Day 41: MCAS Scores & Double Number Line

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

Quote of the Day: “Marva Collins taught Chicago children who had been judged and discarded. For many, her classroom was their last stop. One boy had been in and out of thirteen schools in four years. One stabbed children with pencils and had been thrown out of a mental health center. One eight-year-old would remove the blade from the pencil sharpener and cut up his classmates’ coats, hats, gloves, and scarves. One hit another student with a hammer on his first day. These children hadn’t learned much in school, but everyone knew it was their own fault. Everyone except Mrs. Collins. When 60 Minutes did a segment on Collins’s classroom, Morley Safer [the person doing the interview] tried his best to get a child to say he didn’t like the school. ‘It’s so hard here. There’s no recess. There’s no gym. They work you all day. You have only forty minutes for lunch. Why do you like it? It’s just too hard.’ But the student replied, ‘That’s why I like it, because it makes your brain bigger.’

Question of the Day: "What's a tape diagram?"

Objective: Interpret your MCAS score; compare two quantities in a double number line

Agenda:

1. MCAS scores explained and review for a whole block by the Title I math teacher
2. Get to 10 
3. QSSQ
4. Homework Review
5. Gummy Bears 

Assessment: I did the first ratio of 23 grams to 10 bears and then had the students fill in the corresponding amount of grams for 20, 30, 40, and 50 bears.

Glass Half-Full: The MCAS review I think was very helpful as far as giving students a wake up call for those that needed the wake up call. Last week for instance on the weekly quiz, only 25% of students in one class got a 100. Now this is a quiz in which I will literally stay after with kids and do the problems with them if the students would like. It's heavily impacted by how much effort is given. These students needed a wake up call.

Regrets: There were also students that did not need a wake up call. For these students that did maybe not as well as they would like, hopefully they don't feel hopeless! These students are working hard and doing their best to reach their potential, so I think good things will come whether the MCAS is reviewed with them or not. And at the end of the day, the MCAS is like the Super Bowl. They can't get to that game and succeed without a great preseason, regular season, and playoffs leading up to that moment. I think we need to continue to draw upon the day to day importance as the bigger part of the process for getting better.

Link: Children and spatial reasoning.

Day 40: Tape Diagrams & Quiz Review

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

Objective: Use a tape diagram to solve ratio problems

Agenda:

1. Self Assessment
2. Quote of the Day, Star Student, Question of the Day
3. Review the quiz - particularly problem #5 
4. Tape Diagram Notes - Completed Version Blank Version
5. Tape Diagram Homework
6. Start WQ #8 

Assessment:

1. Students had time to start the homework in class despite shortened classes so I went around and saw how they were doing on these. I also gave students the opportunity to do the third example problem on their own and stand up when they were done.
2. The quiz was self-assessed. 

Glass Half-Full: Everyone got problem five wrong on the quiz, but there were nothing but thumbs up acknowledging understanding when I went over the problem with the students. Initially I got thumbs sideways and they asked me how I came up with 80 ounces for a second time which was encouraging because there is no way we go from virtually nobody getting something to everyone through a lecture.

Regrets: In the notes and on the homework there are many problems that compare the ratio of girls to boys. At a training this year, a speaker told us we should try to stay away from these examples because some students might be gender neutral and you are essentially dismissing them with a problem like this. I simply photocopied last year's notes quickly because father time was forcing my hand, but there are many other ratio examples to choose from and I can change with time for next year.

Day 39: Ratio Quiz

6th Grade Math Standards: 6.RP.1 6.RP.2 6.RP.3b

Objective: Give a unit rate to describe the relationship between two different quantities; apply unit rates to solve other problems; write a ratio three ways; define ratio

Agenda:

1. QSSQ 
2. Take the Ratio Quiz
3. Fix the Weekly Quiz 
4. Keep the numbers 5, 4, 3, 2, and 1 in that order. Use any operations you want and as many parenthesis as necessary. Get solutions from 1 through 40. 
5. Boorito (from Yummy Math) 

Assessment: The quiz.

Glass Half-Full: The quiz was successfully revamped to interleave the decimal standard from our last quiz with a decimal question right off of the 2016 MCAS test. The most encouraging sign of the quiz though was the way in which students highlighted without instructions from me on how to highlight during the quiz. It gave them a great indication of what they needed to find.

Regrets: I got to the Boorito activity in one class, but I wish we could have done it in all classes. The many factors that we needed to consider about the potential for raising $1 million was something that engaged the students. We even researched how many people were in various countries. And once I introduced the actual numbers of how many people celebrate Halloween, how many Chipotles there are in the world and where they are located, the operations of operation, etc. the students were able to start to make conclusions. I did this in a Socratic style instead of a think pair share or group activity, but I think the format worked given the time we had, and the fact that we had not really seen many problems like this one yet this year.

Link: I like this question about auditing your mathematics classroom. "When you look at your roster, can you identify one way in which every student is mathematically smart?"

Day 38: Ratio Study Guide

6th Grade Math Standards: 6.RP.1 6.RP.2 6.RP.3b

Objective: Give a unit rate to describe the relationship between two different quantities; apply unit rates to solve other problems; write a ratio three ways; define ratio

Agenda:

1. Simplifying fractions practice 
2. QSSQ 
3. Pepper
4. Review the shopping from the previous day
5. Highlight the study guide 
6. Complete the study guide

Assessment: Circumventing the room as students worked on the study guide; checking the homework

Glass Half-Full: In the heat of the moment, I decided to have the students highlight all the units in two different colors on the study guide while also circling either the word to or per before they started any problem on the study guide. There was about ten minutes left in the first class and that's what really enabled me to do this - I knew I had time.

Is it something that they can apply to every problem that they ever do? No, of course not. What it did do for them was help them with the reading comprehension in the problem. They were able to truly focus in on what they were trying to find out.

Regrets: I thought the level of focus in my last class was a little lower, but overall it was a good day. A former student who is now at a different high school had the day off and actually came back to do community service by helping out our class. She was very helpful and allowed me to have students work independently instead of in partners as we normally would do. This gave students a better taste for what their weaknesses were and gave me the opportunity to offer feedback instead of a peer. There are pros and cons to that process of course, but I thought it was good because I could really dig deep in explaining what their mistakes were if it was necessary.

Link: Good blog post here from a teacher of four years on the power in the tools of no opt out, my favorite no, and going with the flow as engagement increases in class.

Day 37: Shopping & Unit Rates

6th Grade Math Standards: 6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” 29

6.RP.3b Solve unit rate problems, including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then, at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

Objective: Apply unit rate in real-world scenarios

Agenda:

1. Estimation 180 with capacity Day 53
2. QSSQ 
3. Review the Unit Rate HW 
4. Shopping Stations in the second class 

Assessment: My chief assessment was getting students to recognize the difference in the quotients of small number divided by large number and large number divided by small number.

Students could recognize for instance that 12 pencils over $3.49 was a ratio. On the bottom of the next ratio in a proportion was $1. They were unsure though if it would be 3.43 pencils for $1 or 0.29 pencils for $1. I sat with groups of four as they came to this station all afternoon and went through what made sense and what did not. Although I was exhausted from this single problem when it was all done, I felt confident that kids could reason that 3.43 pencils per $1 made sense for a number of reasons while 0.29 pencils per $1 did not. We then were able to break into a separate conversation about $0.29 for 1 pencil just before it was time to switch stations.

Glass Half-Full: I accidentally forgot to include Station 5 in the copy machine, but timing wise things worked out just fine as students had enough work to keep them on task. On top of that, I think the variety of questions and ways in which students needed to apply unit rate made for a deeper learning experience. I've used this lesson in the past, but not with this much structure. Groups of three to four were switching every 7 or 8 minutes and for the most part the movement breaks helped students. For full disclosure here are the other pictures used at the various stations:

Regrets: The first station was harder than I meant it to be. The example problem does not appear to be an example or a template for the remaining problems. I would probably just do the problems like Station 2 in the future and revamp Station 2 to ask students if $0.25 per egg makes sense or $2.31 per egg makes more sense and why. That way there is still that variety, but students can take what they learned in Station 1 with me and apply it elsewhere.

I also assigned this as homework. It is probably not necessary because going over it the next day would take a lifetime. Maybe just making one part homework (Pepsi) would be a better use of my time and their time.

Link: I'm not going to do this Halloween task from Yummy Math, but I love the idea of asking students for the questions to consider when planning the most effective route to get their candy. I think it's something that they will actually think back on.

Day 36: Unit Rates

6th Grade Math Standards: 6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

6.RP.3b Solve unit rate problems, including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then, at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

Objective: Define unit rate; describe the relationship between two quantities as a unit rate of each quantity

Agenda:

1. Open Middle - Ratios 
2. QSSQ
3. Pepper
4. Unit Rate Notes
5. Unit Rate HW 

Assessment: I had students stand up when they completed certain sections of the note and then students assessed one another by walking around the room. There was also time left in class to do the homework so I circumvented the room while students worked in partners.

Glass Half-Full: The Open Middle problem was answered by only one out of forty students. I give the hint of "halves" to all classes although that hint is a little misleading since really it's the reciprocal of halves in the answer.

Interleaving with the greatest common factor of 120 and 96 was great because students were forced to plug in their divisibility rules to make it work and about half got a wrong answer among those that attempted it.

Again this year with this lesson I let the students use calculators to check their work. Very good idea as the numbers and the time it takes some students can distract away from the concept of unit rate.

Regrets: The way that students formatted the problems independently was showing division problems when I wanted to see units in many cases. I need to get more emphasis on the setting up a proportion. I also never really introduced the term proportion with the students.

The problem with the ice cream was not done very well by the students. Most students could not show the work effectively and gave up. In my opinion, it was a laziness issue where the homework was mostly done in class, but this problem being the fourth of five, was not done int class. I really like this problem too because it incorporates least common multiple as a method for solving (and probably the most logical way to solve it too).

Link: The author of this Math with Bad Drawings article is basically saying that students subjected to these should have every right to rip up the paper. I don't disagree. If the assignment was changed though to making the drawings make sense as the author did though you may have a very challenging assignment for some students.

Day 34 Nana's Paint Mix Up

6th Grade Math Standards: 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

The Learning Objective: Determine if two ratios are equivalent; make two unequal ratios equivalent by manipulating the units

Quote of the Day: Born into poverty, Lincoln was faced with defeat throughout his life. He lost eight elections, twice failed in business and suffered a nervous breakdown. He could have quit many times - but he didn't and because he didn't quit, he became one of the greatest presidents in the history of our country.

Here is a sketch of Lincoln's road to the White House:

1816 His family was forced out of their home. He had to work to support them.

1818 His mother died.

1831 Failed in business.

1832 Ran for state legislature - lost.      

l832 Also lost his job - wanted to go to law school but couldn't get in.         

1833 Borrowed some money from a friend to begin a business and by the

end of the year he was bankrupt. He spent the next 17 years of his life

paying off this debt.

1834 Ran for state legislature again - won.         

1835 Was engaged to be married, sweetheart died and his heart was broken.

1836 Had a total nervous breakdown and was in bed for six months.         

1838 Sought to become speaker of the state legislature - defeated.

1840 Sought to become elector - defeated.        

1843 Ran for Congress - lost.  

1846 Ran for Congress again - this time he won - went to Washington and

did a good job.   

1848 Ran for re-election to Congress - lost.       

1849 Sought the job of land officer in his home state - rejected.   

1854 Ran for Senate of the United States - lost.

1856 Sought the Vice-Presidential nomination at his party's national

convention - got less than 100 votes.    

1858 Ran for U.S. Senate again - again he lost.  

1860 Elected president of the United States.

Question from Yesterday (as always from a student): Does the order matter in a ratio? Is 3 Kittens to 5 puppies the same as 5 puppies to 3 kittens?

What would happen to a ratio that was already put in simplest form if we added one more part to either ingredient? So if we had 20 chickens to 10 wolves and that ratio was simplified to 2:1 could it be 2:2 or even 1:1 if we added one more wolf?

Assessment:

Agenda:

1. Estimation with capactiy Days 51 and 52
2. QSSQ
3. Review homework and exit ticket (for the class that did it)
4. Nana's Paint Mix Up (from Dan Meyer)

Glass Half-Full: Last year when I was doing this lesson, I did the Partial Product from Dan Meyer. This was a good lesson, but as far as I'm concerned Nana's Paint Mix Up might have been the best lesson I've ever done.

I had students write in their notebooks what actually happened on one side and what nana wanted to happen on the other side before the videos were shown. I also had them take out a red colored pencil and another colored pencil of their choosing.

Next I had them partner up before finally showing the video twice to the class. The students were given one minute to decide if the problem was possible to fix. Only two students said it could not be fixed, but they were quickly persuaded to jump off that boat. Next, I had the students to determine how to fix it and that's where the fun started.

One pair of students immediately concluded that by scooping 24 reds the problem would be fixed. They seemed to nail it, so I gave them the sequel question of finding more than one answer to fixing the problem. Other pairs of students struggled. I mean really struggled. When I was set to start going over the problem, I asked one pair of students if they wanted to leave the room so they could not see the answer and they complied. Three other groups followed them out the door into the neighboring class (which is a math class so the teacher did not care).

Then the group that had immediately gotten the answer who I was worried would be bored for the rest of the class opened up Pandora's Box. They argued that 25 red to 5 white was a way to do it. Correct. They then said that 30 red to 10 white was another way to do it. And they would not get rid of that thought. I said nothing. For once in my life. Three other groups kept trying to refute what they said, but that original group just coming back with reasons that their answer worked. Eventually a chart set them straight. Then we invited the seven students back into the room. One group concluded that by adding 8 red, the ratio was now 9:5 which is the same as 5:1. We set them straight with a drawing.

Overall the lesson was an excellent example of having a belief and setting that belief straight with the definition that for every five red there is one white.

Regrets: The book is horrible for the homework. Not only are the problems boring, but there's no room to put a quality answer on the page. The spiral notebook is a necessity. There has to be a better way of getting kids to practice these skills.

Link of the Day: Solve Me Mobile. Good for equations. Could be good for more too I just found it and need to start exploring some more.

Day 33: Ratios Intro

6th Grade Math Standards: 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

The Learning Objective: Define ratio; give an example of a ratio

Question from Yesterday (as always from a student): What was Jeanine's rate of putting together calculators for one hour?

Assessment: Students stood on their own when they were done a problem and were either checked by me or a classmate. Students also journaled their results of the decimal quiz and put a date that they would make up the quiz if they were unsatisfied with their results.

Agenda:

1. Record and reflect on the decimal quiz. I asked the students to write how they studied, how long they studied, a question that they have, and what day/time they will make up the quiz if they are unsatisfied.
2. Review the decimal quiz
3. More depth to the ratio notes (you can write them three ways, highlight the words before and after "to" in a word problem two different colors. Student copy and my copy
4. Rip out and start the homework from the textbook. 

Glass-Half Full: The notes this year were revamped. I included a problem that was released from the MCAS a year or two ago.

I also liked the idea of making students write a date out that they were going to be retaking the decimal quiz because I have not done this before and this made them slightly more accountable than they have been in the past.

Regrets: I have always used an exit ticket with this lesson and only did so in one of my three classes this time around. It could lead to homework being done in an unsatisfactory manner, which means that homework would be pointless tonight.

Link of the Day: National Council of Teachers of Mathematics is looking into changing a high school model of math that is largely broken. Here is the announcement from the NCTM president Matt Larson.

Day 32: Decimals Quiz

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

The Learning Objective: Use decimal operations in real-world and mathematical problems; give an example of a rate

Question from Yesterday (as always from a student): Is dividing by 0.5 and multiplying two the same thing?

Assessment: The decimal quiz (including the post assessment of the pre-assessment we did before starting the unit).

Agenda:

1. QSSQ
2. Decimals quiz
3. Take the post-assessment 
4. Work on WQ #6

Glass-Half Full: There were improvements made in the pre and post test of the decimals assessment.

Regrets: There were low grades on the decimal quiz and the average was the lowest of any assessment we have had this year. That being said, I think that the study guide indicated the previous day that students were making small errors and comprehending their errors after the fact. I think to some extent, we just need to push forward because this will be a skill we continue to build on in ratios and measurement as well as in our daily warm ups and weekly quizzes.

Link of the Day: I just found this one on Twitter courtesy of @DebbieHurtado who found it from NPR Sunday Puzzle by Will Shortz on October 23rd. Use the digits 5, 4, 3, 2, and 1 in that exact order and the four operations as well as parenthesis to find as many numbers from 1 to 40 as you can.

Day 31: Decimal Study Guide

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

The Learning Objective: Divide with decimal divisors and decimal dividends

Quote of the Day: “When your attempt rate is high, each individual failure becomes a lot less significant…Accepting failure doesn’t just make risk-taking easier. In a surprising number of instances, it’s the only reliable path to success.” – Ron Friedman

Question from Yesterday (as always from a student): "Why do we say 'slide' the decimal in division problems? Is it possible to get a quotient that is greater than 1 and less than 1?"

Assessment: Circumventing the classroom; checking the homework; hearing responses during pepper

Agenda:

1. Open Middle Monday - We changed this so that it was only finding the smallest possible sum.
2. Quote, Star Student, and Questions of the Day
3. Review of the word problems from the homework/pepper
4. Study Guide
5. Frayer Model of the 4 problems  (if time)

Glass-Half Full: I caught many students writing 0.9 to the quotient of 0.72 divided by 8 instead of 0.09. This error is easy to catch after the fact, but hard to catch the first time the problem is done. It's why it is so crucial that students have a strong foundation with how money works. I'm finding that students are having less and less of a foundation with money now than they were even eight years ago. Perhaps it is inflation that is causing the problem, but in any case it is creating bigger gaps in these students comprehension of decimals.

Regrets: The open middle problem was not answerable and in many cases a little too difficult because of the plus/minus signs and the issues surrounding adding and subtracting negative decimals. These are not technically in sixth grade standards so I don't like it to go into great depth because our plates are full as it is with the sixth grade curriculum.

Link of the Day: The video on assistments is less than three minutes long. I watched and thought it was a good advertisement, but haven't tried it yet. One of the teachers at my school swears by what it offers, so I'm going to give it a try.

Day 30: Dividing with Decimal Divisors

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

Objective: Divide with divisors that are decimals

Question: When Mr. Stadel poured the liquid into the vase, how did he know how many liters and ounces were leaving one vase and entering the other?

Agenda:

1. What Doesn't Belong Number 6 and Number 18
2. QSSQ
3. Review HW & Pepper
4. Decimal divisor 5 questions to wonder
5. Decimal divisor practice (three sample problems)
6. Decimal divisor homework

Assessment: I was circumventing the room as students worked in partners on the decimal divisor five questions to wonder.

Glass Half-Full: The students were really curious as to what 360 divided by 0 was by the time we got to the end of the paper. What most of them failed to recognize though was that zero was lower than all of the decimal numbers that they were dividing by. They were insisting that the answer had to be zero.

On the spot I thought to have students who were getting zero check the work the same way they would check the work by doing 12 divided by 4 and multiplying their quotient by the divisor. When that did not make sense we had to conclude that the idea of zero being the quotient was also flawed. Ultimately I had them type it into their phone and they received an error message back. 

I think there is room for growth within this lesson as the realization of anything divided by zero is somewhat of a shock to the system they were used to knowing. We worked in strategies with similar numbers (as in how many half dollars can you fit in two dollars and the afore mentioned 12 divided by 4) to make sense of the solutions we were getting with 360. It was only five questions, but I might even shorten it down to four as a result of the amount of time that we can continue to explore the answer to these questions without me giving too much direction. I could just plug in most of the chart where they have to divide in question one. 

Regrets: I'm having a hard time of involving my students that are quieter and more specifically lacking skills or confidence in their number sense when we do the What Doesn't Belong activities. The way I set up this is by having students right reasons and numbers in their notebooks as I go around the room checking homework. The students then are grouped based on the seating in the room on to four separate teams. Each team has a turn to say one thing and then it cannot be repeated again by another group. We generally go around the room three teams with the students pointing out anywhere from four to eight differences. The same people are always participating. Perhaps what I could do is have everyone pass in their work to confirm that certain students are at least participating in writing.

Day 29 Dividing with the Dividends as Decimals

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

Objective: Divide numbers that have a decimal in the dividend.

Question of the Day: Is it possible to have the quotient be higher than the dividend?

Agenda:

1. Estimation 180 - Capacity
2. QSSQ
3. Review Multiplication HW and Pepper
4. My favorite no. 2 divided by 5. 
5. Division with whole number divisors and decimal dividend notes
6. Start the homework 

Assessment: The multiplication homework was checked to see if students were estimating and solving correctly. The My Favorite No problem was checked to see if students knew how to annex a zero and if they knew where to put the dividend and divisor before starting the notes. The notes were done in the format of I do, you do so students stood when they were done and were given feedback from me or a peer.

Glass Half-Full: As a way to differentiate, I had students determine the quotients to many common fractions. Once they had shown the My Favorite No problem without any issue and the same students had also done well on the pre-assessment from last week there was no point in having them take notes. These students then worked in pairs to find what one divided by nine was, two divided by nine, etc. I gave them random fractions including thirds, sixths, sevenths, and elevenths as well.

Regrets: I wish that I had a worksheet for these students with some type of written instructions because they were initially a little confused not by the math as much as they were by what I was asking of them. Good differentiation, but it could have been better.

Link: I really like the chart that MARS (Mathematics Assessment Project) uses for differentiating between GCF and LCM in this lesson.

Day 28: Multiplying Decimals

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

Objective: Multiply decimals to find a product; justify the answer to a multiplication of decimals problem in a real-world and mathematical context

Agenda:

1. Visual Pattern #16
2. QSSQ
3. Review Homework
4. Multiplication of Decimals My Favorite No
5. Multiplication of Decimal Notes or students who mastered it already could do the Yummy Math NBA Best Player with a partner
6. Multiplication of Decimals Practice 

Assessment: My favorite no was assessed to see what students would come up with for an estimate to the problem 4.2 x 8.53. I asked students to first write a number that did not make sense for a product. Then I told them to write an answer that would make sense, but not do any calculations. They come up from fifth grade either without the skill or they simply rehearse that the decimal point needs to slide. I want them to have the number sense to be able to check their answers quickly and see if the answer makes sense or not. I have also found in the past that some kids cannot memorize the rule of sliding the decimal over, so my strategy was to have students put an estimate in as a way of making sense of their answers.

Glass Half-Full: I crossed out many of the problems students needed to do on the homework and instead told them to put in an estimate on the problems that they did have to do which was about seven problems in each class. I wanted the idea of estimating to be drilled in because students have a hard time doing this on their own for whatever reason - perhaps it is perceived as more work. To me though this skill (making sense of the answer) is the most essential part of multiplying decimals because it is apparent that they will have the tools to calculate these problems in their pockets anyway, but that will not save them from knowing when and knowing why. That is what needs to be built in.

Regrets: This is good effort. I think.

Visual patterns are designed to teach students that they can do this, but should look for an alternative. The student who did this was really proud and asked if I wanted her to finish at home since I took a picture of it. I said she was nuts.

Link: Lessons from Illuminations.

Day 27: Adding & Subtracting Decimals Continued

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

Objective: Add and subtract decimal numbers to find a sum or difference

Agenda:

1. Open Middle - Adding Decimals to Get to 1
2. QSSQ 
3. NBA Yummy Math or Adding & Subtracting Decimal Practice from a worksheet
4. Weekly Quiz

Assessment: I circumvented the room throughout both #1 and #3 on the agenda.

Glass Half-Full: There was a good deal of retention after the students had three days off from class which was encouraging. The Open Middle problem was very effective for getting students to be engaged and persistent, but I did have to carefully model and explain the directions to the students. I have not used Open Middle much in past years, so I think this might just be a learning curve similar to what students experience with Visual Patterns every year. Nonetheless, once they got going it was great to see their work - even in the cases where students were not able to achieve the best potential answer. I even had a student get exactly one on a sum, but as another student correctly pointed out the digit nine was used twice.

Regrets: It was interesting to see how different classes handled the Open Middle problems. I did a think, pair, share in all of my classes. In one of those classes we came up with several correct answers and in the other two we came up with none. The variety of depth to which the students in each class understood the problem was fairly significant and not something I accounted for in planning. I'm not sure what I could have done differently other than to have something ready such as come up with a second way to get to 0.999.

Day 26: Adding Decimals

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

Objective: Add decimal numbers and subtract decimal numbers to find a sum or difference

Agenda:

1. What Doesn't Belong?
2. Collect WQs 
3. My Favorite No - subtracting decimals (8 - .6)
4. Decimal Notes or Yummy Math Best NBA Player
5. Exit Tickets 
6. Decimal Addition and Subtraction practice from the textbook 

Assessment: The exit ticket was based on this photo.  On an index card, students needed to tell me what was wrong and how it could be fixed.

Glass Half-Full: It was good to differentiate. The students that did the Yummy Math activity really struggled with the directions because it is a good deal of reading comprehension on top of the math involved. I was able to get to them between the moments that students were thinking on the notes. I think it indirectly served as a good way to keep my pace at an appropriate level for processing time.

Regrets: Textbooks are horrible. Especially last thing on a Friday. There has to be a Yummy Math version of beginner decimals.

Day 25: School Fundraiser - The Rollathon

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

Objective: Perform the four operations in decimals problems

Agenda:

1. Self-Assessment from Prime Factorization Quiz
2. Review the prime factorization quiz
3. Decimal pre-assessment
4. Decimal Place Value Notes - we just wrote a number and put the place values in by tilting a notebook sideways and putting one number between each of the blue lines
5. Destination Elimination

Assessment: The decimals pre-assessment was pretty important because it sets the table for the next week or so. The students that did not do the problems correctly will be taking notes on how to line up decimals, estimating to get products, etc. The students that did these problems correctly will be doing the Yummy Math NBA best player activity instead of the notes. It's a good opportunity to differentiate the students, but also give the students that need the remediation an opportunity to go at a little slower pace.

Glass Half-Full: Shortened classes and distracted classes today as a result of the school fundraiser which let students ride their bikes and rollerblade around the school. It was productive for me and engaging enough on a day where students were either hyper or exhausted (depending on what time they were in the room).

Regrets: Kids struggle to do the Destination Elimination game without very explicit directions from me. I learned in the second class, but it was quite annoying in the first class.

Day 24: Open Middle, Visual Patterns Let Me Grade

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.

Objective: Determine if two numbers are relatively prime; find the product of prime numbers given a composite number

Agenda:

1. QSSQ
2. Quiz on Prime Factorization
3. Students work on their weekly quiz or read a book
4. At the start of the second class, students were given this packet to do in partners. I focused on getting them to write what they know, what they're finding and estimates instead of worrying about the answer since some problems were especially difficult (most notably Visual Pattern #3 - see picture below)

Assessment: The quiz was graded and I got mixed results, but it seemed like the students were at least willing to admit that they were well prepared. I had many students check off simple mistake to wrong answers the next day in class.

Glass Half-Full: Doing the Open Middle, What Wouldn't Belong, Visual Patterns, and 7 Puzzles questions after the quiz was a great way to break up the day. Students had more creative freedom on these and I could hear partnerships working through problems together. In two out of my three classes I did not need to leave my desk once to redirect students so these problems were appropriate challenges. All the while, I got to give students feedback on the weekly quiz and the quiz as I was grading them one on one.

Regrets: My only regret would be the lack of time the next day spent on reviewing the challenge packet for after the quiz. In one of the classes we really got into visual pattern number three (although nobody ultimately had it solved). The chart above was done at the bell and the student who wrote it ordered it not to be erased. I did not erase it. I made another student do it.

Link of the Day: "At some point, self-conciously 'understanding' why you do what you do just slows you down and interrupts flow, resulting in worse decisions," Barbara Oakley stated in this article about her STEM journey that cries out for the need to develop fluency in order to understand complex subjects.

Day 23: Study Guide & Sieve of Erastothenes

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.

Objective: Find the prime factorization of a composite number; identify a number as prime or composite; determine if two numbers are relatively prime

Quote of the Day: “Colonel Stas Preczewski, coach of the army crew team at West Point a few years ago, faced a baffling problem. Through extensive testing he had determined the strengths and abilities of every rower on his team. He had measured each man’s power on ergometers and had composed crews in every possible combination in order to calculate each member’s contribution. He was able to rank his rowers objectively and precisely from best to worst. He then put the eight best in his varsity boat and the eight others, the weakest, in the junior varsity boat. The problem: The JV boat beat the varsity boat two-thirds of the time...The varsity boat was full of resentment over who was contributing the most, while the JV rowers, feeling they had nothing to lose, supported one another happily.
One day he [Coach Preczewski] lined up the varsity crew in four pairs. He told them they were to wrestle for ninety seconds. Only rule: no punching. ‘It was like WWF,’ he recalls. When he stopped them, he noticed that no one was winning. Each man was discovering that his opponent was just as strong and determined as he was. Preczewski then had them change opponents and wrestle again. By the third round they were choosing their own opponents - ‘One guy would point at another and say, ‘You!’ Peczewski says. On the fourth or fifth round, one of the rowers started laughing, and they all piled into a general brawl. Eventually someone said, ‘Coach, can we go row now?’ From then on the varsity boat flew, and made it to the semifinals in the national tournament.” - Geoff Colvin
Question of the Day: "Is there any case where two numbers don't have a common factor including one?"

Agenda:

1. Visual Pattern #12
2. QSSQ
3. Review Homework
4. Study guide on prime factorization
5. Coloring the 100s grid (Sieve of Erastothenes)

Assessment: The study guides were done in pairs, so I went around the room to check in with students. Given the dearth of problems on the study guide, if I saw an issue I would create another problem on the spot and have a student do that or get a partner who had the right information to teach the other partner in front of me.

Glass Half-Full: I had two students who really have struggled to this point in the year write everything they know based on the drawing of the visual pattern. One made a chart, wrote how many green and how many black diamonds there were, and from there we were able to have a very good conversation. All of it started though with what we know and it only took two minutes (I timed it).

Regrets: The Sieve of Erastothenes was not done as well as I would like to see. I could have given the students written directions that told them to circle the prime and then color its multiples instead of doing it orally.

Link of the Day: Dan Meyer has done it again. In a lesson that teaches the math and the morals. Pokemon Go.

Day 22: Greatest Common Factor Via Prime Factorization

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.

Objective: Find the greatest common factor of two numbers using prime factorization

Question of the Day: "Are all numbers less than one negative?"

Agenda:

1. Open Middle Largest Product
2. QSSQ
3. Review the homework problems on prime factorization
4. Pepper
5. GCF with prime factorization notes
6. GCF with prime factorization marker board practice
7. GCF with prime factorization homework

Assessment: Reviewing the homework, pepper, making students stand up when they were done a problem on the notes.

Glass Half-Full: I had to rush through the notes because Open Middle got us off on a tangent and took longer than I had anticipated for the students to recognize what strategy made the most sense. In rushing through the notes, when I went to assess the students formatively at the end of the block it was pretty apparent that in many instances they just were not ready for the homework. Thus, I had the students skip four out of six of the problems where they had to find the greatest common factor using prime factorization. The sections on the homework that they had to list prime and composite numbers was still relevant, quick, and informative (for me not them) review so that part was done. And the students were basically given the go ahead to get the other two problems wrong by me if need be so that they could at least be curious to see how it should be done in class the next day.

Regrets: Open Middle was awesome. To me. The students missed the point to some extent because they got hung up on multiplying the wrong numbers and then assuming that they were right. Perhaps if they had a calculator, they would have tried more numbers and been better able to explain the theory behind why the product was biggest when the tens place had a 9 and the smaller tens place had the larger ones place. This also would have allowed for more opportunities to get practice on greatest common factor with prime factorization. There's a time and a place for fluency of course, but I also have not let students use calculators all year and I do believe the standards ask us to use tools appropriately (MP.5) and look for and make use of structure (MP.7).

Link of the Day: Apparently prime factorization is part of the cryptographic method behind electronic bank transfers. I read that in this post about how prime numbers are being calculated much faster with computers thanks to a new algorithm.

Days 17 - 21: Factors, Multiples, Zombies

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

Objective: Find the least common multiple of two or more numbers by listing the multiples; find the greatest common factor of two or more numbers by listing the factors; find the prime factorization of a number; determine whether two or more numbers are relatively prime.

Quote of the Day: “One study asked a group of people to be measurably more truthful in their dealings with others. When the study group members told three fewer lies per week than the control group participants, they experienced a variety of statistically significant health-related and emotional benefits.” - Andrew Sobel

“Immigrants are four times as likely to become millionaires as American-born citizens. This startling statistic boils down to one thing: a world-class work ethic.” -Steve Siebold

“Most people are fully engaged in microwave thinking - a deep belief that compensation should immediately follow any effort. Champions are different. They believe every effort performed with good intentions yields some form of compensation at some point.” - Steve Siebold

“As it turns out, the more types of relationships a person has the less susceptible they are to developing a full-blown cold, even after direct exposure to a cold-causing virus. When people have a wide range of connections, it provides them with a sense of psychological security that buffers them from day-to-day stress. And because they experience stress less often, their bodies are better conditioned to fend off physiological challenges when they occur.” – Ron Friedman

Agenda:

• Monday we reviewed for the greatest common factor and least common multiple test.
• Tuesday we gave the least common multiple and greatest common factor test.
• Wednesday was a half day. It was a team day in which students did not go to normal classes.
• Thursday was a review of the Test from Tuesday and prime and composite numbers.
• Friday was the introduction to prime factorization.

Glass Half-Full: The half-day was the best day of the week. Every half day rather than see the students for eighteen minutes and spit them out, our team joins forces and we focus on character development. During this week the focus was on teamwork. We chose this because many of our students are coming from different elementary schools and do not know each other well. We wanted to emphasize at this vulnerable time for them that often in life you will be placed on teams with new people, your best friends, and people that you do not particularly care for. In any case, it is important to make the most of your situation for the betterment of everyone.

In the morning, students were only with us for about fifteen minutes, so the assistant principal explained a fundraiser that was taking place the following week (the Rollathon). The students then went to their encore classes.

When they returned to homeroom all five teachers showed them the Kid President video in reference to teamwork. Then the students picked one word that summed up teamwork to them. Cooperation. Unselfishness. Together. Trust. They were compiled onto a poster and it was hung on our doors. Next we went up to the cafeteria as a whole team. Students were placed in teams completely randomly using two decks of cards (the people with the Patriots cards that had 8s and 7s went to one room while the people with the K's and Q's on the Celtics cards went to another room). There were four people per team.

When they got to the classroom, they all got instructions on the Zombie Bridge problem. I was a mobile teacher for this since it has something I have utilized in the past and it is a math problem. I went from room to room explaining to students that they would want to write what they know, create a chart, act it out, or even draw a picture.

We had three groups solve it in five different classes. It took me an hour to solve at grad school, so that was pretty impressive that three groups could get it without teachers helping them.

After working on Zombie Bridge for roughly a half hour the students made their own bridge using gumdrops and tooth picks. We stayed away from giving the students constraints such as the longest bridge or using the least amount of toothpicks. We wanted them to have artistic freedom and the task on Zombie Bridge was enough math according to the other teachers on the team. Hard to argue.

Link of the Day: Which one doesn't belong is something that can be done in all grades. This is an example of kindergarten and second grade using it. The key line in the blog post is that students never ask "Is this right?"