Upper El’s Week

We have packed as much as possible into this week before our two-week March Break.

Everyone had updated individual lessons in math, with many students moving on to new concepts. We will hit the ground running when we return from break! In geometry, fourths continued their lessons on proving equivalence between two figures. Fifths are working with area formulas, most recently finding the area of acute and right triangles.

In history, students started learning about their ancient civilizations for our extensive research project. They will spend the next few weeks researching their assigned civilizations and working with their group members to write papers, prepare presentations, and make three-dimensional models of their civilizations. Then, on Research Night, April 13th, at 5:00, students will present their research to you and their peers. They are very excited to work together on this project. I will send more information about Research Night and the work leading up to it when we return from March Break.

Thank you to Raquel for coming in this week and working on our class plate, and gift for the Here We Grow Spring Gala and Auction! The children enjoyed expressing their creativity while painting the plate and cornhole game.

Wishing you a marvelous March Break,
Karen and Angie

Upper El: Ancient Civilizations

The time has finally come for our big Ancient Civilizations Research Project!

Upper El students study ancient civilizations to learn to see them as an evolutionary stage and to identify with the process of civilization. They learn to challenge the notion of a simplistic, linear progression of human development and discover the most significant events of civilization. We will explore the contributions of cultures, and we hope these studies will arouse each student’s curiosity for expanded studies of civilizations. As we learn about the development of civilizations, we will explore how each group satisfied specific fundamental needs. We will look for ways they expressed basic human tendencies and compare and contrast groups. Each study will focus on geography, cultural activities, everyday life, and political and economic systems. Upper el students will work in small groups, each focusing on one civilization. Working together, they will complete their research in school. They will present to their peers and parents at Research Night on Thursday, April 13th.

After a week of introductory lessons and browsing our classroom library of books on ancient civilizations, students ranked their top four choices. The cultures were narrowed down to Aztecs, Greeks, Vikings, and Egyptians. They received their research group assignments on Friday at the end of the day. The majority, if not all, of the research and presentation preparations, will be completed in school. I’ll update you as we go and let you know if any work is to be completed at home. The children are very excited and look forward to collaborating to present this project to you!

We hope you have a wonderful weekend,
Karen and Angie

Upper El – Binomial Equations

Thank you for taking the time to come in and chat about your child’s progress in school! It was a pleasure spending time with each of you. We also thank you for your generous donations to the Brian Bags we assembled on Valentine’s Day. We were fortunate to receive photos of appreciative recipients of the bags.

We want to extend a warm welcome to a new member of our class this week. We are so happy Virginia has joined Upper El!

After learning about fractions and decimals for the last few weeks, this week, we will look at squaring and preparation for finding square roots.

These lessons “test” multiplication abilities and give children experience in complex, multi-step multiplications with geometric and hierarchical relationships becoming apparent and predictable with practice. Students are looking at the shape and value of a product and thinking ahead.

The first two lessons in this series focus on multiplying a binomial by a binomial, first (7+3) x (4+2), and then 23 x 25. First, the problem is represented with bead bars, focusing on the shape the beads form (rectangles), and then the equation is recorded.

From here, we move on to squaring a binomial, 16². This is in preparation for finding the square root of a number. Like in the first two lessons, bead materials are used to geometrically represent the parts of the equation, 10² + 2(10×6) + 6². The point is for students to see that when a number is multiplied by itself, the product of that multiplication is a square, which is a measurement of surface, not a linear measure.

Let me know if you’d like a lesson. I’m happy to demonstrate this for you.

Wishing you a lovely weekend,
Karen and Angie

Upper El Math – Decimals

Last week I shared information about how Upper El students learn operations with fractions. This week we’ll look at decimals.

As with all Montessori math, sequences of the work with decimal numbers move from simple to complex and from concrete to increasingly abstract calculations. Decimal work begins with the passage from ordinary fractions to decimal numbers. After learning to build decimal numbers with materials, students work with the four operations, starting with addition and subtraction before moving on to multiplication and division.

The first material students work with is called the decimal fraction board. This material lays out the hierarchy of numbers from millions to millionths, with units in the center of the board. Using this board to add, subtract, and multiply numbers helps students understand place value and guides them in learning to read decimal numbers.

After moving through many passages with the decimal fraction board material, work transitions to the decimal checkerboard to complete compound multiplication problems. The decimal checkerboard allows students to experience a geometric representation of decimal multiplication and continues to emphasize place value. While working with this material, students learn to record partial products as they work through their problems.

After completing their work with multiplication, students learn to divide decimal numbers, with the final step being learning the Property of Invariance (if we multiply or divide both the dividend and the divisor by the same whole number, the result does not change, and the remainder, if any, is automatically multiplied or divided by the same number). The property of invariance in traditional schools is the starting point for the division of decimals. Here it is the point of arrival. This order helps construct the mathematical mind because, with these demonstrations, children are doing rational arithmetic.

We look forward to talking with you next week at Parent Teacher Conferences!

Wishing you a wonderful weekend,
Karen and Angie

Upper El’s Week

We are a small but mighty group this week. As introduced in last week’s blog, math work starts with the concrete and leads naturally to the abstract. We had lots of progress in math this week.  Many students are working with fractions. They are learning to add and subtract fractions with different denominators and to multiply whole numbers by fractions. All fraction work begins with students using cut pieces of circles, called fraction insets. In their addition and subtraction work, they manipulate the pieces to figure out what the common denominator is. After doing several problems, we look to see if they recognize a pattern in what they are doing. As they work, students notice that:

  1. To add or subtract fractions with different denominators, all fractions must be reduced to the same denominator.
  2. To change the terms of a fraction, they either multiply or divide both terms by the same number.
  3. If they multiply or divide the terms of a fraction by the same number, the value of the fraction doesn’t change.

In their work with the multiplication of whole numbers by fractions, they start by taking the whole circle insets and changing them into the number of fraction pieces they need in order to multiply. Students begin to notice that, as the denominator of the multiplier is increased, the total product is decreased. They then begin to notice the pattern, they simply have to multiply the whole number by the numerator to get their new numerator and the denominator stays the same. All students working with fractions are also learning to reduce their answers to the lowest terms.

We also have students working with decimal numbers, multiplying binomials, and squaring trinomials. I look forward to sharing more details about those lessons with you in the next few weeks.

Wishing you a beautiful weekend,

Karen and Angie

Montessori Math in Upper El

At the Upper Elementary level, Montessori math work continues to begin with hands-on demonstrations and work with materials for each new concept before students move to the abstract. This provides many benefits for students. Concrete math work in Montessori allows students to naturally develop a deep understanding of concepts, with the exploration of each concept leading to an understanding of rules and formulas. Our process is an introduction to a new concept with the material, independent practice of the concept using the material, and demonstration of understanding of the concept through the use of the material. After understanding is demonstrated, a rule or formula is verbalized before students begin to complete the problems without the use of materials. Sometimes the rule or formula is recorded in their math books for later reference by the student.

Students are also encouraged to come up with their own math problems (within the concept they are studying). This process of Guided Discovery leads to children engaging with issues that arise in their exploration, creating opportunities for mini-lessons as those issues arise. Its focus is on the technique or the process instead of on correct answers to each individual problem. This means that students get to move through the curriculum at a pace that holds their interest and makes math engaging for them. Working at their own pace helps students to develop confidence in their problem-solving ability and a strong sense of independence.

Wishing you a wonderful weekend,
Karen and Angie

Our Week in Upper Elementary

We have had a busy, productive, four-day week. We continued our daily class meetings, led by the fifth years. We had group and individual lessons in history, language arts, and math. We started new books in class and finished books in Lit Circle. We also celebrated Dr. Martin Luther King’s birthday and started learning about his life.

Our class meeting agendas this week included a discussion of reorganizing the cubby area, people not doing enough of a variety of work during work cycle, and people needing to do a better job of cleaning up after themselves during and after work cycle. EACH of these agenda items was chosen by students. We are only in our second week of Class Meetings using the Positive Discipline approach and I am already seeing a positive change in the class. They are more settled and focused during work time and they are taking a more active approach to work together to solve their own problems in the classroom.

We started a new unit in History this week, the Timeline of Modern Humans. This is an overview of fourteen cultures of the modern human species, Homo sapiens sapiens. All of the cultures we will look at lived in Europe during the last 40,000 years, the Upper Paleolithic Age. We are focusing on European cultures only because most of the evidence for these stages in the development of humans was found first in Europe, so there are lots of books about these artifacts and the people we imagine using them. In Language Arts, we started a new writing unit this week, Informative/Explanatory Writing. We also completed a review of editing for content, punctuation, and capitalization.

We are excited about our new class read-aloud, A Wrinkle In Time by Madeline L’Engle. We have also been reading about Dr. Martin Luther King Jr. and are currently reading a book about the making of Martin Luther King Day, Ain’t Gonna Let Nobody Turn Me ‘Round, by Kathlyn J. Kirkwood. On Tuesday we celebrated Dr. King by singing Happy Birthday by Stevie Wonder, one of the main figures in the campaign to have the birthday of Martin Luther King Jr. become a national holiday.

Wishing you a wonderful weekend,

Karen and Angie

Upper El Class Meetings

“There is a great sense of community within the Montessori classroom, where children of differing ages work together in an atmosphere of cooperation rather than competitiveness. There is respect for the environment and for the individuals within it, which comes through experience of freedom within the community.” -Dr. Maria Montessori

Last weekend, Mrs. Tryforos and I attended a two-day workshop on Positive Discipline in the Montessori Classroom. This was easily one of the most useful and informative workshops I have ever attended. I returned with many tools to incorporate into the classroom right away. One of these tools is the Class Meeting.

In the past, I have written about our Upper Elementary Community Meetings. The Class Meeting follows the same basic format as those meetings, but with a few changes, which I view as improvements:

  • Class Meetings are held three to five times per week (as opposed to our once-per-week Community Meeting)
  • There are five jobs during Class Meetings:
    • Facilitator (Angie or I do this): Keeps the meeting on track, moves the meeting along, facilitates respectful sharing
    • Agenda Keeper: Anyone can contribute to the agenda and children contribute more than adults. The Agenda Keeper selects the oldest agenda item from the box for the meeting.
    • Time Keeper: Keeps track of the timing of each meeting segment and lets us know when the time is up
    • Scribe: Records the brainstormed suggestions of the class on chart paper
    • Secretary: Records the problem and solutions in a notebook which is a permanent record of the meetings and is accessible to all students, anytime
  • There are four sections to the Class Meeting:
    • Compliments and Appreciations: A five to eight-minute opening where each person has a chance to give and receive a compliment or a thank you
    • Review of a past agenda item: The secretary reads one problem and solution from a previous meeting with a quick discussion to review how it’s going.
    • Brainstorming: The person who added the agenda item being discussed, shares it and we take turns brainstorming solutions. After the brainstorming, we vote (if it’s a class problem) or the person who shared the item chooses a solution (if it’s not a whole-class issue).
    • Connection Activity: A fun closing where we share jokes, riddles, or two-minute mysteries

We held our first three Class Meetings this week and the feedback from the students was very positive. They shared that they like the new format much better than the old one. You can find more information on Class Meetings here.

Wishing you a wonderful long weekend

Karen and Angie