Day 6: Division

6th Grade Math Standards: 6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.

The Learning Objective: Divide multi-digit dividends by multi-digit divisors; identify the parts of a division problem

Quote of the Day: “In a game against the San Francisco 49ers, Jim Marshall spotted the football on the ground. He scooped it up and ran for a touchdown as the crowed cheered. But he ran the wrong way. He scored for the wrong team on national television. It was the most devastating moment of his life. The shame was overpowering. But during halftime he thought, ‘If you make a mistake, you got to make it right. I realized I had a choice. I could sit in my misery or I could do something about it.’ Pulling himself together for the second half, he played some of his best football ever and contributed to his team’s victory.” - Carol Dweck

Assessment: The exit ticket (pictured below), last night's homework, and starting the homework were all assessed by me checking the work. I also did a thumbs up/thumbs down during the division word exclusion.

Agenda:

1. Estimation 180 Days 14 through 16
2. Review the homework
3. Division Word Exclusion
4. Division Notes
5. Division Exit Ticket
6. Division HW started
7. Pascal's Triangle (one again we did not have time) 

Glass Half-Full Take: The lesson started with Estimation 180. The students were asking to do more after we had done two of the days so I said why not and did a third day. I assigned a couple students from each class to ask why the staples came in packs of 5000 instead of 5040 (if you do the estimation exercises yourself you'll see what I mean). I was pleasantly surprised when one student correctly predicted that there were 5040 in the box, but the company put 5000 on the box because it is a "rounded number."

I gave students the opportunity to get out of their seats in the division word exclusion activity. This also gave us an opportunity to construct viable arguments and critique the reasoning of others (Math Practice Standard 3).

In two out of three classes I gave the exit tickets back to students in class. Tomorrow I will give the tickets back to the class that I missed. Students were able to correctly place the quotient, divisor, and dividend much more easily if there was the long division symbol than if it was a fraction. Great to know and it was an easy match up of assessment and objective.

One Regret: I forgot to review the homework in one class. That was unfortunate because there were a couple things that I wanted to touch upon. I forgot the quote of the day in two out of three classes. Tomorrow I will go over the multiplication problems and emphasize how we can find how many students are in the school.

I want something to extend the students thinking next year if they are sailing through the homework. Unlike yesterday I did not have a problem for students to truly think. They were more or less calculators on the homework.

Homework: See link above on step 6 of the agenda.

Link of the Day: During lunch I invited students throughout the sixth grade to partake in fantasy football for the upcoming week. I took most of my numbers from the daily fantasy websites that are out there, but modified the game a little to make it somewhat easier for sixth graders. They made all calculations by hand and I hope that they will calculate all stats by hand as well. Here is the link I will use for all weeks and the player pool for this week.

Day 5: Multiplication Review

6th Grade Math Standards: 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm.

The Learning Objective: Identify the parts of a multiplication problem; multiply multi-digit factors to find a product

Quote of the Day: "Many people believe that a person is born either smart, average, or dumb - and stays that way for life. But new research shows that the brain is more like a muscle - it changes and gets stronger when you use it." - Carol Dweck

Assessment: I collected all of the my favorite no problems at the beginning of class. In one class, 38% of the students answered the problem correctly. The numbers for the other two classes were also slightly under 50%. I have posted a couple pictures below of what students were doing. During the notes, I had students stand up if they finished problems early. I introduced the routine of once you've been checked off by me, you can go around the room and check off others. Students seemed to be doing very well. I circumvented the room as students worked on the estimation to see what they were writing for too low, too high, and their estimates. Finally, I went around the room during homework. Not surprisingly the more digits on a factor, the greater the likelihood that a student makes an error. Overall though I feel confident that we can start division tomorrow.

Agenda:

1. My Favorite No 98 x 76
2. Analyzing My Favorite No
3. 12 dozen donuts video from PBS 
4. Multiplication Notes (end of Class #1)
5. Estimation 180 Days 8-10
6. Finish notes (if necessary)
7. Let students start the homework
8. Time did not allow, but I would have had students work on Pascal's Triangle from Friday

Glass Half-Full Take: I loved Estimation 180 given the topic today of multiplication. We saw a practical use for the operation in which the students had to think in order to solve a problem. I never realized it until this year, but the tissue boxes on Day 10 of Estimation 180 definitely jumps into volume for students. The amount of reasoning that students do during this time makes it ok  to spend more time than is traditionally allotted to a warm up problem.

I also liked going around the room during the time students were doing homework and crossing out problems for students. For some students I gave a new problem of telling me how many people were in the school. Students initially looked at me cross-eyed but eventually started to think when I prompted them by saying, "What's too low?" Again though, estimation 180 was proving it's worth during this time of the lesson.

One Regret: Initially when we did My Favorite No, I gave a class an additional question to see if they knew the vocabulary for factor and product. I think there are many ways to teach vocabulary, but this is a very inefficient way to do it. In a different class, I had students get out of their seats and say it to each other after I felt like I had been lecturing for too long. That was a much better use of time.

Homework: Multiplication Review B

Link of the Day: Just a short way to get them thinking - could be a good one for anyone out there that has been called a witch.

Day 4: The Baseline

6th Grade Math Standards: All of them

After the baseline: Make sense of problems and persevere in solving them; Look for and make use of structure

The Learning Objective: N/A

Quote of the Day: “Circumstances we can’t foresee, understand, or desire can be - and are - imposed on us without warning; random acts happen to people and organizations out of the blue. In my experience, this is not the exception to the rule, but the rule.”

Assessment: The baseline will be used as a means of letting me know what these students are generally weak and strong with heading into this year. Not surprisingly students expressed confusion on the baseline today because the test consists of sixth grade questions.

I also corrected students homework from last night.

Agenda:

1. September 11th Pictures and Quote of the Day to connect to September 11th
2. Baseline Test
3. Challenge - Determine the missing numbers inside Pascal's Triangle

Glass Half-Full Take: The vast majority of class time was used for the baseline test. Like the past couple of years it took up almost two blocks of class time. That said, the students were very respectful of their peers and remained on task after completing the assignment. A good sign for a new group.

Since the students were occupied taking the baseline, I took advantage of the time by first going around and correcting homework from last night and then helping a couple students who expressed confusion navigate through the challenge question. In looking at the homework, it was apparent that students either forgot or did not know how to turn the question around in word problems. In helping them with the challenge question, I was extremely patient in helping students try to find patterns. I only asked questions and let them draw their own conclusions. That ultimately meant that nobody finished all day, which is ok with me. I told students to keep the problem in the daily section of their math binders.

One Regret: I just hope I get the chance to resume helping students with the challenge. Pascal's Triangle is so rich with patterns and I trust some students will enjoy uncovering the patterns.

Homework: None

Day 3 Organizing Binder & Word Problem Strategy

6th Grade Math Standards: MP.1 Make sense of problems and persevere in solving them.

The Learning Objective: Circle what you know and highlight what you are trying to find; add whole numbers; subtract multi-digit whole numbers; define sum and difference

Quote of the Day: “During the final play-off of a U.S. Open tournament, Bobby Jones’s ball ended up in the rough just off the fairway. As he set up to play his shot, he accidentally caused his ball to move. He immediately turned to the marshals and announced the foul. The marshals discussed the situation among themselves. They hadn’t seen the ball move. Neither did anyone in the gallery. They left it up to Jones whether to take the penalty stroke, which he did. Later, when a marshal commended Jones on his high level of integrity, Jones replied, ‘Do you commend a bank robber for not robbing a bank? No you don’t. This is how the game of golf should be played at all times.’ Jones lost the match that day - by one stroke. But he didn’t lose his integrity.” - John Maxwell

The Assessment: Toward the end of class the teachers checked off two of the first three problems that students completed.

Agenda:

1. NFL Home Field Advantage Jumpstart/Check homework
2. Review and debate the jumpstart
3. Organize the binders 
4. Notes on the first two steps of word problems. The first step is to reiterate what we know and what we're trying to find out. The second step is to develop a plan to solve (make a chart, solve a similar problem, draw a picture, write an equation, guess and check, etc.)
5. Define sum and difference
6. Pepper with the terms sum and difference
7. Write the homework in the agenda book
8. Distribute the homework which was Review A 
9. Do the first problem with the students. Many students will prefer to do the homework on the worksheet so it's important to emphasize it needs to be done in the spiral notebook
10. Let students do the rest of the problems on their own while the teachers check off on numbers 2 and 3

Glass Half-Full Take: The binder set up was more thorough than I have ever done. In the past, I have not helped students at all with this process. I finally recognized after several years of students struggling organizationally that spending a block today can save me and the students down the line. I started with the most basic of instructions which was to put their names inside their notebook and on the cover of their binders as well as the class and room number. More than half of the students did not have this already, so it was time well spent.

Next, we broke down each part of the binder. I told students to keep a multiplication chart in the front part of their binder. That was followed by the three tabs (daily, weekly quizzes, and tests/quizzes). The last part of the binder consisted of the rest of the sleeve protectors.

After we had constructed the binders I emphasized how important it was for students to put all math papers in the binder and not the folder. I timed them opening and closing the three rings (less than five seconds) and encouraged them to take the time to put papers away rather than waiting to do it later or sliding them into the agenda book. All the bad habits that I have seen so frequently throughout the last couple of years I am trying to stop now and I feel much more confident in the binder system this year than I ever have.

One other positive from this day was that we took another step forward in the routine. I reminded students about the importance of having homework out before beginning work on the jumpstart so that I could do my job while they did theirs.

One Regret: I wanted to do My Favorite No with the students on a common subtraction mistake and to introduce the routine, but as a result of taking pictures today we had to shorten the class times and did not have time to fit it in.

We could have fit it in if I had eliminated the NFL Home Field Advantage warm up, but given that today is the first Patriots game and this has some excellent questions that we could debate (including number four which was terrific in one class) I think that this assignment was worth our time. In the future I might tell students to skip ahead to problem number four because I only give about 10 minutes to do this assignment.

Homework: Review worksheet A (18 addition and subtraction review problems including three word problems).

Link of the Day: 10 almost completely free sources for an interactive classroom.

Day 2 The Syllabus & First Homework Assignment

6th Grade Math Standards: N/A

The Learning Objective: Analyze rules and procedures

Quote of the Day: "Don't worry about whether you're better than somebody else, but never cease trying to be the best you can become. You have control over that; the other you don't. Time spent comparing yourself to others is time wasted." - John Wooden

The Assessment: Borrowing an idea from the Book Making Thinking Visible, I had the students use red colored pencils and yellow highlighters today as we were reading the syllabus. It is my seventh year teaching, and I have never done this before, but what a difference it made in our discussions. I did not intend on doing this until around 8:30 today (toward the end of my first class, who unfortunately missed out on the activity). It was somewhat bad planning as I actually thought I could assess this originally by just having students and parents sign it. That is not as beneficial as what we did.

I had students use yellow highlighters for anything that made them think. What I mean by this is anything that makes them want to share a past experience, or if they strongly disagree with something in the syllabus, or if they want to expand on what I'm talk about in another way. The red colored pencils were used for anything that made them stop. Words that they did not understand, expectations that did not make sense, etc.

Through using these two writing utensils, today we had conversations about ratios, proportions, what a fair grade looks like after three trimesters, what it means to be ridiculed, what are some examples of statistics in sports, and other rich conversations. The best part for me was that I wouldn't have gotten any response if I used my traditional methods of "Are there any questions, comments or concerns?"

Agenda:

1. Welcome to Math Jumpstart
2. Review the Syllabus
3. Procedures Recap
4. Letter from last year's teacher
5. Write homework in the agenda book 

Glass Half-Full: This was by far the best I have ever done at collecting the slips for the nurse, handbook, and student information in the morning. We have a very small window in homeroom to do this. Inevitably there are students that go to the wrong room, can't open their locker, etc. and time is precious (we only extend homerooms by 5 minutes today instead of an hour). What I did was write on the board the directions for passing in the forms. I told students to place the green sheet, white sheet, and red sheet on the table in the back of the room where there was a manila folder for each of the sheets. Next to the three folders, I had a checklist with their names on it. If they handed in all three sheets, they checked their name off. I still gave verbal directions, but this idea really enhanced the efficiency of this process. 

I was also glad to have the students who did not get a jumpstart when they initially entered the room go back to the front of the room and rehearse entering the classroom the correct way. 

One Regret: With the procedures recap, I wish I had put a timer on the board as a way to motivate students. It's a common routine in my classroom and it would have been a great time to introduce this routine to the students. 

I also wish we had practiced throwing away papers and I was more explicit with my directions. We threw away the procedures jumpstart. Some students crumpled up the paper. I like it to be flat. One class passed their papers to the front. I like every other student to recycle it at the least because it gets students out of their seats for a moment. 

Homework: Here are some samples of the letter students need to write from their fifth grade teacher. I shared these as exemplars with the students. 

Link of the Day: More and more districts are buying personalized computers for students as assessments are being pushed online. 

Day 1: Representing Harry Wong

6th Grade Math Standards: N/A

The Learning Objective: Analyze the classroom procedures

Quote of the Day: "It's not that I'm so smart. I just stay with problems longer." - Albert Einstein

The Assessment: In order to assess that students were understanding the opening day procedures I discussed, I used 10/2 (10 minutes of lecture, 2 minutes for students to digest and discuss the information with the people around them). It was very loose structure as I told students to talk with someone in front, next to, or behind them. After the students had some time, I had them share what they discussed by cold calling and calling on hands. Here were the procedures discussed and the ways in which I introduced them:

• Safety and specifically fire drills. I transitioned by talking about Newtown, Connecticut. It's amazing how quickly we forget. I guarantee people in Newtown don't look at safety procedures the same way that most educators do, but I told all students that I take this very seriously. I cold called students to tell me what we do in the event of a fire drill after I had explained it. 
• Daily warm up. I asked students how we enter the classroom, and when they said quietly, I asked them why. Eventually we came to the point where I told them that they start class, not me. 
• Labeling papers. They told me it takes 15 seconds to correctly label a paper. I said we should do it every time. First and last name, the date, and the block. 
• Sharpened pencils. They asked about erasable pens (good question) to which I said not in my class. I pointed to our pencil sharpeners and they pointed out their own pencil sharpener chambers. 
• Hallway behavior. I told them that there are video cameras in the hallway. I also said that I always look out in the hall between classes. We talked about being quiet, not running, and keeping your hands to yourself. We also discussed how sometimes at lunch the food of their choice might run out. 
• Seating arrangement. Before class started, I had the students either in the hallway or at the back of the room (I like the back of the room better after today). I then called the students individually into their seats. Harry Wong recommends this as a practice to avoid students complaining before they have really even met you about not being able to sit with their friends. I did tell the students we will move the furniture in the room around, work with different partners on occasion, and that if they have an issue with their seat such as not seeing the board to see me in private. 
• Homework. We talked about why we have homework and how we will have time in class to start. In terms of the why question, students told me that it was to get more practice. I made the analogy to sports and music. The more practice, the better the player. I also said that homework could be a way to push your thinking in a different direction than we had done in school. In terms of how, last year at times students would initially refuse to start homework because it was for "home," so I told students this was not what we expected this year. 
• Session. I brought up the session and told students of my discipline plan. I am using this discipline plan for the first time in three years because at times last year I wish I had more consistency and gave students better expectations for what was acceptable with their behavior. 

Agenda:

We didn't have time for step 5 above.

Here is a look at Step 4:

Glass Half-Full: I thought the classes today were extremely respectful on what has turned out to be an unbearably hot day. I feel rejuvenated this year. I thought I did a good job of telling my homeroom to bring back their signed forms. We went through how easy the process really was and how much time was required. Hopefully they will be the first group I've ever had to have everyone bring everything back the very next day.

One Regret: I don't think I emphasized enough of the math mentality that I want students to have this year. I will communicate more clearly to them in the coming days of my desire to have them make mistakes, push their thinking, and talk without fear about what they know - or think that they know.

Link of the Day: We used Kahoot on one of our professional development days last week, and I really like what the site offers. It's similar to TurningPoint, but with cell phones.

Making Thinking Visible: Twenty Takeaways

My district gave every teacher the book Making Thinking Visible by Ron Ritchhart, Mark Church, and Karin Morrison. I just finished reading it. It was predictably a little dry, but definitely had some great insights that I will look to use to improve how I get students to think this coming school year (which as of this writing is two weeks from tomorrow). In no particular order, here are the ten thoughts/ideas/theories/routines that can help reshape how I teach and maybe how you teach:

1. To a certain degree I have ran away from the question of why. Why is it that a quotient gets bigger when we divide by a fraction or a decimal less than one? Why is the area labeled feet squared? Why did pi get to be the number that is used in circles? Students get tested on all of these topics, but only surface testing. The deeper thinking gets pushed to the side in my hurry to cover the material and ultimately the students have been shown what to do without generating as much deep thinking as I could have pushed them toward.
2. What makes you say that? Sometimes getting a student to elaborate on their thinking becomes intimidating when we follow it up by asking why with our arms crossed and a cold stare. Research has shown that by getting students to verbalize their thinking, their understanding is deeper.
3. From day one students need to recognize that school is no longer about the quick right answer. Learning happens upon reflection of mistakes. That's what I learned when I tried to parallel park on my driver's test, but some days I ignore it in the classroom. 
4. If the theories in the book are applied correctly, every grade and every content area can benefit. Understanding is a direct outcome of thinking, and understanding only comes from a small umbrella of what the authors call "thinking moves." These include observing closely and describing what's there, building explanations and interpretations, reasoning with evidence, making connections, considering different viewpoints and perspectives, capturing the heart and forming conclusions. The authors also added that wondering and asking questions as well as uncovering complexity and going below the surface of things after some time within this theory. These are thinking moves that take place from kindergarten through high school, so the more teachers that jump on board, the better off the student will be. 
5. The students should become familiar with their thinking moves. Students that only worry about test performance are incentivized to be rote learners. To avoid this age-old problem, teachers should give immediate feedback to students by naming the type of thinking a student just demonstrated instead of giving generic praise (another age-old problem). 
6. Ask questions to which we do not know the answer. For instance without a GPS, how long do you think it would take us to drive from Belmonte to Canobe Lake Park? This helps model the thinking process for students and also makes use of takeaway #2 (there is no quick right answer). 
7. Any student that can ask a question that gets everyone thinking - including the teacher - is a great question. Great questions need to be celebrated. Great questions need to be posted. Great questions need reflection. Great questions need to be revisited. Great questions could be as simple as, "What makes you say that?" 
8. In group work listening skills are more valuable than academic skills. Being able to acknowledge each person's contributions, probe their thinking, and ask clarifying questions is a much deeper and richer academic experience for everyone. I think in order to make group work more efficient, groups have to buy into Takeaway #3 (learning through mistakes) first. 
9. See, think, wonder is an excellent way to look at a chart or even any picture or video from Estimation 180, Visual Patterns, etc. The key to me is in the "see" portion of this routine because it gets students started. The authors advocate for two minutes of silent reflection, which in my experience can be classroom management torture. In seeing, students are not trying to make any bold discoveries - just stating what they see. In thinking, there is more engagement than the typical math question because similar to a 3-act math problem, students need to find the question. And of course the wonder is the part where they can fill in the blank and try to solve. That said, the word, wonder is much more "mistake friendly" than answer. It promotes risk taking and does not require students to discover the answer. The other great part about this activity is that the authors actually advocate against worksheets and writing for much of the activity. I find that this is a good break from the norm for students. 
10. Think, Puzzle, Explore was a routine that I would like to implement with measurement. Students come into sixth grade with some background of three dimensional shapes, finding area, and finding a perimeter. I think it would be beneficial for them from the outset to get what they know documented (probably by me on the computer in PowerPoint). My favorite part of this though would be the puzzle to see if they ask questions that eventually we will cover. The hard part of both puzzle and explore is that I can see students stopping simply at "How will we use this in real life?" and "Look it up on the internet." for those two parts of the routine respectively. The authors talk about pushing the thinking further and also using any routine more than just once. 
11. Chalk Talk is a routine that would kill two birds with one stone since it would enable students to put their thinking down on paper and get them out of their seat (which I try to do every class). One thing I could do is use a chalk talk with solving ratio problems. I could have one chart paper that uses ratio tables, another with double number lines, another with tape diagrams, and another with just getting the two ratios equal to each other. I could see what students felt most comfortable with which issue. 
12. 3-2-1 Bridge is a routine I could use in many entirely new topics to sixth graders including the distributive property. I think the most valuable parts would obviously be the questions (Takeaway #7) and also the metaphor. I imagine it would be a huge struggle for most students to come up with a metaphor, but for the one student who does sharing it could provide benefits to the whole class and for me going forward in my teaching. 
13. Headlines as a form of exit ticket. Instead of asking students to do a problem about what we just learned, I could get back to Takeaway #1 and see if they understand the main point of the class in one phrase or sentence. 
14. Getting students to write before they discuss will more often lead to richer discussion. I am aware of this, but often don't bother trying because certain students do not have something to write on or certain students prefer not to write. At least I should give students a choice though so as not to deprive all students of optimal thought. 
15. I used to think...now I think... can be used for social emotional teaching. I always have a hard time transitioning from an assembly about drug awareness or bullying into the surface area of a rectangular prism. I could use the I used to think...now I think to make students reflect on what they just learned because social emotional learning is as important if not more important than any math I teach. 
16. Step Inside is a routine that can get students engaged and using creativity to think about a math concept. I was thinking of having groups of four each take on a different role in an algebraic expression. What might that person believe? What might that person think about those around him/her? Students could also make a game of it by telling the rest of the class about them in 3 hints for instance and then having the class guess who they are. 
17. Red Light, Yellow Light is an excellent routine for a math teacher whenever we are building on a multiple step word problem or a vocabulary intensive portion of the curriculum. Students can take red markers and direct the teacher to anything that causes them to halt or yellow next to anything that causes them to hesitate. There are those days where students just fall apart in reading comprehension and this will give them an opportunity to have an explanation that there will be a challenge and direct their focus to get over that hump. I also like that the authors said if the whole sheet is colored red to stop at one point only and then redirect students. 
18. In addition to discussing behavior and work completion, I need to discuss the expectations for thinking from day one through day one eighty. I want the thinking moves posted on the wall, something about listening to others posted on the wall, and I want something about great questions posted on the wall. 
19. If thinking is going to be promoted less curriculum is going to be covered. I'm not saying that my class was even close to lecture based in the past, but there were certainly moments of me passing along the information without soliciting students to thinking in the past. I'm convinced that student mastery needs to be the goal as opposed to me telling the students everything I know. I've always believed in that, but after reading this book I'm convinced I haven't been practicing that. 
20. Often worksheets force students to think about the work rather than learning what the worksheet is asking for.