Sunday, May 22, 2016

Day 157: Vacation Projects Start

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“When faced with a task that daunts you, a project that you find difficult, begin by doing something. Choose a small component that seems potentially relevant to the task. While it seems sensible to plan everything before you start, mostly you can’t: Objectives are not clearly enough defined, the nature of the problem keeps shifting, it is too complex and you lack sufficient information. The direct approach is simply impossible. Every writer has stared at a blank page, waiting for inspiration. The wait is often lengthy. Get it down.” - John Kay

Question from Yesterday (as always from a student): "What are the dimensions of a rectangular prism with a surface area of 180 ft squared?"

"Why don't we call steak cow?"

The Learning Objective:

Assessment:

Agenda:

  1. Visual Pattern # 60
  2. QSSQ
  3. Flight
  4. Hotel 
  5. Rental Car
  6. Activities
Glass Half-Full: I really enjoyed the dialogue that took place in Visual Pattern #60. By now we're good about writing something down that we know (that's why I picked this quote), but going from that to problem solving strategies is not always great. This was an excellent open-middle problem (thank you Robert Kaplinsky for a fancy new term).


S1: From Step 1 to Step 2 it increases by 4.

S2: The second and third shapes have squares in them.

S1: On top of the squares is a chimney. The chimney goes up by the step number.

S3: The squares have the same dimensions as the step number.

S4: That must mean the 43rd square will have a 43 x 43 rhombus pile and 43 rhombuses going up the chimney.

Me: So, how about that 43rd step calculation Kenny?

S2: 43 x 43 + 43

Me: Uh huh. What's the rule?

Silence. Guesses.

S4: s x s + 1

Me: Write it on the board.

Several students from the peanut gallery: Include parenthesis.

Another student from the peanut gallery: If you just made a chart, you multiply 2 x 3 for step 2, 3 x 4 for step 3, etc. so you could just 43 x 44 and get the same thing.

Me: Why does that work?

Silence.

S2: Well you are adding one more group of 43 so it's like having 44 groups.

Regrets: I'm tired of kids asking me where to find the flight number. It's on the website look for it. Then again, I could just not make it a requirement for the project, but I feel like just introducing this concept to them will prove helpful to one of them later in life.

Link of the Day: This was an article on creating an environment for kids to thrive in and belong to. Eliminating competition, peer to peer insults, and making sure the students are feeling good about being in math.

Day 156: An Impromptu Surface Area Struggle

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

6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface areas of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Quote of the Day: "“Here are some examples of what putting ‘first things first’ might look like for a player:

  • Commit to seeking wisdom everyday
  • Skipping parties to put in extra training
  • Focus on the process rather than results
  • Focus on progress rather than achievement
  • Focus on developing your game versus getting exposure
  • Focus on using your sport to develop more true mental toughness rather than being used by your sport by focusing on results that are outside your control.” – Joshua Medcalf

Question from Yesterday (as always from a student): "If we know the surface area can we find the volume of a rectangular prism?"

"Can lactose intolerant people drink almond milk?"

The Learning Objective: Balance a budget by subtracting decimals

Assessment: Write around

Agenda:

  1. Turn in cereal projects 
  2. QSSQ 
  3. Vacation Directions Explained 
  4. Pick a destination

Glass Half-Full: The connection between the quote of the day and the question of the day was especially powerful.

It started out with if we know the surface area can we find the volume?

Student 1: Yes.

S2: Well I think we can get the dimensions.

S3: If the surface area is 180 feet squared, could we find the dimensions?

Me: Let's try.

And try we did. For twenty-five minutes. The teachers were trying with the students. I asked the students if they wanted to move on and there was a forceful no. Finally.

S4: I figured it out.

Me: Good for you, but more importantly good for everyone in the room. Don't be focused on the results as we said in the quote of the day. Focus on the process. Nobody wanted to give up.

Regrets: I think the vacation project is too open-ended. I need more firm deadlines for each part of the project, and if kids don't get the job done in school, they can finish at home. It's almost like the project has too much autonomy.

Link of the Day: Speaking of open-ended, Robert Kaplinsky explains the difference between open-ended and open-middle questions. I actually commented on his post that I think there is significant value in open-ended questions (which can also function as open-middle questions).

Monday, May 16, 2016

Day 151 - Day 155 MCAS and Cereal Boxes

6th Grade Math Standards: 6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface areas of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

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

Quote of the Day: "Especially for fostering creative, conceptual work, the best way to use money as a motivator is to take the issue of money off the table so people concentrate on the work." - Daniel Pink

Question from Yesterday (as always from a student): "If I get an answer that is not 540 for the surface area is it wrong?" - In reference to finding the surface area of a box with a volume of 540 inches cubed.

The Learning Objective: On days 151 and 152 we took MCAS, so all standards were in play. In Days 153, 154, and 155 we were working on a project in which the students were asked to create their own cereal. For this project, students had to find the dimensions given a volume, find the surface area based on that volume, and then give the cost to charge for creating a box if each square inch was $0.25.

Assessment: The MCAS results will be given to us in September of next year. When I asked my students what they wish they had more practice with after they had taken it, here is what they said and my response in italics (although some of them I did not say out loud, because well...):

Game night a few weeks before MCAS Would you actually show up? Class says yes. Ok cool idea.
Flashcards I recommended this exact idea to everyone. Three of you took me up on it! Three. 
Weekly quizzes can be MCAS questions More often than not, they are.
Go on CTC & Print out blank weekly quizzes I like your attitude
More challenge problems Agreed, but we need fundamentals too. Without the fundamentals it's really hard to challenge people. And oh by the way, we have a Math Academy in the morning on Fridays. 
Reviewing the day before We did. Where were you?
What concept don’t you get (give out a list of all the standards and check off what’s not there). This is a good call. It's essentially standard based. That said, it's very difficult because you have a class working all over the map. It would be my utopia, and I'd love to learn from someone who does this instead of the "factory model." 
Video review of the concepts for the pep rally Yeah. That's exactly what the pep rally was for. 
Review more of everything we’ve learned this year. Forgot greatest common factor and least common multiple We played pepper twice to three times per week. I definitely hit that standard the day before in every class too. 
Mean Absolute Deviation We could have done this better. I wish we had spent one more day on it at the end. 
Pie charts That's another good call. We had a weekly quiz on this, but to some extent this could have been covered in greater depth. 
Radius/Diameter Relationship Really? I thought we had this pretty covered.
Multiplication/division facts That's on you kid. 
Constant Rate That's on me kid. Next year we'll add it in to the linear function conversation.
Number line with negative numbers and the opposite. Why are the two numbers related? Absolute value! Next year we'll add it in to the absolute value conversation. 
PARCC questions True. A little more rigor there. 
Strategies, songs, etc. I feel like I'm beating my head against the wall sometimes...I think we did about 20 visual patterns this year and every time we talked about making a chart. I think we did about 45 Estimation 180 problems and every time we talked about too high and too low. We wrote what we know on word problems and underlined what we were trying to find. We used similar problems. We journaled about our strategies the day before the test. 
Inequalities Could have been reviewed better toward the end of the year, but all in all the unit was pretty extensive. 
Fractions into decimals, decimals into fractions, also percentages Literally every grade I give out has a fraction on it. Did you go through the year not knowing any of your grades? 

Agenda:

  1. QSSQ
  2. Persuasive Language Discussion for writing on why their cereal box is best
  3. Chomp Cereal Company work
  4. WQ #26 
  5. Rectangle ABCD courtesy of Fawn Ngyuen 


Glass Half-Full: For many of the things which students cited that we needed more help on with MCAS, there seemed to be a student who would counter what that student was saying by arguing we had it covered. Not all the work that was put into the year was lost on everyone.

Regrets: The other teacher did a 3-2-1 summary. Three things that were positive, two things to work on, and one question. That would have put a more positive spin on the MCAS debriefing.

Link of the Day: A colleague shared this opinion piece on someone who reflected on seeing classrooms in Finland. A few things that I already knew include the teacher following students up through the early grades and the overall philosophy that less is more (shorter school days and starting school later in life). Her opinion that there are still good and bad teachers was something new and different for me as I was under the impression that bad teachers are generally weeded out.

Tuesday, May 10, 2016

Day 150: MCAS Eve

6th Grade Math Standards: All of them

Quote of the DayWe asked people, ranging from grade schoolers to young adults, ‘When do you feel smart?’ The differences were striking. People with the fixed mindset said: ‘It’s when I don’t make any mistakes.’ ‘When I finish something fast and it’s perfect.’ ‘When something is easy for me, but other people can’t do it.’ It’s about being perfect now, but people with the growth mindset said: ‘When it’s really hard, and I try really hard, and I can do something I couldn’t do before.’ ‘When I work on something a long time and I start to figure it out.’” – Carol Dweck

The Learning Objective: Get excited for MCAS

Assessment: I had students journal what they do when they are stuck on a problem. It was more of a spontaneous idea, but led to great discussion.

Agenda:

  1. Journal when you are stuck
  2. Pair and share your responses
  3. We went over the responses as a class
  4. Review the weekly quiz (MCAS simulation) 
  5. Clickers assessing percent problem, coefficient, and equations
  6. Vocabulary bag games

Glass Half-Full: The videos to pump students up for MCAS were shown as part of an assembly at the end of the day. Thanks to Jason Derulo and Disturbed for the music.

What is the Distributive Property

It's MCAS

Regrets: I really liked the idea of having the students journal strategies to use when they are stuck. This could have been something to build in more throughout the year. I have gradually gotten away from journaling and writing, and it is a necessity for math teachers to have this skill built into their classrooms.

Saturday, May 7, 2016

Day 149 MAD Continued & Year in Review

6th Grade Math Standards: 6.SP.5 Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

Quote of the Day"How wonderful it is that nobody need wait a single moment before starting to improve the world." - Anne Frank

Question from Yesterday (as always from a student): "If the data set is all number one through five and then there are three 25's is the 25 an outlier or no because there are three of them?"

"Do we include a number as part of the mean absolute deviation if it is zero away from the mean?"

The Learning Objective: Find the mean absolute deviation; solve expressions that feature absolute value brackets; reflect a point across an axis in the coordinate plane; simplify expressions by combining like terms

Assessment: The clickers were brought in in the second class to assess every learning objective above besides the mean absolute deviation. For mean absolute deviation, it was assessed by circumventing the room as students worked to find how many moons each planet had. The students seemed to grasp the idea with the notes that were given to them as a reference.

Agenda:

  1. Jumpstart asking students how many paperclips could be chained in 24 hours if 1 paperclip was chained every four seconds
  2. Thumbs up/Thumbs down practice on mean absolute deviation (this is one of the most useful things I did in graduate school!) 
  3. Mean absolute deviation practice in pairs
  4. Jumpstart with reflections (this was a huge issue yesterday with clickers). Highlighters passed out so students would know which access was to be reflected.
  5. Clickers assessing the reflection questions as well as questions about the other issues covered in today's objectives
  6. Paper bag vocabulary. 30 seconds per person in groups. 1 minute per group on teacher to group questions. 10 seconds for a group member to draw a picture of the vocabulary term for their group before anyone could guess. 

Glass Half-Full: I came up with the last game of giving a student a word (such as inverse) to draw an example of on the board and that person's group had ten seconds to guess it on the fly. Once the ten seconds was up, anyone in the class could guess. It was very exciting and loud. I think the teachers next door would not have liked it as much.

Regrets: Mean absolute deviation is what it is. I was talking with a cousin who is a sixth grader in another district and she has no idea what mean absolute deviation is. In other words, she has not been taught that concept. It's pretty silly to ask sixth graders for this because it does not mean anything to them at this age, but I teach it cause of the standards. Teach might not even be the best word for it - gloss over it. For some students it's great, but then there are those students who are still struggling with division, so finding the mean is hard enough. I wish this standard was removed from the common core.

Link of the Day: Really cool idea for presentations that gives the audience a larger role. I'll be having the students present something probably a week from Friday.

Thursday, May 5, 2016

Day 148 Mean Absolute Deviation Intro

6th Grade Math Standards: Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

Quote of the Day: It was a very long quote about the life of a child to slave parents who started a school by the name of Mary Bethune.

Question from Yesterday (as always from a student): Why is that a product can be smaller than a factor?

The Learning Objective: Describe measures of central tendency and variation based on a data display

Assessment: Clickers, self-assessment form

Agenda:

  1. Self-Assessment
  2. QSSQ
  3. Quiz Review
  4. Clickers (combining like terms, identifying a coefficient, reflecting a point across an axis, determining a ratio, and identifying the formula to find the circumference of a circle). 
  5. Pepper
  6. M.A.D. Introduction


Glass Half-Full: On identifying a coefficient, determining what formula to use to find the circumference of a circle, and determining a ratio my classes were more than 80% correct.

Regrets: Students were sitting in groups of four today during the mean absolute deviation lesson and really should have been sitting in rows because it is a large deal of direct instruction. Whenever I was talking it seemed like every student just tuned me out. I need to use simpler numbers perhaps and just do several examples with them instead of one giant example.

Link of the Day: Football analytics form Ravens linebacker John Urschel.

Day 147 Displaying Data Quiz

6th Grade Math Standards: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. MA.4.a. Read and interpret circle graphs.

Quote of the Day“What really motivates people? Is it money? Titles? The answer – which is supported by extensive research – is personal recognition for doing a good job.” - Andrew Sobel

Question from Yesterday (as always from a student): "Is it possible to find an outlier by looking at a histogram?"

The Learning Objective: Describe measures of variation and central tendency in data displays; construct histograms, box plots, and line plots

Assessment: The quiz on displaying data.

Agenda:

  1. QSSQ
  2. Take the quiz
  3. Fix the weekly quiz 
  4. Clickers
  5. Vocabulary bags (one round of 30 seconds for each person in groups of six followed up by one round of one minute each with me giving the questions)


Glass Half-Full: The vocabulary bag activity was an excellent ten minute filler. I had two students stand at each side of the room as "hawks" for any groups that were not paying attention during the second round. If the hawks saw that these groups were not paying attention they took a point away. It's important that before picking the hawks they know that the hawk must have honesty and responsibility to carry out their roles.

Regrets: The problem about what range of numbers is covered in a histogram was not well understood by the students. Also students were unaware that the first quartile to the median was 25% of the data set.


Tuesday, May 3, 2016

Day 146 Displaying Data Study Guide

6th Grade Math Standards: 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. MA.4.a. Read and interpret circle graphs.

Quote of the Day“Many people believe that if they could just make more money, they would enjoy their work. Ironically, it’s the other way around: If people viewed their work with the right mental attitude, they would probably make more money.” - Napoleon Hill

Question from Yesterday (as always from a student): "How does a paper cut work?" "If the bars are not connected on a histogram wouldn't it just be a bar graph?" "Is the outlier of the data set with Tom Brady's interceptions 8?"

The Learning Objective: Construct a histogram, line plot, and box plot

Assessment: Study guide, clickers

Agenda:

  1. May Mayhem jumpstart on volume with fractional edges, surface area, distributive property, and combining like terms 
  2. Homework review of the histograms
  3. QSSQ
  4. Study guide done either with a partner or indivdually
  5. Encore performance of May Mayhem with the same types of questions as part one but different numbers
  6. Weekly Quiz (if time allows)


Glass Half-Full: The second time around with the May Mayhem there was significant improvement compared with the first time around. That should not be a surprise or anything, but what was nice was actually doing this a second time in the same day. I'm going to assess the same four concepts tomorrow during May Mayhem and hope that they have stuck.

Regrets: One idea I had today not just for this lesson but for all lessons was to create a challenge component to every worksheet/assignment we do. Again, this is not a novel concept (it's called differentiation), but it is something that I do not currently do. This is of course a huge undertaking though.

Link of the Day: It's just under 100 days until the Olympics begin! Mathalicious has a cool lesson for the occasion.

Monday, May 2, 2016

Day 145 Histograms Day Two

6th Grade Math Standards: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. MA.4.a. Read and interpret circle graphs.

Quote of the Day“Psychologist Jeremy Dean notes that we have a name for people who don’t experience negative emotions: pyschopaths.” – Ron Friedman

Question from Yesterday (as always from a student): "Why is there no space between the bars of a histogram?" - Kyle Hogan

The Learning Objective: Design a frequency table to construct a histogram

Assessment: Tom Brady's touchdowns by season (exit ticket)

Agenda:

  1. Jumpstart on box plots
  2. Weekly Quiz Review
  3. QSSQ
  4. Pepper
  5. May Mayhem Day 1 (questions revisiting area of a triangle, surface area of a rectangular prism, volume of a rectangular prism, and distributive property)
  6. Tom Brady Histograms practice (interceptions)
  7. Tom Brady Histograms exit ticket (touchdowns)
  8. Histogram homework

Glass Half-Full: Getting students to do the Tom Brady histograms problem as the exit ticket in the second class was perfect. I was able to quickly point out the common errors I was seeing (unequal intervals, lack of a title or labels, and using a scale unnecessarily too large for the frequency portion of the graph). I also was able to clarify to students that intervals need not start and end with a number in the data set.

Regrets: There was about a ten minute lull period in one of my classes today for students that finished the homework early and also did fine on their MCAS simulation. Some sort of challenge could have alleviated this type of scenario.

Day 144: Intro to Histograms

6th Grade Math Standards: 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. MA.4.a. Read and interpret circle graphs.

Quote of the Day: "-Young lady, how long would it take you to become a psychologist?
•“About seven years,” she replied.
•-How old would you be by then?
•“I will be twenty-five.”
•-How old will you be in seven years if you don’t become a psychologist?
•“Well, I guess I would be about twenty-five.”
Five years from today you will be five years older. The question to ask is, Will you be five years wiser?” - Napoleon Hill 
Question from Yesterday (as always from a student): Why is it always that each box of the data set represents 25% of the numbers?

The Learning Objective: Describe the data in a histogram

Assessment: Page 875 #13 - 16 in the textbook

Agenda:

  1. Jumpstart
  2. Review the box plot homework
  3. QSSQ 
  4. Histogram definition and description from the textbook (page 872)
  5. Exit ticket from page 875
  6. Constructing a histogram notes

Glass Half-Full: Today we had an assembly last block which cut the size of the blocks by a few minutes each. That was not an issue in terms of getting to the assessment of the objective.

Regrets: The word interval is a tremendous hurdle for students to walk over. The textbook does not really highlight it as a vocabulary word, but it appears to be brand new for everyone. There needs to be a good amount of time devoted first to the term interval and then we can launch the lesson here.

Day 143 Constructing a Box Plot

6th Grade Math Standards: 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. MA.4.a. Read and interpret circle graphs.

Quote of the Day: "The greatest compliment to any player is that he or she is a great teammate. We can’t all be great players, but we can all be great teammates.” - Jay Bilas

Question from Yesterday (as always from a student): "Will the number line ever be shorter than the whiskers in a box and whisker plot?" - Melisa Omerovic

The Learning Objective: Construct a box plot

Assessment: Eric's Cell phone problem was done as an exit ticket. I put the notes on two separate sheets instead of front to back as it is in the attachment so that students could still have a copy of the notes after the exit ticket was passed in.

Agenda:

  1. Jumpstart/check homework
  2. Passback exit tickets 
  3. Review the homework and jumpstart
  4. QSSQ
  5. Pepper
  6. Creating box plots car problem & Eric's cell phone
  7. Box plot homework

Glass Half-Full: I had students doing the Eric's cell phone problem as an exit ticket. From this I was able to help students that needed clarity on where to end the whiskers or even just how to get started. It was a very challenging question in terms of finding the quartiles and median because there were twelve numbers in the data set. At the same time, when it was all said and done, it made a little sense that there were three numbers in each whisker and each box.

Regrets: The answers to question four were all given on the homework. That can change for next year because questions one through three are all pretty similar.