# The Binomial and Trinomial Cube

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The binomial cube is a cube that has the following pieces: one red cube, three black and red prisms, three black and blue prisms, and one blue cube. A box with eight prisms represent the elements of $(a+b)^3$ or: $a^3 + 3a^2b + 3ab^2 + b^3$

The material is not designed as for math education until the elementary years of Montessori education. In the primary levels (ages 3–6), it is used as sensorial material.

The trinomial cube is similar to the binomial cube, but has the following pieces instead:

• 1 red cube and 6 black and red prisms (varying in size)
• 1 blue cube and 6 black and blue prisms (varying in size)
• 1 yellow cube and 6 black and yellow prisms (varying in size)
• 6 black prisms (same size)

This is similar to the binomial cube, but is a physical representation of this formula:

$(a+b+c)^3 = a^3 + 3a^2b + 3a^2c + b^3 + 3ab^2 + 3b^2c + c^3 + 3ac^2 + 3bc^2 + 6abc$

(Reference: http://en.wikipedia.org/wiki/Montessori_sensorial_materials#The_trinomial_cube)

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The brown stair helps to develop the child’s visual discrimination of differences in two dimensions. It indirectly prepares the child for later work in geometry and for the concept of numbers, in demonstrating the unit difference in height and width between the ten successively thicker prisms. The child will build the brown stair from the thickest to the thinnest.

(Reference: http://www.justmontessori.com/sensorial/)

# Happy New Year!

I. TODDLER NEWS
Happy New Year! We hope everyone enjoyed their vacation with their families. We are so happy to welcome back our toddlers. It may take some time for the children to return to their regular schedule, so we will be busy establishing our normal routine and diligently reviewing our classroom rules.

It is the beginning of January and we are looking forward to having a great year. We will start our year with our Montessori lessons in math. Also during this month we will be talking about cold weather and snow and we will be making some art projects about winter time.
We are happy to have new friends in our class; we say welcome to Chandler and twins Eden and Asha, who joined us in December.

II. PRESCHOOL NEWS
Happy New Year! We are glad to welcome all of you back to school. I hope you all had a happy holiday and got relaxed and ready for a new semester. We are happy to welcome Kaleen to our class this month; she just graduated from our toddler class. For the first week we will review what we learned last semester; then we will continue to gain new knowledge. We have many new materials for our students to explore and new concepts for them to grasp. Our students love learning with our Montessori materials and methods. This is one of the reasons our students are so successful. I have heard many times from our students how much they want to work on the materials. With their curiosity, ambition and confidence in learning, we believe that will be having another successful semester.

We have a lot of fun activities prepared for the science experiments. They will be testing how chemicals, such as soap or detergent react with different things. In art we will work on winter related projects; the snowman and snowflakes are some of our favorites. Since the weather is cold, we will have more playtime indoors than outdoors. We have prepared indoor games and physical activities for the children to enjoy and use up some of their energy.

III. ELEMENTARY NEWS
December 2014 was full of excitement. We celebrated two birthdays in December, Tavian turned 5 on the 14th and Ethan turned 5 on the 18th. We made some holiday crafts played games for the holiday. They enjoyed learning fractions and were enthusiastic about learning the body parts of the fish, the tortoise and the bird.

During January, we will continue to work on our family chart project. The children have started to organize their family pictures. We will begin working on the pictures of your child from infant to present age and still need a few more pictures for this project. This project will serve as a keepsake for your child to remember their childhood as they grow older. Some of their favorite class work will also be included in this album. You might also like to add some of the work they are bringing home weekly.

This month we will have three students from the primary classes joining the elementary class. We are happy to welcome Trenton, Isaac and Andrew to our elementary.

Welcome back to school! We hope that you enjoyed your winter break. We are ready to start another great year. 2015 is going to be a fun filled learning experience!

# The Importance of the Uninterrupted Work Period

We wanted to give you a little bit of background on why we are such “sticklers” about arriving on time to school. We do understand that life happens and sometimes things are out of your control. Our intention is not to punish parents and create conflicts and stress. We hope that this background information helps you.

One of the things that sets Montessori apart from other educational philosophies is the emphasis on the child’s freedom within a prepared environment (the classroom). The Montessori teacher, or “guide” is there to entice and invite the children to explore with the learning materials rather than dictate what to do. Children should be presented with information when they are interested and developmentally ready, and not according to the schedule or time of day. In order to allow for this exploration, the uninterrupted work period of at least 3 hours is required. Through much trial and error and observation, Maria Montessori found this to be the necessary amount of time and so it has been the standard in true Montessori schools for over 100 years! The purpose of this block of time is to allow children to select materials freely, and to become absorbed in their work. They are absorbed because they have the freedom to choose to work with something that is fascinating to them in their particular stage of development. The children are also hesitant to choose challenging work if they are not expecting to have enough time to complete it. Any interruption to the child’s work period disrupts the fragile focus, concentration, critical thinking, problem solving, and exploration which is being developed. For this reason, our drop-off policy has evolved. In order to allow time for a beautiful classroom community lunch and outdoor playtime, the work period must begin by 8:30 and continue without disruption. Each child deserves this opportunity, and a late arrival to the class not only takes away from that child’s experience, but disrupts the others as well. Each child wants to pause from his or her work to greet and welcome the friend or see whose “Mommy” or “Daddy” has come. Our goal is not to make parents feel stressed or guilty when arriving late, or to charge fees. It is our top priority to have this uninterrupted work time for the children to have the best opportunity for learning and development. Please help us with this commitment by bringing your children to school on time!

We consider our parents as partners in providing the best environment for the children and truly have a great desire to work with you in a harmonious way.

### (source: http://www.kinderhousemontessori.com/the-uninterrupted-work-period/)

The Montessori learning method, founded by Maria Montessori, emphasizes a collaborative environment without grades or tests, multi-aged classrooms, as well as self-directed learning and discovery for long blocks of time, primarily for young children ages 2 1/2 to 7.

By the end of kindergarten, among 5-year-olds, “Montessori students proved to be significantly better prepared for elementary school in reading and math skills than the non-Montessori children,” according to the researchers. “They also tested better on “executive function,” the ability to adapt to changing and more complex problems, an indicator of future school and life success.”

Of course, Montessori methods go against the grain of traditional educational methods. We are given very little opportunity, for instance, to perform our own, original experiments, and there is also little or no margin for failure or mistakes. We are judged primarily on getting answers right. There is much less emphasis on developing our creative thinking abilities, our abilities to let our minds run imaginatively and to discover things on our own.

But most highly creative achievers don’t begin with brilliant ideas, they discover them.

Google, for instance, didn’t begin as a brilliant vision, but as a project to improve library searches, followed by a series of small discoveries that unlocked a revolutionary business model. Larry Page and Sergei Brin didn’t begin with an ingenious idea. But they certainly discovered one.

Reference:
Sims, Peter. “The Montessori Mafia.” Ideas Market RSS. The Wall Street Journal, n.d. Web. 08 Dec. 2014. <http://blogs.wsj.com/ideas-market/2011/04/05/the-montessori-mafia/&gt;.