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.