Unit 1: Working with Factors and Multiples

This unit solidifies our understanding of multiplication by exploring the relationship of factors and multiples.  Students will be able to find the greatest common factor and the least common multiple of any two whole numbers.  The learning targets for the unit are as follows:

  1. I can find the greatest common factor of two whole numbers up to 100 (or greater than 100). 6.NS.4
  2. I can find the least common multiple of two whole numbers less than or equal to 12 (or greater than 12). 6.NS.4
  3. I can find the prime factorization for a whole number. (6.ns.4)
  4. I can use the distributive property to translate between expanded form and factored form.  6.NS.4
  5. I can apply greatest common factors and least common multiples to contextual situations. 6.NS.4

I have linked helpful Khan Academy video lessons below:

Welcome to Pond’s Math Class!!

I expect we will all have a wonderful year, and I want to inform you of a few details about how I run the daily routine in class.  Our classes will be 50 minutes long, and will be composed of four main components.  The class will travel through “rotations” in small groups.  First, the class will have a whole group lesson or presentation (ex. notes and practice with surface area of prisms).  On Tuesdays and Thursdays, we will then split into two or three groups and each group will visit stations during the class period.  One station is the small group lesson, where I sit with a group and reinforce the lesson material for the day.  Another station is the independent practice station, where groups will work together to investigate and solve problems or puzzles.  The third station is the tech-work station.  This station has students on technology doing various math based software and games.  Our class time will be busy, and time will fly, so I expect we will move quickly, quietly, and safely through all or our rotations.  We will spend much of the first few days practicing the routine so we get it down smoothly.  

Students in Mr. Pond’s class will be studying math in the investigative style and doing many different tasks to demonstrate their learning.  There will be group work, multi-media lessons, digital learning, and traditional pen and paper type of assignments.  I will use a standards based grading system to gauge student learning.  I will be assessing students on their mastery of learning targets aligned to the state standards.  Students will be offered multiple opportunities to show their mastery of any given learning target.  We will review mistakes and misconceptions to foster critical problem solving methods.  Students will not be penalized for mistakes and misunderstanding.  They will be given additional opportunities to demonstrate their understanding in the form of corrections and make-up work.  There will be equal weight given to all learning targets, as they are aligned to state standards.  This policy motivates students by giving multiple opportunities to demonstrate mastery of a given standard over the course of the semester.  This should not discourage students who struggle at the beginning and will not punish them for their struggles.  Assessments of learning will consist of performance tasks, student work, and unit/section tests.  Assessments for learning will consist of self-assessments and review before summative tests.  I will take the learning styles of each student into account when planning activities and tasks.  Students will access different media to allow multiple opportunities for demonstration of mastery.  The world allows us chances to learn from our mistakes and try again, so will I.  I will locate Math materials in other languages as needed, and I will work with EC staff to properly modify assignments and provide accommodations to students with special needs.

I will expect All students to uphold the code of conduct.  Misbehavior will be dealt with according to schoolwide expectations: 1. Warning  2. Reflection sheet  3. Bounce to another classroom  4. Office referral and call home.  We will create a safe and inviting class environment, so we all can take risks and learn.  We will be open to the ideas of others and listen to different viewpoints.  We will take time to center and calm ourselves when we feel frustrated or stressed.  We will help others in the class as we are a family.  

Education and school are wonderful tools that we are lucky enough to have, and I want students to understand that school is there for them.  I, the teacher, am there for you, the student!  I am here to help you students on your way to becoming intelligent, kind, and self-aware adults.  

 

Cheers!

Andy Pond

 

6th grade Math teacher

IC Imagine

andypond@icimagine.org

Greetings!! Here is a personal reflection on education…

I never would have imagined that I would call myself an existentialist.  I was first introduced to the philosophy in high school through both AP French and Advanced Drama.  In french class, we read Sartre’s “No Exit” and Beckett’s “Waiting for Godot.”  In drama, I was a part of the production that my high school put on of “Waiting for Godot”.   I felt a bit distant from my ideas of existentialism back then.  It seemed so amorphous and bleak, and I was a “yellow dog” optimist. I have come to a new definition of existential philosophy, and I feel a connection with it at this point in my life.  I have spent many hours thinking about people, perceptions, and thinking itself, and I find in the words of existentialist thinkers a keen focus on perception and meaning as relates to individual experience.  To me, this approach to understanding relationship, and even reality, is quite helpful for anyone who works with people, and especially students and children.
We need to put our perceptions into perspective. We must know the limitations of our own knowledge and be sure to maintain awareness when what we “know” or “don’t know” is clouding our perceptions of present experience.  These ideas are existential in that we must take a deep personal involvement in our conviction to realize that all people perceive and create from their own limited perceptions and knowledge. As the late banjo player and riverboat captain, John Hartford, so aptly puts it, “Our style is a product of our limitations.” This phrase is obviously about musical technique, but it corresponds to any activity where thinking is involved. Existentialism requires one to understand the deeply personal nature of thought and experience. Once this understanding about perception and thought is in place, it is only natural to question the nature of “truth”.

This idea uproots all our traditional  foundations of knowledge and thinking. It shows us we can never really capture truth, especially in words. It places truth and knowledge in the realm of subjectivity, which allows us to change our relationship to our own ideas and ideas about people and things. This thinking is difficult for many people because there is no certainty or fixity in it. This is especially challenging for education. It seems obvious, one teacher’s interpretation of the truth in a kernel of knowledge will naturally be different from another’s, and, consequently, will affect the symbols and modes of transmission which are employed in the learning transaction.  Truth cannot be taught. What can be taught is only a subjective interpretation based on the background and experiences of the teacher. That is why a constant watchfulness and awareness of the limiting factors of thought and the influence of background is necessary for any true educator.

Teachers must ignite a spirit of inquiry and discontent in their students so they can begin to engage in the sort of questioning that will lead them to self-discovery. Teachers need to create an environment that enables students to use imagination freely and go beyond themselves. This reaching beyond opens the capacity of empathy and encourages us to think about and question what we are doing with our lives.
This sort of perspective cannot be taught through words.  It can only be modeled in action by the individual teacher. This idea makes for the old adage, “practice what you preach”.  If we model our awareness of behavior and reaction, than we must partake in the practice of “wide awakeness” ourselves, to use a term from Maxine Greene.  If we attempt a practice in this way, regardless of our ideas of success or failure in this endeavor, our teaching will never become a dull routine, and children will learn the ways of actual experience as opposed to the imposition of a process for an expected product or result.
Can this subjective, interpersonal, and self-reflective philosophy be put into practice in modern education?  I believe that an existentialist approach is possible within the constraints of our current system.  While the subject matter within public schools is fairly fixed, the existential philosophy can be implemented in many ways.  The teacher must always be on guard against falling into mechanized routines in thought or behavior, thereby, alienating the students’ reactions and input.  The teacher must make great effort to understand the preferences and interests of each student.  Through the watchful awareness of the class, a teacher will be able to craft lessons that allow the students to explore, empathize, and go beyond themselves.  Regardless of the subject to be taught, teachers can model the sort of self-awareness, wide awakeness, and consideration that existentialism seeks to nourish.  Teachers should not compel or coerce the students into action.  The participation in learning must be voluntary, and the teacher should tell this to the students. Teachers must cultivate true dialogue between themselves and the students, and encourage the students to do the same amongst themselves. This can only be done by offering the students respect, patience, and understanding. Again, regardless of the subject being taught, the teacher is there for the student, not the other way around.
To me, the existentialist tradition exemplifies thoughtfulness, love, and intelligence.  The highly awakened mind knows its own limitations.  Part of existentialist thought encourages us to reflect on our own reactions in order to go beyond them and understand the world more deeply. We have used logic, categorized, and scientifically ordered so much of our world without taking the time to understand what is closest to us, our own thoughts and their relationship to truth. It is time to awaken ourselves to our own inner relationships in order to show the students how to relate to and interact with ideas and their interpretations of them. With increased empathy, consideration, and compassion, our society can take the next steps, in unison with science and technology, towards breaking through our current social barriers and problems. I never would have imagined I would call myself an existentialist.