Day 63: Area of Rectangles Lesson

6th Grade Math Standards: 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

The Learning Objective: Find the area of a rectangle

Quote of the Day:  “When you say you’ll do it, do it. Don’t give your word unless you intend to keep it.” - John Wooden

Agenda:

1. Jumpstart
2. Area Rectangles Notes
3. Area Rectangles Practice
4. Tiles Jumpstart
5. Area of Rectangles Homework

The Assessment: The students were assessed on the area of rectangles practice as well as some of the problems from the notes.

Homework: The area of rectangles homework worksheet as well as the weekly quiz being online.

My Glass Half-Full Take: I really liked the questions that made this lesson harder for students that came with a solid background in area of rectangles. Questions such as if a square has an area of 196 square feet, what is the length and height? Another question that students got hung up on was if a rectangular yard has a rectangular fountain in the middle, what will be the area that gets mowed?

One Thing to Do Differently: I did not anticipate that the notes, which consisted of four questions would take as long as they did. I just wish I had known this going in and I wouldn't have taken as long going over the jumpstart as I did. Although I will add that the jumpstart was very engaging and challenging (only about five students had the right answer all day). I also could have given students larger graph paper for the tiles jumpstart to help them arrange the tiles into all the factors of 48.

Day 62: Perimeter Intro

6th Grade Math Standards: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

MP1 Make sense of problems and persevere in solving them

The Learning Objective: Find the perimeter of a figure

Quote of the Day: “By applying yourself to the task of becoming a little better each and every day over a period of time, you will become a lot better.” - John Wooden

Agenda:

1. Jumpstart 
2. Quiz Review
3. Perimeter Practice
4. Staircase Practice

The Assessment: Circumventing the room as students worked in partners on their perimeter practice worksheet. Also circumventing the room as students tried to come up with the third and fourth staircases in the pattern, the rule for the perimeter, and summarizing the patterns that they found in three sentences. I collected their summaries.

Homework: Work on Weekly Quiz #9

My Glass Half-Full Take: I really enjoyed the staircase activity. The entire class was engaged and one student caught a pattern that I did not care to investigate (the perimeter of the stair part always matched the pattern number). I also liked teaching perimeter even though it's in the fourth grade standards. I thought this lesson added value in terms of talking about units. Students need to know why we write area in units squared and volume in units cubed. Understanding why we write perimeter in just plain units is a step in the direction of doing just that. I also got to ask valuable questions such as what does one tickle mark mean (the answer was feet but students would say an exponent and A prime - which were both appropriate answers in other scenarios). Another question we got value from is what to do when the numbers don't have units next to them.

One Thing to Do Differently: I wish I had targetted certain problems for students to do on the perimeter practice. They had the opportunity to work on adding fractions on a couple problems and also had several problems with multiple steps. The last question was a theory type of question in which students were asked to uncover what ways a rectangle could have a perimeter of 24.

Day 61: Reflections & Rational Numbers Quiz

6th Grade Math Standards: 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.
b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the
coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of
the points are related by reflections across one or both axes.
c. 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: Reflect a point across an axis, order rational numbers, find a point on a number line

Quote of the Day: “He understood that no matter your circumstances, resources, or natural talent, certain things were always within your control - your ability to work harder and smarter than anybody else.” - John Maxwell on Alexander Hamilton

Agenda:

1. Jumpstart
2. Homework Review (we did these problems on the board
3. Study guides 
4. Rational/Reflections Quiz
5. Weekly Quiz #9 

The Assessment: The reflections and rational number quiz and study guide.

Homework: Work on Weekly Quiz #9

My Glass Half-Full Take: The quizzes went pretty well overall after I had a frustrating time reviewing the homework with students as they probably did not give their best effort going into today's lesson. Of course the students not giving their best effort could also be attributed to a lack of self-confidence from an inferior lesson, so I need to make adjustments as well. Nonetheless the basic skills that students needed were successfully demonstrated on the quiz.

One Thing to Do Differently: There were probably too many homework problems. Questions with denominators of 37 and denominators like it made it difficult for students with poor calculation skills. Obviously we want the students to work on these skills, but in doing so we took away the students best effort when it came to logic questions on the homework like where a point is on a number line. Reviewing the homework on this day in general was painful as students did not complete a large portion of their work for whatever reason.

Day 60: Coordinate Plane & Rational Numbers Combined

6th Grade Math Standards: 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.
b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the
coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of
the points are related by reflections across one or both axes.
c. 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: Reflect a point across an axis, define rational number, differentiate between terminating and repeating decimals

Quote of the Day: “Success is not an event; it is a process.” - John Maxwell

Agenda:

1. Jumpstart
2. Homework Review
3. Reflections Exit Ticket 
4. Rational Numbers Notes
5. Rational Numbers Practice

The Assessment: The exit ticket was checked by me as was the homework for understanding. Students had trouble rationalizing which quadrants had the same sign (it was more the vocabulary and the wording of the question out of the book than the concept). I had students do a couple homework problems independently and checked them on the rational numbers practice (converting a fraction to a decimal).

Homework: Rational numbers practice, weekly quiz number nine, practice for the rational numbers quiz.

My Glass Half-Full Take: I was pretty encouraged by how common place the skill of graphing points had become. This is a skill I would say that most students have truly mastered at this juncture of the year.

One Thing to Do Differently: I would like to start the rational numbers lesson by asking students what was bigger -2/3 or -0.6 and to show the work to prove it. Most students cannot do this, but will be motivated by a challenge.

Day 59 Reflections Across the Coordinate Plane

Teacher Note**Starting in this class I'm making posts every week rather than everyday. 

6th Grade Math Standards: 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.
b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the
coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of
the points are related by reflections across one or both axes.
c. 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: Reflect a point across an axis

Quote of the Day: “Do those things necessary to bring forth your personal best and don’t lose sleep worrying about the competition. Let the competition lose sleep worrying about you.” - John Wooden

Agenda:

1. Jumpstart
2. Thanksgiving Recap
3. Reflection Experimenting (hands on with the boards and no writing)
4. Reflections Notes
5. Reflections Practice
6. Reflections HW

The Assessment: Reflections Practice was a homework ticket starter and the reflections experimenting involved me circumventing the classroom.

Homework: Pg 398 #4 & 5, Pg 399 #13, Pg. 400 all, pg. 401 #31, pg. 402 #32-34 & Weekly Quiz #9

My Glass Half-Full Take: I enjoy the experimenting component. Giving the students an opportunity to talk and see the math, and not write is sometimes a good remedy for getting students that have trouble engaging more engaged. It's also a great way to make sense of patterns and make generalizations about what happens in a reflection.

One Thing to Do Differently: I let students circle the term x or y axis in a problem with a colored pencil and then trace over that axis to help them see which axis a point gets reflected over. I didn't emphasize that that they have to do this initially in my first two classes. By the third class I realized that was a mistake as students were opting not to circle and highlight the axis, and that resulted in wrong answers (reflections in the wrong quadrant).

Day 58 Social Studies Film

This day's class was uneventful as far as the math curriculum is concerned. It was a half-day and the last day before Thanksgiving, so rather than shorten classes we lengthened a class as a sixth grade team to show a social studies film. It was a good way to go into the break.

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.