## 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