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?