Learning The Square of a Number Using Montessori Short Bead Chain with Square

We find ourselves working on the Short Bead Chain once again as Mavi reviews his multiplication table.  If you skim through my posts, you will find that we’ve been doing this since Mavi was 5 years old.  Now that he’s older (and wiser!) he finds a deeper meaning in learning the square of a number.

Yes folks, in mathematical terms, the short bead chain materials (and the squares) are used to present the precise squares of a number (2 squared, 4 squared).  Using manipulatives, children can easily grasp the concept and eventually memorize the squares.


Materials needed for this activity

• short bead chains 
• bead squares
• bead chain notation paper (optional)
• short bead chain labels

How the Short Bead Chain works

Invite your child to work on the short bead chain.  Introduce the materials and show where it is placed in your shelf.  In our case, it was Mavi who asked to work on this as he was reviewing his multiplication table.  He is now 9 years old and is working on this independently.

Choose a number to work on.  Start laying out your chain, and place the corresponding square of that bead chain at the end of the chain.  Show the child how you can form the bead chain into a square.  To show the child that they’re exactly the same, place the bead square on top of the square beach chain you formed.  Put back the bead chain in a straight position and prepare your bead chain labels for the counting.

As an example, here’s the chain of 5 with a square of 5.  Start counting from the beginning of the first link: one, two, three, four, five.  Point to the end of the bead, and place your “5” arrow / bead chain label here. Continue counting, pausing and placing the corresponding label at the end of each bead until you reach the end of the chain.


Mavi later on formed the chain into a square again and laid out the arrows as shown below.


Here’s the first time I introduced this activity to Mavi.  Now, he’s working on this independently from 1 to 10, especially when he needed to review.



This how the entire setup looks like from 1 to 9.  Excuse our arrow “16” in the square of 4, we lost the original so we replaced it with whatever we have (red).


As an additional work, you can also let your child record the count using the Bead Chain notation paper.  On where to get and how to use this, visit Montessori Print Shop.


Mavi enjoys learning whenever he uses concrete materials in  math.  There’s always a feeling of satisfaction whenever we use concrete materials(with control of error) because the child learns through discovery.  He knows that it is called a “square” for a reason, not just because some random mathematician wanted to name it like that.  This leads to better understanding of mathematical concepts, without even memorizing them.

If you have further questions on how to use this material, just leave a message and I will try to answer them as soon as possible. Happy learning!