Teaching Integer Operations Activities and Strategies

I love teaching integers! I think it's probably my favorite concept to teach. I've already blogged about the Wii activity I did with my LLD class to introduce real-life integer situations, so I thought I'd write this post about the rest of the activities and strategies I use to teach integer operations.

Since this is my LLD class, I really take my time to ensure my students understand each operation before moving on to the next. I try to give them as many tools and strategies as possible to help them feel successful.

Addition with Chips

I spend a few days on integer addition. One integer addition strategy that many teachers use with students is two-sided chip manipulatives. When I started teaching, this was my go-to activity for integer operations.

Then I discovered the Interactive Integers iPad app, which I've blogged about previously. Unfortunately, our tech people were re-imaging all of the iPads, so they were not available to use. I had to fall back on the two-sided chips.

I knew from previous experience with my OCR classes that my LLD class would have a hard time remembering which color was positive and which was negative, so I wrote + and − on each side with a Sharpie.

I begin by demonstrating on the SmartBoard using an infinite cloner for the chips so I can drag out as many as needed, just like the app. We discuss what a “zero pair” is and first relate it to money:

“If I had $1, but owed my friend $1, how much money would I have left? Right, $0!”

I repeat this a few times with different amounts. Then I go around the room asking each student what their favorite number is. For example, if they tell me 7, I say, “So positive 7 and negative 7 equal...?” and wait for them to answer 0. I repeat this with each student.

Now it's their turn. I write an integer addition problem on the SmartBoard and have students write it on their individual whiteboards. Then I give them chips and ask them to set up or model the problem before attempting to remove any zero pairs.

I'm a real stickler for having them set up their chips neatly and lining up the chips under the correct number on their whiteboards. Once I know they can model the problems correctly, I have them start the “game.”

“Can you make a move and take away a zero pair?”

Once they do that, I ask, “Can you still make a move, or is your turn over?” They like thinking of this as a game. Once they cannot make any more moves, they count the remaining chips to find the final answer.

Addition with a Number Line

Then we move to the number-line method. I explain that most students end up liking this method better. It's one they can use anywhere because, as long as they have scrap paper, they can draw their own number line.

I even show them that if there is a coordinate plane somewhere on a test, they can use the x-axis as a number line. All of my students' desks have these stick-on number lines from Nasco.

On the SmartBoard, I use a template with “start” and “move” boxes and a number line.

I give students communicators with the same number line and plenty of empty space at the top for them to write the problem. I have them draw a dot at the start number, then use the move number to travel the correct number of spaces in the correct direction.

I remind them that negative means move left and positive means move right, just as negative numbers are located to the left and positive numbers are located to the right on a number line. Most students pick up on this strategy very quickly.

Subtraction

Once we finish addition, I tell students that I do not like subtraction, so we're going to change subtraction problems into addition problems. That allows us to use either of the two addition strategies we just learned.

I use the slogan “add a line, change the sign” to teach them how to do this.

After students work with subtraction for a day, I give them a mix of addition and subtraction problems. They must pay attention to the operation and determine whether they need to change subtraction into addition before using one of the strategies.

This is where I see the most difficulty. Students may forget to change subtraction to addition, change the operation but forget to change the sign of the second number, or attempt to use “add a line, change the sign” on an addition problem.

I make sure to give them plenty of practice so they become comfortable switching between addition and subtraction. For my LLD students, I kept the operations separate on the integer-operations quiz and clearly indicated which problems were addition, which were subtraction, and when they should use “add a line, change the sign.”

One way I provide practice with integer addition and subtraction is through a friendly game of bingo. Students love the friendly competition and don't mind doing the work when it's fun.

I use BingoBaker.com to create my online bingo games. I also blogged about Bingo a few years ago.

Multiplication and Division

On to the easy part! I explain the rules for multiplication and division and tell students that they can use a basic four-function calculator for the fact part, but they must use the sign rules to determine whether the answer is positive or negative.

I emphasize that for addition and subtraction, they should use the number line rather than the calculator. For multiplication and division, they cannot use the number line and should either solve the fact mentally or use the calculator.

I still saw a few students try to use the number line for multiplication and division or the calculator for addition and subtraction, but not too many!

Integer Operations Centers

On Wednesday, we completed centers for review. This is my favorite day! The centers included:

1. Integer Operations Cubes
2. Integer Operations Notes and Puzzle
3. Math Practice iPad App

Students had about 10 minutes at each center. Partners worked together on the cubes and puzzle, while students worked independently on the app.

Integer Operations Quiz

While students worked on the study guide Thursday and took the quiz Friday, I left the integer-operation rules on the board for them to reference.

Now that the unit is over, I will allow my students to use scientific calculators so they can use the negative button to complete calculations. Integers are such a big part of the eighth-grade curriculum, so I want students to understand that working with negative numbers is not the same as working only with positive numbers.

At the same time, I'm realistic. Even if students correctly learn the procedures for solving equations, they may still get an incorrect answer if they make a mistake with the integer operations. Calculator use is also included in each of their IEPs.

Looking for Integer Operations Activities?

These hands-on resources give students extra practice with adding, subtracting, multiplying, and dividing integers.

View Integer Operations Cubes View Integer Notes and Puzzle

"Pre-Reflecting"??

One of the new practices I have this school year comes from the ideas I got from my summer reading.  Before I begin a new topic this year, I am "pre-reflecting" (not sure if that's a real word or if I just made it up).  I am more cognizant of the prerequisite skills my students need coming into each topic and thinking about how I can incorporate more real world applications to help my students better relate to and understand how it applies to their lives.  Sometimes, with math topics as abstract as they can be at times, this is difficult.

George Couros quotes Chicago-area teacher Josh Stumpenhorst in his book The Innovator's Mindset: “Innovative teaching is constant evolution to make things better for student learning.”  George rephrases this as “What is best for this learner?”  The students in my resource classes come to me with all ability levels, so this is a question I am constantly asking myself about each and every one of my students every day.

Most "reflections" are done post-lesson, looking back at what went wrong or right.  I'm calling this "pre-reflection" because I'm looking ahead at what I can do to make the lessons I'm teaching this week better for my students before I even teach them.  I'm rethinking activities I have used in the past and modifying them to fit my new teaching/learning model.  In the past I have used a lot of technology, but after being a part of the amazing #IMMOOC group the past few weeks, I realized innovation is not all about the tech that you use.

I’m defining innovation as a way of thinking that creates something new and better. Innovation can come from either "invention" (something totally new) or "iteration" (a change of something that already exists), but if it does not meet the idea of "new and better," it is not innovative.   - George Couros

So innovative doesn't necessarily mean I have to throw tech at it.  It just has to be a change that makes it better than it was before.  My goal is to get my students from point A to point B and sometimes I don't need tech to do that.  I've incorporated more hands on materials this year to help my learners.  As Katie Martin said during last night's #IMMOOC live session, "You can't measure innovation but you can measure student outcomes".  I've narrowed down and fine-tuned my list of go-to tech apps this year and I'm only using the ones that really help my students understand the concepts better and improve their learning outcomes.

Innovation is something new and better.  This blog started out as me writing about all of our 'tech adventures in a middle school math class', but this year is a turning point for this blog, hopefully new and better.  I was even thinking of changing the name of it but couldn't come up with a good title.  George says "change is an opportunity to do something amazing".  I hope I'm making my students math experience this year at least somewhat amazing and memorable.

My new approach to "Do Nows"

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“Do Nows,” “bell ringers,” “warm ups”... whatever you call them, I've been wanting to change my daily routine for a few years now. But up until this year, my Do Nows always consisted of a quick review of what we learned the day before. While there's nothing wrong with this approach, and I occasionally still revert to it, what I've been wanting to do is use this time to focus on improving my students' number sense and mental math abilities.

It's something I've always wanted to work on with them but could never find the time while trying to “cover” (my math supervisor hates that term!) the required curriculum. This summer, after reading a lot about building number sense and daily routines, I decided the perfect place to build this practice into our daily routine was to steal the time from the Do Now time.

My Favorite Number Sense Resources

My three favorite resources for these new routines are Jessica Shumway's Number Sense Routines, Sherry Parrish's Number Talks, and a PDF I discovered online from San Diego City Schools entitled “Middle Level Mathematics Routine Bank.”

Number Sense Routines

Number Talks

Number of the Day

The second week of school I started out with the “Number of the Day” routine from the “Middle Level Mathematics Routine Bank.” I gave my students a random number and they had to write down three different ways to express that number. At first, they looked at me like I had two heads—they had no idea what I was asking them to do. So I gave them a few examples.

Unfortunately, most of them wrote down the super easy “+1” or “×1” expressions, so I had to include in the directions that they could not use 1 as one of their numbers. The next day I gave them the stipulation that each of the three ways had to use a different operation. Gradually throughout that week I expanded the task so they had to use multiple operations in their expressions. I was very proud of one student who thought outside the box and was using exponents and parentheses!

Mental Math and Counting Around the Room

I started out the third week of school with what I thought was a fairly easy routine—using mental math to add 10 to a random number, such as 37 or 148. While most of my students found this easy, there were a few students for whom this was quite a challenge. I gave those students a hundreds chart and showed them that adding 10 just means moving down one row on the chart. After a few days, they began to understand this concept.

So after the two-problem Do Now of adding 10 to a number, we did a “Count Around the Room” activity (Shumway calls it “Count Around the Circle” in her book). They actually loved this and never wanted to stop! I ended up going around the room twice each day. Each day that week and the next I upped the ante and increased the number they were counting by to 20, 30, 40, and 50. Some days we would count forwards, and some days we would count backwards. The trickiest turns were the ones that required them to jump across a century (197 to 207, for example), but they improved on this as time went on.

Multiplication Strategies and Number Talks

The next week I changed it up and we multiplied a random number by 10, 20, 30, 40, and 50. We discussed strategies for doing these calculations mentally. I had explained to them that I wanted them to improve their number sense and be able to take apart numbers and put them back together again, so this was the perfect activity to demonstrate how that works.

We had “Number Talks” about all the different strategies they had used. This brought us into the following week's Do Nows, in which I taught them how to use the area model for multiplication so they were breaking numbers into their hundreds, tens, and ones, multiplying using our mental math strategies from the previous weeks, and putting the numbers back together again. That week I also showed them how to use the partial products method instead of the traditional multiplication algorithm. At one point we had five or six ways recorded on the board for solving one problem—being the math geek that I am, I was super excited!

Building Confidence Without Calculators

What frustrates me is that after a few weeks of Do Nows consisting of “Counting Around the Room” by 30s or multiplying a number by 20 successfully, when my students are faced with the same type of problem in the content we are currently learning, they automatically reach for the calculator for these problems. They are super dependent on their calculators, so trying to break them of this habit is going to be difficult.

I try to anticipate when they are going to reach for the calculator and head them off at the pass! Hopefully after another month or so of doing these types of Do Nows, they will gain more confidence and realize that they don't need the calculator for these mental math problems.

Wii Golf and Integers

So in the spirit of #IMMOOC, I tried my hand at being #innovative today. This year I've been trying to make a concerted effort to connect real world situations to the concepts I teach my students. Today I had a surprise for my first class - we were going to play Wii golf! A few years ago I bought Teach Math with the Wii by Meghan Hearn and Matthew C. Winner, but I never followed through with actually reading it and implementing it in my classroom.

I wanted to surprise my students with this so when we left the classroom right after the Pledge of Allegiance and headed down to the auxiliary gym where we have a really big screen TV, they had no idea what we were going to do. This is what they saw when they walked in and sat down in front of the white board:

Then I pointed to the Wii that I had set up under the TV. They were all super excited, even though they knew that somehow I would weave some math into the game. Yesterday we talked about real world integer examples, such as bank accounts, sports, temperature, and weight. So we started off today just reviewing that in most cases, negative numbers are viewed as a bad thing, but in golf, we want to see lots of negatives because the lower the score, the better.

I gave everyone a quick overview of how to use the controller and how to try to keep the ball as straight as possible. I had everyone grab a clipboard with the scorecard. The students played as one player, each taking their turn on a different hole. They cheered each other on and coached each other on how to correct their swings. After each golfer finished, everyone recorded the score on their scorecard.

After the nine holes were complete, we regrouped at the whiteboard. I modified the par that each hole had been assigned in the actual Wii game so that we would have some positives and negatives to work with. We went through each hole and decided whether the number of strokes was over par (+) or under par (-) and recorded each value in the bottom row of the scorecard.

Time flies when you're having fun, so we didn't get a chance to add up the total score. We will do that next week. I plan on introducing the concept of zero pairs and the use of 2-sided chips for this to help them with the totals.

So my attempt at being #innovative was a big success with the students. I hope this will be a memorable lesson for them and that it has helped them with the concept of integers. I guess I'll find out for sure next week when we continue our journey into the world of integers!

Exponential Innovation

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While I was on my vacation this summer in Sanibel Island, I read The Classroom Chef by John Stevens and Matt Vaudrey. What, you say?! You read a professional development book when you were supposed to be relaxing on vacation?! Well, yes, I'm a math geek, so while most people were reading trashy romance novels on the beach, I was reading about how to pump up my math lessons.

That reading, along with other conversations and books about innovative teaching, inspired me to take a fresh look at my lessons. I was remotivated to bring innovation into my classroom. I just love how educators can inspire each other! I was also lucky enough to hear Dave Burgess speak on my district's opening day that year—he was amazing and inspiring!

At the same time, I was participating in an online course inspired by The Innovator’s Mindset, a book by George Couros, with George Couros and Katie Martin. It was another opportunity to reflect on what innovation could look like in my classroom and to learn from other educators.

So I thought about one of my really boring lessons and tried to figure out how I could be as crazy and innovative as John, Matt, and Dave and make a really memorable lesson for my students. The first topic that came to mind was negative exponents. I looked around the internet to find some ideas that I could run with. One that caught my eye was from Yummy Math. I wanted to be able to relate negative exponents to something in real life that my students could understand. I liked the idea of the beanstalk story, but how could I make it memorable? My first idea, although I loved it, did not happen. I wanted to construct a giant beanstalk (out of paper mache maybe?) in the corner of the room that was so tall it went through a hole in the ceiling tiles. Instead I just made up an elaborate story about a former student named Jack who gave me some beans at the end of the year, and some slides in my Smart notebook to go along with it. (I made my beanstalks with Google Drawings—I just love that app!)

After I told my story and showed my graph, I asked my class to predict what the height of the beanstalk would be at month 6. I told them to look for patterns because math, and nature, are full of patterns. (That's my big push this year—look for patterns.) I had them all answer the question in Google Classroom. Only one student figured out the pattern and predicted correctly. We discussed how the height was changing—I had them figure out that it was changing multiplicatively, not additively. Then I showed them a graph of what the beanstalk would have looked like if it had grown additively.

I used this to introduce the concept of exponential vs. linear growth and we drew in the exponential curve and linear line. We also explored what this data would look like in a table and then we graphed with Desmos. I pointed out that one equation had an exponent and one didn't. I also noted that things that grow exponentially grow faster than things that grow at a linear rate—we compared the heights at month 5 in both graphs.

The next day, I had the class do a Desmos card sort with the concepts of exponential and linear. I was happy to see that most of them had remembered the concepts from the beanstalk lesson! Then I finally got around to introducing negative exponents. In Google Classroom, I asked them to predict what the beanstalk's height would have been at month 1 if I had thought to measure it. This time a few of them saw the pattern and figured it out. From here, I gave out my guided notes. I taught them how to use the calculator to find exponents with the ^ button. I had them complete the positive exponents in the Powers of 2 table on their own. I reiterated the first point in the notes that said negative exponents are reciprocals of positive exponents so we went through the negative exponents together. Then I had them complete the next two tables independently.

After the tables were complete, I showed them my method of circling the base and negative exponent so they are aware that the negative exponent only affects the base and not any coefficients. I showed them how to "swing it down" to the denominator and leave the coefficient in the numerator. They picked up on this procedure fairly quickly.

So the first day, the beanstalk story that captured my students' attention wasn't about negative exponents, but it set the stage for the discussion on negative exponents the next day and they had a real life situation (sort of) that they could relate it to. After class the first day, my classroom aide told me she was watching one student in particular and he was really into the whole story—this is a student who rarely can focus on a lesson. After school, the student I tutor asked me if that story was real. Even though I didn't have my life-sized beanstalk prop, I think the lesson went well and the students will definitely remember the difference between exponential and linear growth!

The Innovator's Mindset

I just finished watching the 1st live #IMMOOC with George Couros and Katie Martin.  It was great seeing Dave Burgess again - he was our opening day speaker this year and he was amazing!  I started reading George's new book The Innovator's Mindset this week and I'm excited to be part of this huge learning community!  I could write about everything we talked about, but I'm going to let the my favorite Tweets from tonight's live session sum it up:

Dave Burgess on #IMMOOC Live on YouTube! "..it's not about raising test scores but raising Ss potential!"

— Rachael L. Toy (@rltoy) September 18, 2016

Change happens with grassroots movements #immooc #ecslearn @MsSandersECS https://t.co/o0O23fFIJQ

— Christine Strickland (@teachstrickland) September 18, 2016

Change can't happen all at once. Find the people that are enthusiastic and utilize the energy. @burgessdave #immooc

— Cathy Mere (@CathyMere) September 18, 2016

If what you are doing is powerful & what you know can help other people, you have the moral imperative to share it via @burgessdave #IMMOOC

— Jennifer Casa-Todd (@JCasaTodd) September 18, 2016

Yes @burgessdave it is a moral imperative to share when you're doing great things! #IMMOOC

— Jamie Dyra (@jdyra) September 18, 2016

Sharing what you’re doing/blogging about it is not egotistical, it’s helping others to learn and improve. #IMMOOC

— Caryn Trautz (@Mathtechy) September 18, 2016

"We need to provide students real world opportunities for learning in school" via @gcouros #IMMOOC

— Joel Schleicher (@joelschleicher) September 18, 2016

The irony of 1:1 schools that aren't connecting kids to the outside work or engaging them are n real world work @KatieMTLC @gcouros #IMMOOC

— Jamie Dyra (@jdyra) September 18, 2016

How are we preparing students for the real world if we deny them from using real word tools?? #IMMOOC @gcouros

— Karen McClintock (@kmcclintock5) September 18, 2016

"A lot of us are very reluctant to change." from @gcouros #IMMOOC

— Maureen Pandola (@mapand) September 18, 2016

We as teachers need to model risk taking if we want our students to embrace risks #IMMOOC @gcouros

— Karen McClintock (@kmcclintock5) September 18, 2016

Time to embrace educational changes...personalized, inquiry, project-based, student-centered learning opportunities for all. #IMMOOC

— Rona Kaufmann (@drronakaufmann) September 18, 2016

Honored to be a part of #IMMOOC tonight w/AMAZING educators, @gcouros & @KatieMTLC They inspire me!! #tlap #InnovatorsMindset

— Dave Burgess (@burgessdave) September 18, 2016

Interesting question @gcouros What would happen if schools didn't have a photocopier? #IMMOOC #bcedchat

— Laurie Meston (@lauriemeston) September 18, 2016

#immooc how do we give kids opportunities in school that don't exist? #InnovatorsMindset @gcouros

— Sue Tonnesen (@SueTonnesen) September 18, 2016

Every educator can be an innovator! #IMMOOC

— Rebecca Glenton (@MsGlenton) September 18, 2016

Love the example shared by @KatieMTLC about a Chemistry teacher teaching subject through a soap company! #IMMOOC

— Jennifer Casa-Todd (@JCasaTodd) September 18, 2016

Being innovative in the classroom doesn’t necessary mean using technology via @gcouros #IMMOOC

— Caryn Trautz (@Mathtechy) September 18, 2016

@gcouros "If you focus on the basics, your bar is low!" #immooc

— stephanie williams (@swilliams206) September 18, 2016

#InnovatorsMindset #IMMOOC 🙌 pic.twitter.com/URSJ63Y12g

— Lauren Paddick (@L_Paddick) September 18, 2016

"Innovation is moving people from their point a to their point b." from @gcouros #IMMOOC

— Maureen Pandola (@mapand) September 18, 2016

How do you convince the parents of our students that what they experienced is no longer sufficient to prepare for 21st century? #IMMOOC

— Rona Kaufmann (@drronakaufmann) September 18, 2016

"Know people's strengths and help them improve than focus on their weaknesses!" #IMMOOC

— Heather Servant (@HeatherServant) September 18, 2016

Staring with 'What is best for this learner" is crucial to all changes in education. via @gcouros #IMMOOC

— Joel Schleicher (@joelschleicher) September 18, 2016

It's about changing one thing that you do. What's one thing you could replace that would be better for your practice. @gcouros #IMMOOC

— Julie Johnson (@Jreaderwriter) September 18, 2016

"Instead of doing something in addition to what you're doing, think about how you can do something differently." - @gcouros #IMMOOC

— David Carruthers (@pluggedportable) September 18, 2016

Love, love, love #IMMOOC first session! So many great points. Build upon strengths of T's and get them to move needle. @gcouros YOU ROCK!

— Shanna Bumiller (@sbumiller) September 18, 2016

I'm looking forward to reading the next few chapters and next week's live session!

I Made It Through the First Week!

Wow, the title of this post makes it sound like my first week was extremely long and difficult.  It was not; it was actually the total opposite - I had a terrific first week!  I love my new schedule and my new students.  Actually my students are not all new to me - I've had about half of them for the past two years of summer school.

First I thought I would share a few pictures of some new things in my classroom this year, courtesy of Sarah Carter - if you haven't read her blog yet you really should - she's an amazing, creative teacher.

So I started out the first day, Tuesday, by going over my classroom procedures and expectations, but to kill two birds wth one stone, I created a Nearpod presentation so my students could not only learn about my routines, but so they also could learn how to use an application that I use quite often throughout the school year.

The next day, Wednesday, I had them get familiar with a couple of other activities that I use on a regular basis, QR code scavenger hunts and Socrative.  I set up a super easy QR code scavenger hunt where the problems were just multiplication facts, just so they could get the hang of how scavenger hunts work.  In the past, students thought they could just go to random problems or just work their way around the room without using the answers as clues as to where to go next.  Hopefully this will prevent that mistake the next time we do a QR code scavenger hunt for real.  The Socrative activity was another super easy set of questions just so they could see how to get into my "class", what the different types of questions looked like, and to see the feedback they get after they answer the question.  (I also do a lot of "Space Races", but I'll save that for another day.)

We finished up with everyone joining my Google Classroom and completing the first assignment which was an "All About Me" Google Slides - I gave everyone their own copy which had 10 slides of questions to help me get to know them.  They had a lot of fun with this one and some students got really creative with the images they chose to go along with their answers.  My homework this weekend is to read through all of them!

Thursday was probably not their favorite day because I gave them a pre-assessment.  I wanted to find out if they have the prerequisite skills that I feel they should have in order to be able to start learning the 8th grade curriculum, such as their basic multiplication facts, integer operations, exponents, one- and two-step equations, and basic graphing skills like plotting points and naming coordinates on a coordinate plane.  I haven't finished grading them all yet, but from what I've seen, I have my work cut out for me this year!

When they had completed the pre-assessment, I had them create bookmarks for all the applications we will be using throughout the year to avoid the 5-minutes or so spent searching for the applications each time we use them.  I also taught them how to shorten the bookmark so that it's just the icon without words so they can fit more on their bookmark bar, and how to make a folder on their bookmark bar for all the math applications.

I think they probably liked today, Friday, the best.  I started out class with a presentation about growth mindsets which consisted of 6 short video clips. I had been telling them all week about how mistakes are OK, mistakes make your brain grow, mistakes show that you are trying and learning, etc.  The first video was Jo Boaler explaining the scientific research about this so they didn't just think I was making it all up.  Then I had a few cutesy cartoony videos about growth mindset.

The video I felt was the best was basically an analogy between brain growth and building a rope bridge across a really high ravine.  The first time across was really difficult (just like learning a new concept), they made some mistakes along the way (one man slips as he's walking on the rope), but the more times they crossed the ravine the easier it became (they showed the two men adding more and more ropes to the bridge they were building which I related to the brain cells being connected), and then after many times across they finally had a solid foundation (they had added wood planks to walk on).  I watched my students as they watched the video and everyone was really engaged in it.

The last two videos had everyone laughing.  One was about learned helplessness - two people were on an escalator and it stops moving.  They both freak out and get frustrated that this has happened when they're obviously trying to get somewhere important (they're both dressed up in business suits).  They call out for help and look for a cell phone to call for help.  A repair man finally arrives and his escalator also breaks down.  We discussed how if this had been an elevator, their reactions would have made sense, but because it was an escalator they could have easily just walked up the rest of the way, but the thought never crossed their minds because they're so used to the escalator doing all the work for them and they aren't doing any thinking for themselves.  The solution to their problem is so obvious but they're just not looking for it.  One of my new slogans came from this video - "Get off the escalator!" - I think I'm going to make a sign to hang up in my classroom that says this.  Anytime I see one of my students saying they don't understand something before they've even attempted the problem, I'll just say "Get off the escalator!" to them.

The final video was about determination and perseverance.  A dog hears the toaster oven 'ding' and cleverly pushes a chair up to the counter, climbs up onto the counter, opens the toaster oven, and pushed the tray with the food out onto the floor so he can eat it.  I used this to discuss how they also should be determined to learn new concepts and persevere instead of giving up.  So my slogan from this video is now "Be the dog!"

After the videos, I had my classes do the 1-100 group work activity that I got from Sara VanDerWerf's blog.  The kids loved this and were so excited to try to beat their scores and beat the other teams.  I loved watching them working so well together.  After we finished the three rounds (by the way, only one team figured out the secret that the position of the numbers went around the paper from one quadrant to the next), we discussed "What good group work looks like" (also from Sara VanDerWerf) and I pointed out the things I had seen while they were working. When we got to number 2 ("They don't get distracted. They don't notice what other groups or the teacher is doing."), I told them I could have been doing a little jig in the back of the room and no one would have noticed.  I only hope the group work the rest of the year looks as good as today's did.

One final thing I almost forgot to mention was the new Do Now routines I've started this year.  I want to help my students develop better number sense, and I found a great list of math routines.  The one I tried this week was the "Number of the Day".  The first time I gave them the number and asked them to write 3 different expressions, each with a different operation.  The next day I stepped up the challenge and asked them for 3 different expressions, each with 2 different operations, and none of the expressions can use the number 1 (I found the first day students were making this way to easy by just adding, subtracting, multiplying or dividing by 1 - I wanted them to think of more challenging ways to write the expressions).  There were a few students who just couldn't come up with an expression with 2 different operations, so I told them it was OK to just use one operation - we're going to work on this.  Then there was one student who made my day today - her expressions showed she was thinking outside the box - she was the only one who included parenthesis, exponents, and negatives!  She really impressed me!

All in all, I had a great first week of school!  This is my 7th year teaching and it was the first opening day that I didn't have the customary opening day butterflies!  I'm really looking forward to working with my new students this year.

Summer Reading

This summer I made it one of my goals to read all the PD books that I've been wanting to read but just haven't had the time during the school year.  I had heard a lot of good things about these books, and they have not disappointed!  Here's a brief summary of each one that I read this summer:

The Classroom Chef  by John Stevens and Matt Vaudrey

In my opinion, this was the best PD book I've read in a long time!  It was full of inspiring ideas that I can't wait to put into action.  While it's geared towards math classes, I think anyone could apply this to their content area as well.  John and Matt use the cooking analogy to help teachers spice up their lessons.  They give tons of great ideas from "Preparing the Kitchen" and "Setting the Table", to "Appetizers", "Entrees", "Side Dishes", "Desserts", and even "The Bill", "Reviews" and "Take-Home Containers".
How many lessons do we all have that are just plain boring and unmotivating?  Pick one, and make it more exciting for your students with these recipes for success!

Total Participation Techniques  by Persida Himmele and William Himmele

This book is loaded with ideas to get each and every one of your students involved.  No longer will they sit there like bumps on a log waiting for someone else to answer your question!  The shy kids as well as the "answer hogs" (you know, the kids who wants to shout out the answer to every question you ask) will have their own say in the conversations with these TPTs.  What I'm planning on doing is putting a little technology spin on these great ideas since my students have 1:1 Chromebooks.  I've set up a "Template" class in Google Classroom where I can "reuse" my different question types easily.  I have the standard multiple choice, true/false, short answer, and likert scale questions ready to go whenever I need them.

Mathematical Mindsets  by Jo Boaler

I got to hear Jo Boaler speak at NTCM 2015 and was hooked on the idea of helping my students develop a growth mindset instead of a fixed mindset.  Her latest book is filled with ideas on how to do just that.  While I love hearing the science behind what happens in your brain when you make a mistake, having the classroom vignettes was invaluable to help me figure out how to help my student (and collegues!) develop a growth mindset.  I want my students to change the way they look at math - start to enjoy it and have confidence in themselves.

Making Thinking Visible  by Ron Ritchhart, Mark Church, and Karin Morrison

Metacognition has been a big buzz word for quite a while.  But besides students 'thinking about their thinking', teachers need to know what they're thinking too!  This book was filled with strategies (they call them routines) to help make students' thinking visible.  There are thinking routines, routines for introducing and exploring ideas, routines for synthesizing and organizing ideas, and routines for digging deeper into ideas. This is so important in order to know where your students are at and whether you can move on or have to reteach.  The authors talk a lot about 'understanding' and that we need to make sure our students are not just memorizing information for a test only to be forgotten a week or so later.  They need to deeply understand concepts so they can apply what they'e learned to other situations.

Teaching Student-Centered Mathematics  by John A. Van de Walle, Jennifer M. Bay-Williams, Lou Ann H. Lovin, and Karen S. Karp

[I just started this one - I'll update this post when I'm done to let you know how it was.  I've had a lot of people recommend this one to me.  I wanted to get the rest of the reviews out to everyone while there's still a few weeks left of summer break.]





I highly recommend all of these great books!  Try to squeeze in a little time each day to get in some PD in what's left of the summer!