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Last year this student claimed to hate me. This year this student seeks me out when they are frustrated. (Don’t you love how much your students love you once you are not their current teacher!) Several weeks ago this student skipped their math class (out of frustration) can came to the math center where I was working. I was not on my game that day and did not realize they were skipping until the end of the hour. After talking through their frustration about not being able to do math, I told the student to chill out for the remaining 10 minutes so I could work with another student. 2 minutes later this is what I saw the student doing on their phone.

The student was solving a math puzzle I had posted in the hallway several days prior. This student had no idea I had posted it. This student claims to hate math, yet they took time out of their passing time to snap a picture of the puzzle so they could solve it later. When I saw this I shouted, **“HA! I caught you. You do like math. Look, I told you to just chill and you are choosing to do math.”** This student smiled at me and just nodded in agreement. Yes! I love days like this.

Sometime at the beginning of February I decided to do a little experiment. My gut told me that all of us love solving problems. I wanted to see what would happen if I posted a math problem in the hallway. Would anyone stop and try and solve it?

Since returning to the classroom 4 years ago I’ve become much more of a minimalist in my classroom. If I am not referencing the things on the was regularly and/or no one is regularly looking at the things on my wall, then I don’t put it up there. I have removed a bunch of ‘visual noise’ that use to clutter my walls. If I was going to put something in the hallway, then I wanted people to look at it. The walls of my school are littered with tons of announcements I am not sure anyone ever looks at. I did not want this to be one of those things.

So I started with 2 basic rules for posting math puzzles in the hallway of my school.

- Whatever I placed in the hallway needed to be something that could be solved fairly quickly. Our passing time at our school is 4 minutes. I wanted it to be possible that at least a few students could solve the problem in 4 minutes or less. I was totally OK knowing that it may take many others much more time. I wanted problems that invited all learners in.
- I also wanted to post puzzles that did not require the students to do much writing.

Following those 2 rules I posted this puzzle – in color – on an 8.5×11 inch sheet of paper. Someone I know posted this problem on Facebook – I think it may be from the Brilliant app -though I’m not sure. I did NOT include my name. There were no prizes announced. I have never told my classes about this. I just posted it mid-day on a Tuesday.

Then I watched. Nothing happened. At least, I did not see many people looking at it. I was a bit disappointed.

The next morning, I added this sign to the top of the problem.

Things changed immediately. Every time I looked in the hall I saw single students or groups of students or even staff stopping and looking at the problem. I saw students pointing and explaining. At times I watch as students argued over the problem. I heard students excitedly calling over other students so they could explain the solution. They had no idea I was watching. They were solving the problem out of the pure joy of solving things. Lesson learned. If you are going to post a puzzle – make sure you challenge others to solve it.

Click to view slideshow.Then this happened.

Student’s insisted on writing down the solution. So I laminated the ‘Can you solve this puzzle?’ sign. This stopped the writing.

Other teachers would excitedly tell me they caught students in their math classes who do not do well looking at the puzzle.

A couple of weeks later I changed the puzzle. This time I used a puzzle I use in math class with my students.

Most people who solve this problem the first time (including a lot of math teachers) shout out ’16’, When students are solving it I tell them after a minute that the answer is NOT 16. They groan (I’ve just ruined what they thought for sure was the answer) and keep working on it. I use this problem in class to have a discussion about the importance of watching the details in the problem. My student teacher can be often heard in class reminding students to ‘watch for bananas and coconuts’ as they solve other problems. When I posted this problem in the hallway I decided to add a post-it note to the puzzle.

Then this happened.

So I replaced the post-it note with a Desmos post-it note.

Not even the power of Desmos could stop people from writing down the correct answer. So I begged for them not to share the answer in my next post-it note.

That did not work either – people kept writing down correct & incorrect (15) solutions on the post-it note. . Finally I laminated the statement. Problem solved.

Almost everyday I catch people looking at, talking about the problems I post. They do it more when they think no teachers are around. I knew it. At some level we all love doing math. The structure of the classroom can take some of that joy away – even with the best teachers.

**So what are my next steps?**

- I want to continue to look for ways for math to be fun for students. What can I do in my classroom and school so students engage in math out of their free will. I do have one other way that I am doing this in my classroom (PLAY TABLE) that I will blog about soon.
- I want to frequently (more frequently than I currently take the time to do) change these problems out. To do this I plan to collect 30-60 good problems, print them out & laminate them so I always have a puzzle ready to go. Here are some potential problems I may use, including the 2 pictured above. (Word Doc: Math Problems for hallway fun )
**I would love it if you send other problems my way.**Tweet me @Saravdwerf or email me at SaraVDW@gmail.com. Remember, I want problems that can be solved relatively quickly & not require students to write much down. - I want to continue to use classroom tasks that build off of students curiosity.
- I want to continue to watch students and observe when they engage in math naturally. My students have the answers to my questions. I just need to be open to watching for them. What I’ve noticed so far is that students of all achievement levels are trying to solve these problems.
- I want to remember that despite what students are telling me – I never know what they are doing when I am not looking. Even my most challenging students may be out there somewhere right now solving a math problem I gave them on their phone.

As always, I love hearing from you! Let me know what you think. What have you done to encourage students to engage in mathematics outside of the things you do in class?

p.s. After posting this blog, I was reminded that the inkling to do this started last summer during Twitter Math Camp when I introduced Dave Sabol to Jucy Lucy’s at an iconic Minneapolis Restaurant. During our lunch he was telling me about posters he had used the prior year in the hallway’s of his school. He was looking for a new idea and somehow the idea of ‘Which One Doesn’t Belong‘ problems came up. I had wanted to do something similar for a while, but he made it happen at his school right at the start of the school year. Check out Dave’s resources at his blog for WODB posters from his school.

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In training’s with teachers I’ve (highly) encouraged them to focus on the distributive property with students and/or use area models for multiplying binomials. I’ve told teachers to stop using the term FOIL altogether in their classrooms. Honestly, I’ve often shamed them for even thinking about the term FOIL ever.

For those of you not in the know….FOIL is an acronym to help organize students thinking about multiplying out 2 binomials. ‘F’ is for multiplying ‘F’irst terms….and so on…For example:

So what changed my mind? What humbled me? What have I been doing wrong?

**NOTHING!**

You’ve been ‘FOIL’ed if you believed for one second I’ve changed my stance on teaching the FOIL method on my classroom.

For those of you reading this post on another day than today, April 1, 2017 – This post was just to see if people would actually believe I’ve changed my stance on teaching FOIL. **I have not.** I do not think any teacher should teach this method to students. It is a limited method that only works for multiplying binomials. It turns one type of problem where students can use a property they already know – the distributive property – into a ‘trick’. What happens when students multiply a binomial with a trinomial? FOIL will not work, but a deep understanding of the distributive property will.

One thing I may have done in the past is ‘shame’ teachers who use it. I could have been kinder as I told them why I don’t use it and what some alternatives are. Luckily there is a great book from Tina Cardone and the #MTBoS community you can download for free at Nix the Tricks. In the book Tina talks about dozens of math tricks like FOIL you should eliminate from your classroom. She tells why to eliminate them and what to replace them with. Check it out. I promise you will learn a lot.

Since I’ve personally stopped using ‘FOIL’ I’ve noticed my students are so much more proficient at using the distributive property in all situations they encounter. I personally love building off of the partial products/area model for multiplication that students use in elementary school and also use the area model for multiplying polynomials of any size.

The are model or box method can grow with students as opposed to limiting them. I try really hard to not teach rules that stop and don’t work as some point.

I try really hard to not teach rules that stop and don’t work as some point. NCTM has a great article for free on ’12 rules that expire‘ (a.k.a. – things you should not teach). Check it out. Math Rules that Expire from NCTM

This week I met up with 20+ math teachers from around the Minneapolis metro area. Over drinks and chips & queso I heard a teacher almost apologize for her students drawing in the curved arrows instead of using the box method to multiply polynomials. She almost ashamedly said “I let them do this instead of using the box”. In her mind the curved arrows where connected to ‘FOIL’ which she felt was bad. Her shame made me sad. I don’t want any of us to feel that the choices we make in our classroom we have to apologize for. My great hope is that we as teachers continue to be learners. That we take information from our classroom and talk about it with a community of math professionals. We are better together. My hope is we encourage one another and don’t shame one another. I hope that all our students will see multiplying polynomials as an opportunity to use the distributive property.

**True Confession.** During my first years of teaching (20+ years ago), I had a phenomenal wall display on FOIL. I had cleverly constructed the entire method for multiplying binomials out of tin foil. Yes tinfoil for FOIL> So clever. The time and energy I spent on this display did nothing for my students to understand conceptually what they were doing. What a waste (though I was applauded by principals and many other adults on this display in my room). I could look back in these days with shame. I don’t. I use this Maya Angelo quote often to comfort me in my work as a teacher. I leave this with you to encourage you in your worn work.

Happy April’s Fool Day. Next year I will do a post on why I think teaching ‘cross-multiplying’ is the best thing we can do for students.

Go forth and do better. I’m on spring break – so look for several posts this week.

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This quote is well known and has been adapted to include many other groups over the years. (You can read more about the original quote HERE) Though I have loved the message of this quote for years, it is this week, yesterday and today at the start of a new presidency that I find myself so distracted wondering how I need to change where I invest my time, resources and energies moving forward. I find myself distracted from wanting to think about math, math teaching, and so much more and instead worrying about my students, my neighbors and my friends.

I post this post today publicly asking you to hold me accountable in how I stand up on behalf of those around me. There are so many others that have and will write things about what is going on in the world more eloquently than myself. I thank them. You move me to act. I am simply stating to any of you reading this that I commit to stand up and speak for those around me who are being treated unjustly. I am not sure what will be next in my journey. I plan to spend time daily in prayer and meditation seeking truth and guidance as I move forward. I am though also committed to action. It may be quiet. It may be loud. It may be public or private – but all I know for sure is my silence and inaction is wrong and a sin.

I do not support the bans put in place in the last days. I will not stay silent. I will reach out to those in my community with love. I will stand with them. Thank you for listening to my public commitment.

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**UPDATE (2.12.17)**: I created a valentine postcard for all my students on Tuesday. If you want to create one similar to mine, all you need is 1 sheet of card-stock, 8 pixie sticks and 8 adhesive dots, & a colored pencil to create 4 nerdy valentines for your students. Here is the Word Doc if you want to edit and make your own: valentine-card We love it because the front is a bit angsty and the back is a bit sappy. Enjoy.

Update 2.13.17: My former student teacher who now lives in the middle of Superior National Forest near the Canadian border could not find pixie sticks and adhesive dots to make her cards – but made equally lovely ones with smarties and a hot glue gun. Check them out.

Desmos is where it is at for Valentine’s Day. Enjoy using the Math-o-Gram site to send a Desmos Valentine via facebook, twitter, email or to post a link anywhere. Share the site with your students so they can send 2.14 desmos grams to one another. You have 5 options to select from.

Many people have created equations that make hearts. Again, DESMOS is where to use them. If you’ve taken 3 minutes to sign up for a FREE desmos account you can log in and just hit ‘save’ for each of thee links and then you can find them always in the future by clicking on the 3 horizontal parallel lines in the upper left corner. Here are just a couple I have saved. Sierpenski Triangle in Hearts 1 red heart Flower to Heart Click on link and then click ‘save’ once you get to desmos.

Also, check out this amazing new video from @DesmosDude and his youtube channel (bonus – @DesmosDude is from MN! we do great stuff in this state) It’s a Desmos love story set to 80’s themed music. Love. This is a must watch!

Check this card out – if you got a bit of time you could make a Pop-Up Sierpinski Valentine Card. Amazing.

Check out this youtube video on how to make a Two-Mobius-Hearts. Who doesn’t want to do arts and crafts in math class.

Last year I shared told my students that if they had someone they were secretly in love with they could tell them secretly using one of these 2 math equations.

- The first equation requires you to see only half of the story. Check out other versions of this equation below.
- The 2nd equation, I tell my students, tells you if your true love is good enough for you. If they can’t solve it then they will never know the truth. See below.

For some of us Valentines Day is lonely. For those students I shared this sad math story with them.

or in GIF form….

Here are just a few fun things I found connecting mathematics to Valentine’s day or Love or Hearts or Cupids or…. Enjoy.

First a Which One Doesn’t Belong with HEARTs from the amazing (and Minnesota’s own) Christopher Danielson. (Seriously, have you bought his book yet? No, click here and do it NOW – so good)

If you are teaching ‘**ratios**‘, this video entitled ‘Bad Date’ is perfect this week.

If you are teaching (or have taught) ‘geometric mean’, this video will teach you how it is used in identifying good matches for your valentine. (video is called ‘inside OK Cupid’)

Brian Marks, over at Yummy Math, posted a bunch of resources related to Valentines last year. **Check out his resources HERE.**

Check out this Valentine Brain Teaser at NCTM’s site.

If you are wanting to send a math valentine to your loved one, your mom or your child – here are a few pictures for inspiration.

Click to view slideshow.Check out this post from Jennifer Cook who had her students make math valentine cards. She got the idea from Matt Vaudrey’s post **HERE.**

Another youtube video Valentine for Math Nerds

Or try these 15 math pick-up lines out on someone….

Or throw this GIF in your slides:

After writing this post, I search twitter before hitting ‘publish’ and found this… Last year the amazing Annie Forest posted some resources. Some of which overlap with mine. **Check it out HERE** (and if you are not following her on twitter, do it now, go, run, click follow)

Do you have a math valentine/love resource to share? Send it my way and I will add it to my list. Twitter @saravdwerf or email saravdw@gmail.com or post below.

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Here are some questions I have after watching this…

- Is there truth in what Simon is saying? My gut is there is. My sister works as a Dean of Students at a college. We often find ourselves talking about the changes we’ve seen in students over the last 25 years of our careers.
- If there is truth, what is my responsibility as a math teacher?
- I know my job as a math teacher is not just about teaching math. I am called to make sure my students are prepared for the world they will enter after HS. How does what is in this video change what I focus on in my classroom?
- What is the role of technology, social media and phones in my classroom?
- What can I do to build my student’s self esteem?
- Should we be talking to students about what Simon talks about in this video?
- How do I help my students build deep and meaningful relationships and practice this skill set? Should I invest more time in my math classroom on this?
- What is the role of impatience and instant gratification in my math classroom?
- Honestly, after watching this I am personally committed to using my cell phone less around the adults in my life.

I’d love to talk to you about your thoughts. Let me know what you think after watching this. Happy Martin Luther King Jr. Day.

Note: Simon followed up the video above with this video response on New Years Day 2017.

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I get asked pretty frequently for help finding math activities for all levels of math. I know why I get these emails. I led K-12 math for 5 years in my district of 200 math teachers and answered these emails all the time. I also sent frequent emails with all kinds of cool things I found for the classroom. The problem is though for the last 4 years I’ve been back in the classroom full time and I don’t have the same time to research for others the cool stuff out there. That said, I will often send something on to those that ask if I have the time. I’m sure that Chris and Colleen (the people who currently hold my old job) get these emails too.

In the last couple of years my response to these emails has slowly changed. Instead of sending something that I find, I send a response like the one I sent today…

I have changed from giving links to activities I find to sending quick emails telling them how to find what they are looking for. Really, it only takes a few minutes to find great resources for the mathematics classroom. Last summer I blogged about some tips for finding resources **HERE**. I am finding I need to add to this blog post with a bit more information. So this post is part 1 of 3 I will do in the near future.

I sent the advice above without testing if it would work. So after I sent the email I made sure by taking my own advice. I timed myself to see how long it would take to find something great on ‘piecewise functions’. Here is what I did..

- I went to my favorite search engine, Google, and entered the following into the search engine: What came up were pages of possible activities to use. ( By the way, I prefer google’s search engine to the search engine at teacher.desmos because I find activities and also things I can use on the online graphing calculator & videos &…). The key to using google is to add the word ‘DESMOS’ to your searches if that is what you are looking for. The favorite thing I found was the the first thing on page 2 that came up on my search (I am not going to give it to you, you need to go find it yourself, I promise you, you will learn more if you do it yourself and it would only take you 2-3 minutes – go now).
- If I don’t find anything at google (and sometimes even if I do), I go to
**teacher.desmos.com**and sign-in (If you don’t have a FREE account yet, what are you waiting for, SIGN-UP now. It only takes a few minutes). I then search Desmos site for what they offer. Not only do Desmos employees write cool stuff here, but they also look at all the stuff we all make and ask for permission to tweak it and add it to their search features. Here is what I searched: Note: at teacher.desmos I search first using just the one math vocab word I am most interested in. My search brought up 4 things. The introductory POLYGRAPH activity being the best. - Go to twitter (create an account if you need to, it only takes a few minutes) and search ‘piecewise desmos’ on twitter’s search engine. After I did this
**my favorite things I found came up**(by the way, this is my #1 thing I do usually, but I made it #3 since many the people who ask for my help are twitter phobic). Do this and you will find a link to ‘Harry and the purple dot’ and ‘Piecewise functions’ by Nick Corley in the first few tweets that came up. Great stuff. Go find it for yourself. Once found you can click the 3 vertical dots on the right and ‘Copy and edit’ to make these activities your own. - If #1, #2 and #3 bring up nothing, then I tweet the following: I tweeted this at 5:12 pm today. I always hear something in 24 hours or less. (usually way less). It is really important in your tweets to tag the math education on twitter using the hashtag #MTBoS and also tag @Desmos on twitter. I promise, even if you don’t have a ton of followers like I do, someone will answer you. The online math community is where 80% of everything I use in my classroom comes from these days. They are welcoming and want to help. Here are the responses I received after tweeting this out:
- At 5:30pm I received this tweet: with this picture.
- & an hour later I received this tweet from Nick (who I mentioned above…

After spending less than 6 minutes (remember I timed myself) online doing #1, 2, 3 and 4. (note: this 6 minutes included opening up 20+ links I found – I could have opened more…) I found lots and lots of Desmos piecewise activities I could use if I were teaching this topic right now. If you want to find what I found, invest 5-10 minutes yourself. Or if you have a different topic you want to find something on, do #1, 2, 3 and 4 with a different topic.

**Note #1:** I still share activities I find interesting with my coworkers (both at my school and around MN) pretty often. I am not done doing this. If I can help I will. What I do want is others to help me find great things.

**Note #2:** The 3 things I do above do not include my 2 favorite ways to find activities. To do what I do, you need to invest a bit more time into twitter and the #MTBoS community. II will share these things in a future post.

Note #3: An email I love getting from people is the following….”Sara, Can I buy you a coffee sometime soon and you help me learn about twitter and the #MTBoS community?”. I will always make time for you (If you can find your way to Minneapolis) and will happily get you involved in the best place to be now days for math PD and resources.

Peace & love Until, next time…..

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In the early 90’s I taught a curriculum (IMP) that changed me & defined my core values as a teacher for the rest of my career. (I am working on a ‘Love letter to IMP’ post sometime). At the start of IMP year 3 (11th grade), the first unit problem was one I am using as an introductory task with my Advanced Algebra students tomorrow (20+ years later). Here is the task, titled ‘Fireworks’: fireworks-task-sheet

My Goal with this task is to review what students should remember from their 9th grade Quadratics Unit (vertex, intercepts, max/min….) within a contextual problem. In the 90’s I did not have Desmos to help make this task more visual. That changed last year & this is why I LOVE Desmos.

**THIS** is the Desmos graph we used with our class after students struggled with the task. When you open the graph it is pretty basic (only labels on the axes).

To tell the ‘Fireworks’ story we (my colleagues & I) click open the equations in the graph one at a time, saying something like the following….

Resulting in this Desmos graph:

Then we click more equations in Desmos and say…

The animation looks like this (but animated!):

Then we click some more Desmos equations and add mathematics vocabulary connected with quadratic functions (note: for this we turned off the background images first).

The graph then looked like this:

Thank you Desmos for helping me and my students visualize the ‘Fireworks’ task. Love you!

**Note:** Before the ‘Firework’s’ task we taught a 3-day arc of lessons on Fawn Nguyen’s Duck Pattern that I highlighted in my **Number Talks Post**. Following the 3-days we used **THIS DESMOS GRAPH**, to determine if the 5 quadratic rules students wrote were equivalent. (later we will prove equivalence algebraically). We also added quadratics vocabulary to this graph as well. (again, click through the equations-scroll down-& see what happens)

Well, I did it. This post is only 416 words. (way less than my normal posts which are always 1000-3000 words). To be fair, I cheated and incuded words within the images I used. I am working on someday doing posts that are 100-200 words with only 1-2 images/links. (this may take me a while though – I have a lot to say and feel like I need to include it all in every post). LOL.

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I teach Advanced Algebra (Alg 2) and last year (2016) I started with this visual:

I then reminded them of the story of Karl Friedrich Gauss we had looked at the first week of school where as a child he had quickly found the sum of the numbers 1 to 100. . Students went on to write rule for the expression by noticing the patterns Gauss noticed.

In the fall I followed this up with a number talk about a ‘football’ pattern.

Together we found a rule for the extended pattern and introduced the tern ‘triangular number’. We talked about this equation being equivalent to the one Gauss had found. On the first day back in 2016 we reviewed all of this and I told them 2016 was also a triangular number. I asked them how many rows of dots were in this picture – instead of counting them we replicated the equations we had built in the fall using a smaller pattern.

We annotated the pattern and wrote the rule.

Students then threw the quadratic rule (it was so great that this rule was quadratic as that is what we were currently studying….Love it) into Desmos to find the number of rows of dots in the number 2016.

It was a great start to 2016. Now I want to do the same in 2017.

So tomorrow is the start of 2017. This is what I am doing tomorrow….

- First I am going to ask them what they know about the number 2017. Most likely the fact that it is a ‘prime number’ will come up. I am going to use this time to deepen students understanding of ‘prime numbers’. I may use these GIF’s.
- I will then share a bunch of other geeky facts about 2017. I tell students that math teachers are geeky and at midnight on twitter & facebook this is what I found people tweeting about 2017. For example look at all of these……Click to view slideshow.
- One of the tweets I plan to use tomorrow is this one…..I will be teaching my students about ‘i’ and complex numbers soon and I want to create a ‘subaru effect’ for my students so they are looking for ‘i’ and/or the term ‘complex numbers’ in the next month or 2 in my classroom.
- My favorite tweet was this one from David Radcliffe (from St. Paul, MN – love my MN math geeks). His tweet caused me to pull out a piece of paper and figure this one out. I was pleasantly surprised that this pattern was quadratic. Love that the unit I am teaching tomorrow is on quadratic functions. I will be using his puzzle this month in my classroom.

I pulled out Desmos to check the work I did on paper and to solve his challenge. The answer is 2017! - This is the 8.5×11″ sign I will post outside me doorway tomorrow. Yes, it’s intentional that there are 17 boxes of 2017. You can print it out using this word doc. Enjoy. happy-2017

- Check out David Radcliff’s amazing blog about the number 2017. He has tons of geeky number facts you can use tomorrow.
- From Matt Parker

- From Alex Bello’s – a math challenge.
- From Brian Marks & Yummy Math. Is 2017 prime? task.
- Do the
**2017 Challenge**with your students with either The Math Forum or Denise Gaskins! - Here is what Wikipedia says about 2017!

Lastly, here is an image I will be using in my classroom this week for sure. In 2017 I am excited about the opening of ‘Hidden Figures‘. You should be too.

I will be walkin’ into 2017 like…

**Happy New Year to all my friends and family. Love you all.**

p.s. My Christmas card blog post (and videos highlighting a decade of my homemade xmas cards) is coming, but is a bit late. Hopefully later this week. Until then, Which One Doesn’t belong?

Kind of like the credits at the end of the Ferris Bueller movie…I have one more 2017 thing for you. Here are other ‘mathy’ dates in 2017.

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