently for different teachers.

Know what you absolutely value above all things.

For me, it’s respect. Not just respect for me the teacher, but respect for all of us in the room. I don’t always handle this gracefully when disrespect unveils itself in my room because it tops my list of all things that make Ms. Win go ape-shit crazy. But because I know this about myself, and being proactive always yields better results than being reactive, I tell my kids of my zero-tolerance for disrespect from the get-go. I say, “I need you to be respectful. That’s the only way we are going to get along in here. Before we can do any mathematics or have any fun in here, we are going to be respectful to each other.” And may God give me the grace to apologize when I am being disrespectful to my students. I find that doughnuts help them forgive me quicker.

Separate the behavior from the child.

We know this already. But there are adult assholes out there. My hypothesis is that we teachers — and parents and society at large — have allowed the adorable children in our care to morph into assholes without effective intervention. What happened? I don’t know exactly, but I do know that we tend to let misbehaviors slide for fear of hurting the kid’s feeling or that it’s not the best time to deal with it. Well, I always try to immediately find the time and will immediately tell a kid that her actions/words are not okay because while the humans are young, their behaviors are especially removed from their true selves. I’m reprimanding the behavior, but I’m keeping the kid. Being a parent for 22 years and a teacher for 26, I conclude that children are highly manipulative. Not because they think it’s a desirable trait, but because they can’t drive and have no income, being manipulative is their survival mode of choice.

A few years ago I was sitting in the lodge at CMC-North in Asilomar when someone recognized me from my Ignite talk and came over to chit chat. He was lamenting the frequency in which his students were asking to use the restroom pass. I asked some related questions to learn more before I realized that he wasn’t lacking classroom management skills as much as just lacking a good lesson.

So, there’s that, step 0 as I call it — find that great math task.

Posted in Teaching | Tagged , | 13 Responses

Long Live the #MTBoS!

Dan Meyer is calling for the retirement of the hashtag #MTBoS. He’s suggesting and going with #iteachmath or #iteachmaths instead.

I get it. I get it that #iteachmath means I TEACH MATH. I get it that #MTBoS could mean anything. I get it that Dan’s intention is no more than to simply make the math community more inviting and inclusive. After all, Dan is among the first handful of math bloggers who helped transform my teaching, and he continues to inspire and challenge my craft. I’m grateful for Dan’s work.

What I don’t get is folks saying #MTBoS is exclusive and alienating and cliquish.

This kind of statement actually hurts my feelings, like someone just said something negative about my children without ever having met them. I feel hurt and insulted because the #MTBoS that I am grateful to be a part of and the people who are in it are anything but “alienating” and “cliquish.”

That’s because I know of the ENORMOUS amount of TIME, WORK, and LOVE that had been poured into making #MTBoS what it is today.

Don’t know what #MTBoS is? Please start here:

When you’re done there, please see here:

It takes ONE click to learn what #MTBoS is.

Anna Vance’s tweet exactly expresses how I feel.


Posted in Teaching | Tagged | 32 Responses

Euclid’s Algorithm

I show my 6th graders this image, pointing out that this picture represents the two numbers 1 and 1 that I’d entered at the top.

I then ask them to give me two new numbers — any two positive integers [that are 10 or less, for now] — and the computer will draw a new picture. As each set of new numbers is entered and the corresponding picture is generated on the screen, I ask students to jot down their “I notice, I wonder” in Google Form and to draw a rough sketch of it in their journal. After a few sets of numbers, I ask students to imagine and/or draw a rough sketch of what they think the picture will look like before I hit the update button.

These are the pairs of numbers they’d asked for and their corresponding pictures, listed in the order that was asked.


I love that the kids are asking for…

  • 6, 6 after the initial 1, 1
  • 3, 8 after 3, 1 (keeping one number the same)
  • 8, 3 after 3, 8 (reversing the numbers to see if anything changes)

But, when sets 9, 9, and 7, 1 are asked at the end there, I say to the class, “Hey, what if figuring out this puzzle — which is how the computer draws the picture given two numbers — gets you a million dollars. And you get to ask for sample sketches like you’ve been asking, except that each sample costs you some money! So, make each request worth it. Let it prove or disprove your conjecture. Ask carefully.”

I love the OHHHs and AHHHs after each picture is revealed. But no one is claiming that he/she had drawn the same diagram. I pause longer for them to write down their noticing and wondering.

I now say, “You may only ask for four more sets of numbers. Remember, make a request that would test your conjecture.”

I ask a normally quiet student. She says, “10, 3.”

Another student wants to know what “100, 5” looks like.

“What about 8, 5?” I reply, “Sure, but draw it in  your journal first.” They are fully engaged. Then I say, “Now, share your drawing with a neighbor.”

I ask, “Did anyone sketch the same thing as their neighbor?” They’re shaking their heads, and I say, “That’s pretty crazy! Do you think yours is more ‘correct’ than your neighbor’s?”

I reveal 8, 5.

The last request is 23, 75.

What some of them have written [with minor edits from me]:

When we did the same two numbers the shape didn’t change but when we did different numbers it changed. Why does it divide into little parts within a square when we put 3,8? When we did 8,3 the number switched around. I wonder if the two numbers are dividing to make the shape. How can you figure out the number when it can’t divide easily. My drawing for 8,5 was one whole and 5 little squares. The 23,75 was a little confusing to me.

They’re different, they are the length and width, and when the two numbers are the same it’s just one cube. I notice that if it can be simplified, it is. Example: 6,2 = 3,1. I don’t understand 8,3, 5,9, 23,75 or 8,5. But I did notice that the smaller the parts of the shape are, the lighter shade of blue they are.

I observe that when the same numbers are entered it equals to a blue square. If the first number is bigger than 2 then it will add one more square. I wonder if you double the number for each number will it be the same shape. I wonder why for 3,8 it has one square with three parts. I observed that if you divided the first number by the second it will equal to the number of squares. For 8,5 I didn’t get the right sketch. The sketch was one square with half of a square cut in half, then in one half is has a strip that is cut in half. I wonder why it has half of a square. I think that my answer for how it figures it out is right, but I don’t know how it comes up with that picture for 8,5.

When you do 1 and 1 it doesn’t change because we tried 6 and 6 it didn’t change and if we put 3 and 1 it did change. I saw that when we did any number like 3 and 1 is 3 ones. So I think that all you have to do is divide something by something = the first number that you put in but if you can’t divide by 2 then I’m wrong. I’m not sure that I got this right but this is what I think.

For the first one 1 and 1 I thought it would be a small one by one cube. What threw my off was the 6 by 6 because the size did not change. For the 8 and 5 I drew a big block and and 5 little ones, but my image was wrong. I also wondered if the first number was the amount of shapes that would appear, but I was wrong again. I don’t understand yet. I tried looking for a pattern, but couldn’t find one.

When I tried 8,5, my answer was almost right. I had the one big square right, the half square right, but then I got the little squares wrong. I think that the way the computer does it is dividing the first number by the second number. I am confident that if you put the numbers 10 and 5 in, it will show 2 squares. When using the diagram, the second number will represent the vertical side.

What I’ve been noticing was that if you put the bigger # in the front and the small # last then it would be like a rectangle. I’ve also been noticing that if you put the same #’s it would like keep on drawing a square. So someone said what could (8,5) look like and Ms.Nguyen showed us the drawing and the I notice that nobody got it right. I was expecting something like smaller because the #’s were small they weren’t as big, but at least I tried to get it correct but I drew something a little bit smaller than that. I also wondered why when we put the same #’s together why do they all become a square that’s what I wonder.

For 5, 12 I notice that it is two big squares, two smaller squares, and two tiny squares, I thought it was going to show 1 big block and another big block but that one would be cut off at the bottom or not a whole block. I also notice that the pattern is the first number multiplied by what equals the second number and the number that is missing is the amount of blocks that is created. I thought I knew it but I don’t really get the ones with a bigger number first and the smaller one last. I thought I knew what 9, 23 was going to be but it the result was surprising. It didn’t look at all how I thought it was going to. The website is pretty cool, but one thing I didn’t understand was the placement of the small blocks and what they stand for. Like some were really tiny and some were small but I don’t know what they stand for. But I bet if someone explains it to me I probably will understand perfectly and feel dumb.

The only thing that I am sure that I know is that when the first number is larger than the second, the shape is wide and when the second number is larger, the shape is tall. Other than that I am very confused.

Then, together as a whole class, they agree on the following;

  1. When both numbers are the same, then the picture is one square.
  2. The computer simplifies the two numbers, such that a picture for 6, 3 is the same for 2, 1.
  3. When the second number is a 1, then the picture shows the first number of squares. For example, 7 and 1 would form a picture of 7 squares, and 100 and 1 would form 100 squares.
  4. The first number is the horizontal dimension, while the second is the vertical.
  5. They are all squares.

The dismissal bell is about to ring, and I want to teach forever.

Tomorrow, we’ll spend some time with one set of numbers, like 10, 3 or 8, 5. We’ll dissect the diagram. Play around with a few more. Practice sketching a few. We’ll write out the equations that go with each diagram. I’ll guide them into noticing the size of the smallest square in relation to the two numbers.

I found this investigation at underground mathematics. The site describes itself as having “rich resources for teaching A level mathematics.” From what I understand, “A level” means advanced level mathematics consisting of core modules ranging from quadratic, logarithms, geometric/arithmetic series, differentiation/integration, etc.

Perfect for my 6th graders who continue to torment me with their arithmetic atrocities, such as, 3² = 6 and 5 ÷ 10 = 2.

While the original task is scripted for older and more advanced students, I found in it what I needed to make it rich and appropriately complex for my 6th graders.

Hail, Euclid’s algorithm!

Posted in Course 1 (6th Grade Math), Math 8, Problem Solving | Tagged , , , , , , , , | 10 Responses

Community Circle

We have Core time with our homeroom students — mine are 8th graders — for 3o minutes at the end of each day. Core is our SSR time, but ELD students are in ELD during this time.

Once a month, however, we use this Core time to do a Community Circle (CC). We’re in our first year of implementation, and because my kids have shown genuine engagement in CC time, we hold it almost every Friday.

I normally pick one or two questions/topics for us to go around and share our answers/thoughts. Questions such as, “If you could be any animal, what would it be, and why?” and “What is your favorite food?” are light-hearted and fun.

But, if the topic gets any deeper than that, then I’m pretty much a wreck.

I don’t know what the hell is wrong with me.

I cried when talking with my students about my father, about my son, Gabriel, about the time when I ran away from home.

I get all choked up at workshops when I speak about a specific student.

Just last week, our school invited Kaiser Permanente to put on a play called, Someone Like Me, for our junior high students. It’s about adolescent bullying awareness, and one of the characters had written in her diary that she wanted to kill herself.

The thought of one of my students ever contemplating suicide makes my heart ache, my chest heavy, my head throbs. After the assembly, we were instructed to hold a CC with our students back in our classroom, but I was too emotional to even talk. Luckily, my colleague was there, and I’d asked her to facilitate the discussion.

I don’t want to know what my kids tell their parents when they get home. I wouldn’t be surprised if it went like this, “Jesus, Dad, Ms. Win cried again in our community circle today. And we were just talking about Jell-O.”

Oh, my God, that reminds me. One time — in the evening of our school’s Continuation Ceremony some years ago — a student pulled her father toward me to introduce us, “Dad, this is Ms. Win, she cried just the other day because she was afraid we girls would get pregnant.”

Seriously, I’d signed up to teach math. What is all this crying bullshit? I want to be a badass teacher, and badass teachers don’t cry, for Pete’s sake!

But, there’s still hope for me because one of my student’s moms tweeted this:

Posted in Teaching | Tagged , , | 3 Responses