Math = Love: August 2018

Sunday, August 26, 2018

Eight Lettered Squares Puzzle

I ran across a new-to-me puzzle last night, and I had to stop everything and try it out. Then, I had to make my husband stop everything and try it out with me. Math puzzles on a Saturday evening. Yes, we are THAT family!

The puzzle comes from The Little Giant Encyclopedia of Puzzles by The Diagram Group (affiliate link). The book has been around since 1996, so there are several super-cheap copies on Amazon.

The puzzle that caught my eye was the 82nd (of 318) puzzles in the book. The premise is simple. Take a rectangular piece of paper including eight letters. Fold the paper so that the letters end up in alphabetical order, one on top of the other.  No cutting allowed!

Source: The Little Giant Encyclopedia of Puzzles by The Diagram Group
I immediately opened up Publisher and got to typing up the puzzle. This is what I came up with:

The husband and I cut out our rectangles and started folding.

Here was my thought process:

Hmmm...this is fun.

Nope. This is impossible. 

Wait. This is just like Manifold (affiliate link)! FYI - as I write this Amazon is having a SUPER DEAL on Manifold. Only $2.92! (Be careful before clicking purchase to make sure this deal is still a deal!)

If I can do Manifold, I can do this.


I can't do this.

I think I can do this.


Meanwhile, the husband is still folding and folding and folding and folding. For once, I figured out a puzzle BEFORE Shaun. This is rare. He usually solves puzzles at least twice as fast as me. I think my years of fiddling with origami may have put me at a slight advantage when it came to solving this puzzle.

One thing I realized while solving the puzzle was that I needed to find a better solution for using it with students. The way I typed up the puzzle uses one page/student.

So, I decided to type up a version with multiple puzzles to one page to make it a bit more friendly on your copy budget!
My last period Pre-AP Algebra 2 class has become a bit obsessed with puzzles over the last few days. On Friday, I had a few students ask to stay AFTER SCHOOL (ON A FRIDAY) to work on the Color Square Puzzle

I'm excited to let them tackle this new puzzle! 

Want to try this puzzle yourself or with your students? I've uploaded the full page version and the three to a page version here

Saturday, August 25, 2018

My 2018-2019 Math Classroom Decorations

Well, I've successfully taught my full week of school (plus a two day week before that) at my new old school. In case you missed the announcement a few months ago, I have returned to the high school I graduated from to teach Algebra 2 and Pre-Calculus.

The past couple of weeks have been crazy with learning how things at my new school work. My new district adopted digital textbooks for math, and there have definitely been a few unexpected snafus, but we are working through them. Sadly, this has meant that a lot of the energy I've usually had at the beginning of the year to write blog posts has been redirected towards emails to the tech department and administrators about what has been working and what hasn't. Now that things are being figured out, I figured it's time to share with you all what I've been up to in regards to my classroom!

So, what better way to start than showing you my newly decorated classroom?

Let's start with the door since that's where you enter my classroom which is really my "home away from home." 

Above my door hangs my Mrs. Carter sign that was a gift from my old school when I got married and changed my name from Ms. Hagan to Mrs. Carter.

Below that, I have two decorations. First, my We Learn Math. What's Your Superpower? poster. You can download a copy of this poster here.

Below the window, I have my When you enter this classroom... quote poster of sorts. This was one of my very first projects for my very first classroom as a first year teacher. I'm now in my seventh year of teaching, and this quote is still welcoming students into my classroom! You can download the files to make your own version of this quote here

Beside my door is one of my all-time favorite classroom decorations - my math-y welcome sign. You can find the file for these posters here

Okay. Enough pictures from outside my classroom. Let's head inside! This is the view from the door.

You just thought we were done with the door. Let's turn around now and check out the other side of the door.

Like last year, I decided to hang my GEMDAS order of operations posters on the door with my grouping symbols poster. You can find these posters here.

Above the door, I hung my pennants from the universities where I earned my bachelor's and master's degrees. Last year after I was named one of twelve finalists for 2018 Oklahoma Teacher of the Year, I received a care package from UTA that included a pennant and a scarf in my school's colors. I asked my sister to get me a TU pennant for Christmas last year so that I would be able to hang them both in my classroom. I'm super happy with how they look in my classroom!

Next to the door, I hung a copy of the bell schedule that I reformatted to fit on 11 x 17 cardstock (affiliate link). My new school has different bell schedules for Monday-Thursday, Friday, and Friday Early Release. This means a lot more different times to keep track of than I'm used to!

Next to that, I hung my Red/Yellow/Green Team Cups posters. I look forward to using these cups for formative assessment as students work in groups. It also helps me to focus on which groups need my help ASAP and which groups can continue for a bit without my immediate assistance. You can find the posters here and read more about the cup strategy here.

My classroom still has a SMART Board, but my school is slowly phasing these out. The math department was chosen to receive 65" televisions to replace our SMARTboards this year. The projector hooked to my SMARTboard still works, but whenever it dies it will not be replaced. So, I'm trying to rely completely on my TV and not use my SMARTboard this year. Maybe I should hang some posters on it to take advantage of this space...

Here's what my tv looks like.

Next to my SMARTboard, I have my posters that remind students what they need to check for when making a graph. I stole this TULSA mnemonic device from @druinok. It helps that we both teach in a suburb of Tulsa! I made the title say "Are your graphs OK?" with an outline of Oklahoma. I realize this is super region specific, but I LOVE it. You can find the download here

I was so excited when I saw that my new classroom still had a wall of cabinets. I've had this in my last two classrooms, and I didn't know how I was going to adjust to having a classroom without built in storage. Plus, cabinets are awesome for hanging posters!

My Roman Numerals poster can be downloaded here. The Naming Polynomials poster can be found here

To the right of these posters, I have my inequality and equality symbol posters. These posters are part of a larger set of math symbols posters that I blogged about several years ago. I didn't have room for all of the math symbols, so I chose these since they seem to be referenced the most.

My SOH CAH TOA posters are a must this year since I'll be teaching trigonometry as a part of Pre-Calc. I've uploaded the files for these posters here. To the right are my Includes vs Excludes posters. These posters are constantly referenced by my students! In years past, I have had students complain when I took them down only a few days before the school year ended because they were trying to reference them while retaking a quiz. They have already came in great use this year as we've been doing domain and range! Download them here.

My last cabinet decoration is my Pythagorean Triple posters. I'm hoping these will be useful in our trig units in pre-calc. These posters can be found here.

My prime number chart was a labor of love this summer. It's humongous, so you can see it no matter where you are in the classroom. Not sure how to read this chart? There's a helpful tutorial here. I will hopefully get the files for this poster up on the blog soon! 

The only wall big enough to hold this humongous poster was above my desk.

One thing I'm not used to about my new classroom is that there is only one bulletin board. You won't find me complaining, though, because this is because I have three whiteboards (31 feet total of whiteboard space)!

For my bulletin board, I decided to start the year off by hanging up my Truth Signs posters that I made several years ago.

Above the Truth Signs, I put up my Perfect Squares and Perfect Cubes posters. I blogged about these and shared the files here.

Next to these posters, you can catch a glimpse of my stellated icosahedrons that I made a few years ago from straws and curling ribbon. I found a very helpful tutorial here. (Update 5/18/2020: The original link was broken. But I managed to find an archived version of the webpage.)

I love the visuals these posters provide for my students. I even find myself referencing them!

At the end, I hung another poster titled "More Perfect Squares."

Here's the other two of my dry erase boards. I wasn't completely sure about the tv's placement at first, but it turns out it's placed perfectly.

Next to the dry erase board by my desk, I posted the parent functions posters that I stole from my husband since he's taking the next two years off from teaching high school to pursue his master's degree in applied mathematics. I will need to make a few more when we get a bit farther in pre-calc. You can download these posters from his blog here.

Students have already been referencing these posters a lot. They were a huge resource to my students when they were working on their first Desmos marbleslides challenge!

This little corner is one of my favorites. I didn't realize how many posters I had printed off in the same color scheme until I started hanging posters on this chalk board coordinate plane. I stuck a dry erase coordinate plane over the top of it and put posters around the blank space.

I've had a lot of questions about the magnetic coordinate plane. It's manufactured by EAI Education, and it comes in four separate magnets that are assembled together to make the coordinate plane. You can purchase one from Amazon (affiliate link). You can download the files for my parts of the coordinate plane magnets here.

As for the other posters, here are the appropriate download links:

My long dry erase board is meant to be the focal point of the room with the tv hanging to the side of it. I put my number line above this board. We reference this number line ALL THE TIME. I firmly believe every math classroom needs a number line! I often find my students holding their pencils up in the air to count things off on the number line. As we've been doing domain and range in Algebra 2, the positive and negative infinity posters have been especially helpful.

The number line file is from Frank Tapson. I shared a link to it here. The positive and negative infinity symbols can be downloaded here

To the left of my dry erase board, I have my TI-84 reference poster.

Above my number line, I hung the function/expression/equation poster that I shared on twitter earlier this summer. I found an image on twitter, and my amazing husband, Shaun, turned it into a poster for me. He shared the files for this poster on his blog.

Next to that, I put my posters that differentiate from Roots, Solutions, Zeros, and X-Intercepts. I printed these on 11 x 17 cardstock (affiliate link). I uploaded the files for these posters here.

Underneath my dry erase board, I put up my Greek Alphabet posters. Students LOVE looking at these posters. They come in really useful when introducing concepts such as using delta for change in regards to the slope formula in Algebra 1 and theta in Trig. You can download these posters here.

I currently have thirty desks in my room (and two of my class periods have exactly thirty students). So, I have my desks arranged in six groups of five. Here's what that ends up looking like. I love that there is still an open space in the center of the room. I look forward to using this space for activities! Maybe even for pulling out my shower curtain coordinate plane!

Seeing this last picture reminded me of a poster I didn't show you earlier. My clock pi sign! This was inspired by Annie Forest, and you can download a copy here.

If I missed any download links, please let me know! And, if you decide to use some of my posters, I'd love to see pictures of them in your space! I'm looking forward to sharing with you guys all the great mathematical discoveries we make in this learning space!

Saturday, August 18, 2018

Twos to Nines Challenges (AKA Best First Day Activity EVER!)

Day one and two are in the books! I'll share a bit more about what I did with my classes on the first two days in a later post, but I want to go ahead and share the mathematical challenge I used with my students on the first day since I have got several questions about it on twitter.

This summer, my husband and I ran across a treasure trove of puzzle books at Goodwill. We *had* to buy them. As Shaun was driving us home, I flipped through the books and would occasionally pose puzzles for us to solve together in the car. We had a lot of fun with this, and in the process I found some puzzles that would be PERFECT for use in the classroom.

One of my favorite new puzzle books from this Goodwill trip is 100 Numerical Games by Pierre Berloquin (affiliate link). If you don't believe me that this book is awesome, just take a look at who wrote the foreword. THE Martin Gardner!

You can a free peek at some of the puzzles in this book by using the "Look Inside" feature from Amazon.

One particular set of puzzles which is sprinkled throughout the book really caught my eye.  This version was based on the number two, but the book also featured puzzles for the numbers three through nine.

The task is to use exactly four twos (or threes, fours, etc) to make each target number. Add arithmetical symbols between the numbers to make every equation true. You may use plus, minus, times, and divide symbols, as well as parentheses and brackets for grouping. 

Originally, I thought about turning this into a puzzle for my puzzle table, but I never got around to it. Fast forward to this past week. I needed an activity to do on day one, and I decided I wanted to do something a bit different than what I've done in the past. For reference on past activities, check out my post on 21 Ideas for the First Week of School!

One of the messages I communicate to my students on the first day of school is that we do math everyday. I can't just say this. I also have to give them math to do on day one.

Yes, there were some groans. We carried on anyway.

My students are arranged in six groups of five, so I decided to set up six challenges around the room. The book featured challenges using the numbers between 2 and 9, so this meant that I had not used the challenges based on the numbers 8 and 9.

To introduce the task, I threw the Eights Challenge up on the TV.  (It's going to take me a while to get used to saying TV and not SMARTBoard!)

After a quick overview of the rules, I gave them a few target numbers to work towards.

Students quickly got to work. Some grabbed paper and a writing utensil. Others got out their graphing calculator or phone calculator. Still others just sat and thought about the task.

Within a couple of minutes, a student in each period would announce that they had found the answer to 10. I asked them to read me their solution so I could write it on the board.

Almost every single time, I ended up hearing 8 + 8 / 8 + 8 = 10. So, I would tell them that we needed to check their work. This was when I asked them what the order of operations says that we need to do first. Unanimously, the class would say divide. Then, a bit of panic would set in. 8/8 is 1. So, 8 + 1 + 8 is 17, not 10.

Without me saying a word, the class would start to suggest either a different way to solve the problem OR a way to salvage this attempt. It usually wasn't long before someone would suggest that we could use PARENTHESES! So, from this, I learned that we do know our order of operations. We're just a bit rusty, but I can deal with that.

After the class found a few of the solutions for the Eights Challenges, I decided to change things up a bit. I told them that now that they understood how the puzzle's structure worked, it was time to try a

Around the room, I had marked off six four-foot sections of white board space so that each group of students could have their own space for working problems throughout the year.

At each station, I had posted a challenge based on a different number.

I typed up the instructions for each challenge. My students didn't really need this since we had done part of the eights challenge as an example, but I did see a few groups reference it. One group used their dry erase marker to actually write symbols between the numbers. Good thing I laminated them!

Then, I typed up the target numbers that students had to find. I thought about making them into magnets so the students could move the target numbers around, but I wasn't sure where all magnets were. Let's just say that moving classrooms sucks. I can't find anything right now!

I ended up just taping them to the dry erase board. This worked just fine. Most groups left the numbers stationary and just wrote their solutions next to the appropriate number. A few groups did move the numbers around. The tape stayed sticky, so they were able to change the number positions without any issues. Since this activity went SO well, I think I will definitely add magnets at some point.

Each table group chose a different number based challenge to work on. They instantly got to work, and the room was soon abuzz with awesome conversations. Students were excited and joyful as they found various solutions. Students were checking other students' ideas and pointing out any issues. Lots of parentheses were being used. Were all their answers perfect? Nope. But, it's day one, and it gave me a great snapshot of where my students are starting from.

It was the first day of school and every kid was engaged. In fact, I would say this was the most engaged my students have ever been on the first day of school. This was my favorite first day of teaching EVER.

Check out this awesome group work! 

Each group was given one dry erase marker and one graphing calculator to encourage collaboration. Every few minutes, I would announce "SWITCH!" This meant that the person holding the marker needed to pass it to another person in the group. The calculator person did the same thing.

Every once in a while, I would introduce a new twist. About five minutes into the activity, I had the groups pause and look at me. I instructed them to nominate one volunteer from each group. This person was to hold their hand up so I could ensure that I had one volunteer from EVERY group. They asked what they were volunteering for. I just said "You'll find out soon."

Once one hand was up from every group, I informed the class that these students would be rotating one group clock-wise. So, each group would lose one member and gain a different member. There were a few groans with this announcement, but students complied. I was excited to try this strategy since each group was working on the same type of challenge, but no two groups had the same problems to solve. This meant that the new group member could bring STRATEGIES from their previous group, but they could not just bring ANSWERS.

After a few times of rotating a single group member, I changed things up yet again with having the entire group rotate to the next station. I did run into a few issues that I hadn't figured out how to handle beforehand. The groups assigned to the challenges based on lower numbers (2s, 3s, and 4s especially) were sometimes able to completely finish their challenge. When this happened, I did one of two things. In my smaller classes, there was often a challenge that had not yet been started. In these classes, I sent the finished group to this untackled challenge. In my larger classes, I had the finished group split apart and join other groups.

The Sevens Challenge ended up being the most difficult for my students to tackle. Often, there would only be two or three target numbers solved by the end of the class period. 

Want to try this activity with your own students? You can find where I typed up the challenges in two different formats: Google Slides and PDF. I hope your students enjoy it as much as mine! This activity had my students finding joy in solving tricky math problems. My job is done.