Day 57: Coordinate Plane Quiz

6th Grade Math Standards: 6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

The Learning Objective: Locate a point in a coordinate plane. Graph points in a coordinate plane. Give the distance between two points that share an axis in a coordinate plane.

Quote of the Day: “When you tell the truth your problems become part of your past, but when you lie they become part of your future.” - Rick Pitino

Agenda:

1. Students cleaned out their binders of all daily and jumpstart materials
2. The students took the quiz on coordinate plane
3. The students worked on another cartesian cartoon if they wanted or did the visual pattern #21
4. In the second part of class we reviewed the quiz and did a self-assessment. The quiz was already graded because I had my prep at an ideal time and I was able to grade some as students from different classes worked on the quiz.
5. Students were given a choice of playing battleship with coordinate plane or doing a cartesian cartoon. 

The Assessment: The coordinate plane quiz went well overall.

Homework: None

My Glass Half-Full Take: With just today and tomorrow (a half-day) before Thanksgiving it was ideal to give back the quizzes today as opposed to after Thanksgiving (I'm not going to see all classes tomorrow). Overall the quiz went well and the cartesian cartoons went well, so students are starting off the trimester on the right foot.

One Thing to Do Differently: There were a couple students that did not do their Cartesian Cartoons. I think I'm to blame in some regard. I am often more tolerant of talking and noise in the classroom than most of the classrooms I walk into. I'm sympathetic to eleven and twelve year olds urges to be children. I think this often causes distraction and perhaps students were not on task. In order to get tougher on a select group of students I may have to be more authoritative in the way that the classroom focuses.

Link of the Day: Kinesthetic way of teaching the coordinate plane.

Day 56: Coordinate Plane Study Guide & Cartesian Cartoon

6th Grade Math Standards: 6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

The Learning Objective: Locate a point in a coordinate plane. Graph points in a coordinate plane. Give the distance between two points that share an axis in a coordinate plane.

Quote of the Day: “Thinking of yourself as the best, is one of the biggest reasons successful people stumble and fail.” - Rick Pitino

Agenda:

1. Jumpstart with mixed numbers and the four major fraction operations
2. Coordinate plane homework review
3. Coordinate plane study guide
4. Journals
5. Cartesian Cartoons

The Assessment: The students accurately drawing their cartoon assessed their ability to graph points in all four quadrants.

The journals was an assessment to me of how the class was going. I asked to write about how they wanted the start of trimester two to go since we have a quiz tomorrow and their cartesian cartoons are counting as a quiz grade. I also asked one thing that I'm doing well to help them learn and one thing that I can do better. I hope they weren't as hard on me as I am on them, but it will keep me humble and help me get better.

The study guides only took some students about five minutes. I worked with a few students during this time, so I was not able to assess all of them. We did go over it as a class when it was done.

Finally I assessed a couple problems from the homework in going around the room. I'm pretty confident students know the quadrants, the vocabulary, graphing points, and plotting points. They have a harder time when it comes to polygons or even circles in a coordinate plane. Finding a distance is something that the students continue to improve upon. It was a smart move in the end to give students not only a problem on the study guide for finding the distance of two points, but also giving them another problem like this immediately after going over it.

Homework: Finishing the cartesian cartoon and prepping for tomorrow's quiz.

My Glass Half-Full Take: The cartesian cartoon is an excellent way to drill without making students think they are being drilled on a skill. I also really liked the journal activity as students showed me how much they were writing. I haven't actually read the content, but the timing of it is perfect since students have a clean slate with a new trimester just underway today.

One Thing to Do Differently: The students were very insecure that their cartesian cartoons were inaccurate. I wish that they were this insecure about all their work and so willing to check on their progress. They kept going up to the pictures of finished products instead of trusting their instincts. This led to them not making as much progress as they could. I wish I had told them from the outset not to worry too much about how the final product looked until they were halfway done plotting the dots. The students worked on this for a full block in the second part of class, and while a few students finished most still had work to do tonight.

Link of the Day: A number that when divided by the product of its digits gives you three and if you add 18 to it, it is inverted. Solution here from the 1991 film Little Man Tate.

Day 55: Coordinate Plane Hands On

6th Grade Math Standards: 6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

The Learning Objective: Find the distance between two points with either the same x or y coordinate.

Quote of the Day: “Many educators think that lowering their standards will give students success experiences, boost their self-esteem, and raise their achievement. It comes from the same philosophy as the overpraising of students’ intelligence."

Agenda:

1. Jumpstart & Collect WQ 
2. Review the homework from the previous class. We highlighted how 0 as one of the coordinates means that the point is on an axis with this homework review.
3. Hands on Coordinate Plane with pegs and a coordinate grid that students could touch instead of write with. 
4. Pass out today's homework
5. Cartesian Cartoon

The Assessment: I partnered students up and gave each partnership a board with orange and blue pegs. I walked around the room to make sure students were doing the task. Here were the details of what students were asked to do:

1. Place an orange peg at the origin. 
2. Place a blue peg at (4, 3).
3. Place a blue peg at (-4, 3)
4. Place an orange peg at (-4, -3)
5. Based on the pattern, what quadrant am I going to ask you to place the next peg? I called on a student for this answer. 
6. What will be the coordinates of the fourth point? I called on a student for this answer.
7. I went through several different partnerships to ask what shape had been created. Some groups said a square while others said a rectangle. 
8. I asked for specific characteristics that a square has. When we got to the characteristic of equal sides, I asked the students how we could find if the shape had equal sides.
9. The students were then asked to measure the distance between the blue peg. The answers I received were mostly wrong. Many said seven because they did not count the last "jump." Thus I counted with them holding up a board of my own and used the analogy of a board game (they still play board games right?).
10. Then we measured the distance from orange to blue peg. It was clear that the students had learned from their previous mistake as all partnerships could answer the distance from one edge to the other. 
11. I asked students if it was a square or rectangle?
12. I asked students to graph the point (-2, 0)
13. I asked students to graph the point (0, -5)
14. I asked the students what quadrant these two points were in.
15. I asked students to graph 4 points that had an absolute value in the y-coordinate of 2. 
16. I asked students to graph 4 points that had an absolute value in the y-coordinate of 2 and that appeared in the third quadrant.
17. I asked students to place a peg at a point so that it was not in a quadrant and the x and y coordinate could not be equal to zero. They were stumped until they one of their classmates shared with us why this was impossible. 

Homework: Coordinate plane practice continued. Students were given more than ten minutes to start this in class.

My Glass Half-Full Take: The 17 steps outlined above were not originally on the plan for today. I was just going to pick a couple of points and call it a day. During curriculum planning time though one of the colleagues shared her line of questions. I liked it. From there I made my own tweaks throughout the day, and by the last class, the questions were differentiated and engaging to my satisfaction.

One Thing to Do Differently: Before students get the Cartesian Cartoon, I need to go over two things. First, they should cross out each point as they plot it. Second, they need to connect the dots each time they plot a dot.

Link of the Day: In this blog post a math teacher argues that immediate feedback isn't always the best type of feedback.

Day 54: Integers Quiz & Coordinate Plane Intro

6th Grade Math Standards: 6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea 

level, credits/debits, positive/negative electric charge); use positive and negative numbers to 

represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and 

coordinate axes familiar from previous grades to represent points on the line and in the plane with 

negative number coordinates. 

a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the 

number line; recognize that the opposite of the opposite of a number is the number itself, 

e.g., –(–3) = 3, and that 0 is its own opposite

6.NS.7 Understand ordering and absolute value of rational numbers. 

a. Interpret statements of inequality as statements about the relative positions of two numbers 

on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to 

the right of –7 on a number line oriented from left to right.

b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 

For example, write –3 degrees C > –7 degrees C to express the fact that –3 degrees C is warmer than –7 degrees C.

c. Understand the absolute value of a rational number as its distance from 0 on the number line; 

interpret absolute value as magnitude for a positive or negative quantity in a real-world 

situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the 

size of the debt in dollars.

d. Distinguish comparisons of absolute value from statements about order. For example, 

recognize that an account balance less than –30 dollars represents a debt greater than 

30 dollars

6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

The Learning Objective: Find the absolute value of an integer, graph a point on the coordinate plane, identify the quadrant a point is located in

Quote of the Day: We 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

Agenda:

1. Integers Jumpstart
2. Homework review
3. Integers Quiz (only took about 15 to 20 minutes)
4. Work on weekly quiz 
5. Visual Patterns challenge problem (end of first block)
6. Coordinate Plane Notes
7. Coordinate Plane Practice
8. Coordinate Plane Homework started

The Assessment: Circumventing the room, integers quiz, fist of five

Homework: Coordinate Plane Practice

My Glass Half-Full Take: The integers quiz went fairly well. Students were able to differentiate between absolute value and actual value well. This was somewhat concerning going into the quiz because I had never taught these topics in double blocks like this year before.

The coordinate plane topic went well because I was patient in my explanations. In the past students are always over confident in what they know, but don't back it up when I set them free to try problems on their own. Today the students that were overconfident were a little humbled as I purposely wrote in wrong answers on the board and nobody called me out for it.

One Thing to Do Differently: There were a couple ways to differentiate and extend the learning that I did not draw upon. I could have asked students when a point does not lie in a quadrant. We saw examples of this, but never made a conclusion about it. It was a question on the homework though, so it's something we'll attack tomorrow.

Link of the Day: Great source for revising a mathematics curriculum map.

Day 53: Absolute Value & Ordering Integers

6th Grade Math Standards: 6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea 

level, credits/debits, positive/negative electric charge); use positive and negative numbers to 

represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and 

coordinate axes familiar from previous grades to represent points on the line and in the plane with 

negative number coordinates. 

a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the 

number line; recognize that the opposite of the opposite of a number is the number itself, 

e.g., –(–3) = 3, and that 0 is its own opposite

6.NS.7 Understand ordering and absolute value of rational numbers. 

a. Interpret statements of inequality as statements about the relative positions of two numbers 

on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to 

the right of –7 on a number line oriented from left to right.

b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 

For example, write –3 degrees C > –7 degrees C to express the fact that –3 degrees C is warmer than –7 degrees C.

c. Understand the absolute value of a rational number as its distance from 0 on the number line; 

interpret absolute value as magnitude for a positive or negative quantity in a real-world 

situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the 

size of the debt in dollars.

d. Distinguish comparisons of absolute value from statements about order. For example, 

recognize that an account balance less than –30 dollars represents a debt greater than 

30 dollars

The Learning Objective: Find the absolute value of a number. Order integers.

Quote of the Day: This was a follow up to yesterday's line about being the smartest doesn't mean you will always end up the smartest.
“More than 50% of all CEOs of Fortune 500 companies had C or C- averages in college. 65% of all U.S. Senators came from the bottom half of their classes. 75% of U.S. presidents were in the lower half club in school. More than 50% of millionaire entrepreneurs never finished college. Talent isn’t everything.” - John Maxwell

Agenda:

1. Self-Assessment 
2. Review Quiz
3. Absolute Value Activator
4. Absolute Value Frayer Model (on back of activator)
5. Absolute Value Exit Ticket
6. Absolute Value Practice (jumpstart to start next class)
7. Integers Skit
8. Ordering Integers Notes
9. Integers Practice

The Assessment: The students were able to put themselves in order in the skit, the integers notes were checked by me for understanding, the absolute value activator was assessed through circumventing the room, the last problem on the absolute value homework models were done by students in partners.

Homework: Study for the quiz on integers tomorrow, weekly quiz #8 due Friday, complete the integers practice

My Glass Half-Full Take: There was a great number of students that correctly identified the absolute value activator as the person being a position of zero on a number line. It was exciting to see the students think independently (or in this case with a partner) and derive what I wanted them to. I enjoyed the fact that I didn't have to show them notes and that they could discover on their own. That's the way math should be taught all the time - although I'm not perfect at doing this myself I'm working on it.

One Thing to Do Differently: I'm not sure if I could do this differently, but before the day was out, students had seven different papers from me. This doesn't include the weekly quiz which is of course ongoing. I gave students a study guide in addition to everything else they got. They flew through some of these papers as many of them had the same concept drilled for them consistently.

Link of the Day: I've let students use their phones occasionally this year. I think I'm going to really open things up soon and try PollEverywhere. My partial worry is for students that do not have smart phones, but I anticipate partnering students up to avoid this problem.

Day 52 Percentage Quiz & Integers Introduction

6th Grade Math Standards: 6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line 
diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea 

level, credits/debits, positive/negative electric charge); use positive and negative numbers to 

represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

The Learning Objective: Find the whole given a part. Find the percent of a number given a whole number percent from 1 to 100.Compare percentages, decimals, and fractions. Order percentages, decimals and fractions.Convert numbers between fractions and percentages. Convert between decimals and percentages.Convert numbers fluently from fractions to decimals and decimals to fractions.

Define an integer. Graph integers.

Quote of the Day: “People have more capacity for lifelong learning and brain development than they ever thought. People may start different...but experience, training, and personal effort take them the rest of the way. It’s not always people who start out the smartest who end up the smartest.” - Carol Dweck

Agenda:

1. Quiz on Percentages
2. Work on WQ #8 which was passed into me today and I gave back as students worked on the quiz
3. Flashcards/3 Column Notes
4. Integers Chant
5. Integers Notes
6. Integers Practice (homework, but it was mostly done in class)

The Assessment: The quiz was assessed. Here's a look back at some of the wrong answers that were common:

The mistakes made in numbers four and five were more common during the study guide than they were today. The student did know that turning a percent into a fraction requires them to use a denominator of 100. That part was basically drilled in. Obviously the directions of simplest form are missed here, but I'm actually more concerned with leaving the % symbol next to the number as part of the answer here. For students that did not simplify I only took off half because I think they demonstrate one of the skills required.

Here is another example of a student getting an answer wrong, but it's not as if the student has learned nothing. Should partial credit be given? In my opinion, the symbol for percent and differentiating between a percent and a fraction is part of mastery of this topic. There is no way of giving partial credit on these two questions. That said, I'm sure the student who answered these wrong will quickly make the note of what was wrong and I would like to retest the topic with them to confirm.

This answer came up a bunch of times. It's why it was my favorite no a few days back. Regardless of the number of times we practice it, it's still going to get a few students. I bet most students will classify this as a simple mistake as opposed to something they don't really understand.

You can't see number nine in the picture here, but it asked for 86% to be made into a decimal. I don't recall anyone getting it wrong. This one stumped them of course because of the decimal. I'm not sure I gave enough practice on this type of problem leading up to the quiz.

Again I see a mistake with place value. Similar to the 0.9 error. This problem is different in some regards though because I would have solved it simply by noting that 5/8 is greater than a half and the other two numbers are not. Of course not every student has this number sense handy, so most of them were dividing and determining what 5/8 was as a decimal or as this student did trying to figure out how to make 100 the denominator. 

Here the student demonstrates the process off to the left side but gets confused about the decimal. After seeing it doesn't make sense, the students proceeds to try division, but still can't make sense of it. I was happy with the perseverance. This problem and the one next to were the problems that were most challenging.

Solid attempt at a proportion here, but the student misses the concept that a percent is a ratio since the number is being compared to 100. 

Here the student can find the part given the whole, but uses the same method to find the whole given the part on number 13. 

I actually never showed the students division as a means to solving these problems. The method could have worked for the problem on the right if the student had made 15 a decimal and carried out the division problem by adding zeros to 75. Interestingly this student successfully converted percentages to decimals earlier in the quiz.

Homework: Integer practice

My Glass Half-Full Take: In one class, we visited another teacher to say the integer chant. "An integer is all whole numbers, their opposites, and zero." It was a great diversion for the kids and I always have fun doing something out of the ordinary. That other class came back later and visited us. I think that particular class will have a more solid understanding of that definition just from the originality of the idea than the other class, but time will tell. If I had thought of it earlier, I would have had the other classes go and pay a visit. Inspiration strikes at weird moments.

One Thing to Do Differently: The standard that we have to teach asks students to explain the meaning of zero. I wouldn't mind hearing what other math teachers have to say about that part of the standard. My interpretation is that zero is when money isn't lost or earned, the temperature doesn't rise or fall, etc. I think it's very basic, but perhaps I'm being too simplistic. I take pride in being rigorous, so hopefully I'm not underselling this concept.

Link of the Day: I really wish I had YouTube in high school. This video taught me something about force. I'm going to build a lever to lift the broken spirits of any students who feel like they can't find the percent of a number tomorrow.

Day 51: Prepping for Percentages Quiz

6th Grade Math Standards: 6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line 
diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
The Learning Objective: Find the whole given a part. Find the percent of a number given a whole number percent from 1 to 100.Compare percentages, decimals, and fractions. Order percentages, decimals and fractions.Convert numbers between fractions and percentages. Convert between decimals and percentages.Convert numbers fluently from fractions to decimals and decimals to fractions.

Quote of the Day: “A lot of people hear the words ‘hard work’ and say ‘oh no - I don’t want to do that.’ I want to coach kids who hear that they are going to have to work hard and then get excited about how much they will improve as a result.” - Coach K

Agenda:

1. Jumpstart 99 Restaurant tip
2. Pass out and read Weekly Quiz #8
3. Study Guide done individually
4. Review study guide with the class
5. Stations: Memory, Grid comparing fractions, decimals, and percentages, Weekly Quiz #8

The Assessment: Circumventing the room during the study guide, sitting at the weekly quiz station as students worked in the second part of class

Homework: Study for the percentage quiz and WQ # 8 is due tomorrow for a homework check

My Glass Half-Full Take: I have never tried to do the study guide as an individual assignment. It has always been done in groups and in partners. I tried it individually today and although the results of the quiz will tell more of the story, I was happy with the focus of the students. The reason I told the class was because I think they are leaving the room overconfident after they do the study guide in groups or with a partner. Answers seem to come much more quickly and easier with two brains (or four) thinking rather than one. I told all students that needed assistance from me to write "wolf" or a "?" to signify it was something that they messed up on the original study guide. My hope was that students would have more urgency to study since many students are admitting that they do not study for math.

One Thing to Do Differently: I did not need to read WQ #8. We did it in the second part of class, and my reading it ahead of time did not seem to service anyone.

Link of the Day: This of course from our decimal standards. Giancarlo Stanton just received a 13-year $365 million contract from the Miami Marlins. How many million dollars is that per season?

Day 50: Find the Whole Given a Part

6th Grade Math Standards: 6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line 
diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
The Learning Objective: Find the whole given a part.

Quote of the Day: “So often we fail to acknowledge what we have because we’re so concerned about what we want. We fail to give real thanks for the many blessings for which we did nothing: our life itself, the flowers, the trees, our family and friends. This moment. All of our blessings we take for granted so much of the time.” - John Wooden

Agenda:

1. Jumpstart - tipping at a restaurant
2. Review the homework
3. Proportions visually
4. Notes
5. My Favorite No. "Isabel got a 70% on her quiz. She answered 21 questions correctly. How many questions were on the quiz?" 
6. Stations - Frayer Model, homework practice, and shopping activity

The Assessment: Students did the last two problems from the notes independently. During stations I had students working in groups of three to four and I sat mostly at the Frayer Model station assessing these students ability to differentiate between a proportion was and was not.

The my favorite no was only done in 2 out of 3 classes. I simply forgot in the middle class.

I looked at the students work from the previous night. The problem that I saw was that students were incorrectly answering the questions that required them to find a new price of something when a percentage was taken off of a number (they didn't subtract).

There was also the jumpstart which challenged all students. Only about three to five got it all day. That was expected because of the way it was worded, but I think it is so essential to teach students how to find a tip.

Homework: Weekly Quiz #8 was made available online. I also had students complete the homework practice if it was not done in class.

My Glass Half-Full Take: The stations activity was done on the fly today as I spoke with colleagues about what they were doing in class during my prep. It was a great way to run Friday afternoon as it gave students the opportunity to get out of their seats about every 10 minutes and got them actively talking about the math instead of having me lecturing.

One Thing to Do Differently: This is such a hard to topic to master. It's hard to say I'd do anything differently for one day, but I know that students would be better off with more time. I think the first concept to master is something like finding 100% of a number, 10% of a number or 1% of a number. I had not taught students this until the end of today's lesson. Having that background though goes a long way toward making sense of answers.

Also, a too high too low with word problems is helpful. In the my favorite no picture above, how can we get 0.4 questions on a test in which there were 21 questions answered correctly?

Link of the Day: Multi-taskers are lousy at multitasking.

Day 49: Percent of a Number

6th Grade Math Standards: 6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line 
diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
The Learning Objective: Find the percent of a number given a whole number percent from 1 to 100.

Quote of the Day: “Adversity can make us stronger, smarter, better, tougher. Blaming your troubles on bad luck makes you weaker. Most worthwhile things in the competitive world come wrapped in adversity.”

Agenda:

1. Jumpstart with a word problem for dividing fractions
2. Review Homework
3. 20% or $20? From Dan Meyer with slight modifications by me
4. Notes
5. Work on the homework 

The Assessment: Circumventing the room as students completed notes and homework

Homework: Page 151 or Percentage Worksheet

My Glass Half-Full Take: The students could meet the objective. I checked every student in the student in the class and they could do what was asked of them.

One Thing to Do Differently: I was not in class for part of the day because of a meeting, so it wasn't a perfect lesson in terms of knowing what went wrong since I did not get to see it. This objective was very easy to meet though as my colleagues pretty much had them master it before I came in (perhaps I should just let them take over all the time). I liked in my second and third classes that I saw that I offered them problems with percentages greater than 100, less than one, and percentages between that had decimals. It was also important to note that more than half the class referred to 8% as 0.8.

Link of the Day: This is a great estimation picture. And a great problem for discussing differences, and how we can all find something in common if we search for it.

Day 48: Comparing & Ordering

6th Grade Math Standards: 6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line 
diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
The Learning Objective: Compare percentages, decimals, and fractions. Order percentages, decimals and fractions.

Quote of the Day: None

Agenda:

1. Review the homework as a class
2. Play Memory (1/2, 1/3, 1/4, 1/5, 5/8, 7/10, 7/100 were the fractions used) 
3. Notes on comparing and ordering 
4. Start the homework in class (first three homework problems were assessed)

The Assessment: The homework problems that the students started in class. I also went from group to group while they were playing Memory. Groups were asked to find the matching fraction, decimal or percentage of a laminated piece of paper that was upside down. Then they had to remember where the matches were once they were flipped over again on the side you couldn't see (it's amazing how you have to explain the game memory - so many kids have never played before).

Homework: Page 133-134 with skipping two of the problems that involved percentages greater than 100 or less than one since these had not been taught as of yet.

My Glass Half-Full Take: Memory was not fully understood by students (it's really hard to explain a game from scratch and get 20 or so students to understand - even I have difficulty learning a new game when someone explains it to me one on one). That being said, students were doing math in groups and reviewing the objective of previous classes. Kids did get the hang of it when I could explain to their small groups and we physically had the cards in front of us. The kids enjoyed it and the block flew by.

One Thing to Do Differently: I think the way I formatted notes could have been done differently. One of the key points to tell students is that they need to be consistent with finding either percentages, decimals or fractions of every number to compare properly. I did not have students write this. Certainly over time with fluency students will need to convert less on paper and can do it more in their heads, but for where they are now I could have given more details to guide them.

Link of the Day: Statistics can do amazing things. Who knew it was so likely to hit deer in West Virginia? I'd say State Farm is a reliable source.

Day 47: Converting to Percentages

6th Grade Math Standards: 6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line 
diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

The Learning Objective: Convert numbers between fractions and percentages. Convert between decimals and percentages.

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

Agenda:

1. Number line jumpstart
2. My favorite no: convert 6/8 into a percentage
3. Notes on common fractions that can be turned into a percent
4. My favorite no: converting 0.3 into a percent and 7% into a decimal
5. Notes on percentages, decimal, and fraction conversions
6. Veteran's Day Homework assignment

The Assessment: My favorite no results were pretty favorable. I'd guess slightly more than half the class could make 6/8 into a percentage (or at least a decimal).

Even the last one written here demonstrates some positive understanding that there needs to be a division problem. The series of questions that I had to ask to help students understand what number was the divisor and which was the dividend went back to our last class.

• Teacher: What is 6/8? Student: A fraction
• Teacher: What is a fraction? Student: A part of a whole
• Teacher: Oh it's a part of a whole, so should you get more or less than one? Student: Less than one
• Teacher: So does 1.33 make sense or 0.75? Student: 0.75

This was the results of the second series of my favorite no. Students always have a hard time with decimals that don't go to the hundredths place or percents that are single digit. Thus I tested students on 7% to a decimal and 0.3 to a percent. Here were the results of 7% to a decimal. The more detail the student shows in the answer, the more encouraged I was.

Homework: Veteran's Day percentage, fraction, and decimal conversion. I have never done something like this before on Veteran's Day, but I think it was a nice way to educate with a dual purpose.

My Glass Half-Full Take: There were a good deal of notes in the class, but there was engagement. That may have had to do with the fact that it was Monday and I generally have my best audience when the students are well rested, but nonetheless the kids enjoyed the notes. They were thoroughly understanding and felt challenged when I went off script and added problems like finding the percentage for 1.25.

One Thing to Do Differently: I created a problem using the Celtics box score from Saturday night. One player made 6 out of 9 shots and another made 7 out of 14. I asked the students when they finished the homework to find the percentage of each player. Then I asked them to determine how many shots the player that made 7 out of 14 would have to make in order to have a better percentage than the player that made 6 out of 9 shots. I thought this was deeper thinking, but ultimately nobody got to it since we ran out of time. For the students that answered My Favorite No correctly, I probably should have given them this problem much sooner.

Link of the Day: Some percentages and fraction conversions are worth memorizing. This game can help.

Day 46: Fraction & Decimal Conversion

6th Grade Math Standards: 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc .) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

The Learning Objective: Convert numbers fluently from fractions to decimals and decimals to fractions.

Quote of the Day: “Perseverance doesn’t really come into play until you are tired. When you’re fresh, excited, and energetic, you approach a task with vigor. Work is fun. Only when you become tired do you need perseverance.” - John Maxwell

Agenda:

1. Review the Fractions Test
2. My favorite no converting fractions to decimals
3. Place value review
4. Fraction & Decimal Conversion Packet

Here a student somehow figured that 3/8 is equivalent to 2 and 2/8. We were trying to convert to a decimal and we ended up with not only a fraction, but a mixed fraction. It's hard to criticize though as this was something the student admitted he had no clue. I'm happy the student tried - at least they were curious in going over it. 

In this instance, a student recognizes the need to divide, but makes the most common mistake of making the 8 a dividend and the 3 a divisor. I told students that a fraction is part of a whole - the key word being part. It's less than one. 

The student did everything right and to celebrate he slid the decimal, and suddenly it all became wrong. 

This will not be the last time I see this. 

Or this...

The Assessment: After I did My Favorite No, I handed back the index cards to students and asked them again to try a problem. They were much more successful the second time - although as a couple pictures below indicate they were not all set by any means.

Homework: None

My Glass Half-Full Take: I like the amount of times I asked students whether or not a fraction which was being converted to a decimal was going to be greater than or less than one. I think this is the biggest obstacle for students in converting fractions to decimals - the decision of what number is the divisor and which is the dividend. If students have a strong understanding of what a proper and improper fraction is though, it is not an issue. I also used "the trick" of put the numerator in the house because it is getting rained on, but I am increasingly trying to show students why mathematically because a trick will only take them so far.

One Thing to Do Differently: I spent almost a full block going over the quiz. I wonder how much learning took place in that time. Sure I gave students a self-assessment checklist but that would take a responsible student a minute to complete. I wonder if I could have given students similar problems instead of just going over the test exclusively. I think that would have made the students take ownership of what we were reviewing and increased the overall focus of the class.

Link of the Day: Granted time is needed to get the best out of this site from the Arizona Department of Education, but the standards are unpacked really well here for middle school mathematics from what I saw taking a quick glance. The site is unique because it offers deeper examples than the way that the common core standards are presented.

Day 45: Fractions Test & Zombie Bridge

6th Grade Math Standards:6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc .) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

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.

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

MP.2 . Reason abstractly and quantitatively.

MP.3 Construct viable arguments and critique the reasoning of others
The Learning Objective: Apply the operations of fractions in order to solve problems

Quote of the Day: “A professor stood before a class of 30 senior molecular biology students. Before he passed out the final exam, he stated, ‘I have been privileged to be your instructor this semester, and I know how hard you have worked to prepare for this test. I also know most of you are off to medical school or grad school next fall. I am well aware of how much pressure you are under to keep you GPAs up, and because I am confident that you know this material, I am prepared to offer an automatic B to anyone who opts to skip taking the final exam.’ The relief was audible. A number of students jumped up from their desks, thanking their professor for the linelife he had thrown them. ‘Any other takers?’ he asked. ‘This is your last opportunity.’ One more student decided to go. The instructor then handed out the final exam, which consisted of two sentences. ‘Congratulations’ it read ‘you have just received an A in this class. Keep believing in yourself.’”

Agenda:

1. Take the Fractions Test
2. Work on WQ #7
3. Zombie Bridge Problem (second part of class) 

The Assessment: The Fractions Test

Homework: Students were to answer these questions after watching this video and this video. The Weekly Quiz is also due tomorrow.

My Glass Half-Full Take: The Zombie Bridge was solved in one class and students tried hard to solve it another. Here were a couple examples of students trying to solve the problems:

The activity does many things to make it a great lesson. Number one it is student driven. I read the problem and then I let the students do the talking - I only ask questions and give suggestions such as underlining what to find, draw a picture, or act it out. It's on the students to discover how to not get eaten by the zombies. It's the first time this year that I have spent an entire class with students trying to solve one problem and although only one student was ultimately able to derive the solution independently (and one teacher for that matter), the thinking and persevering is what makes it worthwhile from a learning perspective. 

One Thing to Do Differently: Fractions. Where to begin. This test did not have the desired results I was looking for especially looking back at my daily assessments and how students were meeting objectives. Although there were students that certainly met their potential, it is always emotionally draining when students are below their potential.

I could have given a quiz on adding and subtracting fractions. The students would have known what to do as far as always finding a common denominator and the word problems would have been much easier to guess at because they would only include two operations. The problem from my perspective with all of this is that it does not show true mastery. Thus the students mixed up the operations they did and made a handful of other errors. It is hardly to say that students were way off or that "they don't know fractions." Looking at their mistakes it was more often small details rather than a total lapse in a certain topic.

In the picture above, this student knew how to find a common denominator. The student also understood that to add you must add the numerators and not the denominators. The problem of course was that the problem was a subtraction problem.

In this problem, again the student knew how to find a common denominator, knew to add the numerators and not the denominators, and even had the correct operation. The problem was that students ignored the fact that she ran around the track twice. My colleagues and I are constantly preaching to students to circle what you know and underline what you're trying to find out. That simple step here would have saved this student (and several more like this student) a simple error. 

In the problem above here, the student correctly put the whole number of one. This student also successfully changed the denominators. The problem was merely that they did not properly subtract four from twenty-one. Again not really an error with the fractions.

Finally, this last photo here uses a very high number of 42,000. There is no doubt that in our world today that an adult would bust out the iPhone and do this problem on the calculator. This student did just fine without the calculator. Except for the fact that the question says how many votes did the winner not receive. Now would an adult pick up on that detail after putting all the information into a calculator? I'm sure some would, but some also wouldn't. This is again an instance in which a student knows what to do with the fractions, but does not know how to solve the word problem.

As I looked at student errors, I came to the conclusion that perhaps I don't need to hit students over the head with fractions. There are those students that still need more practice of course, but in general the bigger issue here might be reading comprehension and just simple calculation mistakes. I have a plan in mind for working out this word problem issue. I might just put together a ton of word problems and in lieu of asking students to solve them, just ask students to find the operations they would need in order to solve them using analogous numbers. I also need to crack down harder on students that do not circle and underline the problems.

Link of the Day: Cool look at how to mislead people with graphs and statistics.

Day 44: Fractions Review

6th Grade Math Standards: 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc .) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

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.

The Learning Objective: Multiply fractions to find a product. Divide fractions in order to find a quotient. Add fractions to get a sum. Subtract fractions to get a difference. Locate a fraction relative to the position of other fractions on a number line.

Quote of the Day: “Confidence must be monitored so that it does not spoil or rot and turn to arrogance. Arrogance or elitism, is the feeling of superiority that fosters the assumption that past success will be repeated without the same hard effort that brought it about in the first place. Thus, I have never gone into a game assuming victory. In fact the quality of our opponent had nothing to do with my own Confidence. Rather I drew strength, Confidence, from the sure knowledge that I had done all things possible to prepare myself and our team to perform at our highest level in competition. The opponent might perform at a higher level - or not. I didn’t concern myself with the other team’s preparation and potential; I just concentrated on ours." - John Wooden

Agenda:

1. Jumpstart with 5 problems that look at 4 different operations and expose students to mixed fractions, regular fractions and whole numbers. I checked weekly quizzes while students did this jumpstart.
2. We reviewed the jumpstart by having 5 students go to the board.
3. The students did this Frayer Model which served as a reminder of how the operations were different and similar to one another. To simplify things for most students my colleagues and I agreed to tell them to just turn all mixed numbers to improper fractions. It was probably not the best long term decision, but I have no regrets as it simplified a complicated topic as it is. 
4. Stations. Cookie recipe, locating fractions on a number line, using fraction tiles to find equivalent fractions, and word problem tactics. 

The Assessment: Students doing the jumpstart on the board, circumventing from group to group as students worked on the Frayer Model and sitting with the students at the number line station during the stations activities. I also checked students weekly quizzes on the spot for them.

Homework: Study for the quiz, finish and fix the weekly quiz

My Glass Half-Full Take: The morning was stressful, but the afternoon was great. It was the first time I had students work in groups of four this year. It was a very positive result. Behavior issues were still prevalent, but nothing more than I would typically get in a lecture (students talking, losing focus or going off topic). Plus for students that were distracted often times their group could bring them back to task and hold them accountable faster than I could.

One Thing to Do Differently: This was somewhat out of my control, but my computer got upgraded to Windows 8 during the professional day yesterday. As a result, I had difficulty using the projector and reviewing the Frayer Model the way I would have liked. By my third class, I was faster and had adjusted well enough to review the Frayer Model in a better manner.

Another part of the lesson that wasn't as strong was that I was one hundred percent reliant on students helping students for the stations with the fraction tiles and the station with the word problems. I'm not sure how much I could have done things differently to get to these stations. Since I was at the number line station, and every student got to the number line station, I did see every student. I also assessed students ability to apply the four operations to fractions during the Frayer Model, so it's not as if I never assessed that skill - I just didn't assess one task of that skill. Perhaps an alternative way to do this would have been to teach students at the number line station and then have those students go and teach other students. That would allow me to see the other stations, but overall I was very happy the way things went and could live with doing today's lesson exactly as it went again (maybe a Mac upgrade instead of Windows though).

Link of the Day: Great article on estimation from Jessica Marks. It's a skill perhaps more valuable than any we can teach given the availability of calculators today to find precise answers. Estimation forces students to think logically.