## Multiples

Multiples of numbers

In this article, I will show you how to find the multiples of one or more numbers with a range of Montessori material:

– the pearl bars,

– the pegs board,

– numbered boards from 1 to 100.

## 1. With the pearl bars:

Let’s find multiples of 2 and of 4:

2 multiple of 2

Let’s find the multiples of 2:

– Set down one green bar with two pearls horizontally and one green bar with two pearls vertically under the first one.

4 multiples of 2

– Next to these bars, set horizontally one under the other, one green bar with two pearls and right under a second green bar with two pearls. Under, vertically, set one yellow bar with four pearls as 2 + 2 = 4

2, 4, 6, 8, 10 multiples of 2

– On the side, set horizontally one under the other, a bar with two green pearls and right under a second green bar with two pearls and a third bar of green pearls. Right under, set vertically a bar of 6 pearls as 2 + 2 + 2 = 6

– On the side, set down horizontally, 4 bars of green pearls and right under vertically a brown bar with 8 pearls as 2 + 2 + 2 + 2 = 8

– On the side, continue setting 5 green bars and right under a golden bar with 10 pearls as 2 + 2 + 2 + 2 + 2 = 10

– On the side, continue setting horizontally 6 green bars and right under a golden bar with ten pearls and a green bar as 2 + 2 + 2 + 2 + 2 + 2 = 12

– And so on…

The multiples of 2 and of 4

– Then, proceed in the same way for the multiples of 4, which you set down under the multiples of 2:

– First, a yellow bar with 4 pearls horizontally and vertically a yellow bar with 4 pearls,

– Then, 2 yellow bars with 4 pearls horizontally and one brown bar with 8 pearls vertically as 4 + 4 = 8

– Then horizontally 3 yellow bars with 4 pearls and vertically one golden bar with 10 pearls and a green bar as 4 + 4 + 4 = 12

– Then horizontally, 4 yellow bars of 4 pearls and vertically a golden bar and a violet bar with 6 pearls as 4 + 4 + 4 + 4 = 16

– And so on…

That way you’ll find the common multiples of 2 and 4: 4, 8, 12, and so on…

## 2. The pegs board:

The pegs board: multiples of 3

Let’s find the multiples of 3 and of 4:

– First, take 3 green nails and set them on the board vertically,

– Under the green nails, set down 3 red nails, then 3 green nails and 3 red nails to reach the bottom of the board.

Take a piece of paper and write down the title “Multiples of 3” and then count:
1, 2, 3 – 3 is a multiple of 3 and write it down on the piece of paper.
Then continue:
4, 5, 6 and write 6 is a multiple of 3.
Continue: 7, 8, 9 and write 9 is a multiple of 3 and go on : 12, 15, 18, 21, 24…

The pegs board the multiples of 4

Do the same thing with the multiples of 4 that you set down vertically next to those of 3 using same colored nails. Take out a piece of paper on which you write the title: “Multiples of 4”.

– Start with 4 green nails and count: 1, 2, 3, 4 and write down 4 in the piece of paper,

– Then continue with 4 red nails and count: 5, 6, 7, 8 and write 8 on the piece of paper

– Then continue with 4 green nails and count: 9, 10, 11, 12 and write down 12 on the piece of paper concerning the multiples of 4 and so on until the bottom of the board.

First common multiple of 3 and of 4

Then take a ruler and set it down horizontally where you can see a color change of the nails and when there is a color change for the first time in both columns of 3 and of 4, say that there is a common multiple of 4 and of 3 (the first one is 12). We also notice that the number12 is found on both pieces of paper.

The pegs board second common multiple of 3 and of 4

You can find all multiples of numbers from 1 to 10 and write them down on paper.

## 3. The sheet with the numbers 1 to 100

The board used to register the multiples – Numbers from 1 to 100

Then, you can use 10 sheets on which you write down numbers from 1 to 100. On the first sheet, write down multiples of 2 and circle each number which is a multiple of 2: 2, 4, 6, 8, 10, 12, 14…. until 100.

Take out a second sheet and entitle it “Multiples of 3” and circle each multiple of 3: 3, 6, 9, 12, 15, 18… until 100.

And so on for all the multiples of numbers from 1 to 10.
Then take out a piece of paper with numbers from 1 to 100 and write down all the multiples of the numbers from 1 to 10 until 100.

Recording the multiples

Then choose a different colored pen for each multiple, for example for the multiples of 2, take a green pen and circle all the multiples of 2 in green, then for the multiples of 3, take an orange pen and circle all the multiples of 3 in orange, then those of 4 in brown, those of 5 in blue….

Show the child that some numbers are circled in more than one color. This means that these numbers are the multiples of more than one number. For example 6 is circled in green, orange and blue which means that 6 is a multiple of 2, 3 and 6. The number 8 is circled in green, brown and red that means that it is a multiple of 2, 4 and 8.

You can also find the multiples of more than one number.

Prime numbers appear.

Then show the child that some numbers are circled with only one color, for example 2 is circled only in green, 3 is circled only in orange, 5 is circled only in blue which means that they are only multiples of themselves. We call these numbers: prime numbers.

Ask the child to take out a piece of paper and to write down as a title “Prime numbers”. Tell him to write down the list of numbers circled in only one color: 1, 2, 3, 5, 7, 11, 13, 17, 19, and so on…

These different ways of working on the notion of the multiples of a number, the common multiples of more than one number and the prime numbers, are very sensory. They involve the visual sense and the touch. Once more, it helps the child build a concrete conception of these notions. The comprehension is therefore facilitated and its memorization as well.

Sylvie d’Esclaibes

## The notion of odd and even numbers

The notion of odd and even numbers is taught very early on in a Montessori school. It is a piece of material we use just after the red and blue bars, the rough numbers and the spindle box. The necessary material is that of numbers and tokens. You will see that it is something that you can easily make at home. It is made of numbers from 1 to 10 and of 55 tokens, preferably red. This material will help your child to set the numbers in order from 1 to 10 and to count the tokens associated to these numbers.

When following the chronology of the presentation of Math material in a kinder garden class, this is the first time that the child sets the numbers in order on his own.

Nonetheless, this material can be presented to a child at the age of primary class to learn the notion of odd and even numbers.

Ask the child to set the numbers horizontally from left to right, and from 1 to 10 (see photo).

Then, show the child number 1 and set one token under it. Then 2, and set 2 tokens horizontally side by side leaving a small space between the two, then 3 and set 2 tokens horizontally side by side leaving a small space between the two and the third token below in the space left by the two above tokens.

Then for number 4, set 2 tokens side by side and 2 tokens below. For number 5, set the 4 first tokens like for number 4 and the fifth token below the empty space left by the above ones. Then, ask the child to continue setting the tokens until number 10.

The error control consists in the fact that all tokens have to be set. Make sure that you have the right number of tokens (55) before you start the exercise.

Look at the way we set the tokens on the picture above as it is essential for the next part of the lesson.

First step: today, I am going to teach you the notion of odd and even. Use your finger (just like in the video) and show odd and even.

Second step: ask your child to show you an odd number and then an even number. Repeat this several times.

Third step: show him a a number and ask him “what is this number?”. Show him another number and ask the same question. Repeat this several times.

Conclusion: Today, you learned that 1, 3, 5, 7, 9 are odd numbers and 2, 4, 6, 8, 10 are even numbers.

With a young child, the lesson ends here. With a child in primary class, you continue the lesson and tell him that all numbers that end in 1, 3, 5, 7, 9 are odd numbers and all numbers that end with 0, 2, 4, 6, and 8 are even numbers. Ask him to give you some even numbers, then some odd numbers and write down numbers on a piece of paper and ask “how is that number?” Repeat this several times.

The child will keep the visual and tactile sensation of what odd and even numbers are and therefore remember them better.

Sylvie d’Esclaibes

## Our Political Science Class

The Lycée International Montessori Athéna proposes a political science class open to our 10th grade students (UK: Year 11) and those of other high schools.

Ideal for motivated students, who are curious of the world that surrounds them, who are ready to improve their knowledge, this class will help them discover political science and offer them the opportunity to present the subject as a credit for the French National Baccalaureate.

The method conferences will take place one Wednesday a week, from 10am to 1pm on our high school premises. The lessons will start on January 29th and will last until the month of June 2014. .

Didier da Silva: will teach this class. He has been a history and geography teacher for 13 years and is also our school performance administrator. Graduated from the French School of “Sciences-Po”, he is a former lecturer there.

Each class is structured like a method conference given at “Sciences-Po”: review of current affairs, followed by an introduction and a lecture on the theme of the day: political science, history of ideas, international relations.

One or two books will be studied in collaboration with their authors.

In order to give a significant added value to the students who will choose to follow the course, the grades obtained will appear on their school report card.

The cost is 350 euros for the whole session (50 % will be paid at registration and the rest by the 30th of March). An invoice will be handed out for tax exemption.

Registrations are opened until the 1rst of February 2014 and the students will start the courses on the 29th of September.

Thanks to this class, we aim at proposing a new method of learning that will help students in their maturity process. It will also help them develop an interest for this type of university studies.

Parents of students from other high schools can obtain further information by writing directly to the lecturer at: didier.dasilva@sciences-po.org

Sylvie d’Esclaibes

REGISTRATION FORM

POLITICAL SCIENCE CLASS

(Please hand back to Didier da Silva before 30th of January 2014)

LYCEE INTERNATIONAL MONTESSORI ATHENA

INFORMATION CONCERNING THE STUDENT

LAST NAME:________________________________________________________________

FIRST NAMES:_________________________________________________________________

DATE OF BIRTH:______________________________________________________

PLACE OF BIRTH:_______________________________________________________

NATIONALITY:____________________________________________________________

PHONE NUMBER:_________________________________________________

INFORMATION CONCERNING THE PARENTS

FATHER’S PROFESSION:____________________________________________________

WORK PHONE NUMBER:________________________________

= Would you be interested in giving a lecture for the political science class? YES – NO

MOTHER’S PROFESSION:_________________________________________________

WORK PHONE NUMBER:_________________________________

= Would you be interested in giving a lecture for the political science class? YES – NO

Regular attendance to the Political Science Class is compulsory. In case of an unjustified absence, a letter will be sent to parents.

The Political Science Class does not convey any particular political position: all political points of view are welcomed and respected.

## Let’s go out and discover the world!

We should always remember the words that Maria Montessori wrote in her book entitled From childhood to adolescence:

“… What we wish for, us to whom the child has shown such power of intelligence, is to go back to Comenius’ fundamental idea, and that is to bring the World to the children.

When the child goes out, the World offers himself to him. Instead of producing objects that represent ideas and to lock them up in a closet, let’s open up the child and show him things in their real perspective…”

Students in middle school and high school enjoyed another nice field trip with their history and geography and English teachers. A former student, who is now an airline pilot, accompanied them.

A visit to Paris

After a long and interesting stroll around the capital, they went to the national film gallery where they were able to see an exhibition on “Jean Cocteau”.

During this nice day, students were able to develop a climate of solidarity between them. It also helps our teachers to see them in a different light and learn more about them. They can easily establish a friendly relationship with their students therefore obtaining the best performances from students who want to please them.

Other trips are being organized, not counting the numerous lunches spent together to celebrate the Epiphany, or just to eat a pizza. On Thursday 30th of January, we will also celebrate the Chinese New Year, which takes place on the 31rst.

These gatherings also make their school year more happy and cheerful and do not leave room to monotony.

Sylvie d’Esclaibes

## We have a new school mascot!

Izia meeting the children

Today, we welcomed the new school mascot: a little Labrador named Izia. After the hens, we now have a little puppy in school!

The children were all thrilled from maternal school students right up to high school students! She will live with our primary school students and they will be responsible for her wellbeing.

Little by little, Izia gets used to the children.

I am impressed by the liability of Montessorian children. They now take care of the hens on their own.

The older students are responsible for the young ones

We generally ask an older student from primary class to help two younger students. They never forget to lay the straw, to give the hens enough to eat and drink and to allow them to walk outside of the cage several times a day.

The child and the puppy

The children are very respectful of our little puppy. When we asked them to let her sleep because she is only two months old, they were very quiet and the atmosphere of the class was more serene than usual.

The joy of the small ones around the puppy

Maria Montessori always pointed out that it is important to open the child’s mind towards nature, and we manage to offer this opportunity to children thanks to our small vegetable gardens, and thanks to the weekly delivery of cut flowers. They can also enjoy the hens and now the brand new puppy.

First time in our garden

We are also negotiating a partnership with a nearby farm.

Children respect their little dog

I am happy to propose a school that is so close to nature.

Sylvie d’Esclaibes

## Let’s bake some cakes!

Our hens taking a stroll!

Now that our hens regularly lay eggs, we can cook! Last Friday, with our primary school students, we made some really nice cakes. The kids were thrilled!

Following the instructions of the recipe can be helpful to work on the tenses of verbs: break the eggs, measure the flour, mix, cook for…

The children prepare the ingredients

We also worked on measures while preparing the ingredients.

Maria Montessori loved this exercise! Children gain independence. They can bake their own cake, measure each ingredient, beat the eggs, turn on the oven, and make sure the cake does not burn…

Nice eggs

The children also noticed that our eggs looked nicer than those found in supermarkets: a nice yellow and shiny color!

The Montessori method involves using concrete exercises especially with young children. Baking and cooking are perfect examples of what you can do with children in respect of the methodology that Maria Montessori left us.

Look at our beautiful cakes!

Pick up the eggs regularly

It is already a thrill for children to pick up the eggs laid by our hens everyday. Now that we are cooking with them, imagine their joy!

This is another great example to be happy in school!

You can also cook with your children at home: prepare your recipes with them. You will have loads of fun and you will be able to introduce notions that are not always easy to grasp!

Sylvie d’Esclaibes

## What is Montessori?

Today, we organized our first “circle” with our high school students.

The circle

In the presence of our history and geography teacher, who is also our performance administrator, Didier da Silva, our French teacher, Bénédicte Dutrieux and one of our English teachers (who also happens to be an ex- student), Paul Belgram, we all sat in a circle and freely talked about different subjects.

This debate is the first of a series that will take place once a month. During our next session, we will ask an ex-student to come and talk about his “Montessori experience”. He will also tell our students how the Montessori method helped him during his college years and his professional life.

A lot of our former students are now attending college and some have just found their first job. We have contacted: Jan who has just finished college and intends to take over his father’s firm; Maxime who has just finished his studies to become an airline pilot; Timothée who is studying chiropody; Hector who is city councilor and on his way to become a lawyer; Maylis who attends a prestigious culinary school; Stanislas who is preparing an MBA in one of the best American colleges; Alexandra who has finished her studies in architecture; Ethan, who worked in show business and is now going to join the kitchen of a famous chef and so on…

This afternoon, the first question was:”“what is Montessori for you?”

• It is a comprehensive school. Teachers and students go through great efforts. If one brings something positive to the class, the teachers are “nice” to them;
• It is a school where we are asked to give our best, and it develops our desire to study.
• We are autonomous and therefore more mature;
• We come freely because in other schools, teachers do not give students the desire to learn anymore;
• The school teaches us to do things on our own;
• We can be successful even if we have to deal with problems,
• The Montessori model adapts itself to the student and not the contrary;
• It is a second family;
• We do not feel stressed out by our teachers.

The second question was for students who come from another system: “what is different?”

• It is the best private school because we are all different when we finish. We are not part of “the mold” like in other schools.
• There are fewer students and therefore more exchange, more discussion between students and teachers;
• In other schools, our personality does not count;
• I had long hours of detention and I became the teachers’ scapegoat. Even if I trespass sometimes, teachers here will not hold it against me;
• It is less stressful here;
• We are fewer in class and everyone has his space. Work is less stressful;
• In my other school, teachers who wanted me to get the best grades stressed me out. The teachers were less available, the homework was just too much and I could never finish it;
• In my former school, we had detention. It is not the case here.

A student who has always attended our school gave the conclusion:

• Here, we find that teachers are our friends, we want to come and we are not scared.

This debate is part of the many actions that I take to promote a privileged, confident and responsible relationship between teachers and students. I aim at creating an appropriate exchange so that my wish to perpetually enrich the teaching methods of my school lives on in respect of what the Montessori model taught me.

Sylvie d’Esclaibes