Day 17 LCM Half Day

6th Grade Math Standards: 6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2). MA.4.a. Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems.

The Learning Objective: Find the least common multiple in a real-world context.

Quote of the Day: “I had the great privilege of being an assistant on the 1992 Olympic team, known as the “Dream Team.” It consisted of some of the greatest players of all time, such as Michael Jordan, Magic Johnson, and Larry Bird. After a team practice, I stood by myself on the sidelines drinking a Diet Coke. Michael Jordan walked over to me and said, ‘Coach K, I would like to do about a half hour of individual work and I was wondering if you could please work with me.” After our workout, Michael shook my hand and said ‘Thanks Coach.’ Michael Jordan had just called me Coach and he had said please and thank you. This was at a time when he was one of the most recognizable faces not only in the game, but throughout the world. That day I learned everyone on Michael Jordan’s team is treated with respect.” - Coach K

Assessment: Checking the weekly quiz

Agenda:

1. Mystery number: 3 clues. The number is more than 50 and less than 100, the number is a multiple of 2 and 7. The number has exactly three prime factors.
2. Review the homework
3. Students worked on a sheet that combined least common multiple and greatest common factor

Glass Half-Full Take: I was glad that I did not assign homework on the half-day. It's the third day we've done least common multiple (if you count the multiples day on Monday), but there wasn't time for a fair assessment in terms of what we did on multiples so giving homework would not yield anything except for the annoying I don't get its and I didn't understands the next day.

One Regret: The classes came and went so fast. I wish I had planned and coordinated the sheet that combined least common multiple and greatest common factor better. I needed to pass out rulers faster, get students organized in partners faster, etc. It was one of those days (as most days tend to go) where the third class got a better lesson than the first.

Homework: Work on weekly quiz

Link of the Day: I love this anecdote from the blog of Tyler Auer (@Mathfireworks). In regards to switching the order of 23 + 59 + 7 to 23 + 7 + 59 it is ok to switch the numbers because the results don't change. He used this point to build on the idea that "we use patterns to manipulate variables and numbers in ways that look different, but don't change the result."

Day 16: Least Common Multiple Word Problems

6th Grade Math Standards: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2).
MA.4.a. Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems.

The Learning Objective: Find the least common multiple of 2 or more numbers in a real-world context.

Quote of the Day: “Listening to others, evaluating - embracing - their opinions and creativity, may seem to suggest uncertainty and doubt about your own judgment and convictions. The ego gets in the way of your eyes and ears.” - John Wooden

Question from Yesterday: "Can we always multiply the numbers together to find the least common multiple?"

Assessment: Checking weekly quizzes and giving feedback; allowing students to work in partners on the homework to get feedback from a peer; checking yesterday's homework

Agenda:

1. Mystery number and homework was checked
2. Review the homework and mystery number
3. Hand back any papers (WQs, partner sheets, etc.)
4. Visual Pattern number three 
5. Least Common Multiple Notes 
6. Least Common Multiple Practice

Glass Half-Full Take: I enjoyed talking today about our star student and how he related to the quote of the day. We were celebrating students who made reference to other students in class when we were having mathematical discussions. This student always references what other students have said and builds upon or refutes those statements.

One Regret: I wish that I had put the students to task on the visual pattern as I was passing back papers. I want them thinking all of the time in class.

Homework: Six word problems on least common multiple (a few students were able to finish in class) and the Weekly Quiz #2.

Link of the Day: I like these pictures of 4 numbers to get students critiquing the arguments of others.

Day 15 Least Common Multiple

6th Grade Math Standards: 6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2).
MA.4.a. Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems.

The Learning Objective: Find the least common multiple of two or more numbers

Quote of the Day: "Don't let yesterday take up too much of today. Learn from the past and get over it" - Will Rogers

Assessment: I had students try a problem on their own during the notes and checked them by going around the room; I checked the homework for understanding of the divisibility rules; the multiples were displayed on the Marvelous Multiples sheet; The clickers helped me see that students had difficulty transitioning from the word multiple to the word factor, but after transitioning they did not have much difficulty.

Agenda:

1. Estimation 180 Day 18 and Day 19 and homework check
2. Cook out ideas
3. Watch Father of the Bride clip
4. Least Common Multiple Notes (definition for each of the three words and two to three homework examples)
5. Start the homework
6. Marvelous Multiples designs 
7. Clickers to check on if students know the difference between factors and multiples

Glass Half-Full Take: On my third slide using the clickers I changed the directions from give a multiple to give a factor and it threw half the class off. That's when I had their attention and they knew to look for the word multiple or factor. The co-teacher told the students that factors always start with one and itself. We said that over and over again in one class to try to make it stick. I'd never done this before, but knowing how hard it is to differentiate between a factor and a multiple, I thought it was a great idea.

One Regret: I wish I posted in my daily agenda pass back and review weekly quiz materials. I forget that the students are still learning routines. I should have carved out the beginning of the block for passing back, passing out, and letting the students pass in various weekly quiz materials.

Homework: I quickly changed the homework when I saw how students were flying through what it was supposed to be. I made them only do two to three problems, but to challenge them I asked them why sometimes multiplying got the least common multiple and sometimes it did not. Differentiating homework has been much more of a routine in my class this year. I don't really care to torture students with busy week. I just want them to think and be challenged a little. As long as effort and thought go into an assignment it is fine by me if they do not reach a valid answer.

Link of the Day: Jognog does much of what the clickers do for me except there are already standards based quizzes created. A former colleague said the fifth and sixth grade teachers in his district are very high on it. 

Day 14: Multiples

6th Grade Math Standards: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2). MA.4.a. Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems.

MP.1 Make sense of problems and persevere in solving them.

The Learning Objective: List the first four multiples of a number

Quote of the Day: “I frequently received letters from custodians after we play an away game telling me our team left the locker room neater and cleaner than anyone who had visited during the year. I believe leaving it clean is just common courtesy. Somebody’s going to have to clean it up, and I see no reason why it shouldn’t be the person who messed it up. I think neatness and courtesy make you feel good about yourself. I believe individuals who feel good about themselves are more productive.” - John Wooden

Assessment: As we were finishing the notes, students stood up to indicate if they could list off the first four multiples of a number; during my favorite no I also checked to see if students would list factors instead of multiples for a number. Many of them (more than half) did.

Agenda:

1. Warm Up Problem and homework check
2. Review the homework
3. My favorite no; list 4 multiples of 12
4. Multiples Notes
5. Pass out the homework
6. Marvelous Multiples

Glass Half-Full Take: The warm up problem took the whole block in one of my classes and it did not bother me at all. Students came away engaged. Two student reactions said it best. "I can't believe that we were just here for 45 minutes." And, "I can't wait to give this to my mom and see her do it." It was amazing to feel the students thinking and interest level. All the while they needed to grasp what a factor was, what a product was, and what a sum was.

One Regret: We did not have time to finish Marvelous Multiples. I came away from the warm up problem feeling good though. Perhaps I could fly through the notes and not tell students what an integer is on this day (integer is inside the definition of multiple we used).

Homework: Multiples practice.

Link of the Day: Mathcounts

Day 13: Greatest Common Factor Goodie Bags

6th Grade Math Standards: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2).
MA.4.a. Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems.

The Learning Objective: Apply the greatest common factor to real world situations

Quote of the Day: "If you want to be successful and to maximize your talent, you need to stop blaming others, take a good look in the mirror, and take responsibility of your own life. Television host Oprah Winfrey says, 'My philosophy is that not only are you responsible for your life, but doing the best at this moment puts you in the best place for the next moment.'" -John Maxwell

Student Question of the Day: What is the greatest common factor of two prime numbers?

Assessment: There were four different assessments that I used today.

1. I checked the homework to see that the process and answers were making sense.
2. I had students start tonight's homework and checked the first two problems for understanding.
3. In groups students put together goodie packages. They had to determine how many people were invited to their party. I listened to their thinking by walking from group to group.
4. I had students write in their journals one thing that they knew based on the Visual Pattern that we showed on the board. Then I listened to them share their ideas first in small groups and then in the whole class. 

Agenda:

1. Jumpstart (3 greatest common factor problems) & check homework
2. Review the homework
3. Start the homework for tonight
4. At the start of class two I rearranged the room so students were sitting in groups and passed out the goodie packages.
5. I explained that students needed to be gentle with the candy and that they could not eat the candy.
6. Students wrote what they were trying to find and what they knew inside their journals (see picture below). 
7. The students worked as a group to determine how many people could attend a party if they had x amount of mints, y amount of lolly pops, and z amount of nerds (the amount changed based on what was in each bag).
8. We discussed Visual Pattern #2. I started by having students think. Then write. Then share in their groups. Then share with the larger group.

Glass Half-Full Take: The second part of class was what I would consider an ideal day from a teaching perspective. Students were sharing their thinking in groups of four and the groups for the most part were extremely respectful and cooperative.

The last two years I have used Visual Patterns as a "throw in" when students are done work or as an extra challenge for certain students in the classroom. This year, I'm putting a much higher emphasis on this after reading Making Thinking Visible. The discussions that I am having in one class in particular are incredibly deep and engaging as every student is determined to find the pattern and explain it to others. Today in one class, a student who typically describes himself as "not good at math" was one of the first to tell me what was happening.

One Regret: I spent $50 on the candy and bags for the lesson. I know the students love the candy, but what I thought all along to myself was 'they better master greatest common factor or else!' Next year I want to do this again, but I could just use construction paper, or paperclips, or used gum, etc.

Homework: 9 problems on greatest common factor plus a challenge problem for students that want it. Every student got at least four problems done in class today. I also crossed out problems for certain students and made the challenge mandatory for others.

Link of the Day: Zipgrade helps analyze any test data. A colleague was explaining it to me. I tried downloading it, but my room was in what scientists call the "mantle" and I don't get service. 

Day 12: Greatest Common Factor

6th Grade Math Standards: 6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2).
MA.4.a. Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems.

The Learning Objective: Determine the greatest common factor of two or three numbers

Quote of the Day: “Nearly every person who develops an idea works at it up to the point where it looks impossible, and then gets discouraged. That’s not the place to become discouraged...Our greatest weakness lies in giving up. The most certain way to succeed is always to try one more time. Many of life’s failures are people who did not realize how close they were to success when they gave up.” - Thomas Edison

Assessment: After showing the students the first two examples in the notes, they did the next two problems on their own. I also had the students do the first two problems in the homework and checked them off. If students completed these problems without any major issues I had them cross out two more problems (which I picked since they were more of the same). Finally I had students write their divisibility rules in the journal to see what they were struggling with. The rule for 4 was giving them the most difficulty.

Agenda:

1. I checked homework while students did estimation
2. Review homework
3. Greatest Common Factor Notes
4. Divisibility Rules in the Journals
5. Greatest Common Factor Homework
6. Greatest Common Factor Challenge (students had the option of doing this on the homework and skipping another homework problem) 

Glass Half-Full Take: Estimation 180 always gets more involved by the third question in terms of the level of thinking on a particular topic (today it was toilet paper).

I also liked a question that a student asked me. What happens when we're trying to find the greatest common factor of two prime numbers?

The challenge problem added some differentiation to the lesson for students.

Grace was supposed to find the greatest common factor of 330 and 462, but she found the greatest common prime factor instead. What is the difference between the number she found and the number she was supposed to find?

One Regret: I had the students sitting in their desks for too long. I have to break that up somehow. Perhaps a vocabulary review or perhaps I could challenge them to show a mistake to a friend. Something needs to be done to keep them active and awake.

Homework: See agenda #5 above (in addition to the weekly quiz).

Day 11: Factors

6th Grade Math Standards: 6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2). MA.4.a. Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems.

The Learning Objective: List the factors for a two digit number.

Quote of the Day: "Americans spend twice as much time on Facebook as they do exercising. And the younger the age, the worse the effects. The average college student spends three hours a day checking social sites. According to a USA Today report, the grade point of average of college students who regularly use Facebook is a full point lower than their peers who do not...American workers are interrupted once every 10.5 minutes by things like emails, texts, and tweets. Once interrupted, it takes an average of 23 minutes for them to get back on task." - Rick Pitino

Assessment: After we review the notes I gave students a problem to try on their own. Typically this problem took place right at the end of the first block we met, so when we met again at the start of block two I gave the class an index card and gave them another number.

The results were mediocre, but got better after I gave students feedback on the first index card problem and gave them a second index card problem. The feedback I gave students was to list factors in numerical order by starting with the factors that are always there (1 and the number itself). What I was noticing was that students were leaving a factor or a pair of factors out.

Agenda:

1. Jumpstart with divisibility rules, prime number, and composite number definitions
2. Review the jumpstart by asking three different students to give each rule of divisibility (so we repeated each other) through cold calling
3. Reviewed the homework by letting six students come to the board and try the six example problems from the homework. As students were at the board, I played a quick round of pepper with the remaining students.
4. We gave thumbs up and thumbs down to students work at the board. It led to great discussion.
5. Factor Notes (Defining factor and two examples where we list all factors in order using the divisibility rules)
6. Exit ticket where we use a two digit composite number and list the factors
7. Starting the next class with listing the factors on an index card
8. Fabulous factors 
9. The Factor Game
10. Pass out the factor homework and put homework in the agenda book

Glass Half-Full Take: Today was a jam packed day, so there's a lot to pick from both in terms of regrets and victories as a class.

I told one student in the middle of class that he was having a great math class. He asked a question skeptically at one point about why 564 was not divisible by since the sum of the digits was 15. He also went up to the board and got one of the homework questions wrong. And he slipped in one more wrong response. He was engaged and when I would cold call him after he had originally got a question he came back with logical understanding. He was pushing himself today and I praised him for it publicly. Tomorrow I'm going to include a slide about him as "Student of the Day" after we do the Quote of the Day. It was growth mindset personified.

One Regret: In the first class, I was a little all over the place in how Fabulous Factors was organized. In the second class, I fixed the situation. Here's what I did.

First, I explained the factor game which is what they would do after finishing Fabulous Factors. This proved effective because students would finish at different times.

I then had students pass out the construction paper, the factors cut outs, a set of markers (one set per two students), and the white paper which they would use the markers on. I distributed scissors to the students. Then I explained the first step in the task which was to cut out a number of their choosing and recycle the scrap paper.

After students had chosen their number, I told them to list the factors in their notebook and have either a neighboring or student or myself check to verify all factors were listed.

Once their "rough draft" was complete, I had them fold the white paper in half (the hamburger way) and then write the factors using markers.

Lastly I passed a slice of masking tape to every student to put the white sheet onto the construction paper.

All the while I was going around the room stapling the numbers to the construction paper and collecting scissors. By the end of the last class, the room was actually clean.

Homework: This factor worksheet

Link of the Day: Cool problem that I intend to tweak a little and then implement for my Math Academy kids. Try it without the answer given to you first cheater!

Day 10: Divisibility Rules

6th Grade Math Standards: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2).
MA.4.a. Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems

The Learning Objective: Determine if a number is divisible by 2, 3, 4, 5, 6, 9, and 10 without using long division or multiplication.

Quote of the Day: "Walt Disney's request for a bank loan was denied 301 times before he got a yes." - John Maxwell

Assessment: During the notes I had students try their own problem and apply the divisibility rules.

Agenda:

1. Self-Assessment of the quiz. This part of the agenda takes up most of the class. It's the first time that students write about their quizzes. It's also the first time that I have them fill out a checklist, so that's a brand new routine I have to teach. I love the checklist for determining why a grade is what it is. So often we give a B and really don't know what that means. This is a loose way of using standards based grading. 
2. Divisibility Notes
3. WQ Information Re-rehearsed 
4. Divisibility Flashcards
5. Divisibility Song
6. Divisibility Homework begins

Glass Half-Full Take: There were many new routines today. Students were passing in their weekly quizzes for the first time into the weekly quiz folder, getting weekly quizzes back with highlights indicating that their problems needed to be corrected, reflecting on how their quizzes went in their journals, filling out their checklist from the quiz, and even putting the checklist and quiz back into their binder. In teaching many routines in a single day (and the 10th day of school at that), it's easy for me as the teacher to make assumptions or the students to get buried in new information overload. Neither happened.

One Regret: As a consequence of all the new routines, much of our first block was spent in review of the quiz. Given how much time I lost there, I would have much rather had students get a print out of the notes and slip it into their binders than to copy the notes into their notebook. We did not have time to internalize and digest the new information today as I would have liked. I think if the students were quizzing themselves instead of writing down information on the rules, more information could have been internalized.

Homework: Students had to continue to fix problems on Weekly Quiz #1, practice their divisibility rules and do step six of the agenda.

Link of the Day: Another thought-provoking problem that I found browsing through Fawn Ngyuen on Twitter. She has way too many engaging problems to share with her followers. 

Day 9 Operations Quiz

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

The Learning Objective: Solve real-world and mathematical problems using division, multiplication, addition, and subtraction; identify the parts of a division problem, define the answers for each of the four operations

Quote of the Day: “I have always told my teams and my three daughters that getting a D on a test, or even in a course is far from the worst thing one can do. You can recover from that. You can study harder for the next test, you can get a tutor; you can even retake the course. The only bad thing would be if you were to cheat. Cheating means you are giving up on yourself. You lose a piece of yourself each time you violate your personal sense of what is right and what is wrong.” - Coach K

Assessment: The students took the quiz. Overall the results were solid on the vocabulary and identifying the parts of a division problem. We had done pepper and really emphasized this vocabulary all week, so it was great to see the hard work from both students and teachers pay off. Their greatest struggles actually came with subtraction. Here's what I saw a good deal of:

On my end, I never did My Favorite No subtraction with the kids this year. The time that I spent doing this a year ago was reallocated to help students organize their binders. Analyzing common errors in subtraction was something we actually did get a chance to do though through the process of long division. In any case, as this picture illustrates, it's hard to argue that students don't understand what they are doing. This student took from the tens place and even correctly rewrote it after taking from the hundreds place. The student simply did not subtract 11 - 3 correctly. More than their understanding of subtraction, my greater issue is the lack of effort to check the work (even though it was in the directions). I only saw this on a handful of the 67 papers I looked at:

And not to say that there weren't errors with regrouping (also known as place value errors). 

All of this would have easily been fixed by doing what kids demonstrated they could do quite proficiently on the first two problems of the quiz - add two numbers to find a sum. Here is another look at a subtraction error and the easy way to prevent that error from being permanent:

On a small scale, does it even matter anymore that students cannot subtract? In my opinion of course, but there are those out there that say no person will be caught dead without their smart phones and their built in calculators. Even if I concede that point the greater issue to me is that we aren't being thorough enough in our approach. Are we not going to take a second look at the dimensions for the bridges that are being built or the surgery that needs to be done? Getting greater proof and more evidence to prove a point is a critical skill that it appears many students do not possess right now. Then again, maybe I as the teacher did not go over how to check will enough heading into this quiz. And maybe in the effort to do the homework or classwork and just get it done, students are not engaged to want to check the work. In any case, it's a problem. We'll discuss on Monday. 

Agenda:

1. Write homework in the agenda books
2. Take the quiz
3. Read the directions for the quiz
4. Let students work on Pascal's Triangle. If they fill it in correctly, they should try to find at least six patterns that are built in. 
5. Review Pascal's Triangles patterns with the class (start of the second block)
6. Clean out the binder
7. Pass out WQ domination sheet and put it in a sleeve of the binder so it never leaves
8. Pass out WQ parent notification form
9. Pass out WQ #1 and let students start it in class 

Glass Half-Full Take: As I said in the assessment it was actually pretty amazing how well the students did with the vocabulary. In peppering the students with questions throughout the week and even having them do the study guide the previous class, it was apparent that the students did not all initially know what the words product, factor, sum, difference, and quotient meant. This was material that was truly learned.

I don't recall who, but I once heard someone comment that mathematics is only a matter of having a mastery of the vocabulary and carrying out a process. The first half of that was covered well by the students on this quiz much to my delight.

I also was glad to finally have some closure with Pascal's Triangle. This was a week in the making. Most of the students still had their original copy which is proof that the binder is working for these students and organization has never been better collectively to start a year for these students.

One Regret: One final mistake I noticed was with lining up the numbers in a division problem. I tried emphasizing to students that there should be one digit in the quotient for every one digit in the dividend. Usually when I gave this advice it was personal rather than to the class as a whole. I think by saying it aloud as a class on Monday in a chanting/singing fashion we will be able to make the message stickier.

Homework: WQ #1 Parent Slip and WQ #1 rough draft is due on Tuesday of next week

Link of the Day: 5 Wolves and 3 sheep (although I'm going to call it 5 wolves and 3 chickens). I have not solved it yet. And I refuse to look up the answer online. 

Day 8: Study Guide for Operations Quiz

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

The Learning Objective: Use division, multiplication, addition, and subtraction in a mathematical and real-world context; identify the parts of all four operations

Quote of the Day: “Children with the fixed mindset want to make sure they succeed. Smart people should always succeed. But for children with the growth mindset, success is about stretching themselves. It’s about becoming smarter. One seventh-grade girl summed it up. ‘I think intelligence is something you have to work for...it isn’t just given to you...Most kids if they’re not sure of an answer will not raise their hand to answer the question. But what I usually do is raise my hand, because if I’m wrong, then my mistake will be corrected. Or I will raise my hand and say How would this be solved? Just by doing that I increase my intelligence.” – Carol Dweck

Assessment: Checking homework; circumventing the room as students did the study guide

Agenda:

1. Visual Patterns #1 for the jumpstart 
2. Review the division homework
3. Sneak peak at tomorrow's quiz
4. Study guide 
5. Product Game

Glass Half-Full Take: The first time we worked on visual patterns as a class was very helpful. Students were building off of one another's ideas. You could sense that students were going from feeling helpless to curious as students shared different ideas. I liked a couple other things that I did on the fly today. The first was that as students did the visual patterns problem (which was projected onto the board), I had other students who got problems wrong on the homework put their solutions on the board. This meant that going over the homework would take less time for everyone in the class when we got to it. It also meant that we could look at mistakes that were made by that student as a class and analyze them.

The other thing that I did on the fly was to put a timer up in the second part of class for how much time I allocated toward the study guide. After the timer expired, I went over the study guide and showed students how to find the answers online so that they could use it as a study tool tonight.

One Regret: In explaining the product game, I should have been more explicit about using a paper clip, pen cap, or other small object to mark the space on the board. In the second class in which I used the product game students had many questions. The game was engaging and a great diversion from the cut and dry math of note-taking or drill and kill, but students initially were unsure how to get started.

Homework: Study for tomorrow's quiz

Link of the Day: A teacher shared this article with me today about How Not to Talk to Your Kids from New York Magazine. It's great for explaining to parents the basic premise of fixed versus growth mindset. 

Day 7: Division Day 2

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

The Learning Objective: Divide multi-digit numbers with two digit divisors

Quote of the Day: “Why waste time proving over and over how great you are, when you could be getting better? Why hide deficiencies instead of overcoming them? The passion for stretching yourself and sticking to it, even (or especially) when it’s not going well, is the hallmark of the growth mindset. This is the mindset that allows people to thrive during some of the most challenging times in their lives.” - Carol Dweck

Assessment: My favorite no problem which was 2438 divided by 23. I used these numbers to see if students would bring down two numbers at a time by accident. It only happened a couple times all day, but it was good to collect the index cards and see what students were where with the topic. Pepper was used to see what students knew and didn't know with regards to vocabulary. I always use no opt out during pepper. I also checked homework and started today's homework within the class period. Students were able to get feedback on their multiplication facts because I had them "speed dating" and switching seats every minute with a deck of cards as a way to give them problems.

In one class I got the problem below done on the board by a student. Needless to say the remainder of 81 with the divisor of 81 led to excellent discussion and thinking on the part of all the students. This is the type of value that is gained when we spend more time letting students do work at the board and less time letting me do work at the board. I don't do enough of this.

Agenda:

1. My Favorite No
2. Review the Homework
3. Pepper
4. Multiplication Speed Partners
5. Division 2 HW
6. Pascal's Triangle

Glass Half-Full: I am trying to give different students different homework assignments this year and also differentiating within the regular class. On the homework today I had some students start in different places. I also personally went by to cross out problems on some papers depending upon the length of time students took or the ease in which they were doing problems. One girl demonstrated proficiency on yesterday's homework and today's homework so I let her work on the Pascal's Triangle paper before she had finished all the problems and told her not to worry about finishing the problems. If she is demonstrating mastery, why should I make her do busy work?

One Regret: Today was a great day to work in groups because it was the second day of the same learning objective. Getting kids to help kids is something I usually implement early in the year and today was a good day for it, but I kept the students in rows.

Homework: Review D; the quiz is two days away

Link of the Day: Good inspirational video passed along from a colleague that's under 5 minutes.

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.