Day 142 Box Plots

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: “All of the 15 actions are appropriate and productive ways of demonstrating emotional openness and the vulnerability that can accompany it.

1.     Say you’re sorry.

2.     Admit you’re wrong.

3.     Empathize

4.     Ask for help.

5.     Talk about how you feel – not just what you think – about an important issue.

6.     Compliment someone

7.     Admit a failure.

8.     Ask for advice.

9.     Use humor – joke about yourself

10. Share problems.

11. Express heartfelt condolences if needed.

12. Share personal issues as appropriate.

13. Help someone else succeed

14. Be honest.

15. Acknowledge others’ contributions.” - Andrew Sobel

Question from Yesterday (as always from a student): "Do we include all the numbers on the number line when finding the mean in a line plot or just the X's?" - Ashlyn Rago

The Learning Objective: Determine three measures of variation when looking at a box plot

Assessment: Students did an exit ticket that was checked by me.

Agenda:

1. Jumpstart on independent variables versus dependent variables
2. QSSQ
3. Students worked in groups on what could be the median, first quartile, and third quartile of a box plot without any instruction for five minutes while I corrected weekly quizzes
4. We reviewed the predictions students made (essentially took notes)
5. Samantha's Family in relation to the box and whisker plots
6. Exit Ticket
7. Start homework
8. Work on the weekly quiz

Glass Half-Full: The exit ticket verified that the students had a solid grasp on the material. I just wish that I had used a consistent exit ticket throughout the lesson (I lost track of the papers in one class and of course found them at the

Regrets: Many students plowed through the homework and weekly quiz. A point in the lesson I did not prep for, but on the fly I had students create data sets that could make sense for a box plot. Next I had them create a potential line plot based on a box and whisker plot. I'd like to have this be a little more organized in the future or even assign the next lesson instead of slowing it down as much as we did today.

Link of the Day: Teacher Appreciation Day deal from Chipotle. I guess they can use the positive PR.

Day 141: Line Plots Continued

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: “Don’t be put off if you have a difficult start with someone. Awkward beginnings can launch wonderful relationships. Work at it. Find a personal connection that will draw you closer.” - Andrew Sobel

Question from Yesterday (as always from a student): “Would it be more cost effective if the school went to tablets instead of using paper for everything?”

"Can you have a data set with only one number?"

The Learning Objective: Describe measures of variation and central tendency in a line plot.

Assessment: Students collaborated on this problem in their groups of four.

Agenda:

1. QSSQ
2. Homework Review
3. Dot plot notes (Mrs. Mullen's class)
4. Pepper
5. Sunshine Problem attached above
6. Start the homework

Glass Half-Full: Tons of differentiation on the homework today for students that had mastered how to find the measures of variation and central tendency, and all it took was a couple of climbs up Bloom's Taxonomy. Among the questions that were popping were when will the IQR and the range be equivalent and when will the mode be the same as the outlier?

Regrets: I would like to have done a little bit of a jumpstart that had nothing to do with this lesson for when students walked in because I didn't really have a great opportunity to check the homework since students were not engaged. It could have been as simple as write ten ways to study for math.

Day 140: Line Plots Introduction

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: “You build strong relationships through great conversations, not one person showing the other how much they know.” – Andrew Sobel

Question from Yesterday (as always from a student): "So if we're finding the range can we just say subtract the two outliers?"

The Learning Objective: Display data sets in line plots

Assessment: Exit ticket with fill in the blank that asked students for two things that a line plot can find, what letter to use to mark data in a line plot, and for another name it is sometimes called.

Agenda:

1. QSSQ
2. Review the Test
3. Review the weekly quiz with a student's work. 
4. Have the students line up by how many colors their shirts have
5. Find the measures of central tendency and variation of the shirt colors in the classroom
6. Pass out the exit ticket
7. Pass out the homework which included 10 practice problems

Glass Half-Full: I was not planning on doing the classroom shirt colors for as long as I did, but students were asking questions and curious, so I went with it. We ended up skipping the problem that I had made ahead of time, which was fine given the results we had during the notes.
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Also of note, everything I'm doing right now and have been doing for several weeks is in groups of four instead of in lecture form. It's much easier for me and I think the students are enjoying the social interactions more as well.

Regrets: The ten problems on the homework were tedious because a few of them repeated each other and ultimately I did not end up going over these the following day. I would cross out the last problem if I were to do this homework assignment again because the extra problem did not add to the skill level for the students and only made them have a disdain for line plots.

Day 138: Variation & Central Tendency Study Guide

6th Grade Math Standards: 6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.
6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
6.SP.3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Quote of the Day:“George Washington Carver was born in 1864 to slave parents. His earliest recollections were the death of his father and the kidnapping of himself and his mother by slave traders in the last year of the Civil War. Though his mother was never heard from again, a racehorse valued at $300 was given in exchange for him.
Five years later, when freed by the Thirteenth Amendment, Carver faced all the disadvantages associated with poverty, race, and ignorance. He was thirteen years old. With an insatiable thirst for knowledge but no school to quench it, he borrowed an old spelling book and, in effect, became his own teacher. For nine years he worked as a servant, laboring by day and studying by night, until he was financially able to attend Iowa State College.
After graduating in 1894 with both bachelor’s and master’s degrees, he joined the school’s faculty, specializing in agricultural research. Carver’s students loved him. His wide knowledge of soils, minerals, birds, and flowers, and his love of nature made study under him a pleasure.” - Napoleon Hill
Question from Yesterday (as always from a student): "Could there be more than one outlier in a data set?"

The Learning Objective: Find the central tendency of a data set; use the appropriate central tendency with data sets that have various distributions; find the range, interquartile range, and outlier of a data set

Assessment: Variation and central tendency study guide done in groups; homework checked for students ability to find the interquartile range, range and outlier

Agenda:

1. Jumpstart using a stem and leaf
2. QSSQ
3. Homework Review
4. Pepper 
5. Study Guide
6. Cheat sheet 

Glass Half-Full: I did not teach stem and leaf prior to today. When students got the jumpstart, I instructed them to work in a group of four and figure out based on the context of the problem how they could find the range, median, etc. "I challenged them by saying I'm not going to help you, but I know you can do it. Take out your homework so I can check it." The response and thinking was tremendous. Only two out of about thirteen groups correctly interpreted the stem and leaf, and both of those groups utilized the key to discover what the numbers in the data set were.

The last group of students got to create their cheat sheet in class. It was amazing to see them work all the way through the bus bell on this individually. The cheat sheet was the size of an index card.

Regrets: I do not like how both the study guide and the quiz give them a number that is missing and the mean is given, but it does not contain a problem in which the students have to make the mean increase or decrease to a certain number. The skill of changing the mean to a certain number is much more meaningful in the real world than having all the data values except for one.

Link of the Day: Visual Pattern #167. Led to a great discussion for sixth graders that need a little more of a challenge. One eighth grade student came up with a different answer than I did this morning at M.A.T.H. Academy.

Day 137: Interquartlie Range

6th Grade Math Standards: 6.SP.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
6.SP.3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
Quote of the Day: “It’s about remaining mentally and emotionally balanced all time, no matter what is taking place around you. You never want to show your opponent a weakness through your words, facial expressions, or body language. No matter what they are saying to you, no matter what the crowd is chanting, if you can show poise you demonstrate to your opponent that they cannot rattle you.” - Coach K

Question from Yesterday (as always from a student): "Is the 21 an outlier in the data set 13, 15, 15, 15, 16, 21?” 

“Would the range ever be the same as any central tendency?” – Nathan Ing

The Learning Objective: Find the interquartile range of a data set

Assessment: Students completed guided practice problems on their own after we did notes; the homework was checked for understanding

Agenda:

1. Estimation 180 - The Bacon
2. Review the homework
3. QSSQ 
4. Pepper (minutes left in class)
5. Measures of Variation Vocabulary at the start of the second class
6. Interquartile range example on the notes
7. Samantha's Family from Laying the Foundation Pre-AP lessons
8. NFL Penalties Practice

Glass Half-Full: When we were doing the Samantha's Family activity, it was good to catch students putting quartiles one and three in the wrong place when the data set had six values. The tendency is for students to put the quartiles between two people, but since the values less than the median and more than the median are three on either side, only one number is needed to represent the quartiles.

Regrets: Students in general are too goofy during the activity to get them to focus on the math aspects of the concept. I would like to warn them ahead of time to have discipline toward the mathematics aspect of the activity.

Link of the Day: Nothing to do with math, but then again we can change that. Fidel Castro wrote a letter to FDR. In it he asked for $10. What is that worth today adjusted for inflation?

Day 136: Measures of Variation Introduction

6th Grade Math Standards: 6.SP.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
6.SP.3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

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

Question from Yesterday: "A square with a side length of 8 has an area of 64 square units and a perimeter of 32 units. Is the perimeter of a square always half the area?"

The Learning Objective: Find the range of a data set; determine the appropriate measure of central tendency with and without outliers

Assessment: Students did two problems with a partner and I circumvented the room as they did this; fist of five

Agenda:

1. Self-Assessment from yesterday's quiz
2. Quiz review
3. Partners to find the range of two data sets with identical median, mean, and mode
4. Outliers examples
5. Appropriate measures discussion and practice
6. Lawyers Salary practice

Glass Half-Full: The appropriate measures practice was done best in my last group today. What I did well in this group was let the students establish an argument that two or even all three central tendencies could describe a data set, but then have them go back and converse about one if they had to pick only one out of the three to describe the data set. This opportunity was only ten seconds in length but proved helpful for these students.

Regrets: I wish that I had more examples and more engaging examples (picture for instance) of outliers. I used the Baseball Reference page for Jose Bautista to show how he was hitting only around 15 home runs per season until 2010. There are many more examples out there, but I need to do a better job of being on the lookout. This lesson became boring at times.

Also, I'm pretty sure 2 out of 70 students could tell me what measures of variation are.

Link of the Day: I got to be at one of these things one day.

Day 135 Central Tendency Quiz

6th Grade Math Standards: 6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
6.SP.3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Quote of the Day: “The starter gun fired and the race began. Almost as soon as it started, a boy tripped and fell, did a couple of somersaults, and started to cry. The eight other runners saw the boy fall and they all slowed down and looked behind them. They stopped and went back to where the boy was lying and crying. A girl with Down syndrome sat down next to him, hugged him, and asked, ‘Are you feeling better now?’ Then all nine held hands and skipped to the finish line. The whole crowd stood and applauded.” – Joe Ehrmann

Question from Yesterday (as always from a student): "Since we're finding a missing value in the data set and that missing value is 10, is the mode now 10 and 15?"

The Learning Objective: Find the mean, median, and mode of a data set; manipulate the mean when adding a new value to the data set

Assessment: Quiz on Central Tendency

Agenda:

1. Assembly (Spread the word to end the word)
2. QSSQ
3. Take the quiz
4. Work on the weekly quiz 

Glass Half-Full: In the morning I was peppering students at their lockers with a question regarding central tendency. Too many did not know what it was. Obviously the students had not studied over the weekend. So, why is this in half-full? Eventually the students knew the definition well enough to put it down on the quiz.

Regrets: The question that had the students bring their average from an 89 after eight quizzes to a 90 after taking a 9th quiz was baffling for the students. The co-teacher suggested I start with smaller numbers and fewer data values next year and get students to master it. To some degree I feel like I did that with finding the mean of 6, but I did not have the students change the mean from 6 to 7.

Link of the Day: Middle school students have an attention span of 10 - 12 minutes on average according to this article. It also alludes to the idea that the brain growth during adolescence is greater than any other time in life. I like the idea of creating five short lessons rather than one long lesson.

Day 134 Central Tendency Study Guide

6th Grade Math Standards: 6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
6.SP.3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Quote of the Day: “Research shows that our natural tendency is to choose others to work with who are very similar to us. But the most creative teams, the teams that solve problems the fastest, are eclectic and combine people with very different backgrounds and personalities…A certain amount of stress and tension is important. If you want to rise above yourself, put in the hard work it takes to accommodate differences. You’ll be handsomely rewarded.” – Andrew Sobel & Jerold Panas

Question from Yesterday (As always asked by a student): "Are mean, median, and mode the only ways to measure central tendency?"

"If a data set is 5, 5, 6, 7, 4, 4 is the mode 4 and 5?"

The Learning Objective: Find the mean, median, and mode of a data set; find a missing data value given the mean

Assessment: Students worked in groups on the study guide and the jumpstart. I assessed them by looking at their work in a jigsaw teaching method.

Agenda:

1. QSSQ
2. Bethel jumpstart
3. Very quick homework review
4. Study guide 
5. Money by month graph

Glass Half-Full: I have been utilizing groups of 4 to do many of the assignments lately it is working as well as it ever has worked. It's hard to say if students would be learning as efficiently or more efficiently if we were in rows, but at the end of the days I feel less stress and have more energy. I think that's because students are teaching each other and I'm forcing them to do more thinking and giving less attention to showing them every detail of what to do. Based on that description it sounds as if I'm not trying as hard, but that is not really the truth. I swear.

Regrets: As the students work in their groups, I'm pulling a heterogeneous group within those groups out three at a time to work with me on the areas that I think they will confront the greatest struggles and helping them work through. I then have them rejoin their groups to review those "struggle spots." I should be modeling this process to students and spending time teaching exactly what I want.

I also regret the amount of time I had to review homework today. It was almost better to not even assign homework because the students with misconceptions on the homework never got them addressed. I think time could have been better spent on the Bethel jumpstart. As students worked on this I worked on their finding of averages one on one in the back of the room. My time would have been better served showing this out in a lecture format instead of one on one. Then if I did a fist of five to see how students felt (though some would lie) I could better use time and actually go over the homework.

Link of the Day: Inside Mathematics is a good resource for problem solving and other things for teachers.

Day 133: Manipulating the Mean

6th Grade Math Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Quote of the Day: From the book 26 Irrefutable Laws of Powerful Relationships. It's too long to type, but it's about a teacher who did not give up on her student and the student eventually became an adult who won a Pulitzer.

Question from Yesterday (as always from a student): Why do the numbers come out to decimals? What happens to the decimals when they are divided by 5 (will they always terminate or will some repeat)?

The Learning Objective: Manipulate the mean of a data set

Assessment: I gave the students their scores using X2 without showing them the average and had the students do three things:

1. Determine their average right now (this part they did just fine)
2. Find how their average could increase by three points (this was much harder)
3. Find how their average could decrease by three points (this was the same as number two, but they ran out of time before they could finish in some cases)

Agenda:

1. Complete a graphic organizer of central tendencies
2. Do several practice problems that vary in their degree of difficulty for finding the three measures of central tendency (mean, median, mode). I found out today through another student that there are other measures of central tendency.
3. Give an example of another student's grade (I made up the information on the fly and used 72, 72, 90, 83 as the scores). Have students calculate the mean and what's needed to bring the grade up to an 83.
4. Have students calculate their own grade and the scores necessary to bring that grade up or down by three points

Glass Half-Full: I really enjoyed teaching and being a teacher today. Perhaps it was the extra hour and a half of sleep I got last night or the two days that I essentially did not teach for because of MCAS testing. I think more likely though is that I enjoyed giving students only a couple issues to dive into and getting them to dive in deep to those issues.

Finding their own mean served a dual purpose of getting them to meet today's objective and also give them awareness of how their grade is scored (which many of them seem to be unaware of). Only about half the students were able to manipulate their averages, so we still have some work to do tomorrow, but I loved that they were challenged and really had to put the pieces of the puzzle together. We broke this problem down with the Polya Problem Solving method.

Regrets: None. Some students did not get the skill according to the exit ticket, but I'm not worried. We will continue to work on it tomorrow. It felt good to have them challenged, to give them time to struggle, and to help some students work it through.

Link of the Day: Interesting read on reward systems among other topics.

Day 131 Vocabulary Practice

6th Grade Math Standards: Everything

The Learning Objective: Use collaboration to identify math vocabulary

Assessment: I sat with a group of three students and we went through about ninety vocabulary words that could only be seen by one person in the group by giving each other definitions, opposites, and examples. We completed the entire list in about thirty minutes. The rest of the class also worked, but they had groups of four and were very engaged just by looking around the room so I did not bother to get up at the risk of slowing down the group of three.

Agenda:

1. MCAS Test
2. Vocabulary review game

Glass-Half Full: Historically we do not like to have students taking normal classes and doing the normal routine after taking the state test. They are cooked and as a teacher I feel guilty asking them for more hard work when they gave so much in the morning. In the past we have done movies or played Scattegories. Today I tried the vocabulary review and it was very well received. There are many positives from a curriculum and cooperation standpoint not to mention that students do not need to write anything so it's a nice change up for students that struggle with calculation.

We identified five vocabulary words that the students struggle with describing (all of them come from the equations and expressions strand): distributive property, linear function, dependent variable, coefficient, and like terms.

Regrets: The rules of the vocabulary review game need to be emphasized from the start. I was introducing them as I was playing with my group because I was catching my group do some things wrong. Here are those rules:

1. Cover the word with your hand so the rest of the group cannot see it. 
2. Give math clues only (do not say it starts with a certain letter)
3. You cannot say a word within the definition when giving clues. For instance, if the word is prime number, you cannot say it's the opposite of a composite number because that is using the word number. 
4. After one minute, pass the bag of words.
5. If you are holding the word in your hand at the end of one minute, it goes back in the bag because nobody guessed it in time. 
6. If it's a word you do not know, you have to eat it for the full one minute. That way it becomes more of a priority for the whole group to talk about its meaning and the context it will be used in math. 

Link of the Day: Another story about how Finlind makes America look bad. This one comes from the LA Times. I love how in this one a child describes a recess experience. They sent us into the woods with a compass and a map and told us to find our way out. Would that fly in the U.S.?

Day 130 Introduction to Median and Mode

6th Grade Math Standards: 6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

The Learning Objective: Find the median; find the mode of a data set

Quote of the Day: "Don't give up just because you've been turned down. Successful people usually admire persistence. You might get a yes on the third try." - Andrew Sobel & Jerold Panas

Question from Yesterday (as always from a student): "If the question is asking for us to find a mean of six using four different data values, can we just write 6, 6, 6, 6?"

Assessment: March Madness was assessed using clickers, the mean, median, and mode were all found by the students in groups as I circumvented the room as well as the co-teachers.

Agenda:

1. QSSQ
2. March Madness (1st question was on finding the mean [2 students scored 40 points, 2 scored 50 points, and 1 scored 90 points], 2nd question on finding the whole given the part of a proportion, third question on volume, fourth question on equivalent fractions)
3. Reviewing the finding the mean practice from the weekend
4. Median of the ages of the students in the room
5. Median and mode practice using notes

Glass-Half Full: The emphasis on crossing out numbers was well received by students.

Regrets: I ignored the possibility of having two modes until a co-teacher brought it to my attention in the last group that I had.

Another thing to consider, though not necessarily a regret, is how much students struggled with the concept of how the mean changes when data values are taken away. When asked what would happen to a data set that described the square footage of celebrity homes if we took the smallest home out of the problem, about 7/8 of the students thought that the average would decrease. When I used the analogy of taking out your worst grade bringing the average up, the students seemed to acknowledge that they were wrong in the first place.

Link of the Day: "We actually expect math to be memorization of disjointed facts, Dan Finkle on his TedX Talk. 92% of people are more likely to accept your assertion if you have a statistic to back it up. Not really, but watch the video because it's funny when he says it.

I really like his 5 talking points:

1. Start with a question rather than answers. 
2. Thinking only happens when we have time to struggle. 
3. You are not the answer key. 
4. Say yes to your students ideas. 
5. Play. Einstein called it the highest form of research.