The Binomial and Trinomial Cube

This slideshow requires JavaScript.

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)

Advertisements

The Broad Stair

Image

IMG_5402

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/)

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;.

Happy Holidays!

Merry-Christmas-Banner-Blue800

I. TODDLER NEWS
I can’t believe December is already here, bringing us 2015 right around the corner. We have been diligently working on introducing the sounds of the letters a to z. As we are working on the last set of letters, you might want to pick up on this great learning opportunity at home, too. Just remember that we are learning the letter sounds, not the letter names. The children really enjoy repeating the sound and then finding an item that starts with that sound. For example, say “a” (sound for short a) then say alligator, apple, etc.

November was full of excitement as the children worked very hard on their November and Thanksgiving art projects. They made a wreath using their hand tracings, a corn stalk, a turkey and a basket with fruits. The children love keeping their little hands busy with arts and crafts.

II. PRESCHOOL NEWS
This semester is almost over and the holiday season is about to start. I am very glad that the students have made significant progress academically and in other areas as well. Their communication skills have tremendously improved; they learned how to take care of themselves and the environments; they learned how and why to respect others, to behave and to use good manners; they gained self-confidence and self-esteem. I am very proud of them. I look forward to the parent-teacher conference to share the detailed information on their progress with you at the end of this semester.

We did our “First Thanksgiving” project. It is our tradition to celebrate the Thanksgiving holiday and learn history at the same time. We also learned rhymes and songs and did art and craft projects about the Pilgrims and Indians and the turkey. We had a wonderful time at our Thanksgiving party and our performance for our friends in the other classes was very successful. In science we studied how materials with different densities reacted in water. They learned the words ‘density’ and ‘volume’ and discovered how to raise and lower water levels using marbles. The students were excited and had so much fun during these experiments.

This month we will continue introducing the children new knowledge while reviewing the concepts we have previously learned. We will be learning and singing holiday songs and doing arts and crafts about Santa, reindeer and other holiday related projects. We are looking forward to meeting with you at our parent-teacher conference.

III. ELEMENTARY NEWS
We have been studying the countries and capital cities of North America and South America. The students are now able to name the body parts of the frog and the fish as well as the parts of a tree. The parts of an atom were introduced and they expressed amazement in learning that everything is made of atoms. We made projects and learned songs related to the Thanksgiving celebration. We discussed the Thanksgiving holiday and reasons for celebrating it.

During the month of December, we will continue to study the structure of the first ten kinds of atoms. We will practice playing different rhythms using rhythm sticks and other percussion instruments.

We will also continue working on reading and spelling skills as well as studying about colors and musical notes. We will begin to name the body parts of the tortoise and bird. We are planning to finish our family chart, using pictures of the child and his/her family members.

May the peace and joy of the holiday season be with you as we culminate the year of 2014 and welcome 2015!