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:
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.
– 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
– 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…
– 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:
Let’s find the multiples of 3 and of 4:
Let’s start with the multiples of 3:
– 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.
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…
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.
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.
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
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.
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.
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.